id	sid	tid	token	lemma	pos
iajs-3094	1	1	386	386	NUM
iajs-3094	1	2	this	this	DET
iajs-3094	1	3	work	work	NOUN
iajs-3094	1	4	is	be	AUX
iajs-3094	1	5	licensed	license	VERB
iajs-3094	1	6	under	under	ADP
iajs-3094	1	7	a	a	DET
iajs-3094	1	8	creative	creative	ADJ
iajs-3094	1	9	commons	common	NOUN
iajs-3094	1	10	attribution	attribution	NOUN
iajs-3094	1	11	4.0	4.0	NUM
iajs-3094	1	12	international	international	ADJ
iajs-3094	1	13	license	license	NOUN
iajs-3094	1	14	ihjpas	ihjpa	NOUN
iajs-3094	1	15	.	.	PUNCT
iajs-3094	2	1	37	37	NUM
iajs-3094	2	2	(	(	PUNCT
iajs-3094	2	3	1	1	NUM
iajs-3094	2	4	)	)	PUNCT
iajs-3094	2	5	2024	2024	NUM
iajs-3094	2	6	ibn	ibn	PROPN
iajs-3094	2	7	al	al	PROPN
iajs-3094	2	8	-	-	PUNCT
iajs-3094	2	9	haitham	haitham	PROPN
iajs-3094	2	10	journal	journal	PROPN
iajs-3094	2	11	for	for	ADP
iajs-3094	2	12	pure	pure	ADJ
iajs-3094	2	13	and	and	CCONJ
iajs-3094	2	14	applied	applied	ADJ
iajs-3094	2	15	sciences	sciences	PROPN
iajs-3094	2	16	journal	journal	PROPN
iajs-3094	2	17	homepage	homepage	NOUN
iajs-3094	2	18	:	:	PUNCT
iajs-3094	2	19	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3094	2	20	pissn	pissn	ADJ
iajs-3094	2	21	:	:	PUNCT
iajs-3094	2	22	1609	1609	NUM
iajs-3094	2	23	-	-	SYM
iajs-3094	2	24	4042	4042	NUM
iajs-3094	2	25	,	,	PUNCT
iajs-3094	2	26	eissn	eissn	NOUN
iajs-3094	2	27	:	:	PUNCT
iajs-3094	2	28	2521	2521	NUM
iajs-3094	2	29	-	-	SYM
iajs-3094	2	30	3407	3407	NUM
iajs-3094	2	31	1nagham	1nagham	NUM
iajs-3094	2	32	muosa	muosa	PROPN
iajs-3094	2	33	neamah	neamah	PROPN
iajs-3094	2	34	2,*bayda	2,*bayda	NUM
iajs-3094	2	35	atiya	atiya	PROPN
iajs-3094	2	36	kalaf	kalaf	PROPN
iajs-3094	3	1	3hamiden	3hamiden	NUM
iajs-3094	3	2	abd	abd	PROPN
iajs-3094	3	3	el	el	PROPN
iajs-3094	3	4	-	-	PUNCT
iajs-3094	3	5	wahed	wahe	VERB
iajs-3094	3	6	khalifa	khalifa	PROPN
iajs-3094	3	7	1,2department	1,2department	NUM
iajs-3094	3	8	of	of	ADP
iajs-3094	3	9	mathematics	mathematic	NOUN
iajs-3094	3	10	,	,	PUNCT
iajs-3094	3	11	college	college	NOUN
iajs-3094	3	12	of	of	ADP
iajs-3094	3	13	education	education	NOUN
iajs-3094	3	14	for	for	ADP
iajs-3094	3	15	pure	pure	ADJ
iajs-3094	3	16	sciences	science	NOUN
iajs-3094	3	17	,	,	PUNCT
iajs-3094	3	18	ibn	ibn	PROPN
iajs-3094	3	19	al	al	PROPN
iajs-3094	3	20	–	–	PUNCT
iajs-3094	3	21	haitham	haitham	PROPN
iajs-3094	3	22	,	,	PUNCT
iajs-3094	3	23	university	university	PROPN
iajs-3094	3	24	of	of	ADP
iajs-3094	3	25	baghdad	baghdad	PROPN
iajs-3094	3	26	iraq	iraq	PROPN
iajs-3094	4	1	3department	3department	NUM
iajs-3094	4	2	of	of	ADP
iajs-3094	4	3	mathematics	mathematic	NOUN
iajs-3094	4	4	,	,	PUNCT
iajs-3094	4	5	college	college	NOUN
iajs-3094	4	6	of	of	ADP
iajs-3094	4	7	science	science	NOUN
iajs-3094	4	8	and	and	CCONJ
iajs-3094	4	9	arts	art	NOUN
iajs-3094	4	10	,	,	PUNCT
iajs-3094	4	11	qassim	qassim	PROPN
iajs-3094	4	12	university	university	PROPN
iajs-3094	4	13	,	,	PUNCT
iajs-3094	4	14	al	al	PROPN
iajs-3094	4	15	-	-	PUNCT
iajs-3094	4	16	badaya	badaya	PROPN
iajs-3094	4	17	51951,saudi	51951,saudi	PROPN
iajs-3094	4	18	arabia	arabia	PROPN
iajs-3094	4	19	.	.	PUNCT
iajs-3094	5	1	3department	3department	NUM
iajs-3094	5	2	of	of	ADP
iajs-3094	5	3	operations	operation	NOUN
iajs-3094	5	4	and	and	CCONJ
iajs-3094	5	5	management	management	NOUN
iajs-3094	5	6	research	research	NOUN
iajs-3094	5	7	,	,	PUNCT
iajs-3094	5	8	faculty	faculty	NOUN
iajs-3094	5	9	of	of	ADP
iajs-3094	5	10	graduate	graduate	ADJ
iajs-3094	5	11	studies	study	NOUN
iajs-3094	5	12	for	for	ADP
iajs-3094	5	13	statistical	statistical	ADJ
iajs-3094	5	14	research	research	NOUN
iajs-3094	5	15	,	,	PUNCT
iajs-3094	5	16	cairo	cairo	PROPN
iajs-3094	5	17	university	university	PROPN
iajs-3094	5	18	,	,	PUNCT
iajs-3094	5	19	giza	giza	PROPN
iajs-3094	5	20	12613	12613	NUM
iajs-3094	5	21	,	,	PUNCT
iajs-3094	5	22	egypt	egypt	PROPN
iajs-3094	5	23	*	*	PUNCT
iajs-3094	5	24	corresponding	correspond	VERB
iajs-3094	5	25	author	author	NOUN
iajs-3094	5	26	.	.	PUNCT
iajs-3094	6	1	baydaa.a.k@ihcoedu.uobaghdad.edu.iq	baydaa.a.k@ihcoedu.uobaghdad.edu.iq	NOUN
iajs-3094	6	2	abstract	abstract	ADJ
iajs-3094	6	3	machine	machine	NOUN
iajs-3094	6	4	scheduling	scheduling	NOUN
iajs-3094	6	5	problems	problem	NOUN
iajs-3094	6	6	(	(	PUNCT
iajs-3094	6	7	msp	msp	PROPN
iajs-3094	6	8	)	)	PUNCT
iajs-3094	6	9	are	be	AUX
iajs-3094	6	10	considered	consider	VERB
iajs-3094	6	11	as	as	ADP
iajs-3094	6	12	one	one	NUM
iajs-3094	6	13	of	of	ADP
iajs-3094	6	14	the	the	DET
iajs-3094	6	15	most	most	ADV
iajs-3094	6	16	important	important	ADJ
iajs-3094	6	17	classes	class	NOUN
iajs-3094	6	18	of	of	ADP
iajs-3094	6	19	combinatorial	combinatorial	ADJ
iajs-3094	6	20	optimization	optimization	NOUN
iajs-3094	6	21	problems	problem	NOUN
iajs-3094	6	22	.	.	PUNCT
iajs-3094	7	1	in	in	ADP
iajs-3094	7	2	this	this	DET
iajs-3094	7	3	paper	paper	NOUN
iajs-3094	7	4	,	,	PUNCT
iajs-3094	7	5	the	the	DET
iajs-3094	7	6	problem	problem	NOUN
iajs-3094	7	7	of	of	ADP
iajs-3094	7	8	job	job	NOUN
iajs-3094	7	9	scheduling	scheduling	NOUN
iajs-3094	7	10	on	on	ADP
iajs-3094	7	11	a	a	DET
iajs-3094	7	12	single	single	ADJ
iajs-3094	7	13	machine	machine	NOUN
iajs-3094	7	14	is	be	AUX
iajs-3094	7	15	studied	study	VERB
iajs-3094	7	16	to	to	PART
iajs-3094	7	17	minimize	minimize	VERB
iajs-3094	7	18	the	the	DET
iajs-3094	7	19	multi	multi	ADJ
iajs-3094	7	20	objective	objective	NOUN
iajs-3094	7	21	and	and	CCONJ
iajs-3094	7	22	multi	multi	ADJ
iajs-3094	7	23	objective	objective	ADJ
iajs-3094	7	24	function	function	NOUN
iajs-3094	7	25	.	.	PUNCT
iajs-3094	8	1	this	this	DET
iajs-3094	8	2	objective	objective	ADJ
iajs-3094	8	3	function	function	NOUN
iajs-3094	8	4	is	be	AUX
iajs-3094	8	5	:	:	PUNCT
iajs-3094	8	6	total	total	ADJ
iajs-3094	8	7	completion	completion	NOUN
iajs-3094	8	8	time	time	NOUN
iajs-3094	8	9	,	,	PUNCT
iajs-3094	8	10	total	total	ADJ
iajs-3094	8	11	lead	lead	NOUN
iajs-3094	8	12	time	time	NOUN
iajs-3094	8	13	and	and	CCONJ
iajs-3094	8	14	maximum	maximum	ADJ
iajs-3094	8	15	tardiness	tardiness	ADJ
iajs-3094	8	16	time	time	NOUN
iajs-3094	8	17	,	,	PUNCT
iajs-3094	8	18	respectively	respectively	ADV
iajs-3094	8	19	,	,	PUNCT
iajs-3094	8	20	which	which	PRON
iajs-3094	8	21	are	be	AUX
iajs-3094	8	22	formulated	formulate	VERB
iajs-3094	8	23	as	as	ADP
iajs-3094	8	24	(	(	PUNCT
iajs-3094	8	25	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	8	26	,	,	PUNCT
iajs-3094	8	27	∑	∑	PROPN
iajs-3094	8	28	𝑬𝒋	𝑬𝒋	PROPN
iajs-3094	8	29	,	,	PUNCT
iajs-3094	8	30	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	8	31	)	)	PUNCT
iajs-3094	8	32	are	be	AUX
iajs-3094	8	33	formulated	formulate	VERB
iajs-3094	8	34	.	.	PUNCT
iajs-3094	9	1	in	in	ADP
iajs-3094	9	2	this	this	DET
iajs-3094	9	3	study	study	NOUN
iajs-3094	9	4	,	,	PUNCT
iajs-3094	9	5	a	a	DET
iajs-3094	9	6	mathematical	mathematical	ADJ
iajs-3094	9	7	model	model	NOUN
iajs-3094	9	8	is	be	AUX
iajs-3094	9	9	created	create	VERB
iajs-3094	9	10	to	to	PART
iajs-3094	9	11	solve	solve	VERB
iajs-3094	9	12	the	the	DET
iajs-3094	9	13	research	research	NOUN
iajs-3094	9	14	problem	problem	NOUN
iajs-3094	9	15	.	.	PUNCT
iajs-3094	10	1	this	this	DET
iajs-3094	10	2	problem	problem	NOUN
iajs-3094	10	3	can	can	AUX
iajs-3094	10	4	be	be	AUX
iajs-3094	10	5	divided	divide	VERB
iajs-3094	10	6	into	into	ADP
iajs-3094	10	7	several	several	ADJ
iajs-3094	10	8	subproblems	subproblem	NOUN
iajs-3094	10	9	and	and	CCONJ
iajs-3094	10	10	simple	simple	ADJ
iajs-3094	10	11	algorithms	algorithm	NOUN
iajs-3094	10	12	have	have	AUX
iajs-3094	10	13	been	be	AUX
iajs-3094	10	14	found	find	VERB
iajs-3094	10	15	to	to	PART
iajs-3094	10	16	find	find	VERB
iajs-3094	10	17	the	the	DET
iajs-3094	10	18	solutions	solution	NOUN
iajs-3094	10	19	to	to	ADP
iajs-3094	10	20	these	these	DET
iajs-3094	10	21	sub	sub	NOUN
iajs-3094	10	22	-	-	NOUN
iajs-3094	10	23	problems	problem	NOUN
iajs-3094	10	24	and	and	CCONJ
iajs-3094	10	25	compare	compare	VERB
iajs-3094	10	26	them	they	PRON
iajs-3094	10	27	with	with	ADP
iajs-3094	10	28	efficient	efficient	ADJ
iajs-3094	10	29	solutions	solution	NOUN
iajs-3094	10	30	.	.	PUNCT
iajs-3094	11	1	for	for	ADP
iajs-3094	11	2	this	this	DET
iajs-3094	11	3	problem	problem	NOUN
iajs-3094	11	4	,	,	PUNCT
iajs-3094	11	5	some	some	DET
iajs-3094	11	6	rules	rule	NOUN
iajs-3094	11	7	that	that	PRON
iajs-3094	11	8	provide	provide	VERB
iajs-3094	11	9	efficient	efficient	ADJ
iajs-3094	11	10	solutions	solution	NOUN
iajs-3094	11	11	have	have	AUX
iajs-3094	11	12	been	be	AUX
iajs-3094	11	13	proved	prove	VERB
iajs-3094	11	14	and	and	CCONJ
iajs-3094	11	15	some	some	DET
iajs-3094	11	16	special	special	ADJ
iajs-3094	11	17	cases	case	NOUN
iajs-3094	11	18	have	have	AUX
iajs-3094	11	19	been	be	AUX
iajs-3094	11	20	introduced	introduce	VERB
iajs-3094	11	21	and	and	CCONJ
iajs-3094	11	22	proved	prove	VERB
iajs-3094	11	23	since	since	SCONJ
iajs-3094	11	24	the	the	DET
iajs-3094	11	25	problem	problem	NOUN
iajs-3094	11	26	is	be	AUX
iajs-3094	11	27	an	an	DET
iajs-3094	11	28	np	np	ADV
iajs-3094	11	29	-	-	PUNCT
iajs-3094	11	30	hard	hard	ADJ
iajs-3094	11	31	problem	problem	NOUN
iajs-3094	11	32	to	to	PART
iajs-3094	11	33	find	find	VERB
iajs-3094	11	34	some	some	DET
iajs-3094	11	35	efficient	efficient	ADJ
iajs-3094	11	36	solutions	solution	NOUN
iajs-3094	11	37	that	that	PRON
iajs-3094	11	38	are	be	AUX
iajs-3094	11	39	efficient	efficient	ADJ
iajs-3094	11	40	for	for	ADP
iajs-3094	11	41	the	the	DET
iajs-3094	11	42	discussed	discuss	VERB
iajs-3094	11	43	problem	problem	NOUN
iajs-3094	11	44	1//	1//	NUM
iajs-3094	11	45	𝐹(∑𝑪𝒋	𝐹(∑𝑪𝒋	NOUN
iajs-3094	11	46	,	,	PUNCT
iajs-3094	11	47	∑𝑬𝒋	∑𝑬𝒋	PROPN
iajs-3094	11	48	,	,	PUNCT
iajs-3094	11	49	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	11	50	)	)	PUNCT
iajs-3094	11	51	,	,	PUNCT
iajs-3094	11	52	and	and	CCONJ
iajs-3094	11	53	good	good	ADJ
iajs-3094	11	54	or	or	CCONJ
iajs-3094	11	55	optimal	optimal	ADJ
iajs-3094	11	56	solutions	solution	NOUN
iajs-3094	11	57	for	for	ADP
iajs-3094	11	58	the	the	DET
iajs-3094	11	59	multiobjective	multiobjective	ADJ
iajs-3094	11	60	functions	function	NOUN
iajs-3094	11	61	1//	1//	NUM
iajs-3094	11	62	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	11	63	+	+	NUM
iajs-3094	11	64	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	11	65	+	+	CCONJ
iajs-3094	11	66	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	11	67	,	,	PUNCT
iajs-3094	11	68	,	,	PUNCT
iajs-3094	11	69	and	and	CCONJ
iajs-3094	11	70	emphasize	emphasize	VERB
iajs-3094	11	71	the	the	DET
iajs-3094	11	72	importance	importance	NOUN
iajs-3094	11	73	of	of	ADP
iajs-3094	11	74	the	the	DET
iajs-3094	11	75	dominance	dominance	NOUN
iajs-3094	11	76	rule	rule	NOUN
iajs-3094	11	77	(	(	PUNCT
iajs-3094	11	78	dr	dr	PROPN
iajs-3094	11	79	)	)	PUNCT
iajs-3094	11	80	,	,	PUNCT
iajs-3094	11	81	which	which	PRON
iajs-3094	11	82	can	can	AUX
iajs-3094	11	83	be	be	AUX
iajs-3094	11	84	applied	apply	VERB
iajs-3094	11	85	to	to	ADP
iajs-3094	11	86	this	this	DET
iajs-3094	11	87	problem	problem	NOUN
iajs-3094	11	88	to	to	PART
iajs-3094	11	89	improve	improve	VERB
iajs-3094	11	90	efficient	efficient	ADJ
iajs-3094	11	91	solutions	solution	NOUN
iajs-3094	11	92	.	.	PUNCT
iajs-3094	12	1	keywords	keyword	NOUN
iajs-3094	12	2	:	:	PUNCT
iajs-3094	12	3	maximum	maximum	ADJ
iajs-3094	12	4	tardiness	tardiness	NOUN
iajs-3094	12	5	,	,	PUNCT
iajs-3094	12	6	multi	multi	ADJ
iajs-3094	12	7	-	-	NOUN
iajs-3094	12	8	criteria	criterion	NOUN
iajs-3094	12	9	,	,	PUNCT
iajs-3094	12	10	multi	multi	ADJ
iajs-3094	12	11	-	-	ADJ
iajs-3094	12	12	objective	objective	ADJ
iajs-3094	12	13	,	,	PUNCT
iajs-3094	12	14	total	total	ADJ
iajs-3094	12	15	completion	completion	NOUN
iajs-3094	12	16	times	time	NOUN
iajs-3094	12	17	,	,	PUNCT
iajs-3094	12	18	total	total	ADJ
iajs-3094	12	19	earliness	earliness	NOUN
iajs-3094	12	20	time	time	NOUN
iajs-3094	12	21	.	.	PUNCT
iajs-3094	13	1	received	receive	VERB
iajs-3094	13	2	13	13	NUM
iajs-3094	13	3	december	december	PROPN
iajs-3094	13	4	2022	2022	NUM
iajs-3094	13	5	,	,	PUNCT
iajs-3094	13	6	received	receive	VERB
iajs-3094	13	7	6	6	NUM
iajs-3094	13	8	january	january	PROPN
iajs-3094	13	9	2023	2023	NUM
iajs-3094	13	10	,	,	PUNCT
iajs-3094	13	11	accepted	accept	VERB
iajs-3094	13	12	13	13	NUM
iajs-3094	13	13	march	march	NOUN
iajs-3094	13	14	2023	2023	NUM
iajs-3094	13	15	,	,	PUNCT
iajs-3094	13	16	published	publish	VERB
iajs-3094	13	17	20	20	NUM
iajs-3094	13	18	january	january	NOUN
iajs-3094	13	19	2024	2024	NUM
iajs-3094	13	20	solving	solve	VERB
iajs-3094	13	21	the	the	DET
iajs-3094	13	22	multi	multi	NOUN
iajs-3094	13	23	-	-	NOUN
iajs-3094	13	24	criteria	criterion	NOUN
iajs-3094	13	25	,	,	PUNCT
iajs-3094	13	26	total	total	ADJ
iajs-3094	13	27	completion	completion	NOUN
iajs-3094	13	28	time	time	NOUN
iajs-3094	13	29	,	,	PUNCT
iajs-3094	13	30	total	total	ADJ
iajs-3094	13	31	earliness	earliness	NOUN
iajs-3094	13	32	time	time	NOUN
iajs-3094	13	33	,	,	PUNCT
iajs-3094	13	34	and	and	CCONJ
iajs-3094	13	35	maximum	maximum	ADJ
iajs-3094	13	36	tardiness	tardiness	ADJ
iajs-3094	13	37	problem	problem	NOUN
iajs-3094	13	38	doi.org/10.30526/37.1.3094	doi.org/10.30526/37.1.3094	PROPN
iajs-3094	13	39	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3094	14	1	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	https://jih.uobaghdad.edu.iq/index.php/j/index#1609-4042	NOUN
iajs-3094	14	2	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	https://jih.uobaghdad.edu.iq/index.php/j/index#2521-3407	VERB
iajs-3094	14	3	mailto:baydaa.a.k@ihcoedu.uobaghdad.edu.iq	mailto:baydaa.a.k@ihcoedu.uobaghdad.edu.iq	ADJ
iajs-3094	14	4	https://orcid.org/0000-0001-5393-4083	https://orcid.org/0000-0001-5393-4083	PROPN
iajs-3094	14	5	mailto:nagham2182011@gmail.com	mailto:nagham2182011@gmail.com	PROPN
iajs-3094	14	6	https://orcid.org/0000-0003-1136-0055	https://orcid.org/0000-0003-1136-0055	PROPN
iajs-3094	14	7	mailto:baydaa.a.k@ihcoedu.uobaghdad.edu.iq	mailto:baydaa.a.k@ihcoedu.uobaghdad.edu.iq	PROPN
iajs-3094	14	8	https://orcid.org/0000-0002-8269-8822	https://orcid.org/0000-0002-8269-8822	PROPN
iajs-3094	14	9	mailto:ha.ahmed@qu.edu.sa	mailto:ha.ahmed@qu.edu.sa	PROPN
iajs-3094	14	10	ihjpas	ihjpa	VERB
iajs-3094	14	11	.	.	PUNCT
iajs-3094	15	1	37	37	NUM
iajs-3094	15	2	(	(	PUNCT
iajs-3094	15	3	1	1	NUM
iajs-3094	15	4	)	)	PUNCT
iajs-3094	15	5	2024	2024	NUM
iajs-3094	15	6	387	387	NUM
iajs-3094	15	7	1	1	NUM
iajs-3094	15	8	.	.	PUNCT
iajs-3094	15	9	introduction	introduction	NOUN
iajs-3094	15	10	scheduling	scheduling	NOUN
iajs-3094	15	11	involves	involve	VERB
iajs-3094	15	12	distributing	distribute	VERB
iajs-3094	15	13	a	a	DET
iajs-3094	15	14	set	set	ADJ
iajs-3094	15	15	number	number	NOUN
iajs-3094	15	16	of	of	ADP
iajs-3094	15	17	resources	resource	NOUN
iajs-3094	15	18	over	over	ADP
iajs-3094	15	19	a	a	DET
iajs-3094	15	20	period	period	NOUN
iajs-3094	15	21	of	of	ADP
iajs-3094	15	22	time	time	NOUN
iajs-3094	15	23	to	to	ADP
iajs-3094	15	24	various	various	ADJ
iajs-3094	15	25	tasks[1	tasks[1	NOUN
iajs-3094	15	26	]	]	PUNCT
iajs-3094	15	27	.	.	PUNCT
iajs-3094	16	1	one	one	NUM
iajs-3094	16	2	or	or	CCONJ
iajs-3094	16	3	more	more	ADJ
iajs-3094	16	4	objectives	objective	NOUN
iajs-3094	16	5	may	may	AUX
iajs-3094	16	6	be	be	AUX
iajs-3094	16	7	optimized	optimize	VERB
iajs-3094	16	8	as	as	ADP
iajs-3094	16	9	a	a	DET
iajs-3094	16	10	result	result	NOUN
iajs-3094	16	11	of	of	ADP
iajs-3094	16	12	this	this	DET
iajs-3094	16	13	decision	decision	NOUN
iajs-3094	16	14	-	-	PUNCT
iajs-3094	16	15	making	make	VERB
iajs-3094	16	16	process	process	NOUN
iajs-3094	16	17	.	.	PUNCT
iajs-3094	17	1	as	as	ADV
iajs-3094	17	2	well	well	ADV
iajs-3094	17	3	as	as	ADP
iajs-3094	17	4	,	,	PUNCT
iajs-3094	17	5	the	the	DET
iajs-3094	17	6	scheduling	scheduling	NOUN
iajs-3094	17	7	problem	problem	NOUN
iajs-3094	17	8	is	be	AUX
iajs-3094	17	9	defined	define	VERB
iajs-3094	17	10	as	as	ADP
iajs-3094	17	11	the	the	DET
iajs-3094	17	12	arrangement	arrangement	NOUN
iajs-3094	17	13	of	of	ADP
iajs-3094	17	14	entities	entity	NOUN
iajs-3094	17	15	(	(	PUNCT
iajs-3094	17	16	people	people	NOUN
iajs-3094	17	17	,	,	PUNCT
iajs-3094	17	18	tasks	task	NOUN
iajs-3094	17	19	,	,	PUNCT
iajs-3094	17	20	vehicles	vehicle	NOUN
iajs-3094	17	21	,	,	PUNCT
iajs-3094	17	22	lecture	lecture	NOUN
iajs-3094	17	23	,	,	PUNCT
iajs-3094	17	24	etc	etc	X
iajs-3094	17	25	.	.	X
iajs-3094	17	26	)	)	PUNCT
iajs-3094	17	27	into	into	ADP
iajs-3094	17	28	a	a	DET
iajs-3094	17	29	pattern	pattern	NOUN
iajs-3094	17	30	in	in	ADP
iajs-3094	17	31	space	space	NOUN
iajs-3094	17	32	-	-	PUNCT
iajs-3094	17	33	time	time	NOUN
iajs-3094	17	34	in	in	ADP
iajs-3094	17	35	such	such	DET
iajs-3094	17	36	a	a	DET
iajs-3094	17	37	way	way	NOUN
iajs-3094	17	38	that	that	PRON
iajs-3094	17	39	constraints	constraint	NOUN
iajs-3094	17	40	are	be	AUX
iajs-3094	17	41	satisfied	satisfied	ADJ
iajs-3094	17	42	and	and	CCONJ
iajs-3094	17	43	certain	certain	ADJ
iajs-3094	17	44	goals	goal	NOUN
iajs-3094	17	45	are	be	AUX
iajs-3094	17	46	achieved	achieve	VERB
iajs-3094	17	47	[	[	PUNCT
iajs-3094	17	48	2	2	NUM
iajs-3094	17	49	-	-	SYM
iajs-3094	17	50	4	4	NUM
iajs-3094	17	51	]	]	PUNCT
iajs-3094	17	52	.	.	PUNCT
iajs-3094	18	1	up	up	ADV
iajs-3094	18	2	until	until	ADP
iajs-3094	18	3	the	the	DET
iajs-3094	18	4	late	late	ADJ
iajs-3094	18	5	1980s	1980	NOUN
iajs-3094	18	6	,	,	PUNCT
iajs-3094	18	7	mainstream	mainstream	NOUN
iajs-3094	18	8	research	research	NOUN
iajs-3094	18	9	has	have	AUX
iajs-3094	18	10	concentrated	concentrate	VERB
iajs-3094	18	11	on	on	ADP
iajs-3094	18	12	a	a	DET
iajs-3094	18	13	certain	certain	ADJ
iajs-3094	18	14	single	single	ADJ
iajs-3094	18	15	object	object	NOUN
iajs-3094	18	16	problem	problem	NOUN
iajs-3094	18	17	.	.	PUNCT
iajs-3094	19	1	when	when	SCONJ
iajs-3094	19	2	more	more	ADJ
iajs-3094	19	3	than	than	ADP
iajs-3094	19	4	one	one	NUM
iajs-3094	19	5	objective	objective	NOUN
iajs-3094	19	6	(	(	PUNCT
iajs-3094	19	7	criteria	criterion	NOUN
iajs-3094	19	8	)	)	PUNCT
iajs-3094	19	9	is	be	AUX
iajs-3094	19	10	needed	need	VERB
iajs-3094	19	11	,	,	PUNCT
iajs-3094	19	12	scheduling	scheduling	NOUN
iajs-3094	19	13	problems	problem	NOUN
iajs-3094	19	14	become	become	VERB
iajs-3094	19	15	more	more	ADV
iajs-3094	19	16	difficult	difficult	ADJ
iajs-3094	19	17	to	to	PART
iajs-3094	19	18	model	model	VERB
iajs-3094	19	19	and	and	CCONJ
iajs-3094	19	20	solve	solve	VERB
iajs-3094	19	21	.	.	PUNCT
iajs-3094	20	1	it	it	PRON
iajs-3094	20	2	is	be	AUX
iajs-3094	20	3	frequently	frequently	ADV
iajs-3094	20	4	implausible	implausible	ADJ
iajs-3094	20	5	that	that	SCONJ
iajs-3094	20	6	different	different	ADJ
iajs-3094	20	7	objectives	objective	NOUN
iajs-3094	20	8	will	will	AUX
iajs-3094	20	9	be	be	AUX
iajs-3094	20	10	best	well	ADV
iajs-3094	20	11	served	serve	VERB
iajs-3094	20	12	by	by	ADP
iajs-3094	20	13	the	the	DET
iajs-3094	20	14	same	same	ADJ
iajs-3094	20	15	set	set	NOUN
iajs-3094	20	16	of	of	ADP
iajs-3094	20	17	decision	decision	NOUN
iajs-3094	20	18	variables	variable	NOUN
iajs-3094	20	19	[	[	X
iajs-3094	20	20	5	5	NUM
iajs-3094	20	21	-	-	SYM
iajs-3094	20	22	8	8	NUM
iajs-3094	20	23	]	]	PUNCT
iajs-3094	20	24	.	.	PUNCT
iajs-3094	21	1	as	as	ADP
iajs-3094	21	2	a	a	DET
iajs-3094	21	3	result	result	NOUN
iajs-3094	21	4	,	,	PUNCT
iajs-3094	21	5	there	there	PRON
iajs-3094	21	6	is	be	VERB
iajs-3094	21	7	a	a	DET
iajs-3094	21	8	trade	trade	NOUN
iajs-3094	21	9	-	-	PUNCT
iajs-3094	21	10	off	off	NOUN
iajs-3094	21	11	between	between	ADP
iajs-3094	21	12	the	the	DET
iajs-3094	21	13	multiple	multiple	ADJ
iajs-3094	21	14	objectives	objective	NOUN
iajs-3094	21	15	.	.	PUNCT
iajs-3094	22	1	this	this	DET
iajs-3094	22	2	type	type	NOUN
iajs-3094	22	3	of	of	ADP
iajs-3094	22	4	problem	problem	NOUN
iajs-3094	22	5	is	be	AUX
iajs-3094	22	6	known	know	VERB
iajs-3094	22	7	as	as	ADP
iajs-3094	22	8	a	a	DET
iajs-3094	22	9	multi	multi	ADJ
iajs-3094	22	10	-	-	ADJ
iajs-3094	22	11	objective	objective	ADJ
iajs-3094	22	12	scheduling	scheduling	NOUN
iajs-3094	22	13	problem	problem	NOUN
iajs-3094	22	14	.	.	PUNCT
iajs-3094	23	1	multi	multi	ADJ
iajs-3094	23	2	-	-	ADJ
iajs-3094	23	3	objective	objective	ADJ
iajs-3094	23	4	scheduling	scheduling	NOUN
iajs-3094	23	5	problems	problem	NOUN
iajs-3094	23	6	are	be	AUX
iajs-3094	23	7	the	the	DET
iajs-3094	23	8	term	term	NOUN
iajs-3094	23	9	used	use	VERB
iajs-3094	23	10	to	to	PART
iajs-3094	23	11	describe	describe	VERB
iajs-3094	23	12	this	this	DET
iajs-3094	23	13	kind	kind	NOUN
iajs-3094	23	14	of	of	ADP
iajs-3094	23	15	problem	problem	NOUN
iajs-3094	23	16	[	[	X
iajs-3094	23	17	9	9	NUM
iajs-3094	23	18	]	]	PUNCT
iajs-3094	23	19	.	.	PUNCT
iajs-3094	24	1	a	a	DET
iajs-3094	24	2	set	set	NOUN
iajs-3094	24	3	of	of	ADP
iajs-3094	24	4	pareto	pareto	ADJ
iajs-3094	24	5	optimal	optimal	ADJ
iajs-3094	24	6	solutions	solution	NOUN
iajs-3094	24	7	(	(	PUNCT
iajs-3094	24	8	efficient	efficient	ADJ
iajs-3094	24	9	solutions	solution	NOUN
iajs-3094	24	10	)	)	PUNCT
iajs-3094	24	11	,	,	PUNCT
iajs-3094	24	12	rather	rather	ADV
iajs-3094	24	13	than	than	ADP
iajs-3094	24	14	a	a	DET
iajs-3094	24	15	single	single	ADJ
iajs-3094	24	16	optimal	optimal	ADJ
iajs-3094	24	17	solution	solution	NOUN
iajs-3094	24	18	,	,	PUNCT
iajs-3094	24	19	are	be	AUX
iajs-3094	24	20	established	establish	VERB
iajs-3094	24	21	using	use	VERB
iajs-3094	24	22	multi	multi	ADJ
iajs-3094	24	23	-	-	ADJ
iajs-3094	24	24	criteria	criteria	ADJ
iajs-3094	24	25	optimization	optimization	NOUN
iajs-3094	24	26	based	base	VERB
iajs-3094	24	27	on	on	ADP
iajs-3094	24	28	competing	compete	VERB
iajs-3094	24	29	objective	objective	ADJ
iajs-3094	24	30	functions	function	NOUN
iajs-3094	24	31	.	.	PUNCT
iajs-3094	25	1	this	this	DET
iajs-3094	25	2	set	set	NOUN
iajs-3094	25	3	includes	include	VERB
iajs-3094	25	4	one	one	NUM
iajs-3094	25	5	(	(	PUNCT
iajs-3094	25	6	many	many	ADJ
iajs-3094	25	7	)	)	PUNCT
iajs-3094	25	8	solution(s	solution(s	NOUN
iajs-3094	25	9	)	)	PUNCT
iajs-3094	25	10	that	that	SCONJ
iajs-3094	25	11	no	no	DET
iajs-3094	25	12	other	other	ADJ
iajs-3094	25	13	solution(s	solution(s	NOUN
iajs-3094	25	14	)	)	PUNCT
iajs-3094	25	15	is	be	AUX
iajs-3094	25	16	better	well	ADJ
iajs-3094	25	17	with	with	ADP
iajs-3094	25	18	respect	respect	NOUN
iajs-3094	25	19	to	to	ADP
iajs-3094	25	20	objective	objective	ADJ
iajs-3094	25	21	functions[[10	functions[[10	NOUN
iajs-3094	25	22	-	-	PUNCT
iajs-3094	25	23	14	14	NUM
iajs-3094	25	24	]	]	PUNCT
iajs-3094	25	25	.	.	PUNCT
iajs-3094	26	1	the	the	DET
iajs-3094	26	2	most	most	ADV
iajs-3094	26	3	important	important	ADJ
iajs-3094	26	4	literature	literature	NOUN
iajs-3094	26	5	survey	survey	NOUN
iajs-3094	26	6	for	for	ADP
iajs-3094	26	7	the	the	DET
iajs-3094	26	8	last	last	ADJ
iajs-3094	26	9	eight	eight	NUM
iajs-3094	26	10	years	year	NOUN
iajs-3094	26	11	.	.	PUNCT
iajs-3094	27	1	[	[	X
iajs-3094	27	2	15	15	NUM
iajs-3094	27	3	]	]	PUNCT
iajs-3094	27	4	discussed	discuss	VERB
iajs-3094	27	5	the	the	DET
iajs-3094	27	6	multi	multi	NOUN
iajs-3094	27	7	-	-	NOUN
iajs-3094	27	8	criteria	criterion	NOUN
iajs-3094	27	9	in	in	ADP
iajs-3094	27	10	order	order	NOUN
iajs-3094	27	11	to	to	PART
iajs-3094	27	12	establish	establish	VERB
iajs-3094	27	13	a	a	DET
iajs-3094	27	14	collection	collection	NOUN
iajs-3094	27	15	of	of	ADP
iajs-3094	27	16	efficient	efficient	ADJ
iajs-3094	27	17	solutions	solution	NOUN
iajs-3094	27	18	for	for	ADP
iajs-3094	27	19	the	the	DET
iajs-3094	27	20	general	general	ADJ
iajs-3094	27	21	problem	problem	NOUN
iajs-3094	27	22	,	,	PUNCT
iajs-3094	27	23	and	and	CCONJ
iajs-3094	27	24	scheduling	scheduling	NOUN
iajs-3094	27	25	problems	problem	NOUN
iajs-3094	27	26	that	that	PRON
iajs-3094	27	27	are	be	AUX
iajs-3094	27	28	researched	research	VERB
iajs-3094	27	29	on	on	ADP
iajs-3094	27	30	a	a	DET
iajs-3094	27	31	single	single	ADJ
iajs-3094	27	32	machine	machine	NOUN
iajs-3094	27	33	are	be	AUX
iajs-3094	27	34	considered	consider	VERB
iajs-3094	27	35	.	.	PUNCT
iajs-3094	28	1	1//	1//	NUM
iajs-3094	28	2	(	(	PUNCT
iajs-3094	28	3	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	28	4	,	,	PUNCT
iajs-3094	28	5	∑𝑻𝒋	∑𝑻𝒋	PROPN
iajs-3094	28	6	,	,	PUNCT
iajs-3094	28	7	𝑻𝑴𝒂𝒙	𝑻𝑴𝒂𝒙	NUM
iajs-3094	28	8	)	)	PUNCT
iajs-3094	28	9	,	,	PUNCT
iajs-3094	28	10	1//	1//	NUM
iajs-3094	28	11	𝑭(∑𝑪𝒋	𝑭(∑𝑪𝒋	NOUN
iajs-3094	28	12	,	,	PUNCT
iajs-3094	28	13	∑𝑬𝒋	∑𝑬𝒋	PROPN
iajs-3094	28	14	,	,	PUNCT
iajs-3094	28	15	𝑬𝑴𝒂𝒙	𝑬𝑴𝒂𝒙	PROPN
iajs-3094	28	16	)	)	PUNCT
iajs-3094	28	17	,	,	PUNCT
iajs-3094	28	18	1//	1//	NUM
iajs-3094	28	19	∑𝑪𝒋	∑𝑪𝒋	PUNCT
iajs-3094	29	1	+	+	CCONJ
iajs-3094	29	2	∑𝑻𝒋	∑𝑻𝒋	PROPN
iajs-3094	29	3	+	+	CCONJ
iajs-3094	29	4	𝑻𝑴𝒂𝒙	𝑻𝑴𝒂𝒙	PROPN
iajs-3094	29	5	,	,	PUNCT
iajs-3094	29	6	1//	1//	NUM
iajs-3094	29	7	∑𝑪𝒋	∑𝑪𝒋	PUNCT
iajs-3094	30	1	+	+	CCONJ
iajs-3094	30	2	∑𝑬𝒋	∑𝑬𝒋	VERB
iajs-3094	30	3	+	+	NUM
iajs-3094	30	4	𝑻𝑴𝒂𝒙.	𝑻𝑴𝒂𝒙.	NOUN
iajs-3094	31	1	[	[	X
iajs-3094	31	2	16	16	NUM
iajs-3094	31	3	]	]	PUNCT
iajs-3094	31	4	examined	examine	VERB
iajs-3094	31	5	the	the	DET
iajs-3094	31	6	multiobjective	multiobjective	ADJ
iajs-3094	31	7	problem	problem	NOUN
iajs-3094	31	8	,	,	PUNCT
iajs-3094	31	9	which	which	PRON
iajs-3094	31	10	is	be	AUX
iajs-3094	31	11	the	the	DET
iajs-3094	31	12	sum	sum	NOUN
iajs-3094	31	13	of	of	ADP
iajs-3094	31	14	completion	completion	NOUN
iajs-3094	31	15	time	time	NOUN
iajs-3094	31	16	,	,	PUNCT
iajs-3094	31	17	tardiness	tardiness	NOUN
iajs-3094	31	18	,	,	PUNCT
iajs-3094	31	19	earliness	earliness	NOUN
iajs-3094	31	20	,	,	PUNCT
iajs-3094	31	21	and	and	CCONJ
iajs-3094	31	22	late	late	ADJ
iajs-3094	31	23	work	work	NOUN
iajs-3094	31	24	.	.	PUNCT
iajs-3094	32	1	1//	1//	NUM
iajs-3094	32	2	∑	∑	PUNCT
iajs-3094	32	3	(	(	PUNCT
iajs-3094	32	4	𝑬𝒋	𝑬𝒋	PROPN
iajs-3094	32	5	+	+	CCONJ
iajs-3094	32	6	𝑻𝒋	𝑻𝒋	PROPN
iajs-3094	32	7	+	+	X
iajs-3094	32	8	𝑪𝒋	𝑪𝒋	ADP
iajs-3094	32	9	+	+	ADJ
iajs-3094	32	10	𝑼𝒋	𝑼𝒋	PROPN
iajs-3094	32	11	+	+	CCONJ
iajs-3094	32	12	𝑽𝒋	𝑽𝒋	PROPN
iajs-3094	32	13	)	)	PUNCT
iajs-3094	32	14	𝒏	𝒏	PROPN
iajs-3094	32	15	=	=	PRON
iajs-3094	32	16	𝟏	𝟏	PROPN
iajs-3094	32	17	,	,	PUNCT
iajs-3094	32	18	1//∑	1//∑	NUM
iajs-3094	32	19	(	(	PUNCT
iajs-3094	32	20	𝜶𝑱𝑬𝒋	𝜶𝑱𝑬𝒋	X
iajs-3094	32	21	+	+	NOUN
iajs-3094	32	22	𝜷𝒋𝑻𝒋	𝜷𝒋𝑻𝒋	NOUN
iajs-3094	32	23	+	+	CCONJ
iajs-3094	32	24	𝜽𝒋𝑪𝒋	𝜽𝒋𝑪𝒋	NOUN
iajs-3094	32	25	+	+	CCONJ
iajs-3094	32	26	𝜸𝒋𝑼𝒋	𝜸𝒋𝑼𝒋	NOUN
iajs-3094	32	27	+	+	NOUN
iajs-3094	32	28	𝝎𝒋𝑽𝒋	𝝎𝒋𝑽𝒋	X
iajs-3094	32	29	)	)	PUNCT
iajs-3094	32	30	𝒏	𝒏	PROPN
iajs-3094	32	31	=	=	PRON
iajs-3094	32	32	𝟏	𝟏	PROPN
iajs-3094	32	33	,	,	PUNCT
iajs-3094	32	34	1/𝑺𝒇/	1/𝑺𝒇/	PROPN
iajs-3094	32	35	∑	∑	PROPN
iajs-3094	32	36	(	(	PUNCT
iajs-3094	32	37	𝜶𝒋𝒇𝑬𝒋𝒇	𝜶𝒋𝒇𝑬𝒋𝒇	NOUN
iajs-3094	32	38	+	+	CCONJ
iajs-3094	32	39	𝒏	𝒏	PROPN
iajs-3094	32	40	=	=	ADJ
iajs-3094	32	41	𝟏	𝟏	X
iajs-3094	32	42	𝜷𝒋𝒇𝑻𝒋𝒇	𝜷𝒋𝒇𝑻𝒋𝒇	NOUN
iajs-3094	32	43	+	+	CCONJ
iajs-3094	32	44	𝜽𝒋𝒇𝑪𝒋𝒇	𝜽𝒋𝒇𝑪𝒋𝒇	PROPN
iajs-3094	32	45	+	+	NUM
iajs-3094	32	46	𝜸𝒋𝒇𝑼𝒋𝒇	𝜸𝒋𝒇𝑼𝒋𝒇	NOUN
iajs-3094	32	47	+	+	NOUN
iajs-3094	32	48	𝝎𝒋𝒇𝑽𝒋𝒇	𝝎𝒋𝒇𝑽𝒋𝒇	NOUN
iajs-3094	32	49	)	)	PUNCT
iajs-3094	32	50	.	.	PUNCT
iajs-3094	33	1	they	they	PRON
iajs-3094	33	2	suggested	suggest	VERB
iajs-3094	33	3	an	an	DET
iajs-3094	33	4	upper	upper	ADJ
iajs-3094	33	5	bound	bind	VERB
iajs-3094	33	6	(	(	PUNCT
iajs-3094	33	7	limits	limit	NOUN
iajs-3094	33	8	)	)	PUNCT
iajs-3094	33	9	ub	ub	NOUN
iajs-3094	33	10	and	and	CCONJ
iajs-3094	33	11	a	a	DET
iajs-3094	33	12	lower	low	ADJ
iajs-3094	33	13	boundary	boundary	NOUN
iajs-3094	33	14	(	(	PUNCT
iajs-3094	33	15	limits	limit	NOUN
iajs-3094	33	16	)	)	PUNCT
iajs-3094	33	17	lb	lb	NOUN
iajs-3094	33	18	be	be	AUX
iajs-3094	33	19	used	use	VERB
iajs-3094	33	20	in	in	ADP
iajs-3094	33	21	the	the	DET
iajs-3094	33	22	application	application	NOUN
iajs-3094	33	23	of	of	ADP
iajs-3094	33	24	the	the	DET
iajs-3094	33	25	branch	branch	NOUN
iajs-3094	33	26	and	and	CCONJ
iajs-3094	33	27	bound	bind	VERB
iajs-3094	33	28	method	method	NOUN
iajs-3094	33	29	.	.	PUNCT
iajs-3094	34	1	[	[	X
iajs-3094	34	2	17	17	NUM
iajs-3094	34	3	]	]	PUNCT
iajs-3094	34	4	studied	study	VERB
iajs-3094	34	5	the	the	DET
iajs-3094	34	6	multi	multi	NOUN
iajs-3094	34	7	-	-	NOUN
iajs-3094	34	8	criteria	criterion	NOUN
iajs-3094	34	9	(	(	PUNCT
iajs-3094	34	10	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	34	11	,	,	PUNCT
iajs-3094	34	12	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	34	13	,	,	PUNCT
iajs-3094	34	14	𝑹𝑳	𝑹𝑳	PROPN
iajs-3094	34	15	)	)	PUNCT
iajs-3094	34	16	,	,	PUNCT
iajs-3094	34	17	multi	multi	ADJ
iajs-3094	34	18	-	-	ADJ
iajs-3094	34	19	objective	objective	ADJ
iajs-3094	34	20	function	function	NOUN
iajs-3094	34	21	(	(	PUNCT
iajs-3094	34	22	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	34	23	+	+	PUNCT
iajs-3094	34	24	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	34	25	+	+	CCONJ
iajs-3094	34	26	𝑹𝑳	𝑹𝑳	PROPN
iajs-3094	34	27	)	)	PUNCT
iajs-3094	34	28	and	and	CCONJ
iajs-3094	34	29	founded	found	VERB
iajs-3094	34	30	the	the	DET
iajs-3094	34	31	optimal	optimal	ADJ
iajs-3094	34	32	solution	solution	NOUN
iajs-3094	34	33	by	by	ADP
iajs-3094	34	34	using	use	VERB
iajs-3094	34	35	the	the	DET
iajs-3094	34	36	bab	bab	PROPN
iajs-3094	34	37	method	method	NOUN
iajs-3094	34	38	with	with	ADP
iajs-3094	34	39	and	and	CCONJ
iajs-3094	34	40	without	without	ADP
iajs-3094	34	41	dr	dr	PROPN
iajs-3094	34	42	then	then	ADV
iajs-3094	34	43	using	use	VERB
iajs-3094	34	44	some	some	DET
iajs-3094	34	45	heuristic	heuristic	ADJ
iajs-3094	34	46	methods	method	NOUN
iajs-3094	34	47	.	.	PUNCT
iajs-3094	35	1	[	[	X
iajs-3094	35	2	18	18	NUM
iajs-3094	35	3	]	]	PUNCT
iajs-3094	35	4	introduced	introduce	VERB
iajs-3094	35	5	a	a	DET
iajs-3094	35	6	heuristic	heuristic	ADJ
iajs-3094	35	7	algorithm	algorithm	NOUN
iajs-3094	35	8	to	to	PART
iajs-3094	35	9	reduce	reduce	VERB
iajs-3094	35	10	the	the	DET
iajs-3094	35	11	(	(	PUNCT
iajs-3094	35	12	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	35	13	+	+	PUNCT
iajs-3094	35	14	𝑬𝒎𝒂𝒙	𝑬𝒎𝒂𝒙	NOUN
iajs-3094	35	15	+	+	CCONJ
iajs-3094	35	16	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	35	17	)	)	PUNCT
iajs-3094	35	18	in	in	ADP
iajs-3094	35	19	a	a	DET
iajs-3094	35	20	single	single	ADJ
iajs-3094	35	21	machine	machine	NOUN
iajs-3094	35	22	scheduling	scheduling	NOUN
iajs-3094	35	23	.	.	PUNCT
iajs-3094	36	1	in	in	ADP
iajs-3094	36	2	this	this	DET
iajs-3094	36	3	paper	paper	NOUN
iajs-3094	36	4	,	,	PUNCT
iajs-3094	36	5	survey	survey	VERB
iajs-3094	36	6	the	the	DET
iajs-3094	36	7	tricriteria	tricriteria	NOUN
iajs-3094	36	8	scheduling	scheduling	NOUN
iajs-3094	36	9	problem	problem	NOUN
iajs-3094	36	10	and	and	CCONJ
iajs-3094	36	11	begin	begin	VERB
iajs-3094	36	12	with	with	ADP
iajs-3094	36	13	some	some	DET
iajs-3094	36	14	basic	basic	ADJ
iajs-3094	36	15	scheduling	scheduling	NOUN
iajs-3094	36	16	concepts	concept	NOUN
iajs-3094	36	17	of	of	ADP
iajs-3094	36	18	multi	multi	ADJ
iajs-3094	36	19	-	-	ADJ
iajs-3094	36	20	criteria	criterion	NOUN
iajs-3094	36	21	problems	problem	NOUN
iajs-3094	36	22	,	,	PUNCT
iajs-3094	36	23	and	and	CCONJ
iajs-3094	36	24	basic	basic	ADJ
iajs-3094	36	25	rules	rule	NOUN
iajs-3094	36	26	are	be	AUX
iajs-3094	36	27	given	give	VERB
iajs-3094	36	28	in	in	ADP
iajs-3094	36	29	section	section	NOUN
iajs-3094	36	30	1	1	NUM
iajs-3094	36	31	.	.	PUNCT
iajs-3094	36	32	section	section	NOUN
iajs-3094	36	33	2	2	NUM
iajs-3094	36	34	provides	provide	VERB
iajs-3094	36	35	information	information	NOUN
iajs-3094	36	36	on	on	ADP
iajs-3094	36	37	problem	problem	NOUN
iajs-3094	36	38	formulation	formulation	NOUN
iajs-3094	36	39	,	,	PUNCT
iajs-3094	36	40	analysis	analysis	NOUN
iajs-3094	36	41	,	,	PUNCT
iajs-3094	36	42	and	and	CCONJ
iajs-3094	36	43	various	various	ADJ
iajs-3094	36	44	algorithms	algorithm	NOUN
iajs-3094	36	45	.	.	PUNCT
iajs-3094	37	1	the	the	DET
iajs-3094	37	2	dominance	dominance	NOUN
iajs-3094	37	3	rule	rule	NOUN
iajs-3094	37	4	is	be	AUX
iajs-3094	37	5	described	describe	VERB
iajs-3094	37	6	in	in	ADP
iajs-3094	37	7	section	section	NOUN
iajs-3094	37	8	3	3	NUM
iajs-3094	37	9	.	.	PUNCT
iajs-3094	38	1	in	in	ADP
iajs-3094	38	2	section	section	NOUN
iajs-3094	38	3	4	4	NUM
iajs-3094	38	4	by	by	ADP
iajs-3094	38	5	proving	prove	VERB
iajs-3094	38	6	several	several	ADJ
iajs-3094	38	7	rules	rule	NOUN
iajs-3094	38	8	,	,	PUNCT
iajs-3094	38	9	we	we	PRON
iajs-3094	38	10	show	show	VERB
iajs-3094	38	11	there	there	PRON
iajs-3094	38	12	exists	exist	VERB
iajs-3094	38	13	is	be	AUX
iajs-3094	38	14	an	an	DET
iajs-3094	38	15	effective	effective	ADJ
iajs-3094	38	16	solution	solution	NOUN
iajs-3094	38	17	to	to	ADP
iajs-3094	38	18	our	our	PRON
iajs-3094	38	19	problem	problem	NOUN
iajs-3094	38	20	.	.	PUNCT
iajs-3094	39	1	the	the	DET
iajs-3094	39	2	conclusions	conclusion	NOUN
iajs-3094	39	3	is	be	AUX
iajs-3094	39	4	given	give	VERB
iajs-3094	39	5	in	in	ADP
iajs-3094	39	6	section	section	NOUN
iajs-3094	39	7	5	5	NUM
iajs-3094	39	8	and	and	CCONJ
iajs-3094	39	9	upcoming	upcoming	ADJ
iajs-3094	39	10	works	work	NOUN
iajs-3094	39	11	.	.	PUNCT
iajs-3094	40	1	2	2	X
iajs-3094	40	2	.	.	X
iajs-3094	40	3	significant	significant	ADJ
iajs-3094	40	4	notations	notation	NOUN
iajs-3094	40	5	.	.	PUNCT
iajs-3094	41	1	in	in	ADP
iajs-3094	41	2	this	this	DET
iajs-3094	41	3	paper	paper	NOUN
iajs-3094	41	4	,	,	PUNCT
iajs-3094	41	5	the	the	DET
iajs-3094	41	6	following	follow	VERB
iajs-3094	41	7	notations	notation	NOUN
iajs-3094	41	8	are	be	AUX
iajs-3094	41	9	used	use	VERB
iajs-3094	41	10	:	:	PUNCT
iajs-3094	41	11	𝑵	𝑵	NOUN
iajs-3094	41	12	:	:	PUNCT
iajs-3094	41	13	jobs	job	NOUN
iajs-3094	41	14	set	set	VERB
iajs-3094	41	15	s.	s.	PROPN
iajs-3094	41	16	t.	t.	PROPN
iajs-3094	41	17	𝑁	𝑁	PROPN
iajs-3094	41	18	=	=	SYM
iajs-3094	41	19	{	{	PUNCT
iajs-3094	41	20	1,2	1,2	NUM
iajs-3094	41	21	,	,	PUNCT
iajs-3094	41	22	…	…	PUNCT
iajs-3094	41	23	,	,	PUNCT
iajs-3094	41	24	𝑛	𝑛	NOUN
iajs-3094	41	25	}	}	PUNCT
iajs-3094	41	26	.	.	PUNCT
iajs-3094	42	1	𝒏	𝒏	NOUN
iajs-3094	42	2	:	:	PUNCT
iajs-3094	42	3	number	number	NOUN
iajs-3094	42	4	of	of	ADP
iajs-3094	42	5	available	available	ADJ
iajs-3094	42	6	jobs	job	NOUN
iajs-3094	42	7	.	.	PUNCT
iajs-3094	43	1	𝒑𝒋	𝒑𝒋	NOUN
iajs-3094	43	2	:	:	PUNCT
iajs-3094	43	3	ttime	ttime	NOUN
iajs-3094	43	4	of	of	ADP
iajs-3094	43	5	the	the	DET
iajs-3094	43	6	job	job	NOUN
iajs-3094	43	7	𝑗′𝑠	𝑗′𝑠	NOUN
iajs-3094	43	8	processing	processing	NOUN
iajs-3094	43	9	,	,	PUNCT
iajs-3094	43	10	which	which	PRON
iajs-3094	43	11	means	mean	VERB
iajs-3094	43	12	it	it	PRON
iajs-3094	43	13	must	must	AUX
iajs-3094	43	14	be	be	AUX
iajs-3094	43	15	processed	process	VERB
iajs-3094	43	16	for	for	ADP
iajs-3094	43	17	a	a	DET
iajs-3094	43	18	period	period	NOUN
iajs-3094	43	19	of	of	ADP
iajs-3094	43	20	length	length	NOUN
iajs-3094	43	21	𝒑𝒋.	𝒑𝒋.	PROPN
iajs-3094	43	22	𝒅𝒋	𝒅𝒋	X
iajs-3094	43	23	:	:	PUNCT
iajs-3094	43	24	the	the	DET
iajs-3094	43	25	due	due	ADJ
iajs-3094	43	26	date	date	NOUN
iajs-3094	43	27	for	for	ADP
iajs-3094	43	28	job	job	NOUN
iajs-3094	43	29	𝑗	𝑗	NOUN
iajs-3094	43	30	(	(	PUNCT
iajs-3094	43	31	or	or	CCONJ
iajs-3094	43	32	the	the	DET
iajs-3094	43	33	jobs	job	NOUN
iajs-3094	43	34	’	'	PUNCT
iajs-3094	43	35	due	due	ADJ
iajs-3094	43	36	date	date	NOUN
iajs-3094	43	37	)	)	PUNCT
iajs-3094	43	38	,	,	PUNCT
iajs-3094	43	39	the	the	DET
iajs-3094	43	40	optimal	optimal	ADJ
iajs-3094	43	41	date	date	NOUN
iajs-3094	43	42	for	for	ADP
iajs-3094	43	43	finishing	finish	VERB
iajs-3094	43	44	the	the	DET
iajs-3094	43	45	jobs	job	NOUN
iajs-3094	43	46	;	;	PUNCT
iajs-3094	43	47	job	job	NOUN
iajs-3094	43	48	termination	termination	NOUN
iajs-3094	43	49	after	after	SCONJ
iajs-3094	43	50	the	the	DET
iajs-3094	43	51	deadline	deadline	NOUN
iajs-3094	43	52	is	be	AUX
iajs-3094	43	53	allowed	allow	VERB
iajs-3094	43	54	but	but	CCONJ
iajs-3094	43	55	will	will	AUX
iajs-3094	43	56	result	result	VERB
iajs-3094	43	57	in	in	ADP
iajs-3094	43	58	a	a	DET
iajs-3094	43	59	penalty	penalty	NOUN
iajs-3094	43	60	.	.	PUNCT
iajs-3094	44	1	ihjpas	ihjpas	PROPN
iajs-3094	44	2	.	.	PUNCT
iajs-3094	45	1	37	37	NUM
iajs-3094	45	2	(	(	PUNCT
iajs-3094	45	3	1	1	NUM
iajs-3094	45	4	)	)	PUNCT
iajs-3094	45	5	2024	2024	NUM
iajs-3094	45	6	388	388	NUM
iajs-3094	45	7	𝒔𝒋	𝒔𝒋	NOUN
iajs-3094	45	8	:	:	PUNCT
iajs-3094	45	9	the	the	DET
iajs-3094	45	10	job	job	NOUN
iajs-3094	45	11	's	's	PART
iajs-3094	45	12	slack	slack	NOUN
iajs-3094	45	13	time	time	NOUN
iajs-3094	45	14	for	for	ADP
iajs-3094	45	15	𝑗	𝑗	PROPN
iajs-3094	45	16	s.	s.	PROPN
iajs-3094	45	17	t.	t.	PROPN
iajs-3094	45	18	𝑠𝑗	𝑠𝑗	PROPN
iajs-3094	45	19	=	=	SYM
iajs-3094	45	20	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	45	21	−	−	PROPN
iajs-3094	45	22	𝑝𝑗.	𝑝𝑗.	PROPN
iajs-3094	46	1	𝑪𝒋	𝑪𝒋	PROPN
iajs-3094	46	2	:	:	PUNCT
iajs-3094	46	3	the	the	DET
iajs-3094	46	4	job	job	NOUN
iajs-3094	46	5	𝑗′𝑠	𝑗′𝑠	ADP
iajs-3094	46	6	completion	completion	NOUN
iajs-3094	46	7	time	time	NOUN
iajs-3094	46	8	where	where	SCONJ
iajs-3094	46	9	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	46	10	=	=	SYM
iajs-3094	46	11	∑	∑	PUNCT
iajs-3094	46	12	𝑝𝑘	𝑝𝑘	ADP
iajs-3094	46	13	𝑗	𝑗	NOUN
iajs-3094	46	14	𝑘=1	𝑘=1	NOUN
iajs-3094	46	15	.	.	PUNCT
iajs-3094	47	1	𝑳𝒋	𝑳𝒋	NOUN
iajs-3094	47	2	:	:	PUNCT
iajs-3094	47	3	the	the	DET
iajs-3094	47	4	lateness	lateness	NOUN
iajs-3094	47	5	time	time	NOUN
iajs-3094	47	6	of	of	ADP
iajs-3094	47	7	jobs	job	NOUN
iajs-3094	47	8	,	,	PUNCT
iajs-3094	48	1	s.	s.	PROPN
iajs-3094	48	2	t.	t.	PROPN
iajs-3094	49	1	𝐿𝑗	𝐿𝑗	PROPN
iajs-3094	49	2	=	=	PUNCT
iajs-3094	49	3	−(𝑑𝑗	−(𝑑𝑗	PROPN
iajs-3094	50	1	−	−	NUM
iajs-3094	50	2	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	50	3	)	)	PUNCT
iajs-3094	50	4	=	=	PUNCT
iajs-3094	51	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	51	2	−	−	NOUN
iajs-3094	51	3	𝑑𝑗.	𝑑𝑗.	PROPN
iajs-3094	51	4	𝑬𝒋	𝑬𝒋	PROPN
iajs-3094	51	5	:	:	PUNCT
iajs-3094	51	6	the	the	DET
iajs-3094	51	7	earliness	earliness	NOUN
iajs-3094	51	8	of	of	ADP
iajs-3094	51	9	job	job	NOUN
iajs-3094	51	10	𝑗	𝑗	INTJ
iajs-3094	51	11	s.	s.	PROPN
iajs-3094	51	12	t.	t.	PROPN
iajs-3094	52	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	52	2	=	=	PUNCT
iajs-3094	52	3	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-3094	52	4	{	{	PUNCT
iajs-3094	52	5	−𝐿𝑗	−𝐿𝑗	X
iajs-3094	52	6	,	,	PUNCT
iajs-3094	52	7	0	0	NUM
iajs-3094	52	8	}	}	PUNCT
iajs-3094	52	9	=	=	PUNCT
iajs-3094	52	10	𝑚𝑎𝑥{𝑑𝑗	𝑚𝑎𝑥{𝑑𝑗	PUNCT
iajs-3094	52	11	−	−	PROPN
iajs-3094	52	12	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	52	13	,	,	PUNCT
iajs-3094	52	14	0	0	NUM
iajs-3094	52	15	}	}	PUNCT
iajs-3094	52	16	.	.	PUNCT
iajs-3094	53	1	𝑻𝒋	𝑻𝒋	ADP
iajs-3094	53	2	:	:	PUNCT
iajs-3094	53	3	the	the	DET
iajs-3094	53	4	tardiness	tardiness	NOUN
iajs-3094	53	5	of	of	ADP
iajs-3094	53	6	job	job	NOUN
iajs-3094	53	7	𝑗	𝑗	INTJ
iajs-3094	53	8	s.	s.	PROPN
iajs-3094	53	9	t.	t.	PROPN
iajs-3094	53	10	𝑇𝑗	𝑇𝑗	PROPN
iajs-3094	53	11	=	=	PUNCT
iajs-3094	53	12	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-3094	53	13	{	{	PUNCT
iajs-3094	53	14	𝐿𝑗	𝐿𝑗	PROPN
iajs-3094	53	15	,	,	PUNCT
iajs-3094	53	16	0	0	NUM
iajs-3094	53	17	}	}	PUNCT
iajs-3094	53	18	=	=	SYM
iajs-3094	53	19	𝑚𝑎𝑥{𝐶𝑗	𝑚𝑎𝑥{𝐶𝑗	NOUN
iajs-3094	53	20	−	−	NOUN
iajs-3094	53	21	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	53	22	,	,	PUNCT
iajs-3094	53	23	0	0	NUM
iajs-3094	53	24	}	}	PUNCT
iajs-3094	53	25	.	.	PUNCT
iajs-3094	54	1	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	54	2	:	:	PUNCT
iajs-3094	54	3	total	total	ADJ
iajs-3094	54	4	completion	completion	NOUN
iajs-3094	54	5	time	time	NOUN
iajs-3094	54	6	.	.	PUNCT
iajs-3094	55	1	∑𝑬𝒋	∑𝑬𝒋	VERB
iajs-3094	55	2	:	:	PUNCT
iajs-3094	55	3	total	total	ADJ
iajs-3094	55	4	earliness	earliness	NOUN
iajs-3094	55	5	time	time	NOUN
iajs-3094	55	6	.	.	PUNCT
iajs-3094	56	1	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	NOUN
iajs-3094	56	2	:	:	PUNCT
iajs-3094	56	3	maximum	maximum	ADJ
iajs-3094	56	4	tardiness	tardiness	NOUN
iajs-3094	57	1	s.	s.	PROPN
iajs-3094	57	2	t.	t.	PROPN
iajs-3094	57	3	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	57	4	=	=	PUNCT
iajs-3094	57	5	𝑚𝑎𝑥𝑗∈𝑁{𝑇𝑗	𝑚𝑎𝑥𝑗∈𝑁{𝑇𝑗	ADJ
iajs-3094	57	6	}	}	PUNCT
iajs-3094	57	7	.	.	PUNCT
iajs-3094	58	1	𝑭	𝑭	NOUN
iajs-3094	58	2	:	:	PUNCT
iajs-3094	58	3	the	the	DET
iajs-3094	58	4	₱	₱	PROPN
iajs-3094	58	5	-problem	-problem	PROPN
iajs-3094	58	6	's	's	PART
iajs-3094	58	7	objective	objective	ADJ
iajs-3094	58	8	function	function	NOUN
iajs-3094	58	9	.	.	PUNCT
iajs-3094	59	1	𝑭𝟏	𝑭𝟏	NOUN
iajs-3094	59	2	:	:	PUNCT
iajs-3094	59	3	the	the	DET
iajs-3094	59	4	(	(	PUNCT
iajs-3094	59	5	𝑆₱)-problem	𝑆₱)-problem	PROPN
iajs-3094	59	6	's	's	PART
iajs-3094	59	7	objective	objective	ADJ
iajs-3094	59	8	function	function	NOUN
iajs-3094	59	9	.	.	PUNCT
iajs-3094	60	1	shortest	short	ADJ
iajs-3094	60	2	processing	processing	NOUN
iajs-3094	60	3	tim	tim	PROPN
iajs-3094	60	4	(	(	PUNCT
iajs-3094	60	5	spt	spt	PROPN
iajs-3094	60	6	):	):	PUNCT
iajs-3094	60	7	jobs	job	NOUN
iajs-3094	60	8	are	be	AUX
iajs-3094	60	9	sequencing	sequence	VERB
iajs-3094	60	10	in	in	ADP
iajs-3094	60	11	non	non	ADJ
iajs-3094	60	12	-	-	ADJ
iajs-3094	60	13	decreasing	decrease	VERB
iajs-3094	60	14	order	order	NOUN
iajs-3094	60	15	of	of	ADP
iajs-3094	60	16	the	the	DET
iajs-3094	60	17	processing	processing	NOUN
iajs-3094	60	18	times	time	NOUN
iajs-3094	60	19	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	60	20	(	(	PUNCT
iajs-3094	60	21	i.	i.	PROPN
iajs-3094	60	22	e.	e.	PROPN
iajs-3094	60	23	𝑝1	𝑝1	PROPN
iajs-3094	60	24	≤	≤	PROPN
iajs-3094	60	25	𝑝2	𝑝2	PROPN
iajs-3094	60	26	≤	≤	NOUN
iajs-3094	60	27	⋯	⋯	NOUN
iajs-3094	60	28	≤	≤	NOUN
iajs-3094	60	29	𝑝𝑛	𝑝𝑛	ADP
iajs-3094	60	30	)	)	PUNCT
iajs-3094	60	31	,	,	PUNCT
iajs-3094	60	32	this	this	DET
iajs-3094	60	33	rule	rule	NOUN
iajs-3094	60	34	is	be	AUX
iajs-3094	60	35	well	well	ADV
iajs-3094	60	36	known	known	ADJ
iajs-3094	60	37	to	to	PART
iajs-3094	60	38	minimize	minimize	VERB
iajs-3094	60	39	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	60	40	for	for	ADP
iajs-3094	60	41	problem	problem	NOUN
iajs-3094	60	42	1//	1//	NUM
iajs-3094	60	43	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	61	1	[	[	X
iajs-3094	61	2	8	8	NUM
iajs-3094	61	3	]	]	PUNCT
iajs-3094	61	4	.	.	PUNCT
iajs-3094	62	1	earliest	early	ADJ
iajs-3094	62	2	due	due	ADJ
iajs-3094	62	3	date	date	NOUN
iajs-3094	62	4	(	(	PUNCT
iajs-3094	62	5	edd	edd	PROPN
iajs-3094	62	6	):	):	PUNCT
iajs-3094	62	7	jobs	job	NOUN
iajs-3094	62	8	are	be	AUX
iajs-3094	62	9	sequenced	sequence	VERB
iajs-3094	62	10	in	in	ADP
iajs-3094	62	11	non	non	ADJ
iajs-3094	62	12	-	-	ADJ
iajs-3094	62	13	decreasing	decrease	VERB
iajs-3094	62	14	order	order	NOUN
iajs-3094	62	15	of	of	ADP
iajs-3094	62	16	their	their	PRON
iajs-3094	62	17	due	due	ADJ
iajs-3094	62	18	dates	date	NOUN
iajs-3094	62	19	𝑑𝑗(i	𝑑𝑗(i	PROPN
iajs-3094	62	20	.	.	PUNCT
iajs-3094	63	1	e.	e.	PROPN
iajs-3094	63	2	𝑑1	𝑑1	PROPN
iajs-3094	63	3	≤	≤	PUNCT
iajs-3094	63	4	𝑑2	𝑑2	VERB
iajs-3094	63	5	≤	≤	NOUN
iajs-3094	63	6	⋯	⋯	NOUN
iajs-3094	63	7	≤	≤	PROPN
iajs-3094	63	8	𝑑𝑛	𝑑𝑛	NOUN
iajs-3094	63	9	)	)	PUNCT
iajs-3094	63	10	,	,	PUNCT
iajs-3094	63	11	this	this	DET
iajs-3094	63	12	rule	rule	NOUN
iajs-3094	63	13	used	use	VERB
iajs-3094	63	14	to	to	PART
iajs-3094	63	15	minimize	minimize	VERB
iajs-3094	63	16	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	63	17	for	for	ADP
iajs-3094	63	18	problem	problem	NOUN
iajs-3094	63	19	1//	1//	PROPN
iajs-3094	63	20	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	63	21	[	[	X
iajs-3094	63	22	19	19	NUM
iajs-3094	63	23	]	]	PUNCT
iajs-3094	63	24	.	.	PUNCT
iajs-3094	64	1	minimum	minimum	ADJ
iajs-3094	64	2	slack	slack	NOUN
iajs-3094	64	3	time	time	NOUN
iajs-3094	64	4	(	(	PUNCT
iajs-3094	64	5	mst	mst	PROPN
iajs-3094	64	6	):	):	PUNCT
iajs-3094	64	7	jobs	job	NOUN
iajs-3094	64	8	are	be	AUX
iajs-3094	64	9	sequenced	sequence	VERB
iajs-3094	64	10	in	in	ADP
iajs-3094	64	11	non	non	ADJ
iajs-3094	64	12	-	-	ADJ
iajs-3094	64	13	decreasing	decrease	VERB
iajs-3094	64	14	order	order	NOUN
iajs-3094	64	15	of	of	ADP
iajs-3094	64	16	their	their	PRON
iajs-3094	64	17	slack	slack	NOUN
iajs-3094	64	18	time	time	NOUN
iajs-3094	64	19	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	64	20	=	=	NOUN
iajs-3094	64	21	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	64	22	−	−	PROPN
iajs-3094	64	23	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	64	24	(	(	PUNCT
iajs-3094	64	25	i.	i.	PROPN
iajs-3094	64	26	e.	e.	PROPN
iajs-3094	64	27	𝑠1	𝑠1	PROPN
iajs-3094	64	28	≤	≤	NOUN
iajs-3094	64	29	𝑠2	𝑠2	NOUN
iajs-3094	64	30	≤	≤	PROPN
iajs-3094	64	31	⋯	⋯	NOUN
iajs-3094	64	32	≤	≤	ADJ
iajs-3094	64	33	𝑠𝑛	𝑠𝑛	NOUN
iajs-3094	64	34	)	)	PUNCT
iajs-3094	64	35	.	.	PUNCT
iajs-3094	65	1	to	to	PART
iajs-3094	65	2	minimize	minimize	VERB
iajs-3094	65	3	𝐸𝑚𝑎𝑥	𝐸𝑚𝑎𝑥	PROPN
iajs-3094	65	4	using	use	VERB
iajs-3094	65	5	this	this	DET
iajs-3094	65	6	rule	rule	NOUN
iajs-3094	65	7	[	[	X
iajs-3094	65	8	20	20	NUM
iajs-3094	65	9	]	]	PUNCT
iajs-3094	65	10	.	.	PUNCT
iajs-3094	66	1	efficient	efficient	ADJ
iajs-3094	66	2	solution	solution	NOUN
iajs-3094	66	3	(	(	PUNCT
iajs-3094	66	4	efso	efso	PROPN
iajs-3094	66	5	):	):	PUNCT
iajs-3094	66	6	a	a	DET
iajs-3094	66	7	feasible	feasible	ADJ
iajs-3094	66	8	schedule	schedule	NOUN
iajs-3094	66	9	𝛼∗	𝛼∗	NOUN
iajs-3094	66	10	is	be	AUX
iajs-3094	66	11	known	know	VERB
iajs-3094	66	12	as	as	ADP
iajs-3094	66	13	pareto	pareto	ADJ
iajs-3094	66	14	optimal	optimal	ADJ
iajs-3094	66	15	or	or	CCONJ
iajs-3094	66	16	(	(	PUNCT
iajs-3094	66	17	nondominated	nondominate	VERB
iajs-3094	66	18	)	)	PUNCT
iajs-3094	66	19	if	if	SCONJ
iajs-3094	66	20	there	there	PRON
iajs-3094	66	21	is	be	VERB
iajs-3094	66	22	absolutely	absolutely	ADV
iajs-3094	66	23	no	no	DET
iajs-3094	66	24	feasible	feasible	ADJ
iajs-3094	66	25	schedule	schedule	NOUN
iajs-3094	66	26	𝛼	𝛼	NOUN
iajs-3094	66	27	,	,	PUNCT
iajs-3094	66	28	then	then	ADV
iajs-3094	66	29	the	the	DET
iajs-3094	66	30	set	set	NOUN
iajs-3094	66	31	of	of	ADP
iajs-3094	66	32	feasible	feasible	ADJ
iajs-3094	66	33	schedules	schedule	NOUN
iajs-3094	66	34	with	with	ADP
iajs-3094	66	35	regard	regard	NOUN
iajs-3094	66	36	to	to	ADP
iajs-3094	66	37	the	the	DET
iajs-3094	66	38	criteria	criterion	NOUN
iajs-3094	66	39	ℎ1	ℎ1	PROPN
iajs-3094	66	40	,	,	PUNCT
iajs-3094	66	41	ℎ2	ℎ2	NOUN
iajs-3094	66	42	and	and	CCONJ
iajs-3094	66	43	ℎ3	ℎ3	NOUN
iajs-3094	66	44	such	such	ADJ
iajs-3094	66	45	that	that	SCONJ
iajs-3094	66	46	ℎ1(𝛼	ℎ1(𝛼	NOUN
iajs-3094	66	47	)	)	PUNCT
iajs-3094	66	48	≤	≤	PUNCT
iajs-3094	66	49	ℎ1(𝛼	ℎ1(𝛼	NUM
iajs-3094	66	50	∗	∗	NOUN
iajs-3094	66	51	)	)	PUNCT
iajs-3094	66	52	,	,	PUNCT
iajs-3094	66	53	ℎ2(𝛼	ℎ2(𝛼	PROPN
iajs-3094	66	54	)	)	PUNCT
iajs-3094	66	55	≤	≤	NUM
iajs-3094	66	56	ℎ2(𝛼	ℎ2(𝛼	NUM
iajs-3094	66	57	∗	∗	NOUN
iajs-3094	66	58	)	)	PUNCT
iajs-3094	66	59	and	and	CCONJ
iajs-3094	66	60	ℎ3(𝛼	ℎ3(𝛼	X
iajs-3094	66	61	)	)	PUNCT
iajs-3094	66	62	≤	≤	NOUN
iajs-3094	67	1	ℎ3(𝛼	ℎ3(𝛼	CCONJ
iajs-3094	67	2	∗	∗	NOUN
iajs-3094	67	3	)	)	PUNCT
iajs-3094	68	1	,	,	PUNCT
iajs-3094	68	2	are	be	AUX
iajs-3094	68	3	satisfied	satisfied	ADJ
iajs-3094	68	4	with	with	ADP
iajs-3094	68	5	at	at	ADV
iajs-3094	68	6	least	least	ADJ
iajs-3094	68	7	one	one	NUM
iajs-3094	68	8	of	of	ADP
iajs-3094	68	9	the	the	DET
iajs-3094	68	10	inequalities	inequality	NOUN
iajs-3094	68	11	[	[	X
iajs-3094	68	12	21	21	NUM
iajs-3094	68	13	]	]	PUNCT
iajs-3094	68	14	.	.	PUNCT
iajs-3094	69	1	3	3	X
iajs-3094	69	2	.	.	X
iajs-3094	69	3	mathematical	mathematical	ADJ
iajs-3094	69	4	formulation	formulation	NOUN
iajs-3094	69	5	in	in	ADP
iajs-3094	69	6	this	this	DET
iajs-3094	69	7	section	section	NOUN
iajs-3094	69	8	,	,	PUNCT
iajs-3094	69	9	the	the	DET
iajs-3094	69	10	three	three	NUM
iajs-3094	69	11	-	-	PUNCT
iajs-3094	69	12	criteria	criterion	NOUN
iajs-3094	69	13	scheduling	scheduling	NOUN
iajs-3094	69	14	problem	problem	NOUN
iajs-3094	69	15	(	(	PUNCT
iajs-3094	69	16	1//	1//	NUM
iajs-3094	69	17	𝑭(∑𝑪𝒋	𝑭(∑𝑪𝒋	NOUN
iajs-3094	69	18	,	,	PUNCT
iajs-3094	69	19	∑	∑	PUNCT
iajs-3094	69	20	𝑬𝒋	𝑬𝒋	PROPN
iajs-3094	69	21	,	,	PUNCT
iajs-3094	69	22	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	69	23	)	)	PUNCT
iajs-3094	69	24	)	)	PUNCT
iajs-3094	69	25	to	to	PART
iajs-3094	69	26	be	be	AUX
iajs-3094	69	27	studied	study	VERB
iajs-3094	69	28	will	will	AUX
iajs-3094	69	29	be	be	AUX
iajs-3094	69	30	described	describe	VERB
iajs-3094	69	31	.	.	PUNCT
iajs-3094	70	1	let	let	VERB
iajs-3094	70	2	the	the	DET
iajs-3094	70	3	number	number	NOUN
iajs-3094	70	4	of	of	ADP
iajs-3094	70	5	jobs	job	NOUN
iajs-3094	70	6	available	available	ADJ
iajs-3094	70	7	at	at	ADP
iajs-3094	70	8	time	time	NOUN
iajs-3094	70	9	0	0	NUM
iajs-3094	70	10	be	be	AUX
iajs-3094	70	11	represented	represent	VERB
iajs-3094	70	12	by	by	ADP
iajs-3094	70	13	𝑁	𝑁	PROPN
iajs-3094	70	14	=	=	SYM
iajs-3094	70	15	{	{	PUNCT
iajs-3094	70	16	1,2	1,2	NUM
iajs-3094	70	17	,	,	PUNCT
iajs-3094	70	18	…	…	PUNCT
iajs-3094	70	19	,	,	PUNCT
iajs-3094	70	20	𝑛	𝑛	PROPN
iajs-3094	70	21	}	}	PUNCT
iajs-3094	70	22	,	,	PUNCT
iajs-3094	70	23	(	(	PUNCT
iajs-3094	70	24	i.	i.	NOUN
iajs-3094	70	25	e	e	PROPN
iajs-3094	70	26	,	,	PUNCT
iajs-3094	70	27	𝑟𝑗	𝑟𝑗	ADP
iajs-3094	70	28	=	=	NOUN
iajs-3094	70	29	0	0	NUM
iajs-3094	70	30	for	for	ADP
iajs-3094	70	31	all	all	DET
iajs-3094	70	32	𝑗	𝑗	NOUN
iajs-3094	70	33	)	)	PUNCT
iajs-3094	70	34	and	and	CCONJ
iajs-3094	70	35	need	need	VERB
iajs-3094	70	36	processing	processing	NOUN
iajs-3094	70	37	on	on	ADP
iajs-3094	70	38	just	just	ADV
iajs-3094	70	39	one	one	NUM
iajs-3094	70	40	machine	machine	NOUN
iajs-3094	70	41	.	.	PUNCT
iajs-3094	71	1	for	for	ADP
iajs-3094	71	2	each	each	DET
iajs-3094	71	3	job	job	NOUN
iajs-3094	71	4	,	,	PUNCT
iajs-3094	71	5	𝑗	𝑗	PROPN
iajs-3094	71	6	has	have	VERB
iajs-3094	71	7	a	a	DET
iajs-3094	71	8	processing	processing	NOUN
iajs-3094	71	9	time	time	NOUN
iajs-3094	71	10	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	71	11	and	and	CCONJ
iajs-3094	71	12	a	a	DET
iajs-3094	71	13	due	due	ADJ
iajs-3094	71	14	date	date	NOUN
iajs-3094	71	15	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	71	16	,	,	PUNCT
iajs-3094	71	17	given	give	VERB
iajs-3094	71	18	a	a	DET
iajs-3094	71	19	list	list	NOUN
iajs-3094	71	20	of	of	ADP
iajs-3094	71	21	jobs	job	NOUN
iajs-3094	71	22	in	in	ADP
iajs-3094	71	23	the	the	DET
iajs-3094	71	24	sequence	sequence	NOUN
iajs-3094	71	25	𝛼	𝛼	NOUN
iajs-3094	71	26	=	=	SYM
iajs-3094	71	27	(	(	PUNCT
iajs-3094	71	28	𝛼1	𝛼1	NOUN
iajs-3094	71	29	,	,	PUNCT
iajs-3094	71	30	𝛼2	𝛼2	ADJ
iajs-3094	71	31	,	,	PUNCT
iajs-3094	71	32	…	…	PUNCT
iajs-3094	71	33	,	,	PUNCT
iajs-3094	71	34	𝛼𝑛	𝛼𝑛	PROPN
iajs-3094	71	35	)	)	PUNCT
iajs-3094	71	36	,	,	PUNCT
iajs-3094	71	37	the	the	DET
iajs-3094	71	38	earliest	early	ADJ
iajs-3094	71	39	completion	completion	NOUN
iajs-3094	71	40	time	time	NOUN
iajs-3094	71	41	possible	possible	ADJ
iajs-3094	72	1	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	72	2	=	=	SYM
iajs-3094	72	3	∑	∑	ADP
iajs-3094	72	4	𝑝𝛼𝑘	𝑝𝛼𝑘	NOUN
iajs-3094	72	5	𝑛	𝑛	PRON
iajs-3094	72	6	𝑘=1	𝑘=1	PRON
iajs-3094	72	7	,	,	PUNCT
iajs-3094	72	8	the	the	DET
iajs-3094	72	9	tardiness	tardiness	NOUN
iajs-3094	72	10	of	of	ADP
iajs-3094	72	11	job	job	NOUN
iajs-3094	72	12	𝑗	𝑗	NOUN
iajs-3094	72	13	,	,	PUNCT
iajs-3094	72	14	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	72	15	=	=	PUNCT
iajs-3094	72	16	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-3094	72	17	{	{	PUNCT
iajs-3094	72	18	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	72	19	−	−	PROPN
iajs-3094	72	20	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	72	21	,	,	PUNCT
iajs-3094	72	22	0	0	NUM
iajs-3094	72	23	}	}	PUNCT
iajs-3094	72	24	,	,	PUNCT
iajs-3094	72	25	the	the	DET
iajs-3094	72	26	earliness	earliness	NOUN
iajs-3094	72	27	of	of	ADP
iajs-3094	72	28	job	job	NOUN
iajs-3094	72	29	𝑗	𝑗	NOUN
iajs-3094	72	30	,	,	PUNCT
iajs-3094	72	31	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	72	32	=	=	PUNCT
iajs-3094	72	33	𝑚𝑎𝑥	𝑚𝑎𝑥	NOUN
iajs-3094	72	34	{	{	PUNCT
iajs-3094	72	35	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	72	36	−	−	PROPN
iajs-3094	73	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	73	2	,	,	PUNCT
iajs-3094	73	3	0	0	NUM
iajs-3094	73	4	}	}	PUNCT
iajs-3094	73	5	.	.	PUNCT
iajs-3094	74	1	the	the	DET
iajs-3094	74	2	aim	aim	NOUN
iajs-3094	74	3	of	of	ADP
iajs-3094	74	4	this	this	DET
iajs-3094	74	5	problem	problem	NOUN
iajs-3094	74	6	is	be	AUX
iajs-3094	74	7	finding	find	VERB
iajs-3094	74	8	a	a	DET
iajs-3094	74	9	schedule	schedule	NOUN
iajs-3094	74	10	α	α	PRON
iajs-3094	74	11	∈	∈	NOUN
iajs-3094	74	12	𝒮	𝒮	NOUN
iajs-3094	74	13	to	to	PART
iajs-3094	74	14	find	find	VERB
iajs-3094	74	15	a	a	DET
iajs-3094	74	16	schedule	schedule	NOUN
iajs-3094	74	17	,	,	PUNCT
iajs-3094	74	18	(	(	PUNCT
iajs-3094	74	19	where	where	SCONJ
iajs-3094	74	20	𝒮	𝒮	PROPN
iajs-3094	74	21	is	be	AUX
iajs-3094	74	22	the	the	DET
iajs-3094	74	23	set	set	NOUN
iajs-3094	74	24	of	of	ADP
iajs-3094	74	25	all	all	DET
iajs-3094	74	26	possible	possible	ADJ
iajs-3094	74	27	feasible	feasible	ADJ
iajs-3094	74	28	schedules	schedule	NOUN
iajs-3094	74	29	;	;	PUNCT
iajs-3094	74	30	where	where	SCONJ
iajs-3094	74	31	a	a	DET
iajs-3094	74	32	feasible	feasible	ADJ
iajs-3094	74	33	schedule	schedule	NOUN
iajs-3094	74	34	means	mean	VERB
iajs-3094	74	35	it	it	PRON
iajs-3094	74	36	satisfies	satisfy	VERB
iajs-3094	74	37	all	all	DET
iajs-3094	74	38	the	the	DET
iajs-3094	74	39	constraints	constraint	NOUN
iajs-3094	74	40	of	of	ADP
iajs-3094	74	41	the	the	DET
iajs-3094	74	42	problem	problem	NOUN
iajs-3094	74	43	₱	₱	PROPN
iajs-3094	74	44	)	)	PUNCT
iajs-3094	74	45	that	that	PRON
iajs-3094	74	46	minimizes	minimize	VERB
iajs-3094	74	47	the	the	DET
iajs-3094	74	48	multi	multi	NOUN
iajs-3094	74	49	-	-	NOUN
iajs-3094	74	50	criteria	criterion	NOUN
iajs-3094	74	51	(	(	PUNCT
iajs-3094	74	52	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	74	53	,	,	PUNCT
iajs-3094	74	54	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	74	55	,	,	PUNCT
iajs-3094	74	56	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	74	57	)	)	PUNCT
iajs-3094	74	58	,	,	PUNCT
iajs-3094	74	59	which	which	PRON
iajs-3094	74	60	is	be	AUX
iajs-3094	74	61	denoted	denote	VERB
iajs-3094	74	62	by	by	ADP
iajs-3094	74	63	(	(	PUNCT
iajs-3094	74	64	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	74	65	)	)	PUNCT
iajs-3094	74	66	,	,	PUNCT
iajs-3094	74	67	can	can	AUX
iajs-3094	74	68	be	be	AUX
iajs-3094	74	69	formulated	formulate	VERB
iajs-3094	74	70	mathematically	mathematically	ADV
iajs-3094	74	71	as	as	SCONJ
iajs-3094	74	72	follows	follow	VERB
iajs-3094	74	73	:	:	PUNCT
iajs-3094	74	74	𝑀𝑖𝑛{∑𝐶𝑗	𝑀𝑖𝑛{∑𝐶𝑗	NOUN
iajs-3094	74	75	,	,	PUNCT
iajs-3094	74	76	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	74	77	,	,	PUNCT
iajs-3094	74	78	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	74	79	}	}	PUNCT
iajs-3094	74	80	s.	s.	PROPN
iajs-3094	74	81	t.	t.	PROPN
iajs-3094	74	82	𝐶1	𝐶1	PROPN
iajs-3094	75	1	=	=	PUNCT
iajs-3094	75	2	𝑝𝛼1	𝑝𝛼1	PROPN
iajs-3094	75	3	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	75	4	≥	≥	NUM
iajs-3094	75	5	𝑝𝛼𝑗	𝑝𝛼𝑗	NOUN
iajs-3094	75	6	𝑗	𝑗	NOUN
iajs-3094	75	7	=	=	SYM
iajs-3094	75	8	1,2	1,2	NUM
iajs-3094	75	9	,	,	PUNCT
iajs-3094	75	10	…	…	PUNCT
iajs-3094	75	11	,	,	PUNCT
iajs-3094	75	12	𝑛	𝑛	DET
iajs-3094	75	13	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	75	14	=	=	PUNCT
iajs-3094	75	15	𝐶𝛼(𝑗−1	𝐶𝛼(𝑗−1	NOUN
iajs-3094	75	16	)	)	PUNCT
iajs-3094	76	1	+	+	NUM
iajs-3094	76	2	𝑝𝛼𝑗	𝑝𝛼𝑗	NOUN
iajs-3094	76	3	𝑗	𝑗	NOUN
iajs-3094	76	4	=	=	NOUN
iajs-3094	76	5	2	2	NUM
iajs-3094	76	6	,	,	PUNCT
iajs-3094	76	7	…	…	PUNCT
iajs-3094	76	8	,	,	PUNCT
iajs-3094	76	9	𝑛	𝑛	DET
iajs-3094	76	10	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	76	11	≥	≥	NOUN
iajs-3094	77	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	77	2	−	−	PROPN
iajs-3094	77	3	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	77	4	𝑗	𝑗	NOUN
iajs-3094	77	5	=	=	SYM
iajs-3094	77	6	1,2	1,2	NUM
iajs-3094	77	7	,	,	PUNCT
iajs-3094	77	8	…	…	PUNCT
iajs-3094	77	9	,	,	PUNCT
iajs-3094	77	10	𝑛	𝑛	PRON
iajs-3094	77	11	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	77	12	≥	≥	NOUN
iajs-3094	77	13	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	77	14	−	−	PUNCT
iajs-3094	78	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	78	2	𝑗	𝑗	NOUN
iajs-3094	78	3	=	=	SYM
iajs-3094	78	4	1,2	1,2	NUM
iajs-3094	78	5	,	,	PUNCT
iajs-3094	78	6	…	…	PUNCT
iajs-3094	78	7	,	,	PUNCT
iajs-3094	78	8	𝑛	𝑛	DET
iajs-3094	78	9	𝑇𝑗	𝑇𝑗	PROPN
iajs-3094	78	10	≥	≥	NOUN
iajs-3094	78	11	0	0	NUM
iajs-3094	78	12	,	,	PUNCT
iajs-3094	78	13	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	78	14	≥	≥	NOUN
iajs-3094	78	15	0	0	PUNCT
iajs-3094	78	16	𝑗	𝑗	NOUN
iajs-3094	78	17	=	=	SYM
iajs-3094	78	18	1,2	1,2	NUM
iajs-3094	78	19	,	,	PUNCT
iajs-3094	78	20	…	…	PUNCT
iajs-3094	78	21	,	,	PUNCT
iajs-3094	78	22	𝑛	𝑛	PROPN
iajs-3094	78	23	}	}	PUNCT
iajs-3094	78	24	…	…	PUNCT
iajs-3094	78	25	(	(	PUNCT
iajs-3094	78	26	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	78	27	)	)	PUNCT
iajs-3094	78	28	.	.	PUNCT
iajs-3094	79	1	ihjpas	ihjpas	PROPN
iajs-3094	79	2	.	.	PUNCT
iajs-3094	80	1	37	37	NUM
iajs-3094	80	2	(	(	PUNCT
iajs-3094	80	3	1	1	NUM
iajs-3094	80	4	)	)	PUNCT
iajs-3094	80	5	2024	2024	NUM
iajs-3094	80	6	389	389	NUM
iajs-3094	80	7	where	where	SCONJ
iajs-3094	80	8	𝛼𝑗	𝛼𝑗	PROPN
iajs-3094	80	9	indicate	indicate	VERB
iajs-3094	80	10	where	where	SCONJ
iajs-3094	80	11	job	job	NOUN
iajs-3094	80	12	𝑗	𝑗	PROPN
iajs-3094	80	13	falls	fall	VERB
iajs-3094	80	14	in	in	ADP
iajs-3094	80	15	the	the	DET
iajs-3094	80	16	ordering	ordering	NOUN
iajs-3094	80	17	α	α	NOUN
iajs-3094	80	18	and	and	CCONJ
iajs-3094	80	19	𝒮	𝒮	PROPN
iajs-3094	80	20	represents	represent	VERB
iajs-3094	80	21	the	the	DET
iajs-3094	80	22	collection	collection	NOUN
iajs-3094	80	23	of	of	ADP
iajs-3094	80	24	all	all	DET
iajs-3094	80	25	schedules	schedule	NOUN
iajs-3094	80	26	.	.	PUNCT
iajs-3094	81	1	finding	find	VERB
iajs-3094	81	2	the	the	DET
iajs-3094	81	3	set	set	NOUN
iajs-3094	81	4	of	of	ADP
iajs-3094	81	5	all	all	DET
iajs-3094	81	6	efficient	efficient	ADJ
iajs-3094	81	7	solutions	solution	NOUN
iajs-3094	81	8	to	to	ADP
iajs-3094	81	9	the	the	DET
iajs-3094	81	10	problem	problem	NOUN
iajs-3094	81	11	(	(	PUNCT
iajs-3094	81	12	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	81	13	)	)	PUNCT
iajs-3094	81	14	is	be	AUX
iajs-3094	81	15	challenging	challenge	VERB
iajs-3094	81	16	since	since	SCONJ
iajs-3094	81	17	it	it	PRON
iajs-3094	81	18	’s	’	VERB
iajs-3094	81	19	an	an	DET
iajs-3094	81	20	np	np	NOUN
iajs-3094	81	21	-	-	PUNCT
iajs-3094	81	22	hard	hard	ADJ
iajs-3094	81	23	problem	problem	NOUN
iajs-3094	81	24	(	(	PUNCT
iajs-3094	81	25	because	because	SCONJ
iajs-3094	81	26	the	the	DET
iajs-3094	81	27	problem	problem	NOUN
iajs-3094	81	28	1//	1//	NUM
iajs-3094	81	29	∑	∑	ADP
iajs-3094	81	30	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	81	31	𝑛	𝑛	PRON
iajs-3094	81	32	𝑗=1	𝑗=1	PROPN
iajs-3094	81	33	is	be	AUX
iajs-3094	81	34	np	np	INTJ
iajs-3094	81	35	-	-	ADJ
iajs-3094	81	36	hard	hard	ADJ
iajs-3094	81	37	[	[	X
iajs-3094	81	38	22	22	NUM
iajs-3094	81	39	]	]	SYM
iajs-3094	81	40	)	)	PUNCT
iajs-3094	81	41	.	.	PUNCT
iajs-3094	82	1	proposition	proposition	NOUN
iajs-3094	82	2	(	(	PUNCT
iajs-3094	82	3	1	1	NUM
iajs-3094	82	4	):	):	PUNCT
iajs-3094	82	5	there	there	PRON
iajs-3094	82	6	is	be	VERB
iajs-3094	82	7	an	an	DET
iajs-3094	82	8	efficient	efficient	ADJ
iajs-3094	82	9	schedule	schedule	NOUN
iajs-3094	82	10	for	for	ADP
iajs-3094	82	11	the	the	DET
iajs-3094	82	12	problem	problem	NOUN
iajs-3094	82	13	(	(	PUNCT
iajs-3094	82	14	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	82	15	)	)	PUNCT
iajs-3094	82	16	that	that	PRON
iajs-3094	82	17	satisfies	satisfy	VERB
iajs-3094	82	18	the	the	DET
iajs-3094	82	19	spt	spt	PROPN
iajs-3094	82	20	rule	rule	NOUN
iajs-3094	82	21	.	.	PUNCT
iajs-3094	83	1	proof	proof	NOUN
iajs-3094	83	2	:	:	PUNCT
iajs-3094	83	3	(	(	PUNCT
iajs-3094	83	4	a	a	X
iajs-3094	83	5	)	)	PUNCT
iajs-3094	83	6	first	first	ADV
iajs-3094	83	7	,	,	PUNCT
iajs-3094	83	8	assume	assume	VERB
iajs-3094	83	9	that	that	SCONJ
iajs-3094	83	10	𝑝𝑖	𝑝𝑖	VERB
iajs-3094	83	11	≠	≠	PROPN
iajs-3094	83	12	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	83	13	for	for	ADP
iajs-3094	83	14	all	all	DET
iajs-3094	83	15	𝑖	𝑖	ADP
iajs-3094	83	16	,	,	PUNCT
iajs-3094	83	17	𝑗.	𝑗.	VERB
iajs-3094	83	18	the	the	DET
iajs-3094	83	19	unique	unique	ADJ
iajs-3094	83	20	sequence	sequence	NOUN
iajs-3094	83	21	spt	spt	NOUN
iajs-3094	83	22	,	,	PUNCT
iajs-3094	83	23	(	(	PUNCT
iajs-3094	83	24	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	83	25	)	)	PUNCT
iajs-3094	83	26	provides	provide	VERB
iajs-3094	83	27	the	the	DET
iajs-3094	83	28	bare	bare	ADJ
iajs-3094	83	29	minimum	minimum	NOUN
iajs-3094	83	30	of	of	ADP
iajs-3094	83	31	∑𝐶𝑗.	∑𝐶𝑗.	PROPN
iajs-3094	83	32	as	as	ADP
iajs-3094	83	33	a	a	DET
iajs-3094	83	34	result	result	NOUN
iajs-3094	83	35	,	,	PUNCT
iajs-3094	83	36	no	no	DET
iajs-3094	83	37	sequence	sequence	NOUN
iajs-3094	83	38	exists	exist	VERB
iajs-3094	83	39	𝛿	𝛿	ADJ
iajs-3094	83	40	≠	≠	PROPN
iajs-3094	83	41	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	83	42	s.t	s.t	PROPN
iajs-3094	83	43	.	.	PROPN
iajs-3094	83	44	∑𝐶𝑗(𝛿	∑𝐶𝑗(𝛿	PROPN
iajs-3094	83	45	)	)	PUNCT
iajs-3094	83	46	≤	≤	PUNCT
iajs-3094	84	1	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	84	2	(	(	PUNCT
iajs-3094	84	3	𝑆𝑃𝑇	𝑆𝑃𝑇	PROPN
iajs-3094	84	4	∗	∗	NOUN
iajs-3094	84	5	)	)	PUNCT
iajs-3094	84	6	,	,	PUNCT
iajs-3094	84	7	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	84	8	(	(	PUNCT
iajs-3094	84	9	𝛿	𝛿	ADJ
iajs-3094	84	10	)	)	PUNCT
iajs-3094	84	11	≤	≤	NUM
iajs-3094	84	12	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	84	13	(	(	PUNCT
iajs-3094	84	14	𝑆𝑃𝑇	𝑆𝑃𝑇	PROPN
iajs-3094	84	15	∗	∗	NOUN
iajs-3094	84	16	)	)	PUNCT
iajs-3094	84	17	,	,	PUNCT
iajs-3094	84	18	and	and	CCONJ
iajs-3094	84	19	𝑇𝑚𝑎𝑥(𝛿	𝑇𝑚𝑎𝑥(𝛿	PROPN
iajs-3094	84	20	)	)	PUNCT
iajs-3094	84	21	≤	≤	NOUN
iajs-3094	84	22	𝑇𝑚𝑎𝑥(𝑆𝑃𝑇	𝑇𝑚𝑎𝑥(𝑆𝑃𝑇	PROPN
iajs-3094	84	23	∗	∗	NOUN
iajs-3094	84	24	)	)	PUNCT
iajs-3094	84	25	(	(	PUNCT
iajs-3094	84	26	1	1	X
iajs-3094	84	27	)	)	PUNCT
iajs-3094	84	28	the	the	DET
iajs-3094	84	29	presence	presence	NOUN
iajs-3094	84	30	of	of	ADP
iajs-3094	84	31	one	one	NUM
iajs-3094	84	32	or	or	CCONJ
iajs-3094	84	33	more	more	ADV
iajs-3094	84	34	strict	strict	ADJ
iajs-3094	84	35	inequalities	inequality	NOUN
iajs-3094	84	36	.	.	PUNCT
iajs-3094	85	1	(	(	PUNCT
iajs-3094	85	2	b	b	X
iajs-3094	85	3	)	)	PUNCT
iajs-3094	85	4	if	if	SCONJ
iajs-3094	85	5	there	there	PRON
iajs-3094	85	6	is	be	VERB
iajs-3094	85	7	more	more	ADJ
iajs-3094	85	8	than	than	ADP
iajs-3094	85	9	one	one	NUM
iajs-3094	85	10	sequence	sequence	NOUN
iajs-3094	85	11	spt	spt	NOUN
iajs-3094	85	12	(	(	PUNCT
iajs-3094	85	13	the	the	DET
iajs-3094	85	14	processing	processing	NOUN
iajs-3094	85	15	times	time	NOUN
iajs-3094	85	16	of	of	ADP
iajs-3094	85	17	jobs	job	NOUN
iajs-3094	85	18	are	be	AUX
iajs-3094	85	19	equal	equal	ADJ
iajs-3094	85	20	)	)	PUNCT
iajs-3094	85	21	,	,	PUNCT
iajs-3094	85	22	assume	assume	VERB
iajs-3094	85	23	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	85	24	be	be	AUX
iajs-3094	85	25	a	a	DET
iajs-3094	85	26	sequence	sequence	NOUN
iajs-3094	85	27	that	that	PRON
iajs-3094	85	28	satisfies	satisfy	VERB
iajs-3094	85	29	the	the	DET
iajs-3094	85	30	rule	rule	NOUN
iajs-3094	85	31	of	of	ADP
iajs-3094	85	32	spt	spt	NOUN
iajs-3094	85	33	and	and	CCONJ
iajs-3094	85	34	jobs	job	NOUN
iajs-3094	85	35	with	with	ADP
iajs-3094	85	36	equal	equal	ADJ
iajs-3094	85	37	processing	processing	NOUN
iajs-3094	85	38	times	time	NOUN
iajs-3094	85	39	in	in	ADP
iajs-3094	85	40	the	the	DET
iajs-3094	85	41	edd	edd	PROPN
iajs-3094	85	42	and	and	CCONJ
iajs-3094	85	43	mst	mst	PROPN
iajs-3094	85	44	sequence	sequence	NOUN
iajs-3094	85	45	.	.	PUNCT
iajs-3094	86	1	if	if	SCONJ
iajs-3094	86	2	a	a	DET
iajs-3094	86	3	set	set	NOUN
iajs-3094	86	4	of	of	ADP
iajs-3094	86	5	jobs	job	NOUN
iajs-3094	86	6	that	that	PRON
iajs-3094	86	7	are	be	AUX
iajs-3094	86	8	to	to	PART
iajs-3094	86	9	be	be	AUX
iajs-3094	86	10	early	early	ADV
iajs-3094	86	11	or	or	CCONJ
iajs-3094	86	12	partially	partially	ADV
iajs-3094	86	13	early	early	ADV
iajs-3094	86	14	is	be	AUX
iajs-3094	86	15	specified	specify	VERB
iajs-3094	86	16	,	,	PUNCT
iajs-3094	86	17	then	then	ADV
iajs-3094	86	18	this	this	DET
iajs-3094	86	19	edd	edd	PROPN
iajs-3094	86	20	and	and	CCONJ
iajs-3094	86	21	mst	mst	PROPN
iajs-3094	86	22	order	order	NOUN
iajs-3094	86	23	minimized	minimized	NOUN
iajs-3094	86	24	∑𝐸𝑗.	∑𝐸𝑗.	PRON
iajs-3094	86	25	note	note	VERB
iajs-3094	86	26	that	that	SCONJ
iajs-3094	86	27	if	if	SCONJ
iajs-3094	86	28	the	the	DET
iajs-3094	86	29	event	event	NOUN
iajs-3094	86	30	is	be	AUX
iajs-3094	86	31	several	several	ADJ
iajs-3094	86	32	jobs	job	NOUN
iajs-3094	86	33	at	at	ADP
iajs-3094	86	34	the	the	DET
iajs-3094	86	35	same	same	ADJ
iajs-3094	86	36	processing	processing	NOUN
iajs-3094	86	37	times	time	NOUN
iajs-3094	86	38	,	,	PUNCT
iajs-3094	86	39	the	the	DET
iajs-3094	86	40	due	due	ADJ
iajs-3094	86	41	date	date	NOUN
iajs-3094	86	42	is	be	AUX
iajs-3094	86	43	considered	consider	VERB
iajs-3094	86	44	identical	identical	ADJ
iajs-3094	86	45	,	,	PUNCT
iajs-3094	86	46	or	or	CCONJ
iajs-3094	86	47	slack	slack	VERB
iajs-3094	86	48	times	time	NOUN
iajs-3094	86	49	,	,	PUNCT
iajs-3094	86	50	then	then	ADV
iajs-3094	86	51	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	86	52	is	be	AUX
iajs-3094	86	53	not	not	PART
iajs-3094	86	54	unique	unique	ADJ
iajs-3094	86	55	.	.	PUNCT
iajs-3094	87	1	show	show	VERB
iajs-3094	87	2	that	that	SCONJ
iajs-3094	87	3	each	each	DET
iajs-3094	87	4	𝑆𝑃𝑇∗sequence	𝑆𝑃𝑇∗sequence	NOUN
iajs-3094	87	5	is	be	AUX
iajs-3094	87	6	an	an	DET
iajs-3094	87	7	efficient	efficient	ADJ
iajs-3094	87	8	,	,	PUNCT
iajs-3094	87	9	sequence	sequence	NOUN
iajs-3094	87	10	that	that	PRON
iajs-3094	87	11	does	do	AUX
iajs-3094	87	12	not	not	PART
iajs-3094	87	13	satisfy	satisfy	VERB
iajs-3094	87	14	the	the	DET
iajs-3094	87	15	spt	spt	PROPN
iajs-3094	87	16	rule	rule	NOUN
iajs-3094	87	17	which	which	PRON
iajs-3094	87	18	can	can	AUX
iajs-3094	87	19	not	not	PART
iajs-3094	87	20	dominate	dominate	VERB
iajs-3094	87	21	an	an	DET
iajs-3094	87	22	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	87	23	sequence	sequence	NOUN
iajs-3094	87	24	by	by	ADP
iajs-3094	87	25	(	(	PUNCT
iajs-3094	87	26	1.1	1.1	NUM
iajs-3094	87	27	)	)	PUNCT
iajs-3094	87	28	.	.	PUNCT
iajs-3094	88	1	if	if	SCONJ
iajs-3094	88	2	δ	δ	PROPN
iajs-3094	88	3	is	be	AUX
iajs-3094	88	4	an	an	DET
iajs-3094	88	5	spt	spt	ADJ
iajs-3094	88	6	-	-	PUNCT
iajs-3094	88	7	sequences	sequence	NOUN
iajs-3094	88	8	but	but	CCONJ
iajs-3094	88	9	not	not	PART
iajs-3094	88	10	an	an	DET
iajs-3094	88	11	spt	spt	NOUN
iajs-3094	88	12	*	*	NOUN
iajs-3094	88	13	sequence	sequence	NOUN
iajs-3094	88	14	,	,	PUNCT
iajs-3094	88	15	it	it	PRON
iajs-3094	88	16	can	can	AUX
iajs-3094	88	17	not	not	PART
iajs-3094	88	18	dominate	dominate	VERB
iajs-3094	88	19	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	88	20	since	since	SCONJ
iajs-3094	88	21	∑𝐶𝑗(𝛿	∑𝐶𝑗(𝛿	NUM
iajs-3094	88	22	)	)	PUNCT
iajs-3094	89	1	=	=	PUNCT
iajs-3094	90	1	∑𝐶𝑗(𝑆𝑃𝑇	∑𝐶𝑗(𝑆𝑃𝑇	NUM
iajs-3094	90	2	∗	∗	NOUN
iajs-3094	90	3	)	)	PUNCT
iajs-3094	91	1	,	,	PUNCT
iajs-3094	91	2	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	91	3	(	(	PUNCT
iajs-3094	91	4	𝑆𝑃𝑇	𝑆𝑃𝑇	PROPN
iajs-3094	91	5	∗	∗	NOUN
iajs-3094	91	6	)	)	PUNCT
iajs-3094	91	7	≤	≤	NUM
iajs-3094	92	1	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	92	2	(	(	PUNCT
iajs-3094	92	3	𝛿	𝛿	ADJ
iajs-3094	92	4	)	)	PUNCT
iajs-3094	92	5	and	and	CCONJ
iajs-3094	92	6	𝑇𝑚𝑎𝑥(𝑆𝑃𝑇	𝑇𝑚𝑎𝑥(𝑆𝑃𝑇	PROPN
iajs-3094	92	7	∗	∗	NOUN
iajs-3094	92	8	)	)	PUNCT
iajs-3094	92	9	≤	≤	NUM
iajs-3094	92	10	𝑇𝑚𝑎𝑥(𝛿	𝑇𝑚𝑎𝑥(𝛿	PROPN
iajs-3094	92	11	)	)	PUNCT
iajs-3094	92	12	by	by	ADP
iajs-3094	92	13	virtue	virtue	NOUN
iajs-3094	92	14	of	of	ADP
iajs-3094	92	15	the	the	DET
iajs-3094	92	16	edd	edd	PROPN
iajs-3094	92	17	and	and	CCONJ
iajs-3094	92	18	mst	mst	PROPN
iajs-3094	92	19	rule	rule	NOUN
iajs-3094	92	20	.	.	PUNCT
iajs-3094	93	1	hence	hence	ADV
iajs-3094	93	2	all	all	DET
iajs-3094	93	3	the	the	DET
iajs-3094	93	4	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	93	5	sequences	sequence	NOUN
iajs-3094	93	6	are	be	AUX
iajs-3094	93	7	efficient	efficient	ADJ
iajs-3094	93	8	.	.	PUNCT
iajs-3094	94	1	as	as	SCONJ
iajs-3094	94	2	mentioned	mention	VERB
iajs-3094	94	3	in	in	ADP
iajs-3094	94	4	proposition	proposition	NOUN
iajs-3094	94	5	(	(	PUNCT
iajs-3094	94	6	1	1	NUM
iajs-3094	94	7	)	)	PUNCT
iajs-3094	94	8	,	,	PUNCT
iajs-3094	94	9	shown	show	VERB
iajs-3094	94	10	that	that	SCONJ
iajs-3094	94	11	the	the	DET
iajs-3094	94	12	spt	spt	PROPN
iajs-3094	94	13	rule	rule	NOUN
iajs-3094	94	14	is	be	AUX
iajs-3094	94	15	efficient	efficient	ADJ
iajs-3094	94	16	for	for	ADP
iajs-3094	94	17	the	the	DET
iajs-3094	94	18	problem	problem	NOUN
iajs-3094	94	19	(	(	PUNCT
iajs-3094	94	20	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	94	21	)	)	PUNCT
iajs-3094	94	22	but	but	CCONJ
iajs-3094	94	23	the	the	DET
iajs-3094	94	24	edd	edd	PROPN
iajs-3094	94	25	rule	rule	NOUN
iajs-3094	94	26	does	do	VERB
iajs-3094	94	27	not	not	PART
iajs-3094	94	28	,	,	PUNCT
iajs-3094	94	29	as	as	SCONJ
iajs-3094	94	30	shown	show	VERB
iajs-3094	94	31	in	in	ADP
iajs-3094	94	32	the	the	DET
iajs-3094	94	33	example	example	NOUN
iajs-3094	94	34	below	below	ADV
iajs-3094	94	35	.	.	PUNCT
iajs-3094	95	1	example	example	NOUN
iajs-3094	95	2	(	(	PUNCT
iajs-3094	95	3	1	1	NUM
iajs-3094	95	4	):	):	PUNCT
iajs-3094	95	5	suppose	suppose	VERB
iajs-3094	95	6	the	the	DET
iajs-3094	95	7	problem	problem	NOUN
iajs-3094	95	8	(	(	PUNCT
iajs-3094	95	9	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	95	10	)	)	PUNCT
iajs-3094	95	11	has	have	VERB
iajs-3094	95	12	the	the	DET
iajs-3094	95	13	following	follow	VERB
iajs-3094	95	14	data	datum	NOUN
iajs-3094	95	15	in	in	ADP
iajs-3094	95	16	table	table	NOUN
iajs-3094	95	17	1	1	NUM
iajs-3094	95	18	:	:	PUNCT
iajs-3094	95	19	table	table	NOUN
iajs-3094	95	20	1	1	NUM
iajs-3094	95	21	.	.	PUNCT
iajs-3094	96	1	the	the	DET
iajs-3094	96	2	data	datum	NOUN
iajs-3094	96	3	of	of	ADP
iajs-3094	96	4	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	96	5	,	,	PUNCT
iajs-3094	96	6	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	96	7	,	,	PUNCT
iajs-3094	96	8	and	and	CCONJ
iajs-3094	96	9	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	96	10	for	for	ADP
iajs-3094	96	11	problem	problem	NOUN
iajs-3094	96	12	(	(	PUNCT
iajs-3094	96	13	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	96	14	)	)	PUNCT
iajs-3094	96	15	job1	job1	PROPN
iajs-3094	96	16	job2	job2	PROPN
iajs-3094	96	17	job3	job3	PROPN
iajs-3094	96	18	job4	job4	PROPN
iajs-3094	96	19	job5	job5	PROPN
iajs-3094	96	20	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	96	21	2	2	NUM
iajs-3094	96	22	5	5	NUM
iajs-3094	96	23	7	7	NUM
iajs-3094	96	24	5	5	NUM
iajs-3094	96	25	8	8	NUM
iajs-3094	96	26	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	96	27	6	6	NUM
iajs-3094	96	28	9	9	NUM
iajs-3094	96	29	8	8	NUM
iajs-3094	96	30	11	11	NUM
iajs-3094	96	31	14	14	NUM
iajs-3094	96	32	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	96	33	4	4	NUM
iajs-3094	96	34	4	4	NUM
iajs-3094	96	35	1	1	NUM
iajs-3094	96	36	6	6	NUM
iajs-3094	96	37	6	6	NUM
iajs-3094	96	38	a	a	DET
iajs-3094	96	39	feasible	feasible	ADJ
iajs-3094	96	40	schedule	schedule	NOUN
iajs-3094	96	41	is	be	AUX
iajs-3094	96	42	provided	provide	VERB
iajs-3094	96	43	by	by	ADP
iajs-3094	96	44	the	the	DET
iajs-3094	96	45	spt	spt	PROPN
iajs-3094	96	46	rule(1,2,4,3,5	rule(1,2,4,3,5	NUM
iajs-3094	96	47	)	)	PUNCT
iajs-3094	96	48	and	and	CCONJ
iajs-3094	96	49	(	(	PUNCT
iajs-3094	96	50	1,4,2,3,5	1,4,2,3,5	NUM
iajs-3094	96	51	)	)	PUNCT
iajs-3094	96	52	,	,	PUNCT
iajs-3094	96	53	hence	hence	ADV
iajs-3094	96	54	(	(	PUNCT
iajs-3094	96	55	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	96	56	,	,	PUNCT
iajs-3094	96	57	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	96	58	,	,	PUNCT
iajs-3094	96	59	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	96	60	)	)	PUNCT
iajs-3094	96	61	=	=	SYM
iajs-3094	96	62	(	(	PUNCT
iajs-3094	96	63	67,6,13	67,6,13	NOUN
iajs-3094	96	64	)	)	PUNCT
iajs-3094	96	65	from	from	ADP
iajs-3094	96	66	𝑆𝑃𝑇∗	𝑆𝑃𝑇∗	PROPN
iajs-3094	96	67	order	order	NOUN
iajs-3094	96	68	(	(	PUNCT
iajs-3094	96	69	1,2,4,3,5	1,2,4,3,5	NUM
iajs-3094	96	70	)	)	PUNCT
iajs-3094	96	71	and	and	CCONJ
iajs-3094	96	72	(	(	PUNCT
iajs-3094	96	73	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	96	74	,	,	PUNCT
iajs-3094	96	75	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	96	76	,	,	PUNCT
iajs-3094	96	77	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	96	78	)	)	PUNCT
iajs-3094	96	79	=	=	PUNCT
iajs-3094	96	80	(	(	PUNCT
iajs-3094	96	81	67,7,13	67,7,13	NOUN
iajs-3094	96	82	)	)	PUNCT
iajs-3094	96	83	from	from	ADP
iajs-3094	96	84	spt	spt	ADJ
iajs-3094	96	85	order	order	NOUN
iajs-3094	96	86	(	(	PUNCT
iajs-3094	96	87	1,4,2,3,5	1,4,2,3,5	NUM
iajs-3094	96	88	)	)	PUNCT
iajs-3094	96	89	,	,	PUNCT
iajs-3094	96	90	it	it	PRON
iajs-3094	96	91	is	be	AUX
iajs-3094	96	92	clear	clear	ADJ
iajs-3094	96	93	that	that	SCONJ
iajs-3094	96	94	in	in	ADP
iajs-3094	96	95	the	the	DET
iajs-3094	96	96	𝑆𝑃𝑇∗sequence	𝑆𝑃𝑇∗sequence	NOUN
iajs-3094	96	97	the	the	DET
iajs-3094	96	98	tasks	task	NOUN
iajs-3094	96	99	(	(	PUNCT
iajs-3094	96	100	2,4	2,4	NUM
iajs-3094	96	101	)	)	PUNCT
iajs-3094	96	102	are	be	AUX
iajs-3094	96	103	arranged	arrange	VERB
iajs-3094	96	104	with	with	ADP
iajs-3094	96	105	equal	equal	ADJ
iajs-3094	96	106	processing	processing	NOUN
iajs-3094	96	107	time	time	NOUN
iajs-3094	96	108	in	in	ADP
iajs-3094	96	109	the	the	DET
iajs-3094	96	110	rule	rule	NOUN
iajs-3094	96	111	of	of	ADP
iajs-3094	96	112	the	the	DET
iajs-3094	96	113	mst	mst	PROPN
iajs-3094	96	114	or	or	CCONJ
iajs-3094	96	115	edd	edd	PROPN
iajs-3094	96	116	.	.	PUNCT
iajs-3094	97	1	but	but	CCONJ
iajs-3094	97	2	edd	edd	PROPN
iajs-3094	97	3	rule	rule	NOUN
iajs-3094	97	4	(	(	PUNCT
iajs-3094	97	5	1,3,2,4,5	1,3,2,4,5	NUM
iajs-3094	97	6	)	)	PUNCT
iajs-3094	97	7	with	with	ADP
iajs-3094	97	8	(	(	PUNCT
iajs-3094	97	9	∑𝐶𝑗	∑𝐶𝑗	INTJ
iajs-3094	97	10	,	,	PUNCT
iajs-3094	97	11	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	97	12	,	,	PUNCT
iajs-3094	97	13	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	97	14	)	)	PUNCT
iajs-3094	97	15	=	=	PUNCT
iajs-3094	97	16	(	(	PUNCT
iajs-3094	97	17	71,4,13	71,4,13	NUM
iajs-3094	97	18	)	)	PUNCT
iajs-3094	97	19	and	and	CCONJ
iajs-3094	97	20	mst	mst	PROPN
iajs-3094	97	21	rule	rule	NOUN
iajs-3094	97	22	(	(	PUNCT
iajs-3094	97	23	3,1,2,4,5	3,1,2,4,5	NUM
iajs-3094	97	24	)	)	PUNCT
iajs-3094	97	25	with	with	ADP
iajs-3094	97	26	(	(	PUNCT
iajs-3094	97	27	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	97	28	,	,	PUNCT
iajs-3094	97	29	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	97	30	,	,	PUNCT
iajs-3094	97	31	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	97	32	)	)	PUNCT
iajs-3094	97	33	=	=	PUNCT
iajs-3094	97	34	(	(	PUNCT
iajs-3094	97	35	76,1,13	76,1,13	NOUN
iajs-3094	97	36	)	)	PUNCT
iajs-3094	97	37	hence	hence	ADV
iajs-3094	97	38	𝑆𝑃𝑇∗the	𝑆𝑃𝑇∗the	DET
iajs-3094	97	39	sequence	sequence	NOUN
iajs-3094	97	40	gives	give	VERB
iajs-3094	97	41	an	an	DET
iajs-3094	97	42	efficient	efficient	ADJ
iajs-3094	97	43	solution	solution	NOUN
iajs-3094	97	44	for	for	ADP
iajs-3094	97	45	the	the	DET
iajs-3094	97	46	problem	problem	NOUN
iajs-3094	97	47	(	(	PUNCT
iajs-3094	97	48	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	97	49	)	)	PUNCT
iajs-3094	97	50	.	.	PUNCT
iajs-3094	98	1	for	for	ADP
iajs-3094	98	2	the	the	DET
iajs-3094	98	3	problem(𝑆𝐶𝑆𝐸𝑇	problem(𝑆𝐶𝑆𝐸𝑇	NOUN
iajs-3094	98	4	)	)	PUNCT
iajs-3094	98	5	,	,	PUNCT
iajs-3094	98	6	we	we	PRON
iajs-3094	98	7	can	can	AUX
iajs-3094	98	8	deduce	deduce	VERB
iajs-3094	98	9	seven	seven	NUM
iajs-3094	98	10	sub	sub	NOUN
iajs-3094	98	11	problems	problem	NOUN
iajs-3094	98	12	(	(	PUNCT
iajs-3094	98	13	𝑆₱𝑖	𝑆₱𝑖	PROPN
iajs-3094	98	14	)	)	PUNCT
iajs-3094	98	15	for	for	ADP
iajs-3094	98	16	𝑖	𝑖	NOUN
iajs-3094	98	17	=	=	SYM
iajs-3094	98	18	1	1	NUM
iajs-3094	98	19	to	to	PART
iajs-3094	98	20	7	7	NUM
iajs-3094	98	21	:	:	PUNCT
iajs-3094	98	22	ihjpas	ihjpas	PROPN
iajs-3094	98	23	.	.	PUNCT
iajs-3094	99	1	37	37	NUM
iajs-3094	99	2	(	(	PUNCT
iajs-3094	99	3	1	1	NUM
iajs-3094	99	4	)	)	PUNCT
iajs-3094	99	5	2024	2024	NUM
iajs-3094	99	6	390	390	NUM
iajs-3094	99	7	1	1	NUM
iajs-3094	99	8	)	)	PUNCT
iajs-3094	99	9	1//𝐿𝑒𝑥(∑𝐶𝑗	1//𝐿𝑒𝑥(∑𝐶𝑗	NUM
iajs-3094	99	10	,	,	PUNCT
iajs-3094	99	11	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	99	12	,	,	PUNCT
iajs-3094	99	13	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	99	14	)	)	PUNCT
iajs-3094	99	15	problem	problem	NOUN
iajs-3094	99	16	𝑆₱1	𝑆₱1	NUM
iajs-3094	99	17	.	.	NOUN
iajs-3094	99	18	2	2	NUM
iajs-3094	99	19	)	)	PUNCT
iajs-3094	99	20	1//𝐿𝑒𝑥(∑𝐶𝑗	1//𝐿𝑒𝑥(∑𝐶𝑗	NUM
iajs-3094	99	21	,	,	PUNCT
iajs-3094	99	22	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	99	23	,	,	PUNCT
iajs-3094	99	24	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	99	25	)	)	PUNCT
iajs-3094	99	26	problem	problem	NOUN
iajs-3094	99	27	𝑆₱2	𝑆₱2	NOUN
iajs-3094	99	28	.	.	PUNCT
iajs-3094	100	1	3	3	X
iajs-3094	100	2	)	)	PUNCT
iajs-3094	100	3	1//𝐿𝑒𝑥(𝑇𝑚𝑎𝑥	1//𝐿𝑒𝑥(𝑇𝑚𝑎𝑥	NUM
iajs-3094	100	4	,	,	PUNCT
iajs-3094	100	5	∑𝐶𝑗	∑𝐶𝑗	PRON
iajs-3094	100	6	,	,	PUNCT
iajs-3094	100	7	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	100	8	)	)	PUNCT
iajs-3094	100	9	problem	problem	NOUN
iajs-3094	100	10	𝑆₱3	𝑆₱3	NUM
iajs-3094	100	11	.	.	PROPN
iajs-3094	101	1	4	4	NUM
iajs-3094	101	2	)	)	PUNCT
iajs-3094	101	3	1//𝐿𝑒𝑥(𝑇𝑚𝑎𝑥	1//𝐿𝑒𝑥(𝑇𝑚𝑎𝑥	NUM
iajs-3094	101	4	,	,	PUNCT
iajs-3094	101	5	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	101	6	,	,	PUNCT
iajs-3094	101	7	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	101	8	)	)	PUNCT
iajs-3094	101	9	problem	problem	NOUN
iajs-3094	101	10	𝑆₱4	𝑆₱4	NOUN
iajs-3094	101	11	.	.	PUNCT
iajs-3094	102	1	5	5	NUM
iajs-3094	102	2	)	)	PUNCT
iajs-3094	102	3	1//𝐿𝑒𝑥(∑𝐸𝑗	1//𝐿𝑒𝑥(∑𝐸𝑗	NOUN
iajs-3094	102	4	,	,	PUNCT
iajs-3094	102	5	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	102	6	,	,	PUNCT
iajs-3094	102	7	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	102	8	)	)	PUNCT
iajs-3094	102	9	problem	problem	NOUN
iajs-3094	102	10	𝑆₱5	𝑆₱5	NOUN
iajs-3094	102	11	.	.	PUNCT
iajs-3094	103	1	6	6	NUM
iajs-3094	103	2	)	)	PUNCT
iajs-3094	103	3	1//𝐿𝑒𝑥	1//𝐿𝑒𝑥	NUM
iajs-3094	103	4	(	(	PUNCT
iajs-3094	103	5	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	103	6	,	,	PUNCT
iajs-3094	103	7	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	103	8	,	,	PUNCT
iajs-3094	103	9	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	103	10	)	)	PUNCT
iajs-3094	103	11	problem	problem	NOUN
iajs-3094	103	12	𝑆₱6	𝑆₱6	ADP
iajs-3094	103	13	.	.	PROPN
iajs-3094	103	14	7	7	X
iajs-3094	103	15	)	)	PUNCT
iajs-3094	103	16	1//	1//	NUM
iajs-3094	103	17	(	(	PUNCT
iajs-3094	103	18	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	103	19	+	+	NUM
iajs-3094	103	20	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	103	21	+	+	CCONJ
iajs-3094	103	22	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	103	23	)	)	PUNCT
iajs-3094	103	24	problem	problem	NOUN
iajs-3094	103	25	𝑆₱7	𝑆₱7	NOUN
iajs-3094	103	26	.	.	PUNCT
iajs-3094	104	1	(	(	PUNCT
iajs-3094	104	2	1	1	X
iajs-3094	104	3	)	)	PUNCT
iajs-3094	104	4	1//	1//	NUM
iajs-3094	104	5	𝑳𝒆𝒙(∑𝑪𝒋	𝑳𝒆𝒙(∑𝑪𝒋	NOUN
iajs-3094	104	6	,	,	PUNCT
iajs-3094	104	7	∑𝑬𝒋	∑𝑬𝒋	PROPN
iajs-3094	104	8	,	,	PUNCT
iajs-3094	104	9	𝑻𝒎𝒂𝒙)(𝑺₱𝟏	𝑻𝒎𝒂𝒙)(𝑺₱𝟏	PROPN
iajs-3094	104	10	):	):	PUNCT
iajs-3094	104	11	the	the	DET
iajs-3094	104	12	definition	definition	NOUN
iajs-3094	104	13	of	of	ADP
iajs-3094	104	14	this	this	DET
iajs-3094	104	15	problem	problem	NOUN
iajs-3094	104	16	is	be	AUX
iajs-3094	104	17	as	as	SCONJ
iajs-3094	104	18	follows	follow	VERB
iajs-3094	104	19	:	:	PUNCT
iajs-3094	104	20	𝑀𝑖𝑛	𝑀𝑖𝑛	PROPN
iajs-3094	104	21	{	{	PUNCT
iajs-3094	104	22	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	104	23	}	}	PUNCT
iajs-3094	104	24	s.	s.	PROPN
iajs-3094	104	25	t.	t.	PROPN
iajs-3094	104	26	∑	∑	PROPN
iajs-3094	105	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	105	2	𝑛	𝑛	PRON
iajs-3094	105	3	𝑗=1	𝑗=1	PROPN
iajs-3094	105	4	=	=	SYM
iajs-3094	105	5	𝐶∗	𝐶∗	NOUN
iajs-3094	105	6	where	where	SCONJ
iajs-3094	105	7	𝐶∗	𝐶∗	NOUN
iajs-3094	105	8	=	=	NOUN
iajs-3094	105	9	∑	∑	PROPN
iajs-3094	105	10	𝐶𝑗(𝑆𝑃𝑇	𝐶𝑗(𝑆𝑃𝑇	NUM
iajs-3094	105	11	)	)	PUNCT
iajs-3094	106	1	𝑛	𝑛	PRON
iajs-3094	106	2	𝑗=1	𝑗=1	NOUN
iajs-3094	106	3	∑	∑	PUNCT
iajs-3094	106	4	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	106	5	𝑛	𝑛	DET
iajs-3094	106	6	𝑗=1	𝑗=1	PROPN
iajs-3094	106	7	≤	≤	PROPN
iajs-3094	106	8	𝐸	𝐸	PROPN
iajs-3094	106	9	,	,	PUNCT
iajs-3094	106	10	𝐸	𝐸	PROPN
iajs-3094	106	11	∈	∈	PROPN
iajs-3094	107	1	[	[	X
iajs-3094	107	2	∑	∑	X
iajs-3094	107	3	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	107	4	𝑛	𝑛	PRON
iajs-3094	107	5	𝑗=1	𝑗=1	PROPN
iajs-3094	107	6	(	(	PUNCT
iajs-3094	107	7	𝑀𝑆𝑇),∑	𝑀𝑆𝑇),∑	X
iajs-3094	107	8	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	107	9	𝑛	𝑛	PRON
iajs-3094	107	10	𝑗=1	𝑗=1	X
iajs-3094	107	11	(	(	PUNCT
iajs-3094	107	12	𝑆𝑃𝑇	𝑆𝑃𝑇	PROPN
iajs-3094	107	13	)	)	PUNCT
iajs-3094	107	14	]	]	PUNCT
iajs-3094	107	15	}	}	PUNCT
iajs-3094	107	16	(	(	PUNCT
iajs-3094	107	17	𝑆₱1	𝑆₱1	NUM
iajs-3094	107	18	)	)	PUNCT
iajs-3094	107	19	.	.	PUNCT
iajs-3094	108	1	since	since	SCONJ
iajs-3094	108	2	the	the	DET
iajs-3094	108	3	most	most	ADV
iajs-3094	108	4	important	important	ADJ
iajs-3094	108	5	function	function	NOUN
iajs-3094	108	6	in	in	ADP
iajs-3094	108	7	this	this	DET
iajs-3094	108	8	problem	problem	NOUN
iajs-3094	108	9	(	(	PUNCT
iajs-3094	108	10	s₱1	s₱1	PROPN
iajs-3094	108	11	)	)	PUNCT
iajs-3094	108	12	,	,	PUNCT
iajs-3094	108	13	∑	∑	PUNCT
iajs-3094	108	14	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	108	15	𝑛	𝑛	DET
iajs-3094	108	16	𝑗=1	𝑗=1	PROPN
iajs-3094	108	17	,	,	PUNCT
iajs-3094	108	18	should	should	AUX
iajs-3094	108	19	be	be	AUX
iajs-3094	108	20	optimal	optimal	ADJ
iajs-3094	108	21	,	,	PUNCT
iajs-3094	108	22	the	the	DET
iajs-3094	108	23	following	follow	VERB
iajs-3094	108	24	easy	easy	ADJ
iajs-3094	108	25	algorithm	algorithm	NOUN
iajs-3094	108	26	produces	produce	VERB
iajs-3094	108	27	the	the	DET
iajs-3094	108	28	best	good	ADJ
iajs-3094	108	29	possible	possible	ADJ
iajs-3094	108	30	outcome	outcome	NOUN
iajs-3094	108	31	.	.	PUNCT
iajs-3094	109	1	algorithm	algorithm	NOUN
iajs-3094	109	2	(	(	PUNCT
iajs-3094	109	3	𝑺𝑪𝑺𝑬𝑻𝟏	𝑺𝑪𝑺𝑬𝑻𝟏	PROPN
iajs-3094	109	4	)	)	PUNCT
iajs-3094	109	5	for	for	ADP
iajs-3094	109	6	1//𝑳𝒆𝒙(∑𝑪𝒋	1//𝑳𝒆𝒙(∑𝑪𝒋	NUM
iajs-3094	109	7	,	,	PUNCT
iajs-3094	109	8	∑𝑬𝒋	∑𝑬𝒋	VERB
iajs-3094	109	9	,	,	PUNCT
iajs-3094	109	10	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	109	11	)	)	PUNCT
iajs-3094	109	12	𝐩𝐫𝐨𝐛𝐥𝐞𝐦	𝐩𝐫𝐨𝐛𝐥𝐞𝐦	NOUN
iajs-3094	109	13	(	(	PUNCT
iajs-3094	109	14	𝑺₱𝟏	𝑺₱𝟏	NOUN
iajs-3094	109	15	)	)	PUNCT
iajs-3094	109	16	.	.	PUNCT
iajs-3094	110	1	st1	st1	PROPN
iajs-3094	110	2	:	:	PUNCT
iajs-3094	110	3	is	be	AUX
iajs-3094	110	4	the	the	DET
iajs-3094	110	5	sequencing	sequencing	NOUN
iajs-3094	110	6	of	of	ADP
iajs-3094	110	7	jobs	job	NOUN
iajs-3094	110	8	according	accord	VERB
iajs-3094	110	9	to	to	ADP
iajs-3094	110	10	the	the	DET
iajs-3094	110	11	spt	spt	PROPN
iajs-3094	110	12	rule	rule	NOUN
iajs-3094	110	13	and	and	CCONJ
iajs-3094	110	14	the	the	DET
iajs-3094	110	15	computation(∑𝑪𝒋	computation(∑𝑪𝒋	ADJ
iajs-3094	110	16	,	,	PUNCT
iajs-3094	110	17	∑𝑬𝒋	∑𝑬𝒋	VERB
iajs-3094	110	18	,	,	PUNCT
iajs-3094	110	19	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	110	20	)	)	PUNCT
iajs-3094	110	21	.	.	PUNCT
iajs-3094	111	1	st2	st2	NOUN
iajs-3094	111	2	:	:	PUNCT
iajs-3094	111	3	if	if	SCONJ
iajs-3094	111	4	there	there	PRON
iajs-3094	111	5	are	be	VERB
iajs-3094	111	6	jobs	job	NOUN
iajs-3094	111	7	with	with	ADP
iajs-3094	111	8	equal	equal	ADJ
iajs-3094	111	9	processing	processing	NOUN
iajs-3094	111	10	times	time	NOUN
iajs-3094	111	11	,	,	PUNCT
iajs-3094	111	12	then	then	ADV
iajs-3094	111	13	order	order	VERB
iajs-3094	111	14	these	these	DET
iajs-3094	111	15	jobs	job	NOUN
iajs-3094	111	16	:	:	PUNCT
iajs-3094	111	17	(	(	PUNCT
iajs-3094	111	18	a	a	X
iajs-3094	111	19	)	)	PUNCT
iajs-3094	111	20	using	use	VERB
iajs-3094	111	21	the	the	DET
iajs-3094	111	22	mst	mst	PROPN
iajs-3094	111	23	rule	rule	NOUN
iajs-3094	111	24	and	and	CCONJ
iajs-3094	111	25	the	the	DET
iajs-3094	111	26	calculation	calculation	NOUN
iajs-3094	111	27	(	(	PUNCT
iajs-3094	111	28	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	111	29	,	,	PUNCT
iajs-3094	111	30	∑𝑬𝒋	∑𝑬𝒋	NOUN
iajs-3094	111	31	,	,	PUNCT
iajs-3094	111	32	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	111	33	)	)	PUNCT
iajs-3094	111	34	.	.	PUNCT
iajs-3094	112	1	(	(	PUNCT
iajs-3094	112	2	b	b	X
iajs-3094	112	3	)	)	PUNCT
iajs-3094	112	4	using	use	VERB
iajs-3094	112	5	the	the	DET
iajs-3094	112	6	edd	edd	PROPN
iajs-3094	112	7	rule	rule	NOUN
iajs-3094	112	8	and	and	CCONJ
iajs-3094	112	9	the	the	DET
iajs-3094	112	10	calculation(∑𝑪𝒋	calculation(∑𝑪𝒋	PROPN
iajs-3094	112	11	,	,	PUNCT
iajs-3094	112	12	∑𝑬𝒋	∑𝑬𝒋	PROPN
iajs-3094	112	13	,	,	PUNCT
iajs-3094	112	14	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	112	15	)	)	PUNCT
iajs-3094	112	16	.	.	PUNCT
iajs-3094	113	1	st3	st3	VERB
iajs-3094	113	2	:	:	PUNCT
iajs-3094	113	3	if	if	SCONJ
iajs-3094	113	4	more	more	ADJ
iajs-3094	113	5	than	than	ADP
iajs-3094	113	6	one	one	NUM
iajs-3094	113	7	spt	spt	NOUN
iajs-3094	113	8	schedule	schedule	NOUN
iajs-3094	113	9	appeared	appear	VERB
iajs-3094	113	10	,	,	PUNCT
iajs-3094	113	11	then	then	ADV
iajs-3094	113	12	choose	choose	VERB
iajs-3094	113	13	the	the	DET
iajs-3094	113	14	schedule	schedule	NOUN
iajs-3094	113	15	with	with	ADP
iajs-3094	113	16	minimum	minimum	NOUN
iajs-3094	113	17	∑𝑬𝒋	∑𝑬𝒋	NOUN
iajs-3094	113	18	and	and	CCONJ
iajs-3094	113	19	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	113	20	.	.	PUNCT
iajs-3094	114	1	note	note	NOUN
iajs-3094	114	2	:	:	PUNCT
iajs-3094	114	3	same	same	ADJ
iajs-3094	114	4	as	as	ADP
iajs-3094	114	5	an	an	DET
iajs-3094	114	6	example	example	NOUN
iajs-3094	114	7	(	(	PUNCT
iajs-3094	114	8	1	1	X
iajs-3094	114	9	)	)	PUNCT
iajs-3094	114	10	for	for	ADP
iajs-3094	114	11	𝑆₱1	𝑆₱1	NUM
iajs-3094	114	12	.	.	PUNCT
iajs-3094	115	1	(	(	PUNCT
iajs-3094	115	2	2	2	X
iajs-3094	115	3	)	)	PUNCT
iajs-3094	115	4	1//𝑳𝒆𝒙(∑𝑪𝒋	1//𝑳𝒆𝒙(∑𝑪𝒋	NOUN
iajs-3094	115	5	,	,	PUNCT
iajs-3094	115	6	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	115	7	,	,	PUNCT
iajs-3094	115	8	∑𝑬𝒋)(𝑺₱𝟐	∑𝑬𝒋)(𝑺₱𝟐	NUM
iajs-3094	115	9	):	):	PUNCT
iajs-3094	115	10	this	this	DET
iajs-3094	115	11	problem	problem	NOUN
iajs-3094	115	12	is	be	AUX
iajs-3094	115	13	defined	define	VERB
iajs-3094	115	14	as	as	SCONJ
iajs-3094	115	15	follows	follow	VERB
iajs-3094	115	16	:	:	PUNCT
iajs-3094	115	17	𝑀𝑖𝑛	𝑀𝑖𝑛	PROPN
iajs-3094	115	18	{	{	PUNCT
iajs-3094	115	19	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	115	20	}	}	PUNCT
iajs-3094	115	21	s.	s.	PROPN
iajs-3094	115	22	t.	t.	PROPN
iajs-3094	115	23	∑	∑	PROPN
iajs-3094	116	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	116	2	𝑛	𝑛	PRON
iajs-3094	116	3	𝑗=1	𝑗=1	PROPN
iajs-3094	116	4	=	=	SYM
iajs-3094	116	5	𝐶∗	𝐶∗	NOUN
iajs-3094	116	6	where	where	SCONJ
iajs-3094	116	7	𝐶∗	𝐶∗	NOUN
iajs-3094	116	8	=	=	NOUN
iajs-3094	116	9	∑	∑	PROPN
iajs-3094	116	10	𝐶𝑗(𝑆𝑃𝑇	𝐶𝑗(𝑆𝑃𝑇	NUM
iajs-3094	116	11	)	)	PUNCT
iajs-3094	116	12	𝑛	𝑛	DET
iajs-3094	116	13	𝑗=1	𝑗=1	PROPN
iajs-3094	116	14	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	116	15	≤	≤	PROPN
iajs-3094	116	16	𝑇	𝑇	PROPN
iajs-3094	116	17	,	,	PUNCT
iajs-3094	116	18	𝑇	𝑇	PROPN
iajs-3094	116	19	∈	∈	PROPN
iajs-3094	117	1	[	[	X
iajs-3094	117	2	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	NOUN
iajs-3094	117	3	)	)	PUNCT
iajs-3094	117	4	,	,	PUNCT
iajs-3094	117	5	𝑇𝑚𝑎𝑥(𝑆𝑃𝑇	𝑇𝑚𝑎𝑥(𝑆𝑃𝑇	PROPN
iajs-3094	117	6	)	)	PUNCT
iajs-3094	117	7	]	]	PUNCT
iajs-3094	118	1	}	}	PUNCT
iajs-3094	118	2	(	(	PUNCT
iajs-3094	118	3	𝑆₱2	𝑆₱2	NOUN
iajs-3094	118	4	)	)	PUNCT
iajs-3094	118	5	.	.	PUNCT
iajs-3094	119	1	the	the	DET
iajs-3094	119	2	problem	problem	NOUN
iajs-3094	119	3	(	(	PUNCT
iajs-3094	119	4	s₱2)with	s₱2)with	ADP
iajs-3094	119	5	∑	∑	PUNCT
iajs-3094	119	6	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	119	7	𝑛	𝑛	PRON
iajs-3094	119	8	𝑗=1	𝑗=1	PROPN
iajs-3094	119	9	is	be	AUX
iajs-3094	119	10	the	the	DET
iajs-3094	119	11	most	most	ADV
iajs-3094	119	12	important	important	ADJ
iajs-3094	119	13	function	function	NOUN
iajs-3094	119	14	,	,	PUNCT
iajs-3094	119	15	it	it	PRON
iajs-3094	119	16	must	must	AUX
iajs-3094	119	17	be	be	AUX
iajs-3094	119	18	optimal	optimal	ADJ
iajs-3094	119	19	,	,	PUNCT
iajs-3094	119	20	so	so	CCONJ
iajs-3094	119	21	the	the	DET
iajs-3094	119	22	easy	easy	ADJ
iajs-3094	119	23	algorithm	algorithm	NOUN
iajs-3094	119	24	𝑺𝑪𝑺𝑬𝑻𝟏	𝑺𝑪𝑺𝑬𝑻𝟏	PROPN
iajs-3094	119	25	that	that	PRON
iajs-3094	119	26	gives	give	VERB
iajs-3094	119	27	us	we	PRON
iajs-3094	119	28	the	the	DET
iajs-3094	119	29	best	good	ADJ
iajs-3094	119	30	result	result	NOUN
iajs-3094	119	31	for	for	ADP
iajs-3094	119	32	(	(	PUNCT
iajs-3094	119	33	s₱2	s₱2	ADJ
iajs-3094	119	34	)	)	PUNCT
iajs-3094	119	35	.	.	PUNCT
iajs-3094	120	1	(	(	PUNCT
iajs-3094	120	2	3	3	X
iajs-3094	120	3	)	)	PUNCT
iajs-3094	120	4	1//𝑳𝒆𝒙(𝑻𝒎𝒂𝒙	1//𝑳𝒆𝒙(𝑻𝒎𝒂𝒙	NUM
iajs-3094	120	5	,	,	PUNCT
iajs-3094	120	6	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	120	7	,	,	PUNCT
iajs-3094	120	8	∑𝑬𝒋)(𝑺₱𝟑	∑𝑬𝒋)(𝑺₱𝟑	NUM
iajs-3094	120	9	):	):	PUNCT
iajs-3094	120	10	this	this	DET
iajs-3094	120	11	problem	problem	NOUN
iajs-3094	120	12	is	be	AUX
iajs-3094	120	13	defined	define	VERB
iajs-3094	120	14	as	as	ADP
iajs-3094	120	15	follows	follow	VERB
iajs-3094	120	16	:	:	PUNCT
iajs-3094	120	17	ihjpas	ihjpas	PROPN
iajs-3094	120	18	.	.	PUNCT
iajs-3094	121	1	37	37	NUM
iajs-3094	121	2	(	(	PUNCT
iajs-3094	121	3	1	1	NUM
iajs-3094	121	4	)	)	PUNCT
iajs-3094	121	5	2024	2024	NUM
iajs-3094	121	6	391	391	NUM
iajs-3094	121	7	𝑀𝑖𝑛∑	𝑀𝑖𝑛∑	NOUN
iajs-3094	121	8	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	121	9	𝑛	𝑛	PRON
iajs-3094	121	10	𝑗=1	𝑗=1	PROPN
iajs-3094	121	11	s.	s.	PROPN
iajs-3094	121	12	t.	t.	PROPN
iajs-3094	122	1	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	122	2	=	=	SYM
iajs-3094	122	3	𝑇	𝑇	PROPN
iajs-3094	122	4	∗	∗	NOUN
iajs-3094	122	5	where	where	SCONJ
iajs-3094	122	6	𝑇∗	𝑇∗	NOUN
iajs-3094	123	1	=	=	PRON
iajs-3094	123	2	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	VERB
iajs-3094	123	3	)	)	PUNCT
iajs-3094	123	4	∑	∑	PUNCT
iajs-3094	124	1	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	124	2	≤	≤	PROPN
iajs-3094	124	3	𝐶	𝐶	PROPN
iajs-3094	124	4	,	,	PUNCT
iajs-3094	124	5	𝐶𝑛	𝐶𝑛	PROPN
iajs-3094	124	6	𝑗=1	𝑗=1	PROPN
iajs-3094	124	7	∈	∈	PROPN
iajs-3094	125	1	[	[	X
iajs-3094	125	2	∑	∑	X
iajs-3094	125	3	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	125	4	𝑛	𝑛	PRON
iajs-3094	125	5	𝑗=1	𝑗=1	PROPN
iajs-3094	125	6	(	(	PUNCT
iajs-3094	125	7	𝑆𝑃𝑇),∑	𝑆𝑃𝑇),∑	NOUN
iajs-3094	125	8	𝐶𝑗(𝐸𝐷𝐷	𝐶𝑗(𝐸𝐷𝐷	NUM
iajs-3094	125	9	)	)	PUNCT
iajs-3094	125	10	]	]	PUNCT
iajs-3094	125	11	𝑛	𝑛	PRON
iajs-3094	125	12	𝑗=1	𝑗=1	PROPN
iajs-3094	125	13	}	}	PUNCT
iajs-3094	125	14	(	(	PUNCT
iajs-3094	125	15	s₱3	s₱3	NOUN
iajs-3094	125	16	)	)	PUNCT
iajs-3094	125	17	.	.	PUNCT
iajs-3094	126	1	given	give	VERB
iajs-3094	126	2	that	that	SCONJ
iajs-3094	126	3	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	126	4	is	be	AUX
iajs-3094	126	5	a	a	DET
iajs-3094	126	6	more	more	ADV
iajs-3094	126	7	important	important	ADJ
iajs-3094	126	8	function	function	NOUN
iajs-3094	126	9	in	in	ADP
iajs-3094	126	10	this	this	DET
iajs-3094	126	11	problem	problem	NOUN
iajs-3094	126	12	(	(	PUNCT
iajs-3094	126	13	s₱3	s₱3	NOUN
iajs-3094	126	14	)	)	PUNCT
iajs-3094	126	15	and	and	CCONJ
iajs-3094	126	16	should	should	AUX
iajs-3094	126	17	be	be	AUX
iajs-3094	126	18	optimal	optimal	ADJ
iajs-3094	126	19	,	,	PUNCT
iajs-3094	126	20	the	the	DET
iajs-3094	126	21	following	follow	VERB
iajs-3094	126	22	algorithm	algorithm	NOUN
iajs-3094	126	23	offers	offer	VERB
iajs-3094	126	24	the	the	DET
iajs-3094	126	25	best	good	ADJ
iajs-3094	126	26	solution	solution	NOUN
iajs-3094	126	27	.	.	PUNCT
iajs-3094	127	1	algorithm	algorithm	NOUN
iajs-3094	127	2	(	(	PUNCT
iajs-3094	127	3	𝑺𝑪𝑺𝑬𝑻𝟐	𝑺𝑪𝑺𝑬𝑻𝟐	PROPN
iajs-3094	127	4	)	)	PUNCT
iajs-3094	127	5	for	for	ADP
iajs-3094	127	6	1//𝑳𝒆𝒙(𝑻𝒎𝒂𝒙	1//𝑳𝒆𝒙(𝑻𝒎𝒂𝒙	NUM
iajs-3094	127	7	,	,	PUNCT
iajs-3094	127	8	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	127	9	,	,	PUNCT
iajs-3094	127	10	∑𝑬𝒋	∑𝑬𝒋	NOUN
iajs-3094	127	11	)	)	PUNCT
iajs-3094	127	12	𝐩𝐫𝐨𝐛𝐥𝐞𝐦	𝐩𝐫𝐨𝐛𝐥𝐞𝐦	NOUN
iajs-3094	127	13	(	(	PUNCT
iajs-3094	127	14	𝑺₱𝟑	𝑺₱𝟑	NUM
iajs-3094	127	15	)	)	PUNCT
iajs-3094	127	16	.	.	PUNCT
iajs-3094	128	1	st1	st1	PROPN
iajs-3094	128	2	:	:	PUNCT
iajs-3094	128	3	arrange	arrange	VERB
iajs-3094	128	4	the	the	DET
iajs-3094	128	5	jobs	job	NOUN
iajs-3094	128	6	according	accord	VERB
iajs-3094	128	7	to	to	ADP
iajs-3094	128	8	the	the	DET
iajs-3094	128	9	rule	rule	NOUN
iajs-3094	128	10	of	of	ADP
iajs-3094	128	11	edd	edd	PROPN
iajs-3094	128	12	and	and	CCONJ
iajs-3094	128	13	calculate	calculate	NOUN
iajs-3094	128	14	𝑻𝒎𝒂𝒙(𝑬𝑫𝑫	𝑻𝒎𝒂𝒙(𝑬𝑫𝑫	NOUN
iajs-3094	128	15	)	)	PUNCT
iajs-3094	129	1	=	=	SYM
iajs-3094	129	2	𝑻	𝑻	PROPN
iajs-3094	129	3	∗.	∗.	PROPN
iajs-3094	129	4	st2	st2	NOUN
iajs-3094	129	5	:	:	PUNCT
iajs-3094	129	6	calculated	calculate	VERB
iajs-3094	129	7	𝐷𝑖	𝐷𝑖	PROPN
iajs-3094	129	8	=	=	PUNCT
iajs-3094	129	9	𝑑𝑖	𝑑𝑖	PART
iajs-3094	129	10	+	+	CCONJ
iajs-3094	129	11	𝑇	𝑇	PROPN
iajs-3094	129	12	∗	∗	NOUN
iajs-3094	129	13	,	,	PUNCT
iajs-3094	129	14	for	for	ADP
iajs-3094	129	15	all	all	PRON
iajs-3094	129	16	in	in	ADP
iajs-3094	129	17	𝑁	𝑁	PROPN
iajs-3094	129	18	𝑤ℎ𝑒𝑟𝑒	𝑤ℎ𝑒𝑟𝑒	NOUN
iajs-3094	129	19	𝑁	𝑁	PROPN
iajs-3094	129	20	=	=	SYM
iajs-3094	129	21	{	{	PUNCT
iajs-3094	129	22	1	1	NUM
iajs-3094	129	23	,	,	PUNCT
iajs-3094	129	24	…	…	PUNCT
iajs-3094	129	25	,	,	PUNCT
iajs-3094	129	26	𝑛	𝑛	PROPN
iajs-3094	129	27	}	}	PUNCT
iajs-3094	129	28	.	.	PUNCT
iajs-3094	130	1	st3	st3	PROPN
iajs-3094	130	2	:	:	PUNCT
iajs-3094	130	3	suppose	suppose	VERB
iajs-3094	130	4	𝑡	𝑡	X
iajs-3094	130	5	=	=	NOUN
iajs-3094	130	6	∑	∑	PUNCT
iajs-3094	130	7	𝑝𝑖𝑖∈𝑁	𝑝𝑖𝑖∈𝑁	NOUN
iajs-3094	130	8	and	and	CCONJ
iajs-3094	130	9	𝐾	𝐾	PROPN
iajs-3094	130	10	equals	equal	VERB
iajs-3094	130	11	𝑛.	𝑛.	NOUN
iajs-3094	130	12	st4	st4	NOUN
iajs-3094	130	13	:	:	PUNCT
iajs-3094	130	14	finding	find	VERB
iajs-3094	130	15	a	a	DET
iajs-3094	130	16	job	job	NOUN
iajs-3094	130	17	𝑗	𝑗	INTJ
iajs-3094	130	18	using	use	VERB
iajs-3094	130	19	the	the	DET
iajs-3094	130	20	smith	smith	PROPN
iajs-3094	130	21	backward	backward	ADJ
iajs-3094	130	22	algorithm	algorithm	NOUN
iajs-3094	130	23	and	and	CCONJ
iajs-3094	130	24	satisfying	satisfy	VERB
iajs-3094	130	25	𝐷𝑗	𝐷𝑗	PROPN
iajs-3094	130	26	≥	≥	NUM
iajs-3094	130	27	𝑡	𝑡	NOUN
iajs-3094	130	28	,	,	PUNCT
iajs-3094	130	29	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	130	30	≥	≥	NOUN
iajs-3094	130	31	𝑝𝑖	𝑝𝑖	PROPN
iajs-3094	130	32	(	(	PUNCT
iajs-3094	130	33	choose	choose	VERB
iajs-3094	130	34	the	the	DET
iajs-3094	130	35	job	job	NOUN
iajs-3094	130	36	𝑗	𝑗	NOUN
iajs-3094	130	37	with	with	ADP
iajs-3094	130	38	the	the	DET
iajs-3094	130	39	largest	large	ADJ
iajs-3094	130	40	due	due	ADJ
iajs-3094	130	41	date	date	NOUN
iajs-3094	130	42	if	if	SCONJ
iajs-3094	130	43	there	there	PRON
iajs-3094	130	44	is	be	VERB
iajs-3094	130	45	a	a	DET
iajs-3094	130	46	tie	tie	NOUN
iajs-3094	130	47	)	)	PUNCT
iajs-3094	130	48	.	.	PUNCT
iajs-3094	131	1	assign	assign	NOUN
iajs-3094	131	2	position	position	NOUN
iajs-3094	131	3	𝐾to	𝐾to	VERB
iajs-3094	131	4	job	job	NOUN
iajs-3094	131	5	𝑗.	𝑗.	NOUN
iajs-3094	131	6	st5	st5	NOUN
iajs-3094	131	7	:	:	PUNCT
iajs-3094	131	8	assign	assign	VERB
iajs-3094	131	9	the	the	DET
iajs-3094	131	10	variables	variable	NOUN
iajs-3094	131	11	𝑡	𝑡	PROPN
iajs-3094	131	12	=	=	SYM
iajs-3094	131	13	𝑡	𝑡	PROPN
iajs-3094	131	14	−	−	PROPN
iajs-3094	131	15	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	131	16	,	,	PUNCT
iajs-3094	131	17	𝑁	𝑁	PROPN
iajs-3094	131	18	=	=	SYM
iajs-3094	131	19	𝑁	𝑁	PROPN
iajs-3094	131	20	−	−	PROPN
iajs-3094	131	21	{	{	PUNCT
iajs-3094	131	22	𝑗	𝑗	NOUN
iajs-3094	131	23	}	}	PUNCT
iajs-3094	131	24	and	and	CCONJ
iajs-3094	131	25	𝐾	𝐾	PROPN
iajs-3094	131	26	=	=	SYM
iajs-3094	131	27	𝐾	𝐾	PROPN
iajs-3094	131	28	−	−	PROPN
iajs-3094	131	29	1	1	NUM
iajs-3094	131	30	;	;	PUNCT
iajs-3094	131	31	if	if	SCONJ
iajs-3094	131	32	𝐾	𝐾	PROPN
iajs-3094	131	33	=	=	SYM
iajs-3094	131	34	1	1	NUM
iajs-3094	131	35	proceed	proceed	VERB
iajs-3094	131	36	to	to	PART
iajs-3094	131	37	step	step	VERB
iajs-3094	131	38	6	6	NUM
iajs-3094	131	39	;	;	PUNCT
iajs-3094	131	40	if	if	SCONJ
iajs-3094	131	41	not	not	PART
iajs-3094	131	42	,	,	PUNCT
iajs-3094	131	43	proceed	proceed	VERB
iajs-3094	131	44	to	to	PART
iajs-3094	131	45	step	step	VERB
iajs-3094	131	46	4	4	NUM
iajs-3094	131	47	.	.	PUNCT
iajs-3094	131	48	st6	st6	NOUN
iajs-3094	131	49	:	:	PUNCT
iajs-3094	131	50	find	find	VERB
iajs-3094	131	51	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	131	52	,	,	PUNCT
iajs-3094	131	53	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	131	54	and	and	CCONJ
iajs-3094	131	55	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	131	56	for	for	ADP
iajs-3094	131	57	the	the	DET
iajs-3094	131	58	sequence	sequence	NOUN
iajs-3094	131	59	that	that	PRON
iajs-3094	131	60	results	result	VERB
iajs-3094	131	61	.	.	PUNCT
iajs-3094	132	1	example	example	NOUN
iajs-3094	132	2	(	(	PUNCT
iajs-3094	132	3	2	2	NUM
iajs-3094	132	4	):	):	PUNCT
iajs-3094	132	5	consider	consider	VERB
iajs-3094	132	6	the	the	DET
iajs-3094	132	7	data	datum	NOUN
iajs-3094	132	8	for	for	ADP
iajs-3094	132	9	the	the	DET
iajs-3094	132	10	problem	problem	NOUN
iajs-3094	132	11	𝑆₱3	𝑆₱3	ADP
iajs-3094	132	12	in	in	ADP
iajs-3094	132	13	table	table	NOUN
iajs-3094	132	14	2	2	NUM
iajs-3094	132	15	.	.	PUNCT
iajs-3094	132	16	table	table	NOUN
iajs-3094	132	17	2	2	NUM
iajs-3094	132	18	.	.	PUNCT
iajs-3094	133	1	the	the	DET
iajs-3094	133	2	data	datum	NOUN
iajs-3094	133	3	of	of	ADP
iajs-3094	133	4	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	133	5	,	,	PUNCT
iajs-3094	133	6	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	133	7	,	,	PUNCT
iajs-3094	133	8	and	and	CCONJ
iajs-3094	133	9	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	133	10	for	for	ADP
iajs-3094	133	11	problem	problem	NOUN
iajs-3094	133	12	𝑆₱3	𝑆₱3	PROPN
iajs-3094	133	13	job1	job1	PROPN
iajs-3094	133	14	job2	job2	PROPN
iajs-3094	133	15	job3	job3	PROPN
iajs-3094	133	16	job4	job4	PROPN
iajs-3094	133	17	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	133	18	9	9	NUM
iajs-3094	133	19	3	3	NUM
iajs-3094	133	20	7	7	NUM
iajs-3094	133	21	2	2	NUM
iajs-3094	133	22	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	133	23	12	12	NUM
iajs-3094	133	24	5	5	NUM
iajs-3094	133	25	9	9	NUM
iajs-3094	133	26	10	10	NUM
iajs-3094	133	27	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	133	28	3	3	NUM
iajs-3094	133	29	2	2	NUM
iajs-3094	133	30	2	2	NUM
iajs-3094	133	31	8	8	NUM
iajs-3094	133	32	hence	hence	ADV
iajs-3094	133	33	the	the	DET
iajs-3094	133	34	(	(	PUNCT
iajs-3094	133	35	edd	edd	PROPN
iajs-3094	133	36	)	)	PUNCT
iajs-3094	133	37	schedule	schedule	NOUN
iajs-3094	133	38	(	(	PUNCT
iajs-3094	133	39	2,3,4,1	2,3,4,1	NUM
iajs-3094	133	40	)	)	PUNCT
iajs-3094	133	41	gives	give	VERB
iajs-3094	133	42	(	(	PUNCT
iajs-3094	133	43	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	133	44	,	,	PUNCT
iajs-3094	133	45	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	133	46	,	,	PUNCT
iajs-3094	133	47	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	133	48	)	)	PUNCT
iajs-3094	133	49	=	=	PUNCT
iajs-3094	133	50	(	(	PUNCT
iajs-3094	133	51	46,2,9	46,2,9	NOUN
iajs-3094	133	52	)	)	PUNCT
iajs-3094	133	53	.	.	PUNCT
iajs-3094	134	1	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	VERB
iajs-3094	134	2	)	)	PUNCT
iajs-3094	135	1	=	=	SYM
iajs-3094	135	2	𝑇∗	𝑇∗	PROPN
iajs-3094	135	3	,	,	PUNCT
iajs-3094	135	4	𝑡	𝑡	PROPN
iajs-3094	135	5	=	=	PROPN
iajs-3094	135	6	21	21	NUM
iajs-3094	135	7	,	,	PUNCT
iajs-3094	136	1	𝐷𝑖	𝐷𝑖	PROPN
iajs-3094	136	2	=	=	PUNCT
iajs-3094	136	3	𝑑𝑖	𝑑𝑖	PART
iajs-3094	136	4	+	+	CCONJ
iajs-3094	136	5	𝑇	𝑇	NOUN
iajs-3094	136	6	∗	∗	NOUN
iajs-3094	136	7	=	=	SYM
iajs-3094	136	8	(	(	PUNCT
iajs-3094	136	9	21,14,18,19	21,14,18,19	NUM
iajs-3094	136	10	)	)	PUNCT
iajs-3094	136	11	.	.	PUNCT
iajs-3094	137	1	the	the	DET
iajs-3094	137	2	schedule	schedule	NOUN
iajs-3094	137	3	(	(	PUNCT
iajs-3094	137	4	4,2,3,1	4,2,3,1	NUM
iajs-3094	137	5	)	)	PUNCT
iajs-3094	137	6	is	be	AUX
iajs-3094	137	7	given	give	VERB
iajs-3094	137	8	by	by	ADP
iajs-3094	137	9	smith	smith	PROPN
iajs-3094	137	10	's	's	PART
iajs-3094	137	11	backward	backward	ADJ
iajs-3094	137	12	algorithm	algorithm	NOUN
iajs-3094	137	13	with	with	ADP
iajs-3094	137	14	(	(	PUNCT
iajs-3094	137	15	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	137	16	,	,	PUNCT
iajs-3094	137	17	∑𝐶𝑗	∑𝐶𝑗	PRON
iajs-3094	137	18	,	,	PUNCT
iajs-3094	137	19	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	137	20	)	)	PUNCT
iajs-3094	137	21	=	=	PRON
iajs-3094	137	22	(	(	PUNCT
iajs-3094	137	23	40,8,9	40,8,9	NOUN
iajs-3094	137	24	)	)	PUNCT
iajs-3094	137	25	.	.	PUNCT
iajs-3094	138	1	(	(	PUNCT
iajs-3094	138	2	4	4	X
iajs-3094	138	3	)	)	PUNCT
iajs-3094	138	4	1//𝑳𝒆𝒙(𝑻𝒎𝒂𝒙	1//𝑳𝒆𝒙(𝑻𝒎𝒂𝒙	NUM
iajs-3094	138	5	,	,	PUNCT
iajs-3094	138	6	∑𝑬𝒋	∑𝑬𝒋	AUX
iajs-3094	138	7	,	,	PUNCT
iajs-3094	138	8	∑𝑪𝒋)(𝑺₱𝟒	∑𝑪𝒋)(𝑺₱𝟒	NUM
iajs-3094	138	9	):	):	PUNCT
iajs-3094	138	10	this	this	DET
iajs-3094	138	11	problem	problem	NOUN
iajs-3094	138	12	is	be	AUX
iajs-3094	138	13	defined	define	VERB
iajs-3094	138	14	as	as	SCONJ
iajs-3094	138	15	follows	follow	VERB
iajs-3094	138	16	:	:	PUNCT
iajs-3094	139	1	𝑀𝑖𝑛∑	𝑀𝑖𝑛∑	PROPN
iajs-3094	139	2	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	139	3	𝑛	𝑛	PRON
iajs-3094	139	4	𝑗=1	𝑗=1	PROPN
iajs-3094	139	5	s.	s.	PROPN
iajs-3094	139	6	t.	t.	PROPN
iajs-3094	140	1	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	140	2	=	=	SYM
iajs-3094	140	3	𝑇∗	𝑇∗	PROPN
iajs-3094	140	4	where	where	SCONJ
iajs-3094	140	5	𝑇∗	𝑇∗	NOUN
iajs-3094	141	1	=	=	PRON
iajs-3094	141	2	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	VERB
iajs-3094	141	3	)	)	PUNCT
iajs-3094	141	4	∑	∑	PUNCT
iajs-3094	142	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	142	2	=	=	SYM
iajs-3094	142	3	𝐸	𝐸	PROPN
iajs-3094	142	4	,	,	PUNCT
iajs-3094	142	5	𝐸	𝐸	PROPN
iajs-3094	142	6	𝑛	𝑛	PRON
iajs-3094	142	7	𝑗=1	𝑗=1	PROPN
iajs-3094	142	8	∈	∈	PROPN
iajs-3094	143	1	[	[	X
iajs-3094	143	2	∑	∑	X
iajs-3094	143	3	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	143	4	𝑛	𝑛	PRON
iajs-3094	143	5	𝑗=1	𝑗=1	X
iajs-3094	143	6	(	(	PUNCT
iajs-3094	143	7	𝑀𝑆𝑇	𝑀𝑆𝑇	PROPN
iajs-3094	143	8	)	)	PUNCT
iajs-3094	143	9	,	,	PUNCT
iajs-3094	143	10	∑	∑	PUNCT
iajs-3094	143	11	𝐸𝑗(𝐸𝐷𝐷	𝐸𝑗(𝐸𝐷𝐷	VERB
iajs-3094	143	12	)	)	PUNCT
iajs-3094	143	13	]	]	PUNCT
iajs-3094	143	14	𝑛	𝑛	PRON
iajs-3094	143	15	𝑗=1	𝑗=1	PROPN
iajs-3094	143	16	}	}	PUNCT
iajs-3094	143	17	.	.	PUNCT
iajs-3094	143	18	.	.	PUNCT
iajs-3094	143	19	.	.	PUNCT
iajs-3094	144	1	(	(	PUNCT
iajs-3094	144	2	𝑆₱4	𝑆₱4	NOUN
iajs-3094	144	3	)	)	PUNCT
iajs-3094	144	4	.	.	PUNCT
iajs-3094	145	1	given	give	VERB
iajs-3094	145	2	that	that	SCONJ
iajs-3094	145	3	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	145	4	is	be	AUX
iajs-3094	145	5	a	a	DET
iajs-3094	145	6	more	more	ADV
iajs-3094	145	7	important	important	ADJ
iajs-3094	145	8	function	function	NOUN
iajs-3094	145	9	in	in	ADP
iajs-3094	145	10	this	this	DET
iajs-3094	145	11	problem	problem	NOUN
iajs-3094	145	12	s₱4and	s₱4and	NOUN
iajs-3094	145	13	should	should	AUX
iajs-3094	145	14	be	be	AUX
iajs-3094	145	15	perfect	perfect	ADJ
iajs-3094	145	16	,	,	PUNCT
iajs-3094	145	17	the	the	DET
iajs-3094	145	18	algorithm	algorithm	NOUN
iajs-3094	145	19	𝑺𝑪𝑺𝑬𝑻𝟐	𝑺𝑪𝑺𝑬𝑻𝟐	PROPN
iajs-3094	145	20	offers	offer	VERB
iajs-3094	145	21	the	the	DET
iajs-3094	145	22	best	good	ADJ
iajs-3094	145	23	solution	solution	NOUN
iajs-3094	145	24	.	.	PUNCT
iajs-3094	146	1	ihjpas	ihjpas	PROPN
iajs-3094	146	2	.	.	PUNCT
iajs-3094	147	1	37	37	NUM
iajs-3094	147	2	(	(	PUNCT
iajs-3094	147	3	1	1	NUM
iajs-3094	147	4	)	)	PUNCT
iajs-3094	147	5	2024	2024	NUM
iajs-3094	147	6	392	392	NUM
iajs-3094	147	7	(	(	PUNCT
iajs-3094	147	8	5	5	NUM
iajs-3094	147	9	)	)	PUNCT
iajs-3094	147	10	1//𝑳𝒆𝒙(∑𝑬𝒋	1//𝑳𝒆𝒙(∑𝑬𝒋	NUM
iajs-3094	147	11	,	,	PUNCT
iajs-3094	147	12	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	147	13	,	,	PUNCT
iajs-3094	147	14	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	147	15	)	)	PUNCT
iajs-3094	147	16	(	(	PUNCT
iajs-3094	147	17	𝑺₱5	𝑺₱5	NOUN
iajs-3094	147	18	):	):	PUNCT
iajs-3094	147	19	this	this	DET
iajs-3094	147	20	problem	problem	NOUN
iajs-3094	147	21	is	be	AUX
iajs-3094	147	22	defined	define	VERB
iajs-3094	147	23	as	as	SCONJ
iajs-3094	147	24	follows	follow	VERB
iajs-3094	147	25	:	:	PUNCT
iajs-3094	147	26	𝑀𝑖𝑛	𝑀𝑖𝑛	PROPN
iajs-3094	147	27	{	{	PUNCT
iajs-3094	147	28	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	147	29	}	}	PUNCT
iajs-3094	147	30	s.	s.	PROPN
iajs-3094	147	31	t.	t.	PROPN
iajs-3094	147	32	∑	∑	PROPN
iajs-3094	147	33	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	147	34	=	=	PUNCT
iajs-3094	147	35	𝐸	𝐸	PROPN
iajs-3094	147	36	∗	∗	NOUN
iajs-3094	147	37	where	where	SCONJ
iajs-3094	147	38	𝐸∗	𝐸∗	NOUN
iajs-3094	147	39	=	=	PUNCT
iajs-3094	147	40	∑	∑	PUNCT
iajs-3094	147	41	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	147	42	𝑛	𝑛	PRON
iajs-3094	147	43	𝑗=1	𝑗=1	X
iajs-3094	147	44	(	(	PUNCT
iajs-3094	147	45	𝑀𝑆𝑇	𝑀𝑆𝑇	PROPN
iajs-3094	147	46	)	)	PUNCT
iajs-3094	148	1	𝑛	𝑛	PROPN
iajs-3094	148	2	𝑗=1	𝑗=1	PROPN
iajs-3094	148	3	∑	∑	PUNCT
iajs-3094	149	1	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	149	2	𝑛	𝑛	DET
iajs-3094	149	3	𝑗=1	𝑗=1	PROPN
iajs-3094	149	4	≤	≤	PROPN
iajs-3094	149	5	𝐶	𝐶	PROPN
iajs-3094	149	6	,	,	PUNCT
iajs-3094	149	7	𝐶	𝐶	PROPN
iajs-3094	149	8	∈	∈	PROPN
iajs-3094	150	1	[	[	X
iajs-3094	150	2	∑	∑	NOUN
iajs-3094	150	3	𝐶𝑗(𝑆𝑃𝑇	𝐶𝑗(𝑆𝑃𝑇	NUM
iajs-3094	150	4	)	)	PUNCT
iajs-3094	150	5	𝑛	𝑛	DET
iajs-3094	150	6	𝑗=1	𝑗=1	PROPN
iajs-3094	150	7	,	,	PUNCT
iajs-3094	150	8	∑	∑	PROPN
iajs-3094	150	9	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	150	10	𝑛	𝑛	PRON
iajs-3094	150	11	𝑗=1	𝑗=1	PROPN
iajs-3094	150	12	(	(	PUNCT
iajs-3094	150	13	𝑀𝑆𝑇	𝑀𝑆𝑇	PROPN
iajs-3094	150	14	)	)	PUNCT
iajs-3094	150	15	]	]	PUNCT
iajs-3094	150	16	}	}	PUNCT
iajs-3094	150	17	.	.	PUNCT
iajs-3094	150	18	.	.	PUNCT
iajs-3094	150	19	.	.	PUNCT
iajs-3094	151	1	(	(	PUNCT
iajs-3094	151	2	𝑆₱5	𝑆₱5	NOUN
iajs-3094	151	3	)	)	PUNCT
iajs-3094	151	4	.	.	PUNCT
iajs-3094	152	1	(	(	PUNCT
iajs-3094	152	2	6	6	NUM
iajs-3094	152	3	)	)	PUNCT
iajs-3094	152	4	1//𝑳𝒆𝒙(∑𝑬𝒋	1//𝑳𝒆𝒙(∑𝑬𝒋	NUM
iajs-3094	152	5	,	,	PUNCT
iajs-3094	152	6	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	152	7	,	,	PUNCT
iajs-3094	152	8	∑𝑪𝒋)(𝑺₱6	∑𝑪𝒋)(𝑺₱6	ADP
iajs-3094	152	9	):	):	PUNCT
iajs-3094	152	10	the	the	DET
iajs-3094	152	11	case	case	NOUN
iajs-3094	152	12	can	can	AUX
iajs-3094	152	13	be	be	AUX
iajs-3094	152	14	written	write	VERB
iajs-3094	152	15	as	as	ADP
iajs-3094	152	16	:	:	PUNCT
iajs-3094	152	17	𝑀𝑖𝑛	𝑀𝑖𝑛	PROPN
iajs-3094	152	18	{	{	PUNCT
iajs-3094	152	19	∑	∑	PROPN
iajs-3094	152	20	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	152	21	𝑛	𝑛	PRON
iajs-3094	152	22	𝑗=1	𝑗=1	PROPN
iajs-3094	152	23	}	}	PUNCT
iajs-3094	152	24	s.	s.	PROPN
iajs-3094	152	25	t.	t.	PROPN
iajs-3094	152	26	∑	∑	PROPN
iajs-3094	153	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	153	2	𝑛	𝑛	PRON
iajs-3094	153	3	𝑗=1	𝑗=1	NOUN
iajs-3094	153	4	=	=	SYM
iajs-3094	153	5	𝐸∗	𝐸∗	NOUN
iajs-3094	154	1	where	where	SCONJ
iajs-3094	154	2	𝐸∗	𝐸∗	NOUN
iajs-3094	154	3	=	=	SYM
iajs-3094	154	4	𝑚𝑖𝑛{∑	𝑚𝑖𝑛{∑	NOUN
iajs-3094	154	5	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	154	6	𝑛	𝑛	PROPN
iajs-3094	154	7	𝑗=1	𝑗=1	X
iajs-3094	154	8	(	(	PUNCT
iajs-3094	154	9	𝑀𝑆𝑇	𝑀𝑆𝑇	PROPN
iajs-3094	154	10	)	)	PUNCT
iajs-3094	154	11	}	}	PUNCT
iajs-3094	154	12	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	154	13	≤	≤	PUNCT
iajs-3094	154	14	𝑇	𝑇	PROPN
iajs-3094	154	15	,	,	PUNCT
iajs-3094	154	16	𝑇	𝑇	PROPN
iajs-3094	154	17	∈	∈	PROPN
iajs-3094	155	1	[	[	X
iajs-3094	155	2	𝑇𝑚𝑎𝑥(𝑀𝑆𝑇	𝑇𝑚𝑎𝑥(𝑀𝑆𝑇	NOUN
iajs-3094	155	3	)	)	PUNCT
iajs-3094	155	4	,	,	PUNCT
iajs-3094	155	5	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	VERB
iajs-3094	155	6	)	)	PUNCT
iajs-3094	155	7	]	]	PUNCT
iajs-3094	155	8	}	}	PUNCT
iajs-3094	155	9	.	.	PUNCT
iajs-3094	155	10	.	.	PUNCT
iajs-3094	155	11	.	.	PUNCT
iajs-3094	156	1	(	(	PUNCT
iajs-3094	156	2	𝑆₱6	𝑆₱6	ADV
iajs-3094	156	3	)	)	PUNCT
iajs-3094	156	4	.	.	PUNCT
iajs-3094	157	1	given	give	VERB
iajs-3094	157	2	that	that	SCONJ
iajs-3094	157	3	1//	1//	NUM
iajs-3094	157	4	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	157	5	is	be	AUX
iajs-3094	157	6	an	an	DET
iajs-3094	157	7	np	np	ADJ
iajs-3094	157	8	-	-	PUNCT
iajs-3094	157	9	hard	hard	ADJ
iajs-3094	157	10	problem	problem	NOUN
iajs-3094	157	11	,	,	PUNCT
iajs-3094	157	12	the	the	DET
iajs-3094	157	13	problems	problem	NOUN
iajs-3094	157	14	(	(	PUNCT
iajs-3094	157	15	s₱5	s₱5	PROPN
iajs-3094	157	16	)	)	PUNCT
iajs-3094	157	17	and	and	CCONJ
iajs-3094	157	18	(	(	PUNCT
iajs-3094	157	19	s₱6	s₱6	PROPN
iajs-3094	157	20	)	)	PUNCT
iajs-3094	157	21	are	be	AUX
iajs-3094	157	22	both	both	PRON
iajs-3094	157	23	np	np	NOUN
iajs-3094	157	24	-	-	PUNCT
iajs-3094	157	25	hard	hard	ADJ
iajs-3094	157	26	.	.	PUNCT
iajs-3094	158	1	(	(	PUNCT
iajs-3094	158	2	7	7	X
iajs-3094	158	3	)	)	PUNCT
iajs-3094	158	4	1//	1//	NUM
iajs-3094	158	5	∑𝑪𝒋	∑𝑪𝒋	PUNCT
iajs-3094	159	1	+	+	CCONJ
iajs-3094	159	2	∑𝑬𝒋	∑𝑬𝒋	PROPN
iajs-3094	159	3	+	+	NUM
iajs-3094	159	4	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	159	5	𝐏𝐫𝐨𝐛𝐥𝐞𝐦.	𝐏𝐫𝐨𝐛𝐥𝐞𝐦.	NOUN
iajs-3094	159	6	the	the	DET
iajs-3094	159	7	objective	objective	NOUN
iajs-3094	159	8	of	of	ADP
iajs-3094	159	9	the	the	DET
iajs-3094	159	10	problem	problem	NOUN
iajs-3094	159	11	is	be	AUX
iajs-3094	159	12	to	to	PART
iajs-3094	159	13	find	find	VERB
iajs-3094	159	14	the	the	DET
iajs-3094	159	15	sequence	sequence	NOUN
iajs-3094	159	16	of	of	ADP
iajs-3094	159	17	job	job	NOUN
iajs-3094	159	18	processing	processing	NOUN
iajs-3094	159	19	that	that	PRON
iajs-3094	159	20	will	will	AUX
iajs-3094	159	21	minimize	minimize	VERB
iajs-3094	159	22	∑𝐶𝑗	∑𝐶𝑗	PRON
iajs-3094	159	23	+	+	CCONJ
iajs-3094	159	24	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	160	1	+	+	ADJ
iajs-3094	160	2	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	160	3	.	.	PUNCT
iajs-3094	161	1	following	follow	VERB
iajs-3094	161	2	is	be	AUX
iajs-3094	161	3	a	a	DET
iajs-3094	161	4	definition	definition	NOUN
iajs-3094	161	5	of	of	ADP
iajs-3094	161	6	this	this	DET
iajs-3094	161	7	sub	sub	NOUN
iajs-3094	161	8	-	-	NOUN
iajs-3094	161	9	problem	problem	NOUN
iajs-3094	161	10	:	:	PUNCT
iajs-3094	161	11	suppose	suppose	VERB
iajs-3094	161	12	that	that	SCONJ
iajs-3094	161	13	α	α	PRON
iajs-3094	161	14	is	be	AUX
iajs-3094	161	15	any	any	DET
iajs-3094	161	16	machine	machine	NOUN
iajs-3094	161	17	schedule	schedule	NOUN
iajs-3094	161	18	that	that	PRON
iajs-3094	161	19	is	be	AUX
iajs-3094	161	20	possible	possible	ADJ
iajs-3094	161	21	to	to	PART
iajs-3094	161	22	formulate	formulate	VERB
iajs-3094	161	23	as	as	SCONJ
iajs-3094	161	24	follows	follow	VERB
iajs-3094	161	25	for	for	ADP
iajs-3094	161	26	a	a	DET
iajs-3094	161	27	given	give	VERB
iajs-3094	161	28	schedule	schedule	NOUN
iajs-3094	161	29	𝛼	𝛼	NOUN
iajs-3094	161	30	=	=	SYM
iajs-3094	161	31	(	(	PUNCT
iajs-3094	161	32	𝛼1	𝛼1	NOUN
iajs-3094	161	33	,	,	PUNCT
iajs-3094	161	34	𝛼2	𝛼2	ADJ
iajs-3094	161	35	,	,	PUNCT
iajs-3094	161	36	…	…	PUNCT
iajs-3094	161	37	,	,	PUNCT
iajs-3094	161	38	𝛼𝑛	𝛼𝑛	PROPN
iajs-3094	161	39	)	)	PUNCT
iajs-3094	161	40	.	.	PUNCT
iajs-3094	162	1	assume	assume	VERB
iajs-3094	162	2	that	that	SCONJ
iajs-3094	162	3	α	α	PRON
iajs-3094	162	4	is	be	AUX
iajs-3094	162	5	any	any	DET
iajs-3094	162	6	schedule	schedule	NOUN
iajs-3094	162	7	that	that	PRON
iajs-3094	162	8	can	can	AUX
iajs-3094	162	9	be	be	AUX
iajs-3094	162	10	expressed	express	VERB
iajs-3094	162	11	as	as	SCONJ
iajs-3094	162	12	follows	follow	VERB
iajs-3094	162	13	for	for	ADP
iajs-3094	162	14	a	a	DET
iajs-3094	162	15	certain	certain	ADJ
iajs-3094	162	16	schedule	schedule	NOUN
iajs-3094	162	17	𝛼	𝛼	NOUN
iajs-3094	162	18	=	=	SYM
iajs-3094	162	19	(	(	PUNCT
iajs-3094	162	20	𝛼1	𝛼1	NOUN
iajs-3094	162	21	,	,	PUNCT
iajs-3094	162	22	𝛼2	𝛼2	ADJ
iajs-3094	162	23	,	,	PUNCT
iajs-3094	162	24	…	…	PUNCT
iajs-3094	162	25	,	,	PUNCT
iajs-3094	162	26	𝛼𝑛	𝛼𝑛	PROPN
iajs-3094	162	27	):	):	PUNCT
iajs-3094	163	1	𝐹1	𝐹1	PROPN
iajs-3094	163	2	=	=	PUNCT
iajs-3094	163	3	𝑀𝑖𝑛{∑𝐶𝑗	𝑀𝑖𝑛{∑𝐶𝑗	NOUN
iajs-3094	163	4	+	+	NUM
iajs-3094	163	5	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	163	6	+	+	CCONJ
iajs-3094	163	7	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	163	8	}	}	PUNCT
iajs-3094	163	9	s.	s.	PROPN
iajs-3094	163	10	t.	t.	PROPN
iajs-3094	163	11	𝐶1	𝐶1	PROPN
iajs-3094	164	1	=	=	PUNCT
iajs-3094	164	2	𝑝𝛼1	𝑝𝛼1	PROPN
iajs-3094	164	3	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	164	4	≥	≥	NUM
iajs-3094	164	5	𝑝𝛼𝑗	𝑝𝛼𝑗	NOUN
iajs-3094	164	6	𝑗	𝑗	NOUN
iajs-3094	164	7	=	=	SYM
iajs-3094	164	8	1,2	1,2	NUM
iajs-3094	164	9	,	,	PUNCT
iajs-3094	164	10	…	…	PUNCT
iajs-3094	164	11	.	.	PUNCT
iajs-3094	165	1	,	,	PUNCT
iajs-3094	165	2	𝑛	𝑛	DET
iajs-3094	165	3	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	165	4	=	=	PUNCT
iajs-3094	165	5	𝐶𝛼(𝑗−1	𝐶𝛼(𝑗−1	NOUN
iajs-3094	165	6	)	)	PUNCT
iajs-3094	166	1	+	+	NUM
iajs-3094	166	2	𝑝𝛼𝑗	𝑝𝛼𝑗	NOUN
iajs-3094	166	3	𝑗	𝑗	NOUN
iajs-3094	166	4	=	=	NOUN
iajs-3094	166	5	2	2	NUM
iajs-3094	166	6	,	,	PUNCT
iajs-3094	166	7	…	…	PUNCT
iajs-3094	166	8	.	.	PUNCT
iajs-3094	167	1	,	,	PUNCT
iajs-3094	167	2	𝑛	𝑛	DET
iajs-3094	167	3	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	167	4	≥	≥	NOUN
iajs-3094	168	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	168	2	−	−	PROPN
iajs-3094	168	3	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	168	4	𝑗	𝑗	NOUN
iajs-3094	168	5	=	=	SYM
iajs-3094	168	6	1,2	1,2	NUM
iajs-3094	168	7	,	,	PUNCT
iajs-3094	168	8	…	…	PUNCT
iajs-3094	168	9	.	.	PUNCT
iajs-3094	169	1	,	,	PUNCT
iajs-3094	169	2	𝑛	𝑛	DET
iajs-3094	169	3	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	169	4	≥	≥	NOUN
iajs-3094	169	5	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	169	6	−	−	PUNCT
iajs-3094	170	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	170	2	𝑗	𝑗	NOUN
iajs-3094	170	3	=	=	SYM
iajs-3094	170	4	1,2	1,2	NUM
iajs-3094	170	5	,	,	PUNCT
iajs-3094	170	6	…	…	PUNCT
iajs-3094	170	7	.	.	PUNCT
iajs-3094	170	8	,	,	PUNCT
iajs-3094	170	9	𝑛	𝑛	PRON
iajs-3094	170	10	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	170	11	≥	≥	NOUN
iajs-3094	170	12	0	0	NUM
iajs-3094	170	13	,	,	PUNCT
iajs-3094	170	14	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	170	15	≥	≥	NOUN
iajs-3094	170	16	0	0	PUNCT
iajs-3094	170	17	𝑗	𝑗	NOUN
iajs-3094	170	18	=	=	SYM
iajs-3094	170	19	1,2	1,2	NUM
iajs-3094	170	20	,	,	PUNCT
iajs-3094	170	21	…	…	PUNCT
iajs-3094	170	22	.	.	PUNCT
iajs-3094	170	23	,	,	PUNCT
iajs-3094	170	24	𝑛	𝑛	PROPN
iajs-3094	170	25	}	}	PUNCT
iajs-3094	170	26	…	…	PUNCT
iajs-3094	170	27	(	(	PUNCT
iajs-3094	170	28	s₱7	s₱7	PROPN
iajs-3094	170	29	)	)	PUNCT
iajs-3094	170	30	.	.	PUNCT
iajs-3094	171	1	finding	find	VERB
iajs-3094	171	2	a	a	DET
iajs-3094	171	3	processing	processing	NOUN
iajs-3094	171	4	order	order	NOUN
iajs-3094	171	5	𝛼	𝛼	NOUN
iajs-3094	171	6	=	=	SYM
iajs-3094	171	7	(	(	PUNCT
iajs-3094	171	8	𝛼1	𝛼1	NOUN
iajs-3094	171	9	,	,	PUNCT
iajs-3094	171	10	…	…	PUNCT
iajs-3094	171	11	,	,	PUNCT
iajs-3094	171	12	𝛼𝑛	𝛼𝑛	PROPN
iajs-3094	171	13	)	)	PUNCT
iajs-3094	171	14	for	for	ADP
iajs-3094	171	15	the	the	DET
iajs-3094	171	16	jobs	job	NOUN
iajs-3094	171	17	on	on	ADP
iajs-3094	171	18	a	a	DET
iajs-3094	171	19	single	single	ADJ
iajs-3094	171	20	machine	machine	NOUN
iajs-3094	171	21	that	that	PRON
iajs-3094	171	22	minimizes	minimize	VERB
iajs-3094	171	23	the	the	DET
iajs-3094	171	24	sum	sum	NOUN
iajs-3094	171	25	of	of	ADP
iajs-3094	171	26	the	the	DET
iajs-3094	171	27	total	total	ADJ
iajs-3094	171	28	completion	completion	NOUN
iajs-3094	171	29	times	time	NOUN
iajs-3094	171	30	,	,	PUNCT
iajs-3094	171	31	the	the	DET
iajs-3094	171	32	total	total	ADJ
iajs-3094	171	33	earliness	earliness	NOUN
iajs-3094	171	34	,	,	PUNCT
iajs-3094	171	35	and	and	CCONJ
iajs-3094	171	36	the	the	DET
iajs-3094	171	37	maximum	maximum	ADJ
iajs-3094	171	38	tardiness	tardiness	NOUN
iajs-3094	171	39	(	(	PUNCT
iajs-3094	171	40	∑𝐶𝑗(𝛼	∑𝐶𝑗(𝛼	PUNCT
iajs-3094	171	41	)	)	PUNCT
iajs-3094	172	1	+	+	CCONJ
iajs-3094	172	2	∑𝐸𝑗(𝛼	∑𝐸𝑗(𝛼	NOUN
iajs-3094	172	3	)	)	PUNCT
iajs-3094	172	4	+	+	CCONJ
iajs-3094	172	5	𝑇𝑚𝑎𝑥(𝛼	𝑇𝑚𝑎𝑥(𝛼	NUM
iajs-3094	172	6	)	)	PUNCT
iajs-3094	172	7	)	)	PUNCT
iajs-3094	172	8	,	,	PUNCT
iajs-3094	172	9	𝛼	𝛼	PROPN
iajs-3094	172	10	∈	∈	PROPN
iajs-3094	172	11	𝒮	𝒮	PROPN
iajs-3094	172	12	(	(	PUNCT
iajs-3094	172	13	where	where	SCONJ
iajs-3094	172	14	𝒮	𝒮	PROPN
iajs-3094	172	15	is	be	AUX
iajs-3094	172	16	the	the	DET
iajs-3094	172	17	set	set	NOUN
iajs-3094	172	18	of	of	ADP
iajs-3094	172	19	all	all	DET
iajs-3094	172	20	feasible	feasible	ADJ
iajs-3094	172	21	solutions	solution	NOUN
iajs-3094	172	22	)	)	PUNCT
iajs-3094	172	23	,	,	PUNCT
iajs-3094	172	24	is	be	AUX
iajs-3094	172	25	the	the	DET
iajs-3094	172	26	aim	aim	NOUN
iajs-3094	172	27	of	of	ADP
iajs-3094	172	28	this	this	DET
iajs-3094	172	29	problem	problem	NOUN
iajs-3094	172	30	.	.	PUNCT
iajs-3094	173	1	proposition(2	proposition(2	NOUN
iajs-3094	173	2	):	):	PUNCT
iajs-3094	173	3	the	the	DET
iajs-3094	173	4	optimal	optimal	ADJ
iajs-3094	173	5	solution	solution	NOUN
iajs-3094	173	6	for	for	ADP
iajs-3094	173	7	1//	1//	NUM
iajs-3094	173	8	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	173	9	+	+	CCONJ
iajs-3094	173	10	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	174	1	+	+	CCONJ
iajs-3094	174	2	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	174	3	problem	problem	NOUN
iajs-3094	174	4	is	be	AUX
iajs-3094	174	5	an	an	DET
iajs-3094	174	6	efso	efso	NOUN
iajs-3094	174	7	for	for	ADP
iajs-3094	174	8	the	the	DET
iajs-3094	174	9	1//	1//	NUM
iajs-3094	174	10	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	174	11	,	,	PUNCT
iajs-3094	174	12	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	174	13	,	,	PUNCT
iajs-3094	174	14	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	174	15	)	)	PUNCT
iajs-3094	174	16	.	.	PUNCT
iajs-3094	175	1	proof	proof	NOUN
iajs-3094	175	2	:	:	PUNCT
iajs-3094	175	3	let	let	VERB
iajs-3094	175	4	𝛽	𝛽	NOUN
iajs-3094	175	5	be	be	AUX
iajs-3094	175	6	an	an	DET
iajs-3094	175	7	optimal	optimal	ADJ
iajs-3094	175	8	schedule	schedule	NOUN
iajs-3094	175	9	for	for	ADP
iajs-3094	175	10	1//	1//	NUM
iajs-3094	175	11	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	175	12	+	+	CCONJ
iajs-3094	175	13	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	175	14	+	+	CCONJ
iajs-3094	175	15	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	175	16	problem	problem	NOUN
iajs-3094	175	17	.	.	PUNCT
iajs-3094	176	1	suppose	suppose	VERB
iajs-3094	176	2	that	that	SCONJ
iajs-3094	176	3	𝛽	𝛽	NOUN
iajs-3094	176	4	gives	give	VERB
iajs-3094	176	5	no	no	DET
iajs-3094	176	6	efficient	efficient	ADJ
iajs-3094	176	7	solution	solution	NOUN
iajs-3094	176	8	for	for	ADP
iajs-3094	176	9	the	the	DET
iajs-3094	176	10	problem	problem	NOUN
iajs-3094	176	11	1//	1//	NUM
iajs-3094	176	12	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	176	13	,	,	PUNCT
iajs-3094	176	14	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	176	15	,	,	PUNCT
iajs-3094	176	16	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	176	17	)	)	PUNCT
iajs-3094	176	18	,	,	PUNCT
iajs-3094	176	19	so	so	CCONJ
iajs-3094	176	20	there	there	PRON
iajs-3094	176	21	is	be	VERB
iajs-3094	176	22	a	a	DET
iajs-3094	176	23	schedule	schedule	NOUN
iajs-3094	176	24	α	α	NOUN
iajs-3094	176	25	which	which	PRON
iajs-3094	176	26	is	be	AUX
iajs-3094	176	27	efficient	efficient	ADJ
iajs-3094	176	28	for	for	ADP
iajs-3094	176	29	1//	1//	NUM
iajs-3094	176	30	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	176	31	,	,	PUNCT
iajs-3094	176	32	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	176	33	,	,	PUNCT
iajs-3094	176	34	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	176	35	)	)	PUNCT
iajs-3094	176	36	problem	problem	NOUN
iajs-3094	176	37	such	such	ADJ
iajs-3094	176	38	that	that	SCONJ
iajs-3094	176	39	:	:	PUNCT
iajs-3094	176	40	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	176	41	(	(	PUNCT
iajs-3094	176	42	𝛼	𝛼	NOUN
iajs-3094	176	43	)	)	PUNCT
iajs-3094	176	44	≤	≤	NOUN
iajs-3094	176	45	∑𝐶𝑗(𝛽	∑𝐶𝑗(𝛽	PUNCT
iajs-3094	176	46	)	)	PUNCT
iajs-3094	176	47	and	and	CCONJ
iajs-3094	176	48	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	176	49	(	(	PUNCT
iajs-3094	176	50	𝛼	𝛼	NOUN
iajs-3094	176	51	)	)	PUNCT
iajs-3094	176	52	≤	≤	NOUN
iajs-3094	176	53	∑𝐸𝑗(𝛽	∑𝐸𝑗(𝛽	PROPN
iajs-3094	176	54	)	)	PUNCT
iajs-3094	176	55	and	and	CCONJ
iajs-3094	176	56	𝑇𝑚𝑎𝑥(𝛼	𝑇𝑚𝑎𝑥(𝛼	NUM
iajs-3094	176	57	)	)	PUNCT
iajs-3094	176	58	≤	≤	NOUN
iajs-3094	176	59	𝑇𝑚𝑎𝑥(𝛽	𝑇𝑚𝑎𝑥(𝛽	NUM
iajs-3094	176	60	)	)	PUNCT
iajs-3094	176	61	,	,	PUNCT
iajs-3094	176	62	and	and	CCONJ
iajs-3094	176	63	when	when	SCONJ
iajs-3094	176	64	there	there	PRON
iajs-3094	176	65	are	be	VERB
iajs-3094	176	66	strict	strict	ADJ
iajs-3094	176	67	inequities	inequity	NOUN
iajs-3094	176	68	in	in	ADP
iajs-3094	176	69	at	at	ADV
iajs-3094	176	70	least	least	ADV
iajs-3094	176	71	one	one	NUM
iajs-3094	176	72	.	.	PUNCT
iajs-3094	177	1	as	as	ADP
iajs-3094	177	2	a	a	DET
iajs-3094	177	3	result	result	NOUN
iajs-3094	177	4	,	,	PUNCT
iajs-3094	177	5	it	it	PRON
iajs-3094	177	6	follows	follow	VERB
iajs-3094	177	7	:	:	PUNCT
iajs-3094	177	8	ihjpas	ihjpas	PROPN
iajs-3094	177	9	.	.	PUNCT
iajs-3094	178	1	37	37	NUM
iajs-3094	178	2	(	(	PUNCT
iajs-3094	178	3	1	1	NUM
iajs-3094	178	4	)	)	PUNCT
iajs-3094	178	5	2024	2024	NUM
iajs-3094	178	6	393	393	NUM
iajs-3094	178	7	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	178	8	(	(	PUNCT
iajs-3094	178	9	𝛼	𝛼	NOUN
iajs-3094	178	10	)	)	PUNCT
iajs-3094	178	11	+	+	CCONJ
iajs-3094	178	12	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	178	13	(	(	PUNCT
iajs-3094	178	14	𝛼	𝛼	NOUN
iajs-3094	178	15	)	)	PUNCT
iajs-3094	178	16	+	+	CCONJ
iajs-3094	178	17	𝑇𝑚𝑎𝑥(𝛼	𝑇𝑚𝑎𝑥(𝛼	NUM
iajs-3094	178	18	)	)	PUNCT
iajs-3094	178	19	≤	≤	NOUN
iajs-3094	178	20	∑𝐶𝑗(𝛽	∑𝐶𝑗(𝛽	PUNCT
iajs-3094	178	21	)	)	PUNCT
iajs-3094	178	22	+	+	NUM
iajs-3094	178	23	∑𝐸𝑗(𝛽	∑𝐸𝑗(𝛽	X
iajs-3094	178	24	)	)	PUNCT
iajs-3094	178	25	+	+	CCONJ
iajs-3094	178	26	𝑇𝑚𝑎𝑥(𝛽	𝑇𝑚𝑎𝑥(𝛽	X
iajs-3094	178	27	)	)	PUNCT
iajs-3094	178	28	,	,	PUNCT
iajs-3094	178	29	so	so	ADV
iajs-3094	178	30	,	,	PUNCT
iajs-3094	178	31	for1//	for1//	NOUN
iajs-3094	178	32	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	178	33	+	+	CCONJ
iajs-3094	178	34	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	178	35	+	+	CCONJ
iajs-3094	178	36	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	178	37	,	,	PUNCT
iajs-3094	178	38	𝛼	𝛼	PRON
iajs-3094	178	39	is	be	AUX
iajs-3094	178	40	a	a	DET
iajs-3094	178	41	schedule	schedule	NOUN
iajs-3094	178	42	that	that	PRON
iajs-3094	178	43	gives	give	VERB
iajs-3094	178	44	the	the	DET
iajs-3094	178	45	better	well	ADJ
iajs-3094	178	46	solution	solution	NOUN
iajs-3094	178	47	from	from	ADP
iajs-3094	178	48	𝛽.	𝛽.	NOUN
iajs-3094	178	49	however	however	ADV
iajs-3094	178	50	,	,	PUNCT
iajs-3094	178	51	since	since	SCONJ
iajs-3094	178	52	𝛽is	𝛽i	VERB
iajs-3094	178	53	the	the	DET
iajs-3094	178	54	optimal	optimal	ADJ
iajs-3094	178	55	schedule	schedule	NOUN
iajs-3094	178	56	,	,	PUNCT
iajs-3094	178	57	the	the	DET
iajs-3094	178	58	assumption	assumption	NOUN
iajs-3094	178	59	is	be	AUX
iajs-3094	178	60	contradicted	contradict	VERB
iajs-3094	178	61	,	,	PUNCT
iajs-3094	178	62	so	so	SCONJ
iajs-3094	178	63	𝛽	𝛽	NOUN
iajs-3094	178	64	should	should	AUX
iajs-3094	178	65	give	give	VERB
iajs-3094	178	66	an	an	DET
iajs-3094	178	67	efficient	efficient	ADJ
iajs-3094	178	68	solution	solution	NOUN
iajs-3094	178	69	to	to	ADP
iajs-3094	178	70	1//	1//	NUM
iajs-3094	178	71	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	178	72	+	+	CCONJ
iajs-3094	178	73	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	178	74	+	+	ADJ
iajs-3094	178	75	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	178	76	.	.	PUNCT
iajs-3094	179	1	4	4	X
iajs-3094	179	2	.	.	X
iajs-3094	179	3	special	special	ADJ
iajs-3094	179	4	cases	case	NOUN
iajs-3094	179	5	of	of	ADP
iajs-3094	179	6	the	the	DET
iajs-3094	179	7	problems	problem	NOUN
iajs-3094	179	8	(	(	PUNCT
iajs-3094	179	9	𝑺𝑪𝑺𝑬𝑻)and	𝑺𝑪𝑺𝑬𝑻)and	PROPN
iajs-3094	179	10	(	(	PUNCT
iajs-3094	179	11	𝑺₱𝟕	𝑺₱𝟕	NOUN
iajs-3094	179	12	)	)	PUNCT
iajs-3094	179	13	in	in	ADP
iajs-3094	179	14	this	this	DET
iajs-3094	179	15	part	part	NOUN
iajs-3094	179	16	,	,	PUNCT
iajs-3094	179	17	give	give	VERB
iajs-3094	179	18	some	some	DET
iajs-3094	179	19	special	special	ADJ
iajs-3094	179	20	cases	case	NOUN
iajs-3094	179	21	and	and	CCONJ
iajs-3094	179	22	examples	example	NOUN
iajs-3094	179	23	for	for	ADP
iajs-3094	179	24	problems	problem	NOUN
iajs-3094	179	25	(	(	PUNCT
iajs-3094	179	26	𝑺𝑪𝑺𝑬𝑻)and	𝑺𝑪𝑺𝑬𝑻)and	PROPN
iajs-3094	179	27	(	(	PUNCT
iajs-3094	179	28	𝑺₱𝟕	𝑺₱𝟕	NOUN
iajs-3094	179	29	)	)	PUNCT
iajs-3094	179	30	that	that	PRON
iajs-3094	179	31	lead	lead	VERB
iajs-3094	179	32	to	to	ADP
iajs-3094	179	33	efficient	efficient	ADJ
iajs-3094	179	34	and	and	CCONJ
iajs-3094	179	35	optimal	optimal	ADJ
iajs-3094	179	36	solutions	solution	NOUN
iajs-3094	179	37	respectively	respectively	ADV
iajs-3094	179	38	.	.	PUNCT
iajs-3094	180	1	4.1	4.1	NUM
iajs-3094	180	2	special	special	ADJ
iajs-3094	180	3	cases	case	NOUN
iajs-3094	180	4	of	of	ADP
iajs-3094	180	5	the	the	DET
iajs-3094	180	6	problem(𝑺𝑪𝑺𝑬𝑻	problem(𝑺𝑪𝑺𝑬𝑻	NOUN
iajs-3094	180	7	)	)	PUNCT
iajs-3094	180	8	case(𝟒.	case(𝟒.	NUM
iajs-3094	180	9	𝟏.	𝟏.	NOUN
iajs-3094	180	10	𝟏	𝟏	X
iajs-3094	180	11	):	):	PUNCT
iajs-3094	180	12	if	if	SCONJ
iajs-3094	180	13	𝑝1	𝑝1	NOUN
iajs-3094	180	14	=	=	SYM
iajs-3094	180	15	𝑑1and	𝑑1and	PROPN
iajs-3094	180	16	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	180	17	=	=	SYM
iajs-3094	180	18	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	180	19	−	−	PROPN
iajs-3094	180	20	𝑑𝑗−1	𝑑𝑗−1	NOUN
iajs-3094	180	21	,	,	PUNCT
iajs-3094	180	22	for	for	ADP
iajs-3094	180	23	all	all	DET
iajs-3094	180	24	𝑗	𝑗	NOUN
iajs-3094	180	25	in	in	ADP
iajs-3094	180	26	𝛼	𝛼	PROPN
iajs-3094	180	27	(	(	PUNCT
iajs-3094	180	28	except	except	SCONJ
iajs-3094	180	29	1	1	NUM
iajs-3094	180	30	)	)	PUNCT
iajs-3094	180	31	then	then	ADV
iajs-3094	180	32	spt	spt	PROPN
iajs-3094	180	33	schedule	schedule	NOUN
iajs-3094	180	34	𝛼	𝛼	PRON
iajs-3094	180	35	gives	give	VERB
iajs-3094	180	36	an	an	DET
iajs-3094	180	37	efficient	efficient	ADJ
iajs-3094	180	38	schedule	schedule	NOUN
iajs-3094	180	39	for	for	ADP
iajs-3094	180	40	problem	problem	NOUN
iajs-3094	180	41	(	(	PUNCT
iajs-3094	180	42	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	180	43	)	)	PUNCT
iajs-3094	180	44	.	.	PUNCT
iajs-3094	181	1	proof	proof	NOUN
iajs-3094	181	2	:	:	PUNCT
iajs-3094	181	3	since	since	SCONJ
iajs-3094	181	4	𝑝1	𝑝1	NOUN
iajs-3094	181	5	=	=	SYM
iajs-3094	181	6	𝑑1	𝑑1	NOUN
iajs-3094	181	7	and	and	CCONJ
iajs-3094	181	8	𝑝2	𝑝2	NOUN
iajs-3094	181	9	=	=	SYM
iajs-3094	181	10	𝑑2	𝑑2	NOUN
iajs-3094	181	11	−	−	NOUN
iajs-3094	181	12	𝑑1	𝑑1	NOUN
iajs-3094	181	13	=	=	PUNCT
iajs-3094	181	14	𝑑2	𝑑2	NOUN
iajs-3094	181	15	−	−	PROPN
iajs-3094	181	16	𝑝1	𝑝1	NOUN
iajs-3094	181	17	,	,	PUNCT
iajs-3094	181	18	then	then	ADV
iajs-3094	181	19	𝐶1	𝐶1	NOUN
iajs-3094	181	20	=	=	SYM
iajs-3094	181	21	𝑑1	𝑑1	NOUN
iajs-3094	181	22	and	and	CCONJ
iajs-3094	181	23	𝐶2	𝐶2	ADJ
iajs-3094	181	24	=	=	NOUN
iajs-3094	181	25	𝑝1	𝑝1	NOUN
iajs-3094	181	26	+	+	NOUN
iajs-3094	181	27	𝑝2	𝑝2	NOUN
iajs-3094	181	28	=	=	SYM
iajs-3094	181	29	𝑝1	𝑝1	NOUN
iajs-3094	181	30	+	+	CCONJ
iajs-3094	181	31	𝑑2	𝑑2	NOUN
iajs-3094	181	32	−	−	PROPN
iajs-3094	181	33	𝑝1	𝑝1	NOUN
iajs-3094	181	34	=	=	NOUN
iajs-3094	181	35	𝑑2	𝑑2	NOUN
iajs-3094	181	36	then	then	ADV
iajs-3094	181	37	𝐶2	𝐶2	ADV
iajs-3094	181	38	=	=	VERB
iajs-3094	181	39	𝑑2	𝑑2	NOUN
iajs-3094	181	40	and	and	CCONJ
iajs-3094	181	41	so	so	ADV
iajs-3094	181	42	on	on	ADP
iajs-3094	181	43	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	181	44	=	=	PUNCT
iajs-3094	181	45	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	181	46	for	for	ADP
iajs-3094	181	47	𝑗	𝑗	X
iajs-3094	181	48	=	=	SYM
iajs-3094	181	49	1,2	1,2	NUM
iajs-3094	181	50	,	,	PUNCT
iajs-3094	181	51	.	.	PUNCT
iajs-3094	181	52	.	.	PUNCT
iajs-3094	182	1	,	,	PUNCT
iajs-3094	182	2	𝑛.	𝑛.	NOUN
iajs-3094	182	3	since	since	SCONJ
iajs-3094	182	4	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	182	5	=	=	PUNCT
iajs-3094	182	6	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	182	7	for	for	ADP
iajs-3094	182	8	all	all	DET
iajs-3094	182	9	𝑗	𝑗	NOUN
iajs-3094	182	10	in	in	ADP
iajs-3094	182	11	𝜎	𝜎	PRON
iajs-3094	182	12	hence	hence	ADV
iajs-3094	182	13	𝐿𝑗	𝐿𝑗	PROPN
iajs-3094	182	14	=	=	NOUN
iajs-3094	182	15	0	0	NUM
iajs-3094	182	16	,	,	PUNCT
iajs-3094	182	17	∀𝑗	∀𝑗	NOUN
iajs-3094	182	18	,	,	PUNCT
iajs-3094	182	19	then	then	ADV
iajs-3094	182	20	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	182	21	=	=	PUNCT
iajs-3094	182	22	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	182	23	=	=	SYM
iajs-3094	182	24	0	0	NUM
iajs-3094	182	25	,	,	PUNCT
iajs-3094	182	26	so	so	ADV
iajs-3094	182	27	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	182	28	=	=	SYM
iajs-3094	182	29	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	182	30	=	=	SYM
iajs-3094	182	31	0	0	X
iajs-3094	182	32	.	.	PUNCT
iajs-3094	183	1	then	then	ADV
iajs-3094	183	2	the	the	DET
iajs-3094	183	3	problem	problem	NOUN
iajs-3094	183	4	1	1	NUM
iajs-3094	183	5	//	//	NUM
iajs-3094	183	6	(	(	PUNCT
iajs-3094	183	7	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	183	8	,	,	PUNCT
iajs-3094	183	9	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	183	10	,	,	PUNCT
iajs-3094	183	11	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	183	12	)	)	PUNCT
iajs-3094	183	13	reduced	reduce	VERB
iajs-3094	183	14	to1	to1	PROPN
iajs-3094	183	15	//	//	PROPN
iajs-3094	183	16	∑𝐶𝑗.	∑𝐶𝑗.	PROPN
iajs-3094	183	17	but	but	CCONJ
iajs-3094	183	18	the	the	DET
iajs-3094	183	19	rule	rule	NOUN
iajs-3094	183	20	that	that	PRON
iajs-3094	183	21	solved	solve	VERB
iajs-3094	183	22	this	this	DET
iajs-3094	183	23	problem	problem	NOUN
iajs-3094	183	24	was	be	AUX
iajs-3094	183	25	spt	spt	ADJ
iajs-3094	183	26	.	.	PUNCT
iajs-3094	184	1	then	then	ADV
iajs-3094	184	2	𝛼	𝛼	PRON
iajs-3094	184	3	provides	provide	VERB
iajs-3094	184	4	an	an	DET
iajs-3094	184	5	efficient	efficient	ADJ
iajs-3094	184	6	solution	solution	NOUN
iajs-3094	184	7	to	to	ADP
iajs-3094	184	8	(	(	PUNCT
iajs-3094	184	9	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	184	10	)	)	PUNCT
iajs-3094	184	11	problem	problem	NOUN
iajs-3094	184	12	.	.	PUNCT
iajs-3094	185	1	case(𝟒.	case(𝟒.	NUM
iajs-3094	185	2	𝟏.	𝟏.	SYM
iajs-3094	185	3	𝟐	𝟐	NUM
iajs-3094	185	4	):	):	PUNCT
iajs-3094	185	5	if	if	SCONJ
iajs-3094	185	6	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	185	7	=	=	SYM
iajs-3094	185	8	𝑝	𝑝	PROPN
iajs-3094	185	9	and	and	CCONJ
iajs-3094	185	10	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	185	11	=	=	SYM
iajs-3094	185	12	𝑗𝑝	𝑗𝑝	PROPN
iajs-3094	185	13	for	for	ADP
iajs-3094	185	14	all	all	DET
iajs-3094	185	15	𝑗	𝑗	NOUN
iajs-3094	185	16	in	in	ADP
iajs-3094	185	17	the	the	DET
iajs-3094	185	18	schedule	schedule	NOUN
iajs-3094	185	19	σ	σ	PROPN
iajs-3094	185	20	,	,	PUNCT
iajs-3094	185	21	then	then	ADV
iajs-3094	185	22	𝜎	𝜎	PROPN
iajs-3094	185	23	gives	give	VERB
iajs-3094	185	24	an	an	DET
iajs-3094	185	25	efso	efso	NOUN
iajs-3094	185	26	to	to	ADP
iajs-3094	185	27	(	(	PUNCT
iajs-3094	185	28	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	185	29	)	)	PUNCT
iajs-3094	185	30	.	.	PUNCT
iajs-3094	186	1	proof	proof	NOUN
iajs-3094	186	2	:	:	PUNCT
iajs-3094	186	3	since	since	SCONJ
iajs-3094	186	4	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	186	5	=	=	SYM
iajs-3094	186	6	𝑗𝑝	𝑗𝑝	NOUN
iajs-3094	186	7	=	=	PUNCT
iajs-3094	187	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	187	2	∀𝑗	∀𝑗	NOUN
iajs-3094	187	3	∈	∈	PROPN
iajs-3094	187	4	𝜎	𝜎	PROPN
iajs-3094	187	5	,	,	PUNCT
iajs-3094	187	6	(	(	PUNCT
iajs-3094	187	7	this	this	PRON
iajs-3094	187	8	means	mean	VERB
iajs-3094	187	9	there	there	PRON
iajs-3094	187	10	is	be	VERB
iajs-3094	187	11	no	no	DET
iajs-3094	187	12	job	job	NOUN
iajs-3094	187	13	late	late	ADV
iajs-3094	187	14	and	and	CCONJ
iajs-3094	187	15	early	early	ADJ
iajs-3094	187	16	s.	s.	PROPN
iajs-3094	187	17	t.	t.	PROPN
iajs-3094	188	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	188	2	=	=	PUNCT
iajs-3094	188	3	0	0	PUNCT
iajs-3094	188	4	=	=	SYM
iajs-3094	188	5	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	188	6	)	)	PUNCT
iajs-3094	189	1	then	then	ADV
iajs-3094	189	2	∑	∑	ADP
iajs-3094	189	3	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	189	4	=	=	SYM
iajs-3094	189	5	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	189	6	=	=	SYM
iajs-3094	189	7	0𝑛	0𝑛	PROPN
iajs-3094	189	8	𝑗=1	𝑗=1	PROPN
iajs-3094	189	9	.	.	PUNCT
iajs-3094	190	1	then	then	ADV
iajs-3094	190	2	the	the	DET
iajs-3094	190	3	problem	problem	NOUN
iajs-3094	190	4	1//	1//	NUM
iajs-3094	190	5	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	190	6	,	,	PUNCT
iajs-3094	190	7	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	190	8	,	,	PUNCT
iajs-3094	190	9	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	190	10	)	)	PUNCT
iajs-3094	190	11	reduced	reduce	VERB
iajs-3094	190	12	to	to	ADP
iajs-3094	190	13	1//	1//	NUM
iajs-3094	190	14	∑	∑	PUNCT
iajs-3094	190	15	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	190	16	𝑛	𝑛	PRON
iajs-3094	190	17	𝑗=1	𝑗=1	PROPN
iajs-3094	190	18	.	.	PUNCT
iajs-3094	191	1	now	now	ADV
iajs-3094	191	2	since	since	SCONJ
iajs-3094	191	3	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	191	4	=	=	SYM
iajs-3094	191	5	𝑝	𝑝	PROPN
iajs-3094	191	6	for	for	ADP
iajs-3094	191	7	every	every	DET
iajs-3094	191	8	job	job	NOUN
iajs-3094	191	9	𝑗	𝑗	INTJ
iajs-3094	191	10	in	in	ADP
iajs-3094	191	11	α	α	NOUN
iajs-3094	191	12	,	,	PUNCT
iajs-3094	191	13	then	then	ADV
iajs-3094	191	14	∑	∑	ADP
iajs-3094	191	15	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	191	16	𝑛	𝑛	PRON
iajs-3094	191	17	𝑗=1	𝑗=1	PROPN
iajs-3094	191	18	=	=	SYM
iajs-3094	191	19	𝑝	𝑝	PROPN
iajs-3094	191	20	(	(	PUNCT
iajs-3094	191	21	𝑛2+𝑛	𝑛2+𝑛	PROPN
iajs-3094	191	22	2	2	NUM
iajs-3094	191	23	)	)	PUNCT
iajs-3094	191	24	.	.	PUNCT
iajs-3094	192	1	but	but	CCONJ
iajs-3094	192	2	𝑝	𝑝	PROPN
iajs-3094	192	3	(	(	PUNCT
iajs-3094	192	4	𝑛2+𝑛	𝑛2+𝑛	ADP
iajs-3094	192	5	2	2	NUM
iajs-3094	192	6	)	)	PUNCT
iajs-3094	192	7	is	be	AUX
iajs-3094	192	8	constant	constant	ADJ
iajs-3094	192	9	,	,	PUNCT
iajs-3094	192	10	hence	hence	ADV
iajs-3094	192	11	any	any	DET
iajs-3094	192	12	schedule	schedule	NOUN
iajs-3094	192	13	gives	give	VERB
iajs-3094	192	14	an	an	DET
iajs-3094	192	15	efso	efso	NOUN
iajs-3094	192	16	to	to	ADP
iajs-3094	192	17	(	(	PUNCT
iajs-3094	192	18	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	192	19	)	)	PUNCT
iajs-3094	192	20	.	.	PUNCT
iajs-3094	193	1	as	as	ADP
iajs-3094	193	2	a	a	DET
iajs-3094	193	3	result	result	NOUN
iajs-3094	193	4	,	,	PUNCT
iajs-3094	193	5	every	every	DET
iajs-3094	193	6	schedule	schedule	NOUN
iajs-3094	193	7	provides	provide	VERB
iajs-3094	193	8	an	an	DET
iajs-3094	193	9	efficient	efficient	ADJ
iajs-3094	193	10	solution	solution	NOUN
iajs-3094	193	11	to	to	ADP
iajs-3094	193	12	the	the	DET
iajs-3094	193	13	problem	problem	NOUN
iajs-3094	193	14	.	.	PUNCT
iajs-3094	194	1	case	case	NOUN
iajs-3094	194	2	(	(	PUNCT
iajs-3094	194	3	𝟒.	𝟒.	X
iajs-3094	194	4	𝟏.	𝟏.	X
iajs-3094	194	5	𝟑	𝟑	X
iajs-3094	194	6	):	):	PUNCT
iajs-3094	194	7	if	if	SCONJ
iajs-3094	194	8	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	194	9	=	=	SYM
iajs-3094	194	10	𝑘𝑝𝑗	𝑘𝑝𝑗	NOUN
iajs-3094	194	11	for	for	ADP
iajs-3094	194	12	all	all	DET
iajs-3094	194	13	𝑘	𝑘	PRON
iajs-3094	194	14	≥	≥	NOUN
iajs-3094	194	15	2	2	NUM
iajs-3094	194	16	and	and	CCONJ
iajs-3094	194	17	𝑗	𝑗	PRON
iajs-3094	194	18	∈	∈	ADJ
iajs-3094	194	19	α	α	NOUN
iajs-3094	194	20	=	=	NOUN
iajs-3094	194	21	spt	spt	PROPN
iajs-3094	194	22	schedule	schedule	NOUN
iajs-3094	194	23	then	then	ADV
iajs-3094	194	24	𝛼	𝛼	PROPN
iajs-3094	194	25	is	be	AUX
iajs-3094	194	26	an	an	DET
iajs-3094	194	27	efso	efso	NOUN
iajs-3094	194	28	to	to	ADP
iajs-3094	194	29	the	the	DET
iajs-3094	194	30	(	(	PUNCT
iajs-3094	194	31	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	194	32	)	)	PUNCT
iajs-3094	194	33	.	.	PUNCT
iajs-3094	195	1	proof	proof	NOUN
iajs-3094	195	2	:	:	PUNCT
iajs-3094	195	3	let	let	VERB
iajs-3094	195	4	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	195	5	=	=	VERB
iajs-3094	195	6	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	196	1	−	−	PROPN
iajs-3094	197	1	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	197	2	be	be	AUX
iajs-3094	197	3	the	the	DET
iajs-3094	197	4	slack	slack	NOUN
iajs-3094	197	5	time	time	NOUN
iajs-3094	197	6	of	of	ADP
iajs-3094	197	7	the	the	DET
iajs-3094	197	8	job	job	NOUN
iajs-3094	197	9	j	j	NOUN
iajs-3094	197	10	(	(	PUNCT
iajs-3094	197	11	𝑗	𝑗	NOUN
iajs-3094	197	12	=	=	SYM
iajs-3094	197	13	1	1	NUM
iajs-3094	197	14	,	,	PUNCT
iajs-3094	197	15	…	…	PUNCT
iajs-3094	197	16	,	,	PUNCT
iajs-3094	197	17	𝑛	𝑛	X
iajs-3094	197	18	)	)	PUNCT
iajs-3094	197	19	since	since	SCONJ
iajs-3094	197	20	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	197	21	=	=	SYM
iajs-3094	197	22	𝑘𝑝𝑗	𝑘𝑝𝑗	NOUN
iajs-3094	197	23	then	then	ADV
iajs-3094	197	24	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	197	25	=	=	NOUN
iajs-3094	197	26	𝑘𝑝𝑗	𝑘𝑝𝑗	NOUN
iajs-3094	197	27	−	−	PROPN
iajs-3094	197	28	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	197	29	=	=	SYM
iajs-3094	197	30	(	(	PUNCT
iajs-3094	197	31	𝑘	𝑘	PRON
iajs-3094	197	32	−	−	PROPN
iajs-3094	197	33	1)𝑝𝑗.	1)𝑝𝑗.	NUM
iajs-3094	197	34	since	since	SCONJ
iajs-3094	197	35	spt	spt	NOUN
iajs-3094	197	36	schedule	schedule	NOUN
iajs-3094	197	37	,	,	PUNCT
iajs-3094	197	38	the	the	DET
iajs-3094	197	39	processing	processing	NOUN
iajs-3094	197	40	time	time	NOUN
iajs-3094	197	41	for	for	ADP
iajs-3094	197	42	tasks	task	NOUN
iajs-3094	197	43	is	be	AUX
iajs-3094	197	44	arranged	arrange	VERB
iajs-3094	197	45	in	in	ADP
iajs-3094	197	46	a	a	DET
iajs-3094	197	47	nondescending	nondescending	ADJ
iajs-3094	197	48	sequence	sequence	NOUN
iajs-3094	197	49	(	(	PUNCT
iajs-3094	197	50	this	this	DET
iajs-3094	197	51	meam	meam	NOUN
iajs-3094	197	52	𝑝𝑖	𝑝𝑖	PROPN
iajs-3094	197	53	≤	≤	ADJ
iajs-3094	197	54	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	197	55	for	for	ADP
iajs-3094	197	56	all	all	PRON
iajs-3094	197	57	𝑖	𝑖	ADP
iajs-3094	197	58	≤	≤	NUM
iajs-3094	197	59	𝑗	𝑗	NOUN
iajs-3094	197	60	)	)	PUNCT
iajs-3094	197	61	.	.	PUNCT
iajs-3094	198	1	then	then	ADV
iajs-3094	198	2	(	(	PUNCT
iajs-3094	198	3	𝑘	𝑘	X
iajs-3094	198	4	−	−	PROPN
iajs-3094	198	5	1)𝑝1	1)𝑝1	PROPN
iajs-3094	198	6	≤	≤	NUM
iajs-3094	198	7	(	(	PUNCT
iajs-3094	198	8	𝑘	𝑘	PRON
iajs-3094	198	9	−	−	PROPN
iajs-3094	198	10	1)𝑝2	1)𝑝2	NUM
iajs-3094	198	11	≤	≤	NOUN
iajs-3094	198	12	⋯	⋯	ADP
iajs-3094	198	13	≤	≤	NOUN
iajs-3094	198	14	(	(	PUNCT
iajs-3094	198	15	𝑘	𝑘	PRON
iajs-3094	198	16	−	−	X
iajs-3094	198	17	1)𝑝𝑛	1)𝑝𝑛	NUM
iajs-3094	198	18	,	,	PUNCT
iajs-3094	198	19	hence	hence	ADV
iajs-3094	198	20	𝑠1	𝑠1	PROPN
iajs-3094	198	21	≤	≤	NOUN
iajs-3094	198	22	𝑠2	𝑠2	NOUN
iajs-3094	198	23	≤	≤	PROPN
iajs-3094	198	24	⋯	⋯	NOUN
iajs-3094	198	25	≤	≤	ADJ
iajs-3094	198	26	𝑠𝑛.	𝑠𝑛.	NOUN
iajs-3094	198	27	which	which	PRON
iajs-3094	198	28	is	be	AUX
iajs-3094	198	29	mst	mst	PROPN
iajs-3094	198	30	order	order	NOUN
iajs-3094	198	31	,	,	PUNCT
iajs-3094	198	32	since	since	SCONJ
iajs-3094	198	33	mst	mst	PROPN
iajs-3094	198	34	order	order	NOUN
iajs-3094	198	35	gives	give	VERB
iajs-3094	198	36	efso	efso	NOUN
iajs-3094	198	37	for	for	ADP
iajs-3094	198	38	∑𝐸𝑗.	∑𝐸𝑗.	PROPN
iajs-3094	198	39	hence	hence	ADV
iajs-3094	198	40	spt	spt	PROPN
iajs-3094	198	41	is	be	AUX
iajs-3094	198	42	efficient	efficient	ADJ
iajs-3094	198	43	for	for	ADP
iajs-3094	198	44	(	(	PUNCT
iajs-3094	198	45	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	198	46	)	)	PUNCT
iajs-3094	198	47	.	.	PUNCT
iajs-3094	199	1	case(𝟒.	case(𝟒.	NUM
iajs-3094	199	2	𝟏.	𝟏.	NOUN
iajs-3094	199	3	𝟒	𝟒	X
iajs-3094	199	4	):	):	PUNCT
iajs-3094	199	5	if	if	SCONJ
iajs-3094	199	6	spt	spt	PROPN
iajs-3094	199	7	and	and	CCONJ
iajs-3094	199	8	mst	mst	PROPN
iajs-3094	199	9	are	be	AUX
iajs-3094	199	10	identical	identical	ADJ
iajs-3094	199	11	then	then	ADV
iajs-3094	199	12	they	they	PRON
iajs-3094	199	13	give	give	VERB
iajs-3094	199	14	an	an	DET
iajs-3094	199	15	efficient	efficient	ADJ
iajs-3094	199	16	schedule	schedule	NOUN
iajs-3094	199	17	for	for	ADP
iajs-3094	199	18	(	(	PUNCT
iajs-3094	199	19	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	199	20	)	)	PUNCT
iajs-3094	199	21	.	.	PUNCT
iajs-3094	200	1	proof	proof	NOUN
iajs-3094	200	2	:	:	PUNCT
iajs-3094	200	3	since	since	SCONJ
iajs-3094	200	4	spt	spt	PROPN
iajs-3094	200	5	and	and	CCONJ
iajs-3094	200	6	mst	mst	PROPN
iajs-3094	200	7	are	be	AUX
iajs-3094	200	8	identical	identical	ADJ
iajs-3094	200	9	then	then	ADV
iajs-3094	200	10	∑	∑	ADP
iajs-3094	200	11	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	200	12	𝑛	𝑛	PRON
iajs-3094	200	13	𝑗=1	𝑗=1	PROPN
iajs-3094	200	14	is	be	AUX
iajs-3094	200	15	minimum	minimum	ADJ
iajs-3094	200	16	value	value	NOUN
iajs-3094	200	17	,	,	PUNCT
iajs-3094	200	18	and	and	CCONJ
iajs-3094	200	19	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	200	20	is	be	AUX
iajs-3094	200	21	minimum	minimum	ADJ
iajs-3094	200	22	value	value	NOUN
iajs-3094	200	23	.	.	PUNCT
iajs-3094	201	1	but	but	CCONJ
iajs-3094	201	2	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	201	3	=	=	NOUN
iajs-3094	201	4	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	201	5	−	−	PROPN
iajs-3094	201	6	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	201	7	and	and	CCONJ
iajs-3094	201	8	𝑑1	𝑑1	NOUN
iajs-3094	201	9	−	−	PROPN
iajs-3094	201	10	𝑝1	𝑝1	NOUN
iajs-3094	201	11	≤.	≤.	NOUN
iajs-3094	201	12	.	.	PUNCT
iajs-3094	201	13	.	.	PUNCT
iajs-3094	202	1	≤	≤	NUM
iajs-3094	203	1	𝑑𝑛	𝑑𝑛	PUNCT
iajs-3094	203	2	−	−	PROPN
iajs-3094	203	3	𝑝𝑛	𝑝𝑛	INTJ
iajs-3094	203	4	then	then	ADV
iajs-3094	203	5	𝑑1	𝑑1	NOUN
iajs-3094	203	6	−	−	PROPN
iajs-3094	203	7	𝑝1	𝑝1	PROPN
iajs-3094	203	8	+	+	CCONJ
iajs-3094	203	9	𝑝1	𝑝1	NOUN
iajs-3094	203	10	≤.	≤.	NOUN
iajs-3094	203	11	.	.	PUNCT
iajs-3094	203	12	.	.	PUNCT
iajs-3094	204	1	≤	≤	NUM
iajs-3094	205	1	𝑑𝑛	𝑑𝑛	PUNCT
iajs-3094	205	2	−	−	PROPN
iajs-3094	205	3	𝑝𝑛	𝑝𝑛	NOUN
iajs-3094	205	4	+	+	X
iajs-3094	205	5	𝑝𝑛	𝑝𝑛	X
iajs-3094	205	6	(	(	PUNCT
iajs-3094	205	7	since	since	SCONJ
iajs-3094	205	8	𝑝1	𝑝1	NOUN
iajs-3094	205	9	≤	≤	NOUN
iajs-3094	205	10	⋯	⋯	ADP
iajs-3094	205	11	≤	≤	NOUN
iajs-3094	205	12	𝑝𝑛	𝑝𝑛	NOUN
iajs-3094	205	13	)	)	PUNCT
iajs-3094	205	14	,	,	PUNCT
iajs-3094	205	15	hence	hence	ADV
iajs-3094	205	16	𝑑1	𝑑1	NOUN
iajs-3094	205	17	≤.	≤.	NOUN
iajs-3094	205	18	.	.	PUNCT
iajs-3094	205	19	.	.	PUNCT
iajs-3094	206	1	≤	≤	NOUN
iajs-3094	207	1	𝑑𝑛(which	𝑑𝑛(which	PROPN
iajs-3094	207	2	is	be	AUX
iajs-3094	207	3	edd	edd	PROPN
iajs-3094	207	4	order	order	NOUN
iajs-3094	207	5	)	)	PUNCT
iajs-3094	207	6	,	,	PUNCT
iajs-3094	207	7	since	since	SCONJ
iajs-3094	207	8	the	the	DET
iajs-3094	207	9	edd	edd	PROPN
iajs-3094	207	10	order	order	NOUN
iajs-3094	207	11	gives	give	VERB
iajs-3094	207	12	efso	efso	NOUN
iajs-3094	207	13	for	for	ADP
iajs-3094	207	14	the	the	DET
iajs-3094	207	15	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	207	16	then	then	ADV
iajs-3094	207	17	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	207	18	is	be	AUX
iajs-3094	207	19	minimum	minimum	ADJ
iajs-3094	207	20	.	.	PUNCT
iajs-3094	208	1	hence	hence	ADV
iajs-3094	208	2	all	all	DET
iajs-3094	208	3	schedule	schedule	VERB
iajs-3094	208	4	an	an	DET
iajs-3094	208	5	efso	efso	NOUN
iajs-3094	208	6	for	for	ADP
iajs-3094	208	7	(	(	PUNCT
iajs-3094	208	8	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	208	9	)	)	PUNCT
iajs-3094	208	10	.	.	PUNCT
iajs-3094	209	1	case(𝟒.	case(𝟒.	NUM
iajs-3094	209	2	𝟏.	𝟏.	SYM
iajs-3094	209	3	𝟓	𝟓	NUM
iajs-3094	209	4	):	):	PUNCT
iajs-3094	209	5	if	if	SCONJ
iajs-3094	209	6	the	the	DET
iajs-3094	209	7	processing	processing	NOUN
iajs-3094	209	8	times	time	NOUN
iajs-3094	209	9	of	of	ADP
iajs-3094	209	10	all	all	DET
iajs-3094	209	11	jobs	job	NOUN
iajs-3094	209	12	are	be	AUX
iajs-3094	209	13	identical	identical	ADJ
iajs-3094	209	14	,	,	PUNCT
iajs-3094	209	15	then	then	ADV
iajs-3094	209	16	mst	mst	PROPN
iajs-3094	209	17	ordered	order	VERB
iajs-3094	209	18	is	be	AUX
iajs-3094	209	19	efso	efso	ADJ
iajs-3094	209	20	to	to	ADP
iajs-3094	209	21	problem	problem	NOUN
iajs-3094	209	22	(	(	PUNCT
iajs-3094	209	23	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	209	24	)	)	PUNCT
iajs-3094	209	25	.	.	PUNCT
iajs-3094	210	1	ihjpas	ihjpas	PROPN
iajs-3094	210	2	.	.	PUNCT
iajs-3094	211	1	37	37	NUM
iajs-3094	211	2	(	(	PUNCT
iajs-3094	211	3	1	1	NUM
iajs-3094	211	4	)	)	PUNCT
iajs-3094	211	5	2024	2024	NUM
iajs-3094	211	6	394	394	NUM
iajs-3094	211	7	proof	proof	NOUN
iajs-3094	211	8	:	:	PUNCT
iajs-3094	211	9	since	since	SCONJ
iajs-3094	211	10	the	the	DET
iajs-3094	211	11	processing	processing	NOUN
iajs-3094	211	12	times	time	NOUN
iajs-3094	211	13	of	of	ADP
iajs-3094	211	14	all	all	DET
iajs-3094	211	15	jobs	job	NOUN
iajs-3094	211	16	are	be	AUX
iajs-3094	211	17	identical	identical	ADJ
iajs-3094	211	18	,	,	PUNCT
iajs-3094	211	19	then	then	ADV
iajs-3094	211	20	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	211	21	=	=	SYM
iajs-3094	211	22	𝑝	𝑝	PROPN
iajs-3094	211	23	(	(	PUNCT
iajs-3094	211	24	𝑛(𝑛+1	𝑛(𝑛+1	PROPN
iajs-3094	211	25	)	)	PUNCT
iajs-3094	211	26	2	2	NUM
iajs-3094	211	27	)	)	PUNCT
iajs-3094	211	28	,	,	PUNCT
iajs-3094	211	29	it	it	PRON
iajs-3094	211	30	is	be	AUX
iajs-3094	211	31	the	the	DET
iajs-3094	211	32	same	same	ADJ
iajs-3094	211	33	for	for	ADP
iajs-3094	211	34	any	any	DET
iajs-3094	211	35	sequence	sequence	NOUN
iajs-3094	211	36	.	.	PUNCT
iajs-3094	212	1	since	since	SCONJ
iajs-3094	212	2	mst	mst	PROPN
iajs-3094	212	3	schedule	schedule	NOUN
iajs-3094	212	4	,	,	PUNCT
iajs-3094	212	5	ordered	order	VERB
iajs-3094	212	6	the	the	DET
iajs-3094	212	7	slack	slack	NOUN
iajs-3094	212	8	time	time	NOUN
iajs-3094	212	9	of	of	ADP
iajs-3094	212	10	jobs	job	NOUN
iajs-3094	212	11	in	in	ADP
iajs-3094	212	12	a	a	DET
iajs-3094	212	13	non	non	ADJ
iajs-3094	212	14	-	-	ADJ
iajs-3094	212	15	decreasing	decrease	VERB
iajs-3094	212	16	sequence	sequence	NOUN
iajs-3094	212	17	(	(	PUNCT
iajs-3094	212	18	that	that	PRON
iajs-3094	212	19	mean	mean	VERB
iajs-3094	212	20	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	212	21	≤	≤	NUM
iajs-3094	212	22	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	212	23	for	for	ADP
iajs-3094	212	24	all	all	PRON
iajs-3094	212	25	𝑖	𝑖	ADP
iajs-3094	212	26	≤	≤	NUM
iajs-3094	212	27	𝑗	𝑗	INTJ
iajs-3094	212	28	in	in	ADP
iajs-3094	212	29	mst	mst	PROPN
iajs-3094	212	30	schedule	schedule	NOUN
iajs-3094	212	31	)	)	PUNCT
iajs-3094	212	32	.	.	PUNCT
iajs-3094	213	1	since	since	SCONJ
iajs-3094	213	2	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	213	3	=	=	SYM
iajs-3094	213	4	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	213	5	−	−	PROPN
iajs-3094	213	6	𝑝	𝑝	PROPN
iajs-3094	213	7	,	,	PUNCT
iajs-3094	213	8	using	use	VERB
iajs-3094	213	9	mst	mst	PROPN
iajs-3094	213	10	rule	rule	NOUN
iajs-3094	213	11	and	and	CCONJ
iajs-3094	213	12	adding	add	VERB
iajs-3094	213	13	𝑝	𝑝	NOUN
iajs-3094	213	14	for	for	ADP
iajs-3094	213	15	each	each	DET
iajs-3094	213	16	term	term	NOUN
iajs-3094	213	17	,	,	PUNCT
iajs-3094	213	18	is	be	AUX
iajs-3094	213	19	produced	produce	VERB
iajs-3094	213	20	𝑑𝑖	𝑑𝑖	AUX
iajs-3094	213	21	≤	≤	NUM
iajs-3094	213	22	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	213	23	for	for	ADP
iajs-3094	213	24	all	all	DET
iajs-3094	213	25	𝑖	𝑖	ADP
iajs-3094	213	26	≤	≤	NUM
iajs-3094	213	27	𝑗	𝑗	INTJ
iajs-3094	213	28	(	(	PUNCT
iajs-3094	213	29	which	which	PRON
iajs-3094	213	30	is	be	AUX
iajs-3094	213	31	edd	edd	PROPN
iajs-3094	213	32	order	order	NOUN
iajs-3094	213	33	)	)	PUNCT
iajs-3094	213	34	,	,	PUNCT
iajs-3094	213	35	hence	hence	ADV
iajs-3094	213	36	edd	edd	PROPN
iajs-3094	213	37	and	and	CCONJ
iajs-3094	213	38	mst	mst	PROPN
iajs-3094	213	39	are	be	AUX
iajs-3094	213	40	identical	identical	ADJ
iajs-3094	213	41	.	.	PUNCT
iajs-3094	214	1	since	since	SCONJ
iajs-3094	214	2	mst	mst	PROPN
iajs-3094	214	3	order	order	NOUN
iajs-3094	214	4	gives	give	VERB
iajs-3094	214	5	efficient	efficient	ADJ
iajs-3094	214	6	value	value	NOUN
iajs-3094	214	7	for	for	ADP
iajs-3094	214	8	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	214	9	and	and	CCONJ
iajs-3094	214	10	edd	edd	PROPN
iajs-3094	214	11	order	order	NOUN
iajs-3094	214	12	gives	give	VERB
iajs-3094	214	13	efficient	efficient	ADJ
iajs-3094	214	14	value	value	NOUN
iajs-3094	214	15	for	for	ADP
iajs-3094	214	16	the	the	DET
iajs-3094	214	17	𝑇𝑗	𝑇𝑗	NOUN
iajs-3094	214	18	then	then	ADV
iajs-3094	214	19	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	214	20	is	be	AUX
iajs-3094	214	21	minimum	minimum	ADJ
iajs-3094	214	22	.	.	PUNCT
iajs-3094	215	1	hence	hence	ADV
iajs-3094	215	2	mst	mst	PROPN
iajs-3094	215	3	is	be	AUX
iajs-3094	215	4	an	an	DET
iajs-3094	215	5	efso	efso	NOUN
iajs-3094	215	6	for	for	ADP
iajs-3094	215	7	the	the	DET
iajs-3094	215	8	third	third	ADJ
iajs-3094	215	9	criterion	criterion	NOUN
iajs-3094	215	10	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	215	11	,	,	PUNCT
iajs-3094	215	12	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	215	13	,	,	PUNCT
iajs-3094	215	14	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	215	15	.	.	PUNCT
iajs-3094	216	1	case(𝟒.	case(𝟒.	NUM
iajs-3094	216	2	𝟏.	𝟏.	SYM
iajs-3094	216	3	𝟔	𝟔	NUM
iajs-3094	216	4	):	):	PUNCT
iajs-3094	216	5	if	if	SCONJ
iajs-3094	216	6	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	216	7	=	=	SYM
iajs-3094	216	8	𝑑	𝑑	NOUN
iajs-3094	216	9	,	,	PUNCT
iajs-3094	216	10	and	and	CCONJ
iajs-3094	216	11	spt	spt	PROPN
iajs-3094	216	12	and	and	CCONJ
iajs-3094	216	13	mst	mst	PROPN
iajs-3094	216	14	are	be	AUX
iajs-3094	216	15	identical	identical	ADJ
iajs-3094	216	16	∀𝑗	∀𝑗	NOUN
iajs-3094	216	17	,	,	PUNCT
iajs-3094	216	18	(	(	PUNCT
iajs-3094	216	19	𝑗	𝑗	NOUN
iajs-3094	216	20	=	=	SYM
iajs-3094	216	21	1,2	1,2	NUM
iajs-3094	216	22	,	,	PUNCT
iajs-3094	216	23	.	.	PUNCT
iajs-3094	216	24	.	.	PUNCT
iajs-3094	217	1	.	.	PUNCT
iajs-3094	218	1	,	,	PUNCT
iajs-3094	218	2	𝑛	𝑛	X
iajs-3094	218	3	)	)	PUNCT
iajs-3094	218	4	in	in	ADP
iajs-3094	218	5	a	a	DET
iajs-3094	218	6	schedule	schedule	NOUN
iajs-3094	218	7	α	α	NOUN
iajs-3094	218	8	,	,	PUNCT
iajs-3094	218	9	then	then	ADV
iajs-3094	218	10	𝛼	𝛼	PROPN
iajs-3094	218	11	is	be	AUX
iajs-3094	218	12	efso	efso	ADJ
iajs-3094	218	13	to	to	ADP
iajs-3094	218	14	(	(	PUNCT
iajs-3094	218	15	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	218	16	)	)	PUNCT
iajs-3094	218	17	.	.	PUNCT
iajs-3094	219	1	proof	proof	NOUN
iajs-3094	219	2	:	:	PUNCT
iajs-3094	219	3	since	since	SCONJ
iajs-3094	219	4	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	219	5	=	=	SYM
iajs-3094	219	6	𝑑	𝑑	PROPN
iajs-3094	219	7	,	,	PUNCT
iajs-3094	219	8	there	there	PRON
iajs-3094	219	9	are	be	VERB
iajs-3094	219	10	two	two	NUM
iajs-3094	219	11	cases	case	NOUN
iajs-3094	219	12	:	:	PUNCT
iajs-3094	219	13	a	a	X
iajs-3094	219	14	)	)	PUNCT
iajs-3094	219	15	if	if	SCONJ
iajs-3094	219	16	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	219	17	=	=	SYM
iajs-3094	219	18	𝑑	𝑑	NOUN
iajs-3094	219	19	=	=	SYM
iajs-3094	219	20	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	219	21	,	,	PUNCT
iajs-3094	219	22	hence	hence	ADV
iajs-3094	219	23	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	219	24	≥	≥	NUM
iajs-3094	219	25	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	219	26	for	for	ADP
iajs-3094	219	27	all	all	DET
iajs-3094	219	28	𝑗	𝑗	PROPN
iajs-3094	219	29	(	(	PUNCT
iajs-3094	219	30	this	this	PRON
iajs-3094	219	31	means	mean	VERB
iajs-3094	219	32	all	all	DET
iajs-3094	219	33	jobs	job	NOUN
iajs-3094	219	34	are	be	AUX
iajs-3094	219	35	late	late	ADJ
iajs-3094	219	36	s.	s.	PROPN
iajs-3094	219	37	t.	t.	PROPN
iajs-3094	220	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	220	2	=	=	PUNCT
iajs-3094	220	3	0	0	PUNCT
iajs-3094	220	4	=	=	SYM
iajs-3094	220	5	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	220	6	for	for	ADP
iajs-3094	220	7	all	all	DET
iajs-3094	220	8	𝑗	𝑗	NOUN
iajs-3094	220	9	)	)	PUNCT
iajs-3094	220	10	.	.	PUNCT
iajs-3094	221	1	then	then	ADV
iajs-3094	221	2	1//	1//	NUM
iajs-3094	221	3	(	(	PUNCT
iajs-3094	221	4	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	221	5	,	,	PUNCT
iajs-3094	221	6	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	221	7	,	,	PUNCT
iajs-3094	221	8	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	221	9	)	)	PUNCT
iajs-3094	221	10	reduce	reduce	VERB
iajs-3094	221	11	to	to	ADP
iajs-3094	221	12	1//	1//	NUM
iajs-3094	221	13	(	(	PUNCT
iajs-3094	221	14	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	221	15	,	,	PUNCT
iajs-3094	221	16	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	221	17	)	)	PUNCT
iajs-3094	221	18	,	,	PUNCT
iajs-3094	221	19	as	as	ADP
iajs-3094	221	20	result	result	NOUN
iajs-3094	221	21	,	,	PUNCT
iajs-3094	221	22	the	the	DET
iajs-3094	221	23	spt	spt	PROPN
iajs-3094	221	24	rule	rule	NOUN
iajs-3094	221	25	provides	provide	VERB
iajs-3094	221	26	an	an	DET
iajs-3094	221	27	efso	efso	NOUN
iajs-3094	221	28	to	to	ADP
iajs-3094	221	29	the	the	DET
iajs-3094	221	30	problem	problem	NOUN
iajs-3094	221	31	(	(	PUNCT
iajs-3094	221	32	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	221	33	)	)	PUNCT
iajs-3094	222	1	.where	.where	SCONJ
iajs-3094	222	2	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	223	1	=	=	SYM
iajs-3094	223	2	𝑑	𝑑	PROPN
iajs-3094	223	3	for	for	ADP
iajs-3094	223	4	all	all	DET
iajs-3094	223	5	the	the	DET
iajs-3094	223	6	orders	order	NOUN
iajs-3094	223	7	of	of	ADP
iajs-3094	223	8	𝑗	𝑗	NOUN
iajs-3094	223	9	and	and	CCONJ
iajs-3094	223	10	spt	spt	PROPN
iajs-3094	223	11	gives	give	VERB
iajs-3094	223	12	efso	efso	NOUN
iajs-3094	223	13	for	for	ADP
iajs-3094	223	14	1//	1//	PROPN
iajs-3094	223	15	∑𝐶𝑗.	∑𝐶𝑗.	PROPN
iajs-3094	223	16	b	b	X
iajs-3094	223	17	)	)	PUNCT
iajs-3094	223	18	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	223	19	=	=	SYM
iajs-3094	223	20	𝑑	𝑑	PROPN
iajs-3094	223	21	>	>	X
iajs-3094	223	22	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	223	23	for	for	ADP
iajs-3094	223	24	all	all	PRON
iajs-3094	224	1	𝑗	𝑗	INTJ
iajs-3094	224	2	hence	hence	ADV
iajs-3094	224	3	either	either	CCONJ
iajs-3094	224	4	𝑑	𝑑	PROPN
iajs-3094	224	5	≤	≤	X
iajs-3094	224	6	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	224	7	or	or	CCONJ
iajs-3094	224	8	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	224	9	>	>	X
iajs-3094	224	10	𝑑	𝑑	PROPN
iajs-3094	224	11	,	,	PUNCT
iajs-3094	224	12	since	since	SCONJ
iajs-3094	224	13	spt	spt	PROPN
iajs-3094	224	14	and	and	CCONJ
iajs-3094	224	15	mst	mst	PROPN
iajs-3094	224	16	are	be	AUX
iajs-3094	224	17	identical	identical	ADJ
iajs-3094	224	18	(	(	PUNCT
iajs-3094	224	19	this	this	PRON
iajs-3094	224	20	mean	mean	VERB
iajs-3094	224	21	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	224	22	,	,	PUNCT
iajs-3094	224	23	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	224	24	is	be	AUX
iajs-3094	224	25	minimum	minimum	ADJ
iajs-3094	224	26	values	value	NOUN
iajs-3094	224	27	)	)	PUNCT
iajs-3094	224	28	.	.	PUNCT
iajs-3094	225	1	then	then	ADV
iajs-3094	225	2	a	a	DET
iajs-3094	225	3	schedule	schedule	NOUN
iajs-3094	225	4	𝛼	𝛼	NOUN
iajs-3094	225	5	is	be	AUX
iajs-3094	225	6	an	an	DET
iajs-3094	225	7	efso	efso	NOUN
iajs-3094	225	8	to	to	ADP
iajs-3094	225	9	(	(	PUNCT
iajs-3094	225	10	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	225	11	)	)	PUNCT
iajs-3094	225	12	.	.	PUNCT
iajs-3094	226	1	case	case	NOUN
iajs-3094	226	2	(	(	PUNCT
iajs-3094	226	3	𝟒.	𝟒.	X
iajs-3094	226	4	𝟏.	𝟏.	X
iajs-3094	226	5	𝟕	𝟕	NUM
iajs-3094	226	6	):	):	PUNCT
iajs-3094	226	7	if	if	SCONJ
iajs-3094	226	8	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	226	9	=	=	SYM
iajs-3094	226	10	𝑝	𝑝	NOUN
iajs-3094	226	11	,	,	PUNCT
iajs-3094	226	12	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	226	13	=	=	SYM
iajs-3094	226	14	𝑑	𝑑	PROPN
iajs-3094	226	15	and	and	CCONJ
iajs-3094	226	16	𝑑	𝑑	PROPN
iajs-3094	226	17	≤	≤	NOUN
iajs-3094	226	18	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	226	19	for	for	ADP
iajs-3094	226	20	all	all	DET
iajs-3094	226	21	𝑗	𝑗	NOUN
iajs-3094	226	22	in	in	ADP
iajs-3094	226	23	a	a	DET
iajs-3094	226	24	schedule	schedule	NOUN
iajs-3094	226	25	α	α	NOUN
iajs-3094	226	26	then	then	ADV
iajs-3094	226	27	any	any	DET
iajs-3094	226	28	schedule	schedule	NOUN
iajs-3094	226	29	𝛼	𝛼	NOUN
iajs-3094	226	30	is	be	AUX
iajs-3094	226	31	efso	efso	ADJ
iajs-3094	226	32	to	to	ADP
iajs-3094	226	33	(	(	PUNCT
iajs-3094	226	34	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	226	35	)	)	PUNCT
iajs-3094	226	36	.	.	PUNCT
iajs-3094	227	1	proof	proof	NOUN
iajs-3094	227	2	:	:	PUNCT
iajs-3094	227	3	since	since	SCONJ
iajs-3094	227	4	𝑑	𝑑	NOUN
iajs-3094	227	5	≤	≤	X
iajs-3094	227	6	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	227	7	for	for	ADP
iajs-3094	227	8	all	all	DET
iajs-3094	227	9	𝑗	𝑗	NOUN
iajs-3094	227	10	(	(	PUNCT
iajs-3094	227	11	this	this	PRON
iajs-3094	227	12	means	mean	VERB
iajs-3094	227	13	all	all	DET
iajs-3094	227	14	jobs	job	NOUN
iajs-3094	227	15	are	be	AUX
iajs-3094	227	16	late	late	ADJ
iajs-3094	227	17	s.	s.	PROPN
iajs-3094	227	18	t.	t.	PROPN
iajs-3094	228	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	228	2	=	=	PUNCT
iajs-3094	228	3	0	0	PUNCT
iajs-3094	228	4	=	=	SYM
iajs-3094	228	5	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	228	6	)	)	PUNCT
iajs-3094	228	7	and	and	CCONJ
iajs-3094	228	8	𝑇𝑗	𝑇𝑗	PROPN
iajs-3094	228	9	=	=	SYM
iajs-3094	228	10	𝑚𝑎𝑥{𝐿𝑗	𝑚𝑎𝑥{𝐿𝑗	PROPN
iajs-3094	228	11	,	,	PUNCT
iajs-3094	228	12	0	0	NUM
iajs-3094	228	13	}	}	PUNCT
iajs-3094	228	14	=	=	SYM
iajs-3094	228	15	𝑚𝑎𝑥{𝑗𝑝	𝑚𝑎𝑥{𝑗𝑝	NUM
iajs-3094	228	16	−	−	PROPN
iajs-3094	229	1	𝑑	𝑑	NOUN
iajs-3094	229	2	,	,	PUNCT
iajs-3094	229	3	0	0	NUM
iajs-3094	229	4	}	}	PUNCT
iajs-3094	229	5	then	then	ADV
iajs-3094	229	6	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	229	7	=	=	PUNCT
iajs-3094	229	8	𝑚𝑎𝑥{𝑚𝑎𝑥{𝑗𝑝	𝑚𝑎𝑥{𝑚𝑎𝑥{𝑗𝑝	PUNCT
iajs-3094	229	9	−	−	PROPN
iajs-3094	229	10	𝑑	𝑑	NOUN
iajs-3094	229	11	,	,	PUNCT
iajs-3094	229	12	0	0	NUM
iajs-3094	229	13	}	}	PUNCT
iajs-3094	229	14	}	}	PUNCT
iajs-3094	229	15	=	=	PUNCT
iajs-3094	229	16	𝑛𝑝	𝑛𝑝	ADP
iajs-3094	229	17	−	−	PROPN
iajs-3094	229	18	𝑑.	𝑑.	NOUN
iajs-3094	229	19	hence	hence	ADV
iajs-3094	229	20	1	1	NUM
iajs-3094	229	21	∕∕	∕∕	SYM
iajs-3094	229	22	(	(	PUNCT
iajs-3094	229	23	∑𝐶𝑗	∑𝐶𝑗	INTJ
iajs-3094	229	24	,	,	PUNCT
iajs-3094	229	25	∑	∑	PROPN
iajs-3094	229	26	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	229	27	,	,	PUNCT
iajs-3094	229	28	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	229	29	)	)	PUNCT
iajs-3094	229	30	reduced	reduce	VERB
iajs-3094	229	31	to	to	ADP
iajs-3094	229	32	1//	1//	NUM
iajs-3094	229	33	(	(	PUNCT
iajs-3094	229	34	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	229	35	,	,	PUNCT
iajs-3094	229	36	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	229	37	)	)	PUNCT
iajs-3094	229	38	=	=	PUNCT
iajs-3094	229	39	(	(	PUNCT
iajs-3094	229	40	𝑝	𝑝	PROPN
iajs-3094	229	41	(	(	PUNCT
iajs-3094	229	42	𝑛2+𝑛	𝑛2+𝑛	PROPN
iajs-3094	229	43	2	2	NUM
iajs-3094	229	44	)	)	PUNCT
iajs-3094	229	45	,	,	PUNCT
iajs-3094	229	46	𝑛𝑝	𝑛𝑝	ADP
iajs-3094	229	47	−	−	PROPN
iajs-3094	229	48	𝑑	𝑑	NOUN
iajs-3094	229	49	)	)	PUNCT
iajs-3094	229	50	.	.	PUNCT
iajs-3094	230	1	then	then	ADV
iajs-3094	230	2	any	any	DET
iajs-3094	230	3	schedule	schedule	NOUN
iajs-3094	230	4	is	be	AUX
iajs-3094	230	5	an	an	DET
iajs-3094	230	6	efso	efso	NOUN
iajs-3094	230	7	to	to	ADP
iajs-3094	230	8	(	(	PUNCT
iajs-3094	230	9	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	230	10	)	)	PUNCT
iajs-3094	230	11	because	because	SCONJ
iajs-3094	230	12	the	the	DET
iajs-3094	230	13	three	three	NUM
iajs-3094	230	14	quantities	quantity	NOUN
iajs-3094	230	15	are	be	AUX
iajs-3094	230	16	constant	constant	ADJ
iajs-3094	230	17	.	.	PUNCT
iajs-3094	231	1	case(𝟒.	case(𝟒.	NUM
iajs-3094	231	2	𝟏.	𝟏.	SYM
iajs-3094	231	3	𝟖	𝟖	X
iajs-3094	231	4	):	):	PUNCT
iajs-3094	231	5	if	if	SCONJ
iajs-3094	231	6	𝑑𝛼𝑖	𝑑𝛼𝑖	PROPN
iajs-3094	231	7	+	+	CCONJ
iajs-3094	231	8	𝑝𝛼𝑗	𝑝𝛼𝑗	X
iajs-3094	231	9	≤	≤	NUM
iajs-3094	231	10	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	231	11	for	for	ADP
iajs-3094	231	12	all	all	DET
iajs-3094	231	13	𝑖	𝑖	ADP
iajs-3094	231	14	,	,	PUNCT
iajs-3094	231	15	𝑗	𝑗	INTJ
iajs-3094	231	16	in	in	ADP
iajs-3094	231	17	𝑆𝑃𝑇	𝑆𝑃𝑇	PROPN
iajs-3094	231	18	schedule	schedule	NOUN
iajs-3094	231	19	𝛼	𝛼	NOUN
iajs-3094	231	20	,	,	PUNCT
iajs-3094	231	21	where	where	SCONJ
iajs-3094	231	22	𝑖	𝑖	ADP
iajs-3094	231	23	≤	≤	X
iajs-3094	231	24	𝑗	𝑗	PROPN
iajs-3094	231	25	,	,	PUNCT
iajs-3094	231	26	spt	spt	PROPN
iajs-3094	231	27	and	and	CCONJ
iajs-3094	231	28	edd	edd	PROPN
iajs-3094	231	29	are	be	AUX
iajs-3094	231	30	identical	identical	ADJ
iajs-3094	231	31	,	,	PUNCT
iajs-3094	231	32	then	then	ADV
iajs-3094	231	33	𝛼	𝛼	VERB
iajs-3094	231	34	is	be	AUX
iajs-3094	231	35	the	the	DET
iajs-3094	231	36	efso	efso	NOUN
iajs-3094	231	37	for	for	ADP
iajs-3094	231	38	(	(	PUNCT
iajs-3094	231	39	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	231	40	)	)	PUNCT
iajs-3094	231	41	.	.	PUNCT
iajs-3094	232	1	proof	proof	NOUN
iajs-3094	232	2	:	:	PUNCT
iajs-3094	232	3	since	since	SCONJ
iajs-3094	232	4	𝑑𝛼𝑖	𝑑𝛼𝑖	PROPN
iajs-3094	232	5	+	+	CCONJ
iajs-3094	232	6	𝑝𝛼𝑗	𝑝𝛼𝑗	X
iajs-3094	232	7	≤	≤	NUM
iajs-3094	232	8	𝑑𝛼𝑗	𝑑𝛼𝑗	PROPN
iajs-3094	232	9	∀𝑖	∀𝑖	PROPN
iajs-3094	232	10	,	,	PUNCT
iajs-3094	232	11	𝑗	𝑗	PROPN
iajs-3094	232	12	in	in	ADP
iajs-3094	232	13	𝛼	𝛼	NOUN
iajs-3094	232	14	,	,	PUNCT
iajs-3094	232	15	then	then	ADV
iajs-3094	232	16	𝑑𝛼𝑖	𝑑𝛼𝑖	VERB
iajs-3094	232	17	≤	≤	NUM
iajs-3094	232	18	𝑑𝛼𝑗	𝑑𝛼𝑗	PROPN
iajs-3094	232	19	−	−	PROPN
iajs-3094	232	20	𝑝𝛼𝑗	𝑝𝛼𝑗	NOUN
iajs-3094	232	21	for	for	ADP
iajs-3094	232	22	all	all	DET
iajs-3094	232	23	𝑖	𝑖	SYM
iajs-3094	232	24	,	,	PUNCT
iajs-3094	232	25	𝑗	𝑗	ADJ
iajs-3094	232	26	and	and	CCONJ
iajs-3094	232	27	𝑑𝛼𝑖	𝑑𝛼𝑖	ADJ
iajs-3094	232	28	−	−	PROPN
iajs-3094	232	29	𝑝𝛼𝑖	𝑝𝛼𝑖	ADJ
iajs-3094	232	30	≤	≤	NUM
iajs-3094	233	1	𝑑𝛼𝑗	𝑑𝛼𝑗	PROPN
iajs-3094	233	2	−	−	PROPN
iajs-3094	233	3	𝑝𝛼𝑗	𝑝𝛼𝑗	PROPN
iajs-3094	233	4	,	,	PUNCT
iajs-3094	233	5	for	for	ADP
iajs-3094	233	6	all	all	DET
iajs-3094	233	7	𝑖	𝑖	ADP
iajs-3094	233	8	,	,	PUNCT
iajs-3094	233	9	𝑗	𝑗	INTJ
iajs-3094	233	10	(	(	PUNCT
iajs-3094	233	11	since	since	SCONJ
iajs-3094	233	12	𝑝𝛼𝑖	𝑝𝛼𝑖	ADJ
iajs-3094	233	13	≥	≥	PROPN
iajs-3094	233	14	0	0	NUM
iajs-3094	233	15	and	and	CCONJ
iajs-3094	233	16	𝑝𝛼𝑖	𝑝𝛼𝑖	ADJ
iajs-3094	233	17	≤	≤	ADJ
iajs-3094	233	18	𝑝𝛼𝑗	𝑝𝛼𝑗	NOUN
iajs-3094	233	19	)	)	PUNCT
iajs-3094	233	20	.then	.then	X
iajs-3094	233	21	s𝛼𝑖	s𝛼𝑖	VERB
iajs-3094	233	22	≤	≤	NUM
iajs-3094	233	23	s𝛼𝑗	s𝛼𝑗	NOUN
iajs-3094	233	24	,	,	PUNCT
iajs-3094	233	25	for	for	ADP
iajs-3094	233	26	all	all	DET
iajs-3094	233	27	𝑖	𝑖	ADP
iajs-3094	233	28	,	,	PUNCT
iajs-3094	233	29	𝑗	𝑗	INTJ
iajs-3094	233	30	(	(	PUNCT
iajs-3094	233	31	this	this	DET
iajs-3094	233	32	mean	mean	VERB
iajs-3094	233	33	all	all	DET
iajs-3094	233	34	jobs	job	NOUN
iajs-3094	233	35	are	be	AUX
iajs-3094	233	36	ordered	order	VERB
iajs-3094	233	37	in	in	ADP
iajs-3094	233	38	mst	mst	PROPN
iajs-3094	233	39	order	order	NOUN
iajs-3094	233	40	for	for	ADP
iajs-3094	233	41	all	all	PRON
iajs-3094	233	42	𝑖	𝑖	ADP
iajs-3094	233	43	,	,	PUNCT
iajs-3094	233	44	𝑗	𝑗	INTJ
iajs-3094	233	45	in	in	ADP
iajs-3094	233	46	𝛼	𝛼	NOUN
iajs-3094	233	47	)	)	PUNCT
iajs-3094	233	48	,	,	PUNCT
iajs-3094	233	49	then	then	ADV
iajs-3094	233	50	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	233	51	is	be	AUX
iajs-3094	233	52	minimum	minimum	ADJ
iajs-3094	233	53	.	.	PUNCT
iajs-3094	234	1	hence	hence	ADV
iajs-3094	234	2	spt	spt	PROPN
iajs-3094	234	3	gives	give	VERB
iajs-3094	234	4	the	the	DET
iajs-3094	234	5	optimal	optimal	ADJ
iajs-3094	234	6	solution	solution	NOUN
iajs-3094	234	7	for	for	ADP
iajs-3094	234	8	both	both	DET
iajs-3094	234	9	criteria	criterion	NOUN
iajs-3094	234	10	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	234	11	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
iajs-3094	234	12	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	234	13	,	,	PUNCT
iajs-3094	234	14	and	and	CCONJ
iajs-3094	234	15	𝑇𝑚𝑎𝑥(spt	𝑇𝑚𝑎𝑥(spt	ADJ
iajs-3094	234	16	)	)	PUNCT
iajs-3094	235	1	=	=	VERB
iajs-3094	235	2	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	𝑇𝑚𝑎𝑥(𝐸𝐷𝐷	VERB
iajs-3094	235	3	)	)	PUNCT
iajs-3094	235	4	(	(	PUNCT
iajs-3094	235	5	since	since	SCONJ
iajs-3094	235	6	spt	spt	PROPN
iajs-3094	235	7	and	and	CCONJ
iajs-3094	235	8	edd	edd	PROPN
iajs-3094	235	9	are	be	AUX
iajs-3094	235	10	identical	identical	ADJ
iajs-3094	235	11	)	)	PUNCT
iajs-3094	235	12	.	.	PUNCT
iajs-3094	236	1	then	then	ADV
iajs-3094	236	2	spt	spt	PROPN
iajs-3094	236	3	is	be	AUX
iajs-3094	236	4	an	an	DET
iajs-3094	236	5	efso	efso	NOUN
iajs-3094	236	6	for	for	ADP
iajs-3094	236	7	the	the	DET
iajs-3094	236	8	problem	problem	NOUN
iajs-3094	236	9	(	(	PUNCT
iajs-3094	236	10	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	236	11	)	)	PUNCT
iajs-3094	236	12	.	.	PUNCT
iajs-3094	237	1	case(𝟒.	case(𝟒.	NUM
iajs-3094	237	2	𝟏.	𝟏.	SYM
iajs-3094	237	3	𝟗	𝟗	NUM
iajs-3094	237	4	):	):	PUNCT
iajs-3094	237	5	if	if	SCONJ
iajs-3094	237	6	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	237	7	+	+	NUM
iajs-3094	237	8	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	237	9	≤	≤	NOUN
iajs-3094	237	10	𝐶𝑗+1	𝐶𝑗+1	ADJ
iajs-3094	237	11	for	for	ADP
iajs-3094	237	12	𝑗	𝑗	NOUN
iajs-3094	237	13	=	=	SYM
iajs-3094	237	14	1,2	1,2	NUM
iajs-3094	237	15	,	,	PUNCT
iajs-3094	237	16	.	.	PUNCT
iajs-3094	237	17	.	.	PUNCT
iajs-3094	238	1	,	,	PUNCT
iajs-3094	238	2	𝑛	𝑛	DET
iajs-3094	238	3	−	−	NOUN
iajs-3094	238	4	1	1	NUM
iajs-3094	238	5	then	then	ADV
iajs-3094	238	6	the	the	DET
iajs-3094	238	7	spt	spt	PROPN
iajs-3094	238	8	schedule	schedule	NOUN
iajs-3094	238	9	is	be	AUX
iajs-3094	238	10	an	an	DET
iajs-3094	238	11	efso	efso	NOUN
iajs-3094	238	12	for	for	ADP
iajs-3094	238	13	(	(	PUNCT
iajs-3094	238	14	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	238	15	)	)	PUNCT
iajs-3094	238	16	.	.	PUNCT
iajs-3094	239	1	proof	proof	NOUN
iajs-3094	239	2	:	:	PUNCT
iajs-3094	239	3	let	let	VERB
iajs-3094	239	4	𝜎	𝜎	PRON
iajs-3094	239	5	=	=	SYM
iajs-3094	239	6	(	(	PUNCT
iajs-3094	239	7	𝜎1	𝜎1	PROPN
iajs-3094	239	8	,	,	PUNCT
iajs-3094	239	9	𝜎2	𝜎2	NOUN
iajs-3094	239	10	,	,	PUNCT
iajs-3094	239	11	.	.	PUNCT
iajs-3094	239	12	.	.	PUNCT
iajs-3094	240	1	,	,	PUNCT
iajs-3094	240	2	𝜎𝑛	𝜎𝑛	X
iajs-3094	240	3	)	)	PUNCT
iajs-3094	240	4	by	by	ADP
iajs-3094	240	5	spt	spt	ADJ
iajs-3094	240	6	sequence	sequence	NOUN
iajs-3094	240	7	,	,	PUNCT
iajs-3094	240	8	since	since	SCONJ
iajs-3094	240	9	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	240	10	+	+	NUM
iajs-3094	240	11	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	240	12	≤	≤	NOUN
iajs-3094	240	13	𝐶𝑗+1	𝐶𝑗+1	VERB
iajs-3094	240	14	,	,	PUNCT
iajs-3094	240	15	∀𝑗(𝑗	∀𝑗(𝑗	NOUN
iajs-3094	240	16	=	=	SYM
iajs-3094	240	17	1,2	1,2	NUM
iajs-3094	240	18	,	,	PUNCT
iajs-3094	240	19	.	.	PUNCT
iajs-3094	240	20	.	.	PUNCT
iajs-3094	241	1	,	,	PUNCT
iajs-3094	241	2	𝑛	𝑛	DET
iajs-3094	241	3	−	−	NOUN
iajs-3094	241	4	1	1	NUM
iajs-3094	241	5	)	)	PUNCT
iajs-3094	241	6	.	.	PUNCT
iajs-3094	242	1	then	then	ADV
iajs-3094	242	2	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	242	3	≤	≤	PROPN
iajs-3094	242	4	𝐶𝑗+1	𝐶𝑗+1	ADJ
iajs-3094	242	5	−	−	PROPN
iajs-3094	242	6	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	242	7	=	=	PUNCT
iajs-3094	242	8	∑	∑	PUNCT
iajs-3094	242	9	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	242	10	𝑗+1	𝑗+1	X
iajs-3094	242	11	𝑖=1	𝑖=1	PUNCT
iajs-3094	242	12	−	−	PROPN
iajs-3094	242	13	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	243	1	=	=	PUNCT
iajs-3094	243	2	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	243	3	+	+	NUM
iajs-3094	243	4	𝑝𝑗+1	𝑝𝑗+1	PROPN
iajs-3094	243	5	−	−	NOUN
iajs-3094	243	6	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	243	7	∀𝑗(𝑗	∀𝑗(𝑗	NOUN
iajs-3094	243	8	=	=	SYM
iajs-3094	243	9	1,2	1,2	NUM
iajs-3094	243	10	,	,	PUNCT
iajs-3094	243	11	.	.	PUNCT
iajs-3094	243	12	.	.	PUNCT
iajs-3094	244	1	,	,	PUNCT
iajs-3094	244	2	𝑛	𝑛	DET
iajs-3094	244	3	−	−	NOUN
iajs-3094	244	4	1	1	NUM
iajs-3094	244	5	)	)	PUNCT
iajs-3094	244	6	.	.	PUNCT
iajs-3094	245	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	245	2	+	+	NUM
iajs-3094	245	3	𝑝𝑗+1	𝑝𝑗+1	PROPN
iajs-3094	245	4	−	−	NOUN
iajs-3094	245	5	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	245	6	=	=	PUNCT
iajs-3094	245	7	{	{	PUNCT
iajs-3094	245	8	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	245	9	if	if	SCONJ
iajs-3094	245	10	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	245	11	=	=	SYM
iajs-3094	245	12	𝑝𝑗+1	𝑝𝑗+1	PROPN
iajs-3094	245	13	,	,	PUNCT
iajs-3094	245	14	𝑗	𝑗	NOUN
iajs-3094	245	15	=	=	SYM
iajs-3094	245	16	1,2	1,2	NUM
iajs-3094	245	17	,	,	PUNCT
iajs-3094	245	18	.	.	PUNCT
iajs-3094	245	19	.	.	PUNCT
iajs-3094	246	1	,	,	PUNCT
iajs-3094	246	2	𝑛	𝑛	DET
iajs-3094	246	3	−	−	NOUN
iajs-3094	246	4	1	1	NUM
iajs-3094	247	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	247	2	+	+	NOUN
iajs-3094	247	3	𝑝	𝑝	NOUN
iajs-3094	247	4	if	if	SCONJ
iajs-3094	247	5	𝑝	𝑝	NOUN
iajs-3094	247	6	=	=	SYM
iajs-3094	247	7	𝑝𝑗+1	𝑝𝑗+1	PROPN
iajs-3094	247	8	−	−	PROPN
iajs-3094	247	9	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	247	10	,	,	PUNCT
iajs-3094	247	11	𝑗	𝑗	NOUN
iajs-3094	247	12	=	=	SYM
iajs-3094	247	13	1,2	1,2	NUM
iajs-3094	247	14	,	,	PUNCT
iajs-3094	247	15	.	.	PUNCT
iajs-3094	247	16	.	.	PUNCT
iajs-3094	248	1	,	,	PUNCT
iajs-3094	248	2	𝑛	𝑛	DET
iajs-3094	248	3	−	−	PROPN
iajs-3094	248	4	1	1	NUM
iajs-3094	248	5	}	}	PUNCT
iajs-3094	248	6	(	(	PUNCT
iajs-3094	248	7	1	1	X
iajs-3094	248	8	)	)	PUNCT
iajs-3094	248	9	since	since	SCONJ
iajs-3094	248	10	𝜎	𝜎	PROPN
iajs-3094	248	11	is	be	AUX
iajs-3094	248	12	the	the	DET
iajs-3094	248	13	spt	spt	PROPN
iajs-3094	248	14	schedule	schedule	NOUN
iajs-3094	248	15	,	,	PUNCT
iajs-3094	248	16	there	there	PRON
iajs-3094	248	17	are	be	VERB
iajs-3094	248	18	two	two	NUM
iajs-3094	248	19	cases	case	NOUN
iajs-3094	248	20	:	:	PUNCT
iajs-3094	248	21	ihjpas	ihjpa	NOUN
iajs-3094	248	22	.	.	PUNCT
iajs-3094	249	1	37	37	NUM
iajs-3094	249	2	(	(	PUNCT
iajs-3094	249	3	1	1	NUM
iajs-3094	249	4	)	)	PUNCT
iajs-3094	249	5	2024	2024	NUM
iajs-3094	249	6	395	395	NUM
iajs-3094	249	7	a	a	DET
iajs-3094	249	8	)	)	PUNCT
iajs-3094	249	9	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	249	10	=	=	SYM
iajs-3094	249	11	𝑝𝑗+1	𝑝𝑗+1	PROPN
iajs-3094	249	12	,	,	PUNCT
iajs-3094	249	13	for	for	ADP
iajs-3094	249	14	𝑗	𝑗	NOUN
iajs-3094	249	15	=	=	SYM
iajs-3094	249	16	1,2	1,2	NUM
iajs-3094	249	17	,	,	PUNCT
iajs-3094	249	18	.	.	PUNCT
iajs-3094	249	19	.	.	PUNCT
iajs-3094	250	1	,	,	PUNCT
iajs-3094	251	1	𝑛	𝑛	PRON
iajs-3094	251	2	−	−	NOUN
iajs-3094	251	3	1	1	NUM
iajs-3094	251	4	and	and	CCONJ
iajs-3094	251	5	equation	equation	NOUN
iajs-3094	251	6	(	(	PUNCT
iajs-3094	251	7	1	1	NUM
iajs-3094	251	8	)	)	PUNCT
iajs-3094	251	9	.	.	PUNCT
iajs-3094	252	1	hence	hence	ADV
iajs-3094	252	2	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	252	3	≤	≤	NOUN
iajs-3094	252	4	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	252	5	(	(	PUNCT
iajs-3094	252	6	this	this	PRON
iajs-3094	252	7	means	mean	VERB
iajs-3094	252	8	all	all	DET
iajs-3094	252	9	jobs	job	NOUN
iajs-3094	252	10	are	be	AUX
iajs-3094	252	11	late	late	ADJ
iajs-3094	252	12	s.	s.	PROPN
iajs-3094	252	13	t.	t.	PROPN
iajs-3094	253	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	253	2	=	=	SYM
iajs-3094	253	3	0	0	PUNCT
iajs-3094	253	4	=	=	SYM
iajs-3094	253	5	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	253	6	)	)	PUNCT
iajs-3094	253	7	.	.	PUNCT
iajs-3094	254	1	the	the	DET
iajs-3094	254	2	problem	problem	NOUN
iajs-3094	254	3	1	1	NUM
iajs-3094	254	4	∕∕	∕∕	SYM
iajs-3094	254	5	(	(	PUNCT
iajs-3094	254	6	∑𝐶𝑗	∑𝐶𝑗	INTJ
iajs-3094	254	7	,	,	PUNCT
iajs-3094	254	8	∑	∑	PROPN
iajs-3094	254	9	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	254	10	,	,	PUNCT
iajs-3094	254	11	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	254	12	)	)	PUNCT
iajs-3094	254	13	reduced	reduce	VERB
iajs-3094	254	14	to	to	ADP
iajs-3094	254	15	1//	1//	NUM
iajs-3094	254	16	(	(	PUNCT
iajs-3094	254	17	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	254	18	,	,	PUNCT
iajs-3094	254	19	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	254	20	)	)	PUNCT
iajs-3094	254	21	,	,	PUNCT
iajs-3094	254	22	so	so	ADV
iajs-3094	254	23	spt	spt	ADJ
iajs-3094	254	24	schedule	schedule	NOUN
iajs-3094	254	25	is	be	AUX
iajs-3094	254	26	an	an	DET
iajs-3094	254	27	efso	efso	NOUN
iajs-3094	254	28	.	.	PUNCT
iajs-3094	255	1	b	b	X
iajs-3094	255	2	)	)	PUNCT
iajs-3094	255	3	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	255	4	<	<	X
iajs-3094	255	5	𝑝𝑗+1	𝑝𝑗+1	NUM
iajs-3094	255	6	,	,	PUNCT
iajs-3094	255	7	for	for	ADP
iajs-3094	255	8	𝑗	𝑗	NOUN
iajs-3094	255	9	=	=	SYM
iajs-3094	255	10	1,2	1,2	NUM
iajs-3094	255	11	,	,	PUNCT
iajs-3094	255	12	.	.	PUNCT
iajs-3094	255	13	.	.	PUNCT
iajs-3094	256	1	,	,	PUNCT
iajs-3094	256	2	𝑛	𝑛	DET
iajs-3094	256	3	−	−	NOUN
iajs-3094	256	4	1	1	NUM
iajs-3094	256	5	and	and	CCONJ
iajs-3094	256	6	by	by	ADP
iajs-3094	256	7	(	(	PUNCT
iajs-3094	256	8	4.1),then	4.1),then	PRON
iajs-3094	256	9	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	256	10	≤	≤	PROPN
iajs-3094	257	1	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	257	2	+	+	NUM
iajs-3094	257	3	𝑝	𝑝	PROPN
iajs-3094	257	4	,	,	PUNCT
iajs-3094	257	5	𝑝	𝑝	NOUN
iajs-3094	257	6	>	>	X
iajs-3094	257	7	0	0	PUNCT
iajs-3094	258	1	then	then	ADV
iajs-3094	258	2	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	258	3	−	−	PROPN
iajs-3094	259	1	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	259	2	≤	≤	PROPN
iajs-3094	259	3	𝑝	𝑝	PROPN
iajs-3094	259	4	(	(	PUNCT
iajs-3094	259	5	this	this	PRON
iajs-3094	259	6	means	mean	VERB
iajs-3094	259	7	all	all	DET
iajs-3094	259	8	jobs	job	NOUN
iajs-3094	259	9	are	be	AUX
iajs-3094	259	10	late	late	ADJ
iajs-3094	259	11	𝑠.	𝑠.	NOUN
iajs-3094	259	12	𝑡.	𝑡.	NOUN
iajs-3094	260	1	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	260	2	=	=	SYM
iajs-3094	260	3	0	0	PUNCT
iajs-3094	260	4	=	=	SYM
iajs-3094	260	5	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	260	6	)	)	PUNCT
iajs-3094	260	7	,	,	PUNCT
iajs-3094	260	8	hence	hence	ADV
iajs-3094	260	9	1	1	NUM
iajs-3094	260	10	∕∕	∕∕	SYM
iajs-3094	260	11	(	(	PUNCT
iajs-3094	260	12	∑𝐶𝑗	∑𝐶𝑗	INTJ
iajs-3094	260	13	,	,	PUNCT
iajs-3094	260	14	∑	∑	PUNCT
iajs-3094	260	15	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	260	16	,	,	PUNCT
iajs-3094	260	17	𝑇𝑚𝑎𝑥)reduced	𝑇𝑚𝑎𝑥)reduce	VERB
iajs-3094	260	18	to	to	ADP
iajs-3094	260	19	1//	1//	NUM
iajs-3094	260	20	(	(	PUNCT
iajs-3094	260	21	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	260	22	,	,	PUNCT
iajs-3094	260	23	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	260	24	)	)	PUNCT
iajs-3094	260	25	,	,	PUNCT
iajs-3094	260	26	also	also	ADV
iajs-3094	260	27	spt	spt	ADJ
iajs-3094	260	28	rule	rule	NOUN
iajs-3094	260	29	is	be	AUX
iajs-3094	260	30	an	an	DET
iajs-3094	260	31	efso	efso	NOUN
iajs-3094	260	32	.	.	PUNCT
iajs-3094	261	1	case(𝟒.	case(𝟒.	NUM
iajs-3094	261	2	𝟏.	𝟏.	X
iajs-3094	261	3	𝟏𝟎	𝟏𝟎	NUM
iajs-3094	261	4	):	):	PUNCT
iajs-3094	261	5	if	if	SCONJ
iajs-3094	261	6	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	261	7	≥	≥	NUM
iajs-3094	261	8	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	261	9	and	and	CCONJ
iajs-3094	261	10	spt	spt	PROPN
iajs-3094	261	11	,	,	PUNCT
iajs-3094	261	12	edd	edd	PROPN
iajs-3094	261	13	rules	rule	NOUN
iajs-3094	261	14	are	be	AUX
iajs-3094	261	15	identical	identical	ADJ
iajs-3094	261	16	for	for	ADP
iajs-3094	261	17	all	all	DET
iajs-3094	261	18	𝑗	𝑗	NOUN
iajs-3094	261	19	in	in	ADP
iajs-3094	261	20	a	a	DET
iajs-3094	261	21	schedule	schedule	NOUN
iajs-3094	261	22	𝛼	𝛼	NOUN
iajs-3094	261	23	,	,	PUNCT
iajs-3094	261	24	then	then	ADV
iajs-3094	261	25	𝛼	𝛼	PRON
iajs-3094	261	26	schedule	schedule	NOUN
iajs-3094	261	27	gives	give	VERB
iajs-3094	261	28	an	an	DET
iajs-3094	261	29	efso	efso	NOUN
iajs-3094	261	30	for	for	ADP
iajs-3094	261	31	(	(	PUNCT
iajs-3094	261	32	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	261	33	)	)	PUNCT
iajs-3094	261	34	.	.	PUNCT
iajs-3094	262	1	proof	proof	NOUN
iajs-3094	262	2	:	:	PUNCT
iajs-3094	262	3	let	let	VERB
iajs-3094	262	4	σ	σ	NOUN
iajs-3094	262	5	be	be	AUX
iajs-3094	262	6	an	an	DET
iajs-3094	262	7	spt	spt	ADJ
iajs-3094	262	8	schedule	schedule	NOUN
iajs-3094	262	9	with	with	ADP
iajs-3094	262	10	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	262	11	≥	≥	NUM
iajs-3094	262	12	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	262	13	for	for	ADP
iajs-3094	262	14	each	each	DET
iajs-3094	262	15	𝑗	𝑗	NOUN
iajs-3094	262	16	in	in	ADP
iajs-3094	262	17	𝜎	𝜎	PROPN
iajs-3094	262	18	(	(	PUNCT
iajs-3094	262	19	this	this	PRON
iajs-3094	262	20	means	mean	VERB
iajs-3094	262	21	that	that	SCONJ
iajs-3094	262	22	all	all	DET
iajs-3094	262	23	jobs	job	NOUN
iajs-3094	262	24	in	in	ADP
iajs-3094	262	25	the	the	DET
iajs-3094	262	26	spt	spt	PROPN
iajs-3094	262	27	schedule	schedule	NOUN
iajs-3094	262	28	are	be	AUX
iajs-3094	262	29	late	late	ADJ
iajs-3094	262	30	)	)	PUNCT
iajs-3094	262	31	,	,	PUNCT
iajs-3094	262	32	hence	hence	ADV
iajs-3094	262	33	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	262	34	=	=	SYM
iajs-3094	262	35	0	0	PUNCT
iajs-3094	262	36	=	=	SYM
iajs-3094	262	37	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	262	38	for	for	ADP
iajs-3094	262	39	all	all	DET
iajs-3094	262	40	𝑗	𝑗	PROPN
iajs-3094	262	41	in	in	ADP
iajs-3094	262	42	𝛼.	𝛼.	NOUN
iajs-3094	262	43	then	then	ADV
iajs-3094	262	44	1//	1//	NUM
iajs-3094	262	45	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	262	46	,	,	PUNCT
iajs-3094	262	47	∑	∑	PUNCT
iajs-3094	262	48	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	262	49	,	,	PUNCT
iajs-3094	262	50	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	262	51	)	)	PUNCT
iajs-3094	262	52	reduced	reduce	VERB
iajs-3094	262	53	to	to	ADP
iajs-3094	262	54	1//(∑𝐶𝑗	1//(∑𝐶𝑗	NUM
iajs-3094	262	55	,	,	PUNCT
iajs-3094	262	56	𝑇𝑚𝑎𝑥).hence	𝑇𝑚𝑎𝑥).hence	SCONJ
iajs-3094	262	57	spt	spt	ADJ
iajs-3094	262	58	schedule	schedule	NOUN
iajs-3094	262	59	is	be	AUX
iajs-3094	262	60	efficient	efficient	ADJ
iajs-3094	262	61	for	for	ADP
iajs-3094	262	62	(	(	PUNCT
iajs-3094	262	63	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	262	64	)	)	PUNCT
iajs-3094	262	65	.	.	PUNCT
iajs-3094	263	1	case(4.1.11	case(4.1.11	NOUN
iajs-3094	263	2	):	):	PUNCT
iajs-3094	263	3	if	if	SCONJ
iajs-3094	263	4	the	the	DET
iajs-3094	263	5	spt	spt	PROPN
iajs-3094	263	6	schedule	schedule	NOUN
iajs-3094	263	7	gives	give	VERB
iajs-3094	263	8	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	263	9	≤	≤	NOUN
iajs-3094	263	10	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	263	11	∀𝑖	∀𝑖	PROPN
iajs-3094	263	12	∈	∈	PROPN
iajs-3094	263	13	𝑁	𝑁	PROPN
iajs-3094	263	14	then	then	ADV
iajs-3094	263	15	this	this	DET
iajs-3094	263	16	spt	spt	PROPN
iajs-3094	263	17	schedule	schedule	NOUN
iajs-3094	263	18	gives	give	VERB
iajs-3094	263	19	an	an	DET
iajs-3094	263	20	efso	efso	NOUN
iajs-3094	263	21	for	for	ADP
iajs-3094	263	22	(	(	PUNCT
iajs-3094	263	23	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	263	24	)	)	PUNCT
iajs-3094	263	25	.	.	PUNCT
iajs-3094	264	1	proof	proof	NOUN
iajs-3094	264	2	:	:	PUNCT
iajs-3094	264	3	since	since	SCONJ
iajs-3094	264	4	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	264	5	≤	≤	NOUN
iajs-3094	264	6	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	264	7	for	for	ADP
iajs-3094	264	8	all	all	DET
iajs-3094	264	9	𝑗	𝑗	NOUN
iajs-3094	264	10	in	in	ADP
iajs-3094	264	11	the	the	DET
iajs-3094	264	12	spt	spt	PROPN
iajs-3094	264	13	schedule	schedule	NOUN
iajs-3094	264	14	(	(	PUNCT
iajs-3094	264	15	this	this	PRON
iajs-3094	264	16	means	mean	VERB
iajs-3094	264	17	all	all	DET
iajs-3094	264	18	jobs	job	NOUN
iajs-3094	264	19	are	be	AUX
iajs-3094	264	20	early	early	ADV
iajs-3094	264	21	s.	s.	PROPN
iajs-3094	265	1	t.	t.	PROPN
iajs-3094	265	2	𝑇𝑗	𝑇𝑗	PROPN
iajs-3094	265	3	=	=	SYM
iajs-3094	265	4	0	0	PUNCT
iajs-3094	266	1	=	=	SYM
iajs-3094	266	2	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	266	3	for	for	ADP
iajs-3094	266	4	all	all	DET
iajs-3094	266	5	𝑗	𝑗	NOUN
iajs-3094	266	6	)	)	PUNCT
iajs-3094	266	7	and	and	CCONJ
iajs-3094	266	8	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	266	9	=	=	PUNCT
iajs-3094	266	10	𝑚𝑎𝑥{−𝐿𝑗	𝑚𝑎𝑥{−𝐿𝑗	X
iajs-3094	266	11	,	,	PUNCT
iajs-3094	266	12	0	0	X
iajs-3094	266	13	}	}	PUNCT
iajs-3094	266	14	then	then	ADV
iajs-3094	266	15	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	266	16	=	=	PUNCT
iajs-3094	266	17	∑𝑚𝑎𝑥{−𝐿𝑗	∑𝑚𝑎𝑥{−𝐿𝑗	ADJ
iajs-3094	266	18	,	,	PUNCT
iajs-3094	266	19	0	0	NUM
iajs-3094	266	20	}	}	PUNCT
iajs-3094	266	21	for	for	ADP
iajs-3094	266	22	all	all	DET
iajs-3094	266	23	𝑗.	𝑗.	NOUN
iajs-3094	266	24	hence	hence	ADV
iajs-3094	266	25	1//	1//	NUM
iajs-3094	266	26	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	266	27	,	,	PUNCT
iajs-3094	266	28	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	266	29	,	,	PUNCT
iajs-3094	266	30	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	266	31	)	)	PUNCT
iajs-3094	266	32	reduced	reduce	VERB
iajs-3094	266	33	to	to	ADP
iajs-3094	266	34	1//	1//	NUM
iajs-3094	266	35	(	(	PUNCT
iajs-3094	266	36	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	266	37	,	,	PUNCT
iajs-3094	266	38	∑	∑	ADV
iajs-3094	266	39	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	266	40	)	)	PUNCT
iajs-3094	266	41	.	.	PUNCT
iajs-3094	267	1	hence	hence	ADV
iajs-3094	267	2	spt	spt	PROPN
iajs-3094	267	3	rule	rule	NOUN
iajs-3094	267	4	gives	give	VERB
iajs-3094	267	5	an	an	DET
iajs-3094	267	6	efso	efso	NOUN
iajs-3094	267	7	.	.	PUNCT
iajs-3094	268	1	4.2	4.2	NUM
iajs-3094	268	2	special	special	ADJ
iajs-3094	268	3	cases	case	NOUN
iajs-3094	268	4	for	for	ADP
iajs-3094	268	5	subproblem	subproblem	NOUN
iajs-3094	268	6	(	(	PUNCT
iajs-3094	268	7	s₱7	s₱7	PROPN
iajs-3094	268	8	)	)	PUNCT
iajs-3094	268	9	we	we	PRON
iajs-3094	268	10	introduce	introduce	VERB
iajs-3094	268	11	some	some	DET
iajs-3094	268	12	special	special	ADJ
iajs-3094	268	13	cases	case	NOUN
iajs-3094	268	14	for	for	ADP
iajs-3094	268	15	the	the	DET
iajs-3094	268	16	problem	problem	NOUN
iajs-3094	268	17	(	(	PUNCT
iajs-3094	268	18	s₱7)that	s₱7)that	PRON
iajs-3094	268	19	has	have	AUX
iajs-3094	268	20	optimal	optimal	ADJ
iajs-3094	268	21	solutions	solution	NOUN
iajs-3094	268	22	in	in	ADP
iajs-3094	268	23	this	this	DET
iajs-3094	268	24	section	section	NOUN
iajs-3094	268	25	.	.	PUNCT
iajs-3094	269	1	case(4.2.1	case(4.2.1	NOUN
iajs-3094	269	2	):	):	PUNCT
iajs-3094	269	3	if	if	SCONJ
iajs-3094	269	4	𝑝1	𝑝1	NOUN
iajs-3094	269	5	=	=	SYM
iajs-3094	269	6	𝑑1and	𝑑1and	PROPN
iajs-3094	269	7	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	269	8	=	=	SYM
iajs-3094	269	9	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	269	10	−	−	PROPN
iajs-3094	269	11	𝑑𝑗−1	𝑑𝑗−1	NOUN
iajs-3094	269	12	,	,	PUNCT
iajs-3094	269	13	for	for	ADP
iajs-3094	269	14	all	all	DET
iajs-3094	269	15	𝑗	𝑗	NOUN
iajs-3094	269	16	in	in	ADP
iajs-3094	269	17	𝛼	𝛼	PROPN
iajs-3094	269	18	(	(	PUNCT
iajs-3094	269	19	except	except	SCONJ
iajs-3094	269	20	1	1	NUM
iajs-3094	269	21	)	)	PUNCT
iajs-3094	269	22	then	then	ADV
iajs-3094	269	23	spt	spt	PROPN
iajs-3094	269	24	schedule	schedule	NOUN
iajs-3094	269	25	𝛼	𝛼	PRON
iajs-3094	269	26	gives	give	VERB
iajs-3094	269	27	an	an	DET
iajs-3094	269	28	optimal	optimal	ADJ
iajs-3094	269	29	solution	solution	NOUN
iajs-3094	269	30	for	for	ADP
iajs-3094	269	31	the	the	DET
iajs-3094	269	32	problem	problem	NOUN
iajs-3094	269	33	1//	1//	NUM
iajs-3094	269	34	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	269	35	+	+	NUM
iajs-3094	269	36	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	269	37	+	+	NOUN
iajs-3094	269	38	𝑇𝑚𝑎𝑥.	𝑇𝑚𝑎𝑥.	NOUN
iajs-3094	269	39	proof	proof	NOUN
iajs-3094	269	40	:	:	PUNCT
iajs-3094	269	41	proof	proof	NOUN
iajs-3094	269	42	as	as	ADP
iajs-3094	269	43	in	in	ADP
iajs-3094	269	44	case	case	NOUN
iajs-3094	269	45	(	(	PUNCT
iajs-3094	269	46	4.1.1	4.1.1	NUM
iajs-3094	269	47	)	)	PUNCT
iajs-3094	269	48	and	and	CCONJ
iajs-3094	269	49	(	(	PUNCT
iajs-3094	269	50	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	269	51	+	+	NUM
iajs-3094	269	52	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	269	53	+	+	CCONJ
iajs-3094	269	54	𝑇𝑚𝑎𝑥)=∑𝐶𝑗.	𝑇𝑚𝑎𝑥)=∑𝐶𝑗.	NUM
iajs-3094	270	1	case(4.2.2	case(4.2.2	NUM
iajs-3094	270	2	):	):	PUNCT
iajs-3094	270	3	if	if	SCONJ
iajs-3094	270	4	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	270	5	=	=	SYM
iajs-3094	270	6	𝑝	𝑝	PROPN
iajs-3094	270	7	and	and	CCONJ
iajs-3094	270	8	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	270	9	=	=	SYM
iajs-3094	270	10	𝑗𝑝	𝑗𝑝	PROPN
iajs-3094	270	11	for	for	ADP
iajs-3094	270	12	all	all	DET
iajs-3094	270	13	𝑗	𝑗	NOUN
iajs-3094	270	14	in	in	ADP
iajs-3094	270	15	the	the	DET
iajs-3094	270	16	schedule	schedule	NOUN
iajs-3094	270	17	σ	σ	PROPN
iajs-3094	270	18	,	,	PUNCT
iajs-3094	270	19	then	then	ADV
iajs-3094	270	20	𝜎	𝜎	PROPN
iajs-3094	270	21	gives	give	VERB
iajs-3094	270	22	an	an	DET
iajs-3094	270	23	optimal	optimal	ADJ
iajs-3094	270	24	solution	solution	NOUN
iajs-3094	270	25	for	for	ADP
iajs-3094	270	26	the	the	DET
iajs-3094	270	27	problem	problem	NOUN
iajs-3094	270	28	1//	1//	NUM
iajs-3094	270	29	(	(	PUNCT
iajs-3094	270	30	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	270	31	+	+	NUM
iajs-3094	270	32	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	270	33	+	+	CCONJ
iajs-3094	270	34	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	270	35	)	)	PUNCT
iajs-3094	270	36	.	.	PUNCT
iajs-3094	271	1	proof	proof	NOUN
iajs-3094	271	2	:	:	PUNCT
iajs-3094	271	3	verified	verify	VERB
iajs-3094	271	4	by	by	ADP
iajs-3094	271	5	the	the	DET
iajs-3094	271	6	case	case	NOUN
iajs-3094	271	7	(	(	PUNCT
iajs-3094	271	8	4.1.2	4.1.2	NUM
iajs-3094	271	9	)	)	PUNCT
iajs-3094	271	10	,	,	PUNCT
iajs-3094	271	11	hence	hence	ADV
iajs-3094	271	12	(	(	PUNCT
iajs-3094	271	13	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	271	14	+	+	NUM
iajs-3094	271	15	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	271	16	+	+	CCONJ
iajs-3094	271	17	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	271	18	)	)	PUNCT
iajs-3094	271	19	=	=	PUNCT
iajs-3094	271	20	∑	∑	PUNCT
iajs-3094	271	21	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	271	22	𝓃	𝓃	NOUN
iajs-3094	271	23	𝑗=1	𝑗=1	X
iajs-3094	271	24	=	=	SYM
iajs-3094	271	25	𝑝	𝑝	PROPN
iajs-3094	271	26	(	(	PUNCT
iajs-3094	271	27	𝑛2+𝑛	𝑛2+𝑛	PROPN
iajs-3094	271	28	2	2	NUM
iajs-3094	271	29	)	)	PUNCT
iajs-3094	271	30	.	.	PUNCT
iajs-3094	272	1	case	case	NOUN
iajs-3094	272	2	(	(	PUNCT
iajs-3094	272	3	4.2.3	4.2.3	NUM
iajs-3094	272	4	):	):	PUNCT
iajs-3094	272	5	if	if	SCONJ
iajs-3094	272	6	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	272	7	=	=	SYM
iajs-3094	272	8	𝑘𝑝𝑗	𝑘𝑝𝑗	NOUN
iajs-3094	272	9	for	for	ADP
iajs-3094	272	10	all	all	DET
iajs-3094	272	11	𝑘	𝑘	DET
iajs-3094	272	12	≥	≥	NOUN
iajs-3094	272	13	2	2	NUM
iajs-3094	272	14	then	then	ADV
iajs-3094	272	15	the	the	DET
iajs-3094	272	16	spt	spt	PROPN
iajs-3094	272	17	schedule	schedule	NOUN
iajs-3094	272	18	is	be	AUX
iajs-3094	272	19	an	an	DET
iajs-3094	272	20	optimal	optimal	ADJ
iajs-3094	272	21	solution	solution	NOUN
iajs-3094	272	22	for	for	ADP
iajs-3094	272	23	the	the	DET
iajs-3094	272	24	problem	problem	NOUN
iajs-3094	272	25	(	(	PUNCT
iajs-3094	272	26	s₱7	s₱7	PROPN
iajs-3094	272	27	)	)	PUNCT
iajs-3094	272	28	.	.	PUNCT
iajs-3094	273	1	proof	proof	NOUN
iajs-3094	273	2	:	:	PUNCT
iajs-3094	273	3	proof	proof	NOUN
iajs-3094	273	4	as	as	ADP
iajs-3094	273	5	in	in	ADP
iajs-3094	273	6	case	case	NOUN
iajs-3094	273	7	(	(	PUNCT
iajs-3094	273	8	4.1.3	4.1.3	NUM
iajs-3094	273	9	)	)	PUNCT
iajs-3094	273	10	.	.	PUNCT
iajs-3094	274	1	case	case	NOUN
iajs-3094	274	2	(	(	PUNCT
iajs-3094	274	3	4.2.4	4.2.4	NUM
iajs-3094	274	4	):	):	PUNCT
iajs-3094	274	5	if	if	SCONJ
iajs-3094	274	6	spt	spt	PROPN
iajs-3094	274	7	and	and	CCONJ
iajs-3094	274	8	mst	mst	PROPN
iajs-3094	274	9	are	be	AUX
iajs-3094	274	10	identical	identical	ADJ
iajs-3094	274	11	then	then	ADV
iajs-3094	274	12	they	they	PRON
iajs-3094	274	13	give	give	VERB
iajs-3094	274	14	an	an	DET
iajs-3094	274	15	optimal	optimal	ADJ
iajs-3094	274	16	schedule	schedule	NOUN
iajs-3094	274	17	for	for	ADP
iajs-3094	274	18	the	the	DET
iajs-3094	274	19	problem	problem	NOUN
iajs-3094	274	20	(	(	PUNCT
iajs-3094	274	21	s₱7	s₱7	PROPN
iajs-3094	274	22	)	)	PUNCT
iajs-3094	274	23	.	.	PUNCT
iajs-3094	275	1	proof	proof	NOUN
iajs-3094	275	2	:	:	PUNCT
iajs-3094	275	3	proof	proof	NOUN
iajs-3094	275	4	as	as	ADP
iajs-3094	275	5	in	in	ADP
iajs-3094	275	6	case	case	NOUN
iajs-3094	275	7	(	(	PUNCT
iajs-3094	275	8	4.1.4	4.1.4	NUM
iajs-3094	275	9	)	)	PUNCT
iajs-3094	275	10	.	.	PUNCT
iajs-3094	276	1	case	case	NOUN
iajs-3094	276	2	(	(	PUNCT
iajs-3094	276	3	4.2.5	4.2.5	NUM
iajs-3094	276	4	):	):	PUNCT
iajs-3094	276	5	if	if	SCONJ
iajs-3094	276	6	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	276	7	=	=	SYM
iajs-3094	276	8	𝑝	𝑝	PROPN
iajs-3094	276	9	∀𝑗	∀𝑗	NOUN
iajs-3094	276	10	∈	∈	PROPN
iajs-3094	276	11	𝑁	𝑁	PROPN
iajs-3094	276	12	,	,	PUNCT
iajs-3094	276	13	then	then	ADV
iajs-3094	276	14	the	the	DET
iajs-3094	276	15	edd	edd	PROPN
iajs-3094	276	16	schedule	schedule	NOUN
iajs-3094	276	17	is	be	AUX
iajs-3094	276	18	an	an	DET
iajs-3094	276	19	optimal	optimal	ADJ
iajs-3094	276	20	schedule	schedule	NOUN
iajs-3094	276	21	for	for	ADP
iajs-3094	276	22	(	(	PUNCT
iajs-3094	276	23	s₱7	s₱7	PROPN
iajs-3094	276	24	)	)	PUNCT
iajs-3094	276	25	.	.	PUNCT
iajs-3094	277	1	proof	proof	NOUN
iajs-3094	277	2	:	:	PUNCT
iajs-3094	277	3	proof	proof	NOUN
iajs-3094	277	4	as	as	ADP
iajs-3094	277	5	in	in	ADP
iajs-3094	277	6	case	case	NOUN
iajs-3094	277	7	(	(	PUNCT
iajs-3094	277	8	4.1.5	4.1.5	NUM
iajs-3094	277	9	)	)	PUNCT
iajs-3094	277	10	.	.	PUNCT
iajs-3094	278	1	case(4.2.6	case(4.2.6	PROPN
iajs-3094	278	2	):	):	PUNCT
iajs-3094	278	3	if	if	SCONJ
iajs-3094	278	4	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	278	5	=	=	SYM
iajs-3094	278	6	𝑑	𝑑	NOUN
iajs-3094	278	7	,	,	PUNCT
iajs-3094	278	8	and	and	CCONJ
iajs-3094	278	9	spt	spt	PROPN
iajs-3094	278	10	and	and	CCONJ
iajs-3094	278	11	mst	mst	PROPN
iajs-3094	278	12	are	be	AUX
iajs-3094	278	13	identical	identical	ADJ
iajs-3094	278	14	∀𝑗	∀𝑗	NOUN
iajs-3094	278	15	,	,	PUNCT
iajs-3094	278	16	(	(	PUNCT
iajs-3094	278	17	𝑗	𝑗	NOUN
iajs-3094	278	18	=	=	SYM
iajs-3094	278	19	1,2	1,2	NUM
iajs-3094	278	20	,	,	PUNCT
iajs-3094	278	21	…	…	PUNCT
iajs-3094	278	22	,	,	PUNCT
iajs-3094	278	23	𝑛	𝑛	X
iajs-3094	278	24	)	)	PUNCT
iajs-3094	278	25	in	in	ADP
iajs-3094	278	26	schedule	schedule	NOUN
iajs-3094	278	27	𝛼	𝛼	PRON
iajs-3094	278	28	then	then	ADV
iajs-3094	278	29	the	the	DET
iajs-3094	278	30	𝛼	𝛼	NOUN
iajs-3094	278	31	gives	give	VERB
iajs-3094	278	32	an	an	DET
iajs-3094	278	33	optimal	optimal	ADJ
iajs-3094	278	34	value	value	NOUN
iajs-3094	278	35	for	for	ADP
iajs-3094	278	36	(	(	PUNCT
iajs-3094	278	37	s₱7	s₱7	PROPN
iajs-3094	278	38	)	)	PUNCT
iajs-3094	278	39	.	.	PUNCT
iajs-3094	279	1	proof	proof	NOUN
iajs-3094	279	2	:	:	PUNCT
iajs-3094	279	3	proof	proof	NOUN
iajs-3094	279	4	as	as	ADP
iajs-3094	279	5	in	in	ADP
iajs-3094	279	6	case	case	NOUN
iajs-3094	279	7	(	(	PUNCT
iajs-3094	279	8	4.1.6	4.1.6	NUM
iajs-3094	279	9	)	)	PUNCT
iajs-3094	279	10	,	,	PUNCT
iajs-3094	279	11	and	and	CCONJ
iajs-3094	279	12	ihjpas	ihjpa	VERB
iajs-3094	279	13	.	.	PUNCT
iajs-3094	280	1	37	37	NUM
iajs-3094	280	2	(	(	PUNCT
iajs-3094	280	3	1	1	NUM
iajs-3094	280	4	)	)	PUNCT
iajs-3094	280	5	2024	2024	NUM
iajs-3094	280	6	396	396	NUM
iajs-3094	280	7	∑	∑	PUNCT
iajs-3094	280	8	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	280	9	𝑛	𝑛	PRON
iajs-3094	280	10	𝑗=1	𝑗=1	PROPN
iajs-3094	280	11	+	+	PUNCT
iajs-3094	280	12	∑	∑	PROPN
iajs-3094	280	13	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	280	14	𝑛	𝑛	PRON
iajs-3094	280	15	𝑗=1	𝑗=1	PROPN
iajs-3094	280	16	+	+	CCONJ
iajs-3094	280	17	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	280	18	=	=	PUNCT
iajs-3094	280	19	{	{	PUNCT
iajs-3094	280	20	∑	∑	PROPN
iajs-3094	280	21	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	280	22	𝑛	𝑛	PRON
iajs-3094	280	23	𝑗=1	𝑗=1	PROPN
iajs-3094	280	24	+	+	CCONJ
iajs-3094	280	25	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	280	26	,	,	PUNCT
iajs-3094	280	27	,	,	PUNCT
iajs-3094	280	28	if	if	SCONJ
iajs-3094	280	29	𝑑	𝑑	PRON
iajs-3094	280	30	=	=	VERB
iajs-3094	280	31	𝑝𝑗(𝑖.	𝑝𝑗(𝑖.	NOUN
iajs-3094	280	32	𝑒.	𝑒.	NOUN
iajs-3094	280	33	,	,	PUNCT
iajs-3094	281	1	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	281	2	≥	≥	NUM
iajs-3094	281	3	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	281	4	=	=	SYM
iajs-3094	281	5	𝑑	𝑑	NOUN
iajs-3094	281	6	)	)	PUNCT
iajs-3094	281	7	∑	∑	PUNCT
iajs-3094	281	8	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	281	9	𝑛	𝑛	PRON
iajs-3094	281	10	𝑗=1	𝑗=1	PROPN
iajs-3094	281	11	+	+	PUNCT
iajs-3094	281	12	∑	∑	PROPN
iajs-3094	281	13	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	281	14	𝑛	𝑛	PRON
iajs-3094	281	15	𝑗=1	𝑗=1	PROPN
iajs-3094	281	16	+	+	CCONJ
iajs-3094	281	17	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	281	18	=	=	SYM
iajs-3094	281	19	∑	∑	PART
iajs-3094	281	20	𝑑𝑛	𝑑𝑛	NOUN
iajs-3094	281	21	𝑗=1	𝑗=1	PROPN
iajs-3094	281	22	+	+	CCONJ
iajs-3094	282	1	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	282	2	,	,	PUNCT
iajs-3094	282	3	if	if	SCONJ
iajs-3094	282	4	𝑑	𝑑	PROPN
iajs-3094	282	5	>	>	X
iajs-3094	282	6	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	282	7	then	then	ADV
iajs-3094	282	8	either	either	CCONJ
iajs-3094	282	9	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	282	10	≥	≥	NUM
iajs-3094	282	11	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	282	12	or	or	CCONJ
iajs-3094	282	13	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	282	14	<	<	X
iajs-3094	282	15	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	282	16	.	.	PUNCT
iajs-3094	283	1	case	case	NOUN
iajs-3094	283	2	(	(	PUNCT
iajs-3094	283	3	4.2.7	4.2.7	NUM
iajs-3094	283	4	):	):	PUNCT
iajs-3094	283	5	any	any	DET
iajs-3094	283	6	schedule	schedule	NOUN
iajs-3094	283	7	gives	give	VERB
iajs-3094	283	8	an	an	DET
iajs-3094	283	9	optimal	optimal	ADJ
iajs-3094	283	10	solution	solution	NOUN
iajs-3094	283	11	for	for	ADP
iajs-3094	283	12	the	the	DET
iajs-3094	283	13	problem	problem	NOUN
iajs-3094	283	14	s₱7	s₱7	VERB
iajs-3094	283	15	if	if	SCONJ
iajs-3094	283	16	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	283	17	=	=	SYM
iajs-3094	283	18	𝑝	𝑝	NOUN
iajs-3094	283	19	,	,	PUNCT
iajs-3094	283	20	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	283	21	=	=	SYM
iajs-3094	283	22	𝑑	𝑑	PROPN
iajs-3094	283	23	and	and	CCONJ
iajs-3094	283	24	𝑑	𝑑	PROPN
iajs-3094	283	25	≤	≤	X
iajs-3094	283	26	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	283	27	∀𝑗(𝑗	∀𝑗(𝑗	NOUN
iajs-3094	283	28	=	=	SYM
iajs-3094	283	29	1,2	1,2	NUM
iajs-3094	283	30	,	,	PUNCT
iajs-3094	283	31	…	…	PUNCT
iajs-3094	283	32	.	.	PUNCT
iajs-3094	284	1	,	,	PUNCT
iajs-3094	284	2	𝑛	𝑛	NOUN
iajs-3094	284	3	)	)	PUNCT
iajs-3094	284	4	.	.	PUNCT
iajs-3094	285	1	proof	proof	NOUN
iajs-3094	285	2	:	:	PUNCT
iajs-3094	285	3	proof	proof	NOUN
iajs-3094	285	4	as	as	ADP
iajs-3094	285	5	in	in	ADP
iajs-3094	285	6	case	case	NOUN
iajs-3094	285	7	(	(	PUNCT
iajs-3094	285	8	4.1.7	4.1.7	NUM
iajs-3094	285	9	)	)	PUNCT
iajs-3094	285	10	,	,	PUNCT
iajs-3094	285	11	and	and	CCONJ
iajs-3094	285	12	(	(	PUNCT
iajs-3094	285	13	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	285	14	+	+	NUM
iajs-3094	285	15	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	285	16	+	+	CCONJ
iajs-3094	286	1	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	286	2	)	)	PUNCT
iajs-3094	286	3	=	=	SYM
iajs-3094	286	4	𝑝	𝑝	PROPN
iajs-3094	286	5	(	(	PUNCT
iajs-3094	286	6	𝑛2+𝑛	𝑛2+𝑛	PROPN
iajs-3094	286	7	2	2	NUM
iajs-3094	286	8	)	)	PUNCT
iajs-3094	287	1	+	+	CCONJ
iajs-3094	287	2	𝑛𝑝	𝑛𝑝	ADP
iajs-3094	287	3	−	−	PROPN
iajs-3094	287	4	𝑑	𝑑	NOUN
iajs-3094	287	5	.	.	PUNCT
iajs-3094	288	1	if	if	SCONJ
iajs-3094	288	2	𝑑𝛼𝑖	𝑑𝛼𝑖	PROPN
iajs-3094	288	3	+	+	CCONJ
iajs-3094	288	4	𝑝𝛼𝑗	𝑝𝛼𝑗	X
iajs-3094	288	5	≤	≤	NUM
iajs-3094	288	6	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	288	7	for	for	ADP
iajs-3094	288	8	all	all	DET
iajs-3094	288	9	𝑖	𝑖	ADP
iajs-3094	288	10	,	,	PUNCT
iajs-3094	288	11	𝑗	𝑗	INTJ
iajs-3094	288	12	in	in	ADP
iajs-3094	288	13	schedule	schedule	NOUN
iajs-3094	288	14	𝑆𝑃𝑇	𝑆𝑃𝑇	PROPN
iajs-3094	288	15	𝛼	𝛼	NOUN
iajs-3094	288	16	,	,	PUNCT
iajs-3094	288	17	where	where	SCONJ
iajs-3094	288	18	𝑖	𝑖	ADP
iajs-3094	288	19	≤	≤	X
iajs-3094	288	20	𝑗	𝑗	VERB
iajs-3094	288	21	and	and	CCONJ
iajs-3094	288	22	spt	spt	PROPN
iajs-3094	288	23	and	and	CCONJ
iajs-3094	288	24	edd	edd	PROPN
iajs-3094	288	25	are	be	AUX
iajs-3094	288	26	identical	identical	ADJ
iajs-3094	288	27	,	,	PUNCT
iajs-3094	288	28	then	then	ADV
iajs-3094	288	29	𝛼	𝛼	VERB
iajs-3094	288	30	is	be	AUX
iajs-3094	288	31	the	the	DET
iajs-3094	288	32	efso	efso	NOUN
iajs-3094	288	33	for	for	ADP
iajs-3094	288	34	(	(	PUNCT
iajs-3094	288	35	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	288	36	)	)	PUNCT
iajs-3094	288	37	.	.	PUNCT
iajs-3094	289	1	case	case	NOUN
iajs-3094	289	2	(	(	PUNCT
iajs-3094	289	3	4.2.8	4.2.8	NUM
iajs-3094	289	4	):	):	PUNCT
iajs-3094	289	5	if	if	SCONJ
iajs-3094	289	6	𝑑𝛼𝑖	𝑑𝛼𝑖	PROPN
iajs-3094	289	7	+	+	CCONJ
iajs-3094	289	8	𝑝𝛼𝑗	𝑝𝛼𝑗	X
iajs-3094	289	9	≤	≤	NUM
iajs-3094	289	10	𝑑𝛼𝑗	𝑑𝛼𝑗	NOUN
iajs-3094	289	11	for	for	ADP
iajs-3094	289	12	all	all	DET
iajs-3094	289	13	𝑖	𝑖	ADP
iajs-3094	289	14	,	,	PUNCT
iajs-3094	289	15	𝑗	𝑗	INTJ
iajs-3094	289	16	in	in	ADP
iajs-3094	289	17	schedule	schedule	NOUN
iajs-3094	289	18	𝑆𝑃𝑇	𝑆𝑃𝑇	PROPN
iajs-3094	289	19	𝛼	𝛼	NOUN
iajs-3094	289	20	,	,	PUNCT
iajs-3094	289	21	where	where	SCONJ
iajs-3094	289	22	𝑖	𝑖	ADP
iajs-3094	289	23	≤	≤	X
iajs-3094	289	24	𝑗	𝑗	VERB
iajs-3094	289	25	,	,	PUNCT
iajs-3094	289	26	spt	spt	PROPN
iajs-3094	289	27	and	and	CCONJ
iajs-3094	289	28	edd	edd	PROPN
iajs-3094	289	29	are	be	AUX
iajs-3094	289	30	identical	identical	ADJ
iajs-3094	289	31	,	,	PUNCT
iajs-3094	289	32	then	then	ADV
iajs-3094	289	33	𝛼	𝛼	VERB
iajs-3094	289	34	is	be	AUX
iajs-3094	289	35	the	the	DET
iajs-3094	289	36	optimal	optimal	ADJ
iajs-3094	289	37	solution	solution	NOUN
iajs-3094	289	38	for	for	ADP
iajs-3094	289	39	(	(	PUNCT
iajs-3094	289	40	s₱7	s₱7	PROPN
iajs-3094	289	41	)	)	PUNCT
iajs-3094	289	42	.	.	PUNCT
iajs-3094	290	1	proof	proof	NOUN
iajs-3094	290	2	:	:	PUNCT
iajs-3094	290	3	proof	proof	NOUN
iajs-3094	290	4	as	as	ADP
iajs-3094	290	5	in	in	ADP
iajs-3094	290	6	case	case	NOUN
iajs-3094	290	7	(	(	PUNCT
iajs-3094	290	8	4.1.8	4.1.8	NUM
iajs-3094	290	9	)	)	PUNCT
iajs-3094	290	10	.	.	PUNCT
iajs-3094	291	1	case	case	NOUN
iajs-3094	291	2	(	(	PUNCT
iajs-3094	291	3	4.2.9	4.2.9	NUM
iajs-3094	291	4	):	):	PUNCT
iajs-3094	291	5	if	if	SCONJ
iajs-3094	291	6	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	291	7	+	+	NUM
iajs-3094	291	8	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	291	9	≤	≤	NOUN
iajs-3094	291	10	𝐶𝑗+1	𝐶𝑗+1	ADJ
iajs-3094	291	11	for	for	ADP
iajs-3094	291	12	𝑗	𝑗	NOUN
iajs-3094	291	13	=	=	SYM
iajs-3094	291	14	1,2	1,2	NUM
iajs-3094	291	15	,	,	PUNCT
iajs-3094	291	16	.	.	PUNCT
iajs-3094	291	17	.	.	PUNCT
iajs-3094	292	1	,	,	PUNCT
iajs-3094	292	2	𝑛	𝑛	DET
iajs-3094	292	3	−	−	NOUN
iajs-3094	292	4	1	1	NUM
iajs-3094	292	5	then	then	ADV
iajs-3094	292	6	the	the	DET
iajs-3094	292	7	spt	spt	PROPN
iajs-3094	292	8	schedule	schedule	NOUN
iajs-3094	292	9	is	be	AUX
iajs-3094	292	10	an	an	DET
iajs-3094	292	11	optimal	optimal	ADJ
iajs-3094	292	12	solution	solution	NOUN
iajs-3094	292	13	for	for	ADP
iajs-3094	292	14	(	(	PUNCT
iajs-3094	292	15	𝑆₱7	𝑆₱7	NOUN
iajs-3094	292	16	)	)	PUNCT
iajs-3094	292	17	.	.	PUNCT
iajs-3094	293	1	proof	proof	NOUN
iajs-3094	293	2	:	:	PUNCT
iajs-3094	293	3	verified	verify	VERB
iajs-3094	293	4	by	by	ADP
iajs-3094	293	5	the	the	DET
iajs-3094	293	6	case	case	NOUN
iajs-3094	293	7	(	(	PUNCT
iajs-3094	293	8	4.1.9	4.1.9	NUM
iajs-3094	293	9	)	)	PUNCT
iajs-3094	293	10	.	.	PUNCT
iajs-3094	294	1	case	case	NOUN
iajs-3094	294	2	(	(	PUNCT
iajs-3094	294	3	4.2.10	4.2.10	NUM
iajs-3094	294	4	):	):	PUNCT
iajs-3094	294	5	if	if	SCONJ
iajs-3094	294	6	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	294	7	≥	≥	PRON
iajs-3094	294	8	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	294	9	,	,	PUNCT
iajs-3094	294	10	spt	spt	PROPN
iajs-3094	294	11	and	and	CCONJ
iajs-3094	294	12	edd	edd	PROPN
iajs-3094	294	13	rules	rule	NOUN
iajs-3094	294	14	are	be	AUX
iajs-3094	294	15	identical	identical	ADJ
iajs-3094	294	16	for	for	ADP
iajs-3094	294	17	all	all	DET
iajs-3094	294	18	𝑗	𝑗	NOUN
iajs-3094	294	19	in	in	ADP
iajs-3094	294	20	a	a	DET
iajs-3094	294	21	schedule	schedule	NOUN
iajs-3094	294	22	𝛼	𝛼	NOUN
iajs-3094	294	23	,	,	PUNCT
iajs-3094	294	24	then	then	ADV
iajs-3094	294	25	schedule	schedule	NOUN
iajs-3094	294	26	𝛼	𝛼	PRON
iajs-3094	294	27	gives	give	VERB
iajs-3094	294	28	an	an	DET
iajs-3094	294	29	optmal	optmal	ADJ
iajs-3094	294	30	solution	solution	NOUN
iajs-3094	294	31	for(𝑆₱7	for(𝑆₱7	NOUN
iajs-3094	294	32	)	)	PUNCT
iajs-3094	294	33	.	.	PUNCT
iajs-3094	295	1	proof	proof	NOUN
iajs-3094	295	2	:	:	PUNCT
iajs-3094	295	3	verified	verify	VERB
iajs-3094	295	4	by	by	ADP
iajs-3094	295	5	the	the	DET
iajs-3094	295	6	case	case	NOUN
iajs-3094	295	7	(	(	PUNCT
iajs-3094	295	8	4.1.10	4.1.10	NUM
iajs-3094	295	9	)	)	PUNCT
iajs-3094	295	10	.	.	PUNCT
iajs-3094	296	1	case	case	NOUN
iajs-3094	296	2	(	(	PUNCT
iajs-3094	296	3	4.2.11	4.2.11	NUM
iajs-3094	296	4	):	):	PUNCT
iajs-3094	296	5	if	if	SCONJ
iajs-3094	296	6	the	the	DET
iajs-3094	296	7	spt	spt	PROPN
iajs-3094	296	8	schedule	schedule	NOUN
iajs-3094	296	9	gives	give	VERB
iajs-3094	296	10	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	296	11	≤	≤	NOUN
iajs-3094	296	12	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	296	13	∀𝑖	∀𝑖	PROPN
iajs-3094	296	14	∈	∈	PROPN
iajs-3094	297	1	𝑁	𝑁	PROPN
iajs-3094	297	2	then	then	ADV
iajs-3094	297	3	this	this	DET
iajs-3094	297	4	spt	spt	PROPN
iajs-3094	297	5	schedule	schedule	NOUN
iajs-3094	297	6	gives	give	VERB
iajs-3094	297	7	an	an	DET
iajs-3094	297	8	optimal	optimal	ADJ
iajs-3094	297	9	schedule	schedule	NOUN
iajs-3094	297	10	for	for	ADP
iajs-3094	297	11	(	(	PUNCT
iajs-3094	297	12	𝑆₱7	𝑆₱7	NOUN
iajs-3094	297	13	)	)	PUNCT
iajs-3094	297	14	.	.	PUNCT
iajs-3094	298	1	proof	proof	NOUN
iajs-3094	298	2	:	:	PUNCT
iajs-3094	298	3	proof	proof	NOUN
iajs-3094	298	4	as	as	ADP
iajs-3094	298	5	in	in	ADP
iajs-3094	298	6	case	case	NOUN
iajs-3094	298	7	(	(	PUNCT
iajs-3094	298	8	4.1.11	4.1.11	NUM
iajs-3094	298	9	)	)	PUNCT
iajs-3094	298	10	.	.	PUNCT
iajs-3094	299	1	in	in	ADP
iajs-3094	299	2	table	table	NOUN
iajs-3094	299	3	3	3	NUM
iajs-3094	299	4	,	,	PUNCT
iajs-3094	299	5	an	an	DET
iajs-3094	299	6	examples	example	NOUN
iajs-3094	299	7	give	give	VERB
iajs-3094	299	8	for	for	ADP
iajs-3094	299	9	describing	describe	VERB
iajs-3094	299	10	the	the	DET
iajs-3094	299	11	special	special	ADJ
iajs-3094	299	12	cases	case	NOUN
iajs-3094	299	13	for	for	ADP
iajs-3094	299	14	two	two	NUM
iajs-3094	299	15	problems	problem	NOUN
iajs-3094	299	16	(	(	PUNCT
iajs-3094	299	17	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	299	18	)	)	PUNCT
iajs-3094	299	19	and	and	CCONJ
iajs-3094	299	20	(	(	PUNCT
iajs-3094	299	21	𝑆₱7	𝑆₱7	NOUN
iajs-3094	299	22	)	)	PUNCT
iajs-3094	299	23	by	by	ADP
iajs-3094	299	24	calculating	calculate	VERB
iajs-3094	299	25	the	the	DET
iajs-3094	299	26	objective	objective	ADJ
iajs-3094	299	27	functions(𝐹)and	functions(𝐹)and	NOUN
iajs-3094	299	28	(	(	PUNCT
iajs-3094	299	29	𝐹1)respectively	𝐹1)respectively	ADV
iajs-3094	299	30	,	,	PUNCT
iajs-3094	299	31	using	use	VERB
iajs-3094	299	32	6	6	NUM
iajs-3094	299	33	jobs	job	NOUN
iajs-3094	299	34	.	.	PUNCT
iajs-3094	300	1	ihjpas	ihjpas	PROPN
iajs-3094	300	2	.	.	PUNCT
iajs-3094	301	1	37	37	NUM
iajs-3094	301	2	(	(	PUNCT
iajs-3094	301	3	1	1	NUM
iajs-3094	301	4	)	)	PUNCT
iajs-3094	301	5	2024	2024	NUM
iajs-3094	301	6	397	397	NUM
iajs-3094	301	7	table	table	NOUN
iajs-3094	301	8	3	3	NUM
iajs-3094	301	9	.	.	PUNCT
iajs-3094	301	10	special	special	ADJ
iajs-3094	301	11	cases	case	NOUN
iajs-3094	301	12	of	of	ADP
iajs-3094	301	13	problem	problem	NOUN
iajs-3094	301	14	(	(	PUNCT
iajs-3094	301	15	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	301	16	)	)	PUNCT
iajs-3094	301	17	and	and	CCONJ
iajs-3094	301	18	(	(	PUNCT
iajs-3094	301	19	𝑆₱7	𝑆₱7	NOUN
iajs-3094	301	20	)	)	PUNCT
iajs-3094	301	21	in	in	ADP
iajs-3094	301	22	the	the	DET
iajs-3094	301	23	following	follow	VERB
iajs-3094	301	24	examples	example	NOUN
iajs-3094	301	25	.	.	PUNCT
iajs-3094	302	1	5	5	X
iajs-3094	302	2	.	.	X
iajs-3094	302	3	dominance	dominance	NOUN
iajs-3094	302	4	rules	rule	NOUN
iajs-3094	302	5	for	for	ADP
iajs-3094	302	6	single	single	ADJ
iajs-3094	302	7	machine	machine	NOUN
iajs-3094	302	8	scheduling	scheduling	NOUN
iajs-3094	302	9	problem	problem	NOUN
iajs-3094	302	10	dominance	dominance	NOUN
iajs-3094	302	11	rules	rule	NOUN
iajs-3094	302	12	(	(	PUNCT
iajs-3094	302	13	drs	dr	NOUN
iajs-3094	302	14	)	)	PUNCT
iajs-3094	302	15	are	be	AUX
iajs-3094	302	16	used	use	VERB
iajs-3094	302	17	efficiently	efficiently	ADV
iajs-3094	302	18	in	in	ADP
iajs-3094	302	19	reducing	reduce	VERB
iajs-3094	302	20	the	the	DET
iajs-3094	302	21	current	current	ADJ
iajs-3094	302	22	sequences[23	sequences[23	NOUN
iajs-3094	302	23	-	-	PUNCT
iajs-3094	302	24	25	25	NUM
iajs-3094	302	25	]	]	PUNCT
iajs-3094	302	26	.	.	PUNCT
iajs-3094	303	1	dr	dr	PROPN
iajs-3094	303	2	is	be	AUX
iajs-3094	303	3	used	use	VERB
iajs-3094	303	4	usually	usually	ADV
iajs-3094	303	5	to	to	PART
iajs-3094	303	6	indicate	indicate	VERB
iajs-3094	303	7	whether	whether	SCONJ
iajs-3094	303	8	a	a	DET
iajs-3094	303	9	certain	certain	ADJ
iajs-3094	303	10	node	node	NOUN
iajs-3094	303	11	in	in	ADP
iajs-3094	303	12	a	a	DET
iajs-3094	303	13	bab	bab	PROPN
iajs-3094	303	14	method	method	NOUN
iajs-3094	303	15	can	can	AUX
iajs-3094	303	16	be	be	AUX
iajs-3094	303	17	eliminated	eliminate	VERB
iajs-3094	303	18	before	before	ADP
iajs-3094	303	19	calculating	calculate	VERB
iajs-3094	303	20	its	its	PRON
iajs-3094	303	21	lower	low	ADJ
iajs-3094	303	22	bound	bind	VERB
iajs-3094	303	23	.	.	PUNCT
iajs-3094	304	1	these	these	DET
iajs-3094	304	2	rules	rule	NOUN
iajs-3094	304	3	are	be	AUX
iajs-3094	304	4	been	be	AUX
iajs-3094	304	5	useful	useful	ADJ
iajs-3094	304	6	when	when	SCONJ
iajs-3094	304	7	a	a	DET
iajs-3094	304	8	node	node	NOUN
iajs-3094	304	9	has	have	VERB
iajs-3094	304	10	a	a	DET
iajs-3094	304	11	lower	lower	ADV
iajs-3094	304	12	bound	bind	VERB
iajs-3094	304	13	less	less	ADJ
iajs-3094	304	14	than	than	ADP
iajs-3094	304	15	the	the	DET
iajs-3094	304	16	optimum	optimum	ADJ
iajs-3094	304	17	solution	solution	NOUN
iajs-3094	304	18	and	and	CCONJ
iajs-3094	304	19	can	can	AUX
iajs-3094	304	20	be	be	AUX
iajs-3094	304	21	eliminated	eliminate	VERB
iajs-3094	304	22	[	[	PUNCT
iajs-3094	304	23	26	26	NUM
iajs-3094	304	24	-	-	SYM
iajs-3094	304	25	28	28	NUM
iajs-3094	304	26	]	]	PUNCT
iajs-3094	304	27	.	.	PUNCT
iajs-3094	305	1	when	when	SCONJ
iajs-3094	305	2	the	the	DET
iajs-3094	305	3	nodes	node	NOUN
iajs-3094	305	4	are	be	AUX
iajs-3094	305	5	dominated	dominate	VERB
iajs-3094	305	6	by	by	ADP
iajs-3094	305	7	others	other	NOUN
iajs-3094	305	8	in	in	ADP
iajs-3094	305	9	the	the	DET
iajs-3094	305	10	bab	bab	PROPN
iajs-3094	305	11	procedure	procedure	NOUN
iajs-3094	305	12	,	,	PUNCT
iajs-3094	305	13	drs	dr	NOUN
iajs-3094	305	14	can	can	AUX
iajs-3094	305	15	be	be	AUX
iajs-3094	305	16	used	use	VERB
iajs-3094	305	17	also	also	ADV
iajs-3094	305	18	to	to	PART
iajs-3094	305	19	cut	cut	VERB
iajs-3094	305	20	these	these	DET
iajs-3094	305	21	nodes	node	NOUN
iajs-3094	305	22	.	.	PUNCT
iajs-3094	306	1	such	such	ADJ
iajs-3094	306	2	developments	development	NOUN
iajs-3094	306	3	may	may	AUX
iajs-3094	306	4	heavily	heavily	ADV
iajs-3094	306	5	reduce	reduce	VERB
iajs-3094	306	6	the	the	DET
iajs-3094	306	7	number	number	NOUN
iajs-3094	306	8	of	of	ADP
iajs-3094	306	9	nodes	node	NOUN
iajs-3094	306	10	in	in	ADP
iajs-3094	306	11	searching	search	VERB
iajs-3094	306	12	for	for	ADP
iajs-3094	306	13	an	an	DET
iajs-3094	306	14	efficient	efficient	ADJ
iajs-3094	306	15	solution	solution	NOUN
iajs-3094	306	16	.	.	PUNCT
iajs-3094	307	1	where	where	SCONJ
iajs-3094	307	2	the	the	DET
iajs-3094	307	3	drs	dr	NOUN
iajs-3094	307	4	are	be	AUX
iajs-3094	307	5	also	also	ADV
iajs-3094	307	6	applicable	applicable	ADJ
iajs-3094	307	7	to	to	ADP
iajs-3094	307	8	such	such	ADJ
iajs-3094	307	9	problems[29,30	problems[29,30	PROPN
iajs-3094	307	10	]	]	PUNCT
iajs-3094	307	11	.	.	PUNCT
iajs-3094	308	1	the	the	DET
iajs-3094	308	2	dominance	dominance	NOUN
iajs-3094	308	3	rules	rule	VERB
iajs-3094	308	4	as	as	SCONJ
iajs-3094	308	5	we	we	PRON
iajs-3094	308	6	mentioned	mention	VERB
iajs-3094	308	7	before	before	ADV
iajs-3094	308	8	are	be	AUX
iajs-3094	308	9	used	use	VERB
iajs-3094	308	10	in	in	ADP
iajs-3094	308	11	an	an	DET
iajs-3094	308	12	attempt	attempt	NOUN
iajs-3094	308	13	to	to	PART
iajs-3094	308	14	eliminate	eliminate	VERB
iajs-3094	308	15	nodes	node	NOUN
iajs-3094	308	16	in	in	ADP
iajs-3094	308	17	the	the	DET
iajs-3094	308	18	bab	bab	PROPN
iajs-3094	308	19	method	method	NOUN
iajs-3094	308	20	which	which	PRON
iajs-3094	308	21	makes	make	VERB
iajs-3094	308	22	us	we	PRON
iajs-3094	308	23	reduce	reduce	VERB
iajs-3094	308	24	the	the	DET
iajs-3094	308	25	time	time	NOUN
iajs-3094	308	26	spent	spend	VERB
iajs-3094	308	27	on	on	ADP
iajs-3094	308	28	solving	solve	VERB
iajs-3094	308	29	this	this	DET
iajs-3094	308	30	problem1//	problem1//	PROPN
iajs-3094	308	31	∑𝐶𝑗	∑𝐶𝑗	PROPN
iajs-3094	308	32	+	+	CCONJ
iajs-3094	308	33	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	308	34	+	+	CCONJ
iajs-3094	308	35	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	308	36	.	.	PUNCT
iajs-3094	309	1	rule	rule	NOUN
iajs-3094	309	2	(	(	PUNCT
iajs-3094	309	3	1	1	NUM
iajs-3094	309	4	):	):	PUNCT
iajs-3094	309	5	if	if	SCONJ
iajs-3094	309	6	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	309	7	≤	≤	ADJ
iajs-3094	309	8	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	309	9	and	and	CCONJ
iajs-3094	309	10	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	309	11	≤	≤	NOUN
iajs-3094	309	12	𝑑𝑗	𝑑𝑗	ADV
iajs-3094	309	13	then	then	ADV
iajs-3094	309	14	there	there	PRON
iajs-3094	309	15	is	be	VERB
iajs-3094	309	16	an	an	DET
iajs-3094	309	17	optimal	optimal	ADJ
iajs-3094	309	18	schedule	schedule	NOUN
iajs-3094	309	19	wherein	wherein	SCONJ
iajs-3094	309	20	the	the	DET
iajs-3094	309	21	job	job	NOUN
iajs-3094	309	22	𝑖	𝑖	NOUN
iajs-3094	309	23	processing	processing	NOUN
iajs-3094	309	24	before	before	ADP
iajs-3094	309	25	job	job	NOUN
iajs-3094	309	26	.	.	PUNCT
iajs-3094	310	1	proof	proof	NOUN
iajs-3094	310	2	:	:	PUNCT
iajs-3094	310	3	consider	consider	VERB
iajs-3094	310	4	a	a	DET
iajs-3094	310	5	schedule	schedule	NOUN
iajs-3094	310	6	𝜎	𝜎	NOUN
iajs-3094	310	7	=	=	X
iajs-3094	310	8	𝜎1𝑖𝑗𝜎2	𝜎1𝑖𝑗𝜎2	PROPN
iajs-3094	310	9	and	and	CCONJ
iajs-3094	310	10	a	a	DET
iajs-3094	310	11	schedule	schedule	NOUN
iajs-3094	310	12	�	�	NOUN
iajs-3094	310	13	̇	̇	NOUN
iajs-3094	310	14	�	�	PROPN
iajs-3094	310	15	=	=	PUNCT
iajs-3094	310	16	𝜎1𝑗𝑖𝜎2	𝜎1𝑗𝑖𝜎2	PROPN
iajs-3094	310	17	see	see	VERB
iajs-3094	310	18	figure	figure	NOUN
iajs-3094	310	19	(	(	PUNCT
iajs-3094	310	20	1	1	NUM
iajs-3094	310	21	)	)	PUNCT
iajs-3094	310	22	figure1	figure1	NOUN
iajs-3094	310	23	.	.	PUNCT
iajs-3094	311	1	the	the	DET
iajs-3094	311	2	scheduling	scheduling	NOUN
iajs-3094	311	3	𝜎	𝜎	PROPN
iajs-3094	311	4	and	and	CCONJ
iajs-3094	311	5	�	�	PROPN
iajs-3094	311	6	̈	̈	SYM
iajs-3094	311	7	�	�	PROPN
iajs-3094	311	8	𝐹1	𝐹1	PROPN
iajs-3094	311	9	𝐹	𝐹	PROPN
iajs-3094	311	10	conditions	condition	NOUN
iajs-3094	311	11	𝒑𝒋	𝒑𝒋	AUX
iajs-3094	311	12	𝐚𝐧𝐝	𝐚𝐧𝐝	VERB
iajs-3094	311	13	𝒅𝒋	𝒅𝒋	ADP
iajs-3094	311	14	case	case	NOUN
iajs-3094	311	15	57	57	NUM
iajs-3094	311	16	(	(	PUNCT
iajs-3094	311	17	57,0,0	57,0,0	X
iajs-3094	311	18	)	)	PUNCT
iajs-3094	311	19	𝑝1	𝑝1	NOUN
iajs-3094	311	20	=	=	SYM
iajs-3094	311	21	𝑑1and	𝑑1and	PROPN
iajs-3094	311	22	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	311	23	=	=	SYM
iajs-3094	311	24	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	311	25	−	−	PROPN
iajs-3094	311	26	𝑑𝑗−1	𝑑𝑗−1	NOUN
iajs-3094	311	27	for	for	ADP
iajs-3094	311	28	all	all	DET
iajs-3094	311	29	𝑗	𝑗	PRON
iajs-3094	311	30	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	311	31	=	=	SYM
iajs-3094	311	32	1,2,4,7,5,3	1,2,4,7,5,3	NUM
iajs-3094	311	33	,	,	PUNCT
iajs-3094	311	34	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	311	35	=	=	SYM
iajs-3094	311	36	1,3,10,22,22,15,6	1,3,10,22,22,15,6	PROPN
iajs-3094	311	37	(	(	PUNCT
iajs-3094	311	38	4.1.1	4.1.1	NUM
iajs-3094	311	39	)	)	PUNCT
iajs-3094	311	40	(	(	PUNCT
iajs-3094	311	41	4.2.1	4.2.1	NOUN
iajs-3094	311	42	)	)	PUNCT
iajs-3094	311	43	126	126	NUM
iajs-3094	311	44	(	(	PUNCT
iajs-3094	311	45	126,0,0	126,0,0	NUM
iajs-3094	311	46	)	)	PUNCT
iajs-3094	311	47	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	311	48	=	=	SYM
iajs-3094	311	49	𝑝	𝑝	PROPN
iajs-3094	311	50	and	and	CCONJ
iajs-3094	311	51	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	311	52	=	=	SYM
iajs-3094	311	53	𝑗𝑝	𝑗𝑝	PROPN
iajs-3094	311	54	,	,	PUNCT
iajs-3094	311	55	∀𝑗	∀𝑗	NOUN
iajs-3094	311	56	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	311	57	=	=	SYM
iajs-3094	311	58	6	6	NUM
iajs-3094	311	59	,	,	PUNCT
iajs-3094	311	60	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	311	61	=	=	SYM
iajs-3094	311	62	6,12,18,24,30,36	6,12,18,24,30,36	NUM
iajs-3094	311	63	(	(	PUNCT
iajs-3094	311	64	4.1.2	4.1.2	NUM
iajs-3094	311	65	)	)	PUNCT
iajs-3094	311	66	(	(	PUNCT
iajs-3094	311	67	4.2.2	4.2.2	X
iajs-3094	311	68	)	)	PUNCT
iajs-3094	311	69	94	94	NUM
iajs-3094	311	70	(	(	PUNCT
iajs-3094	311	71	78,12,4	78,12,4	NUM
iajs-3094	311	72	)	)	PUNCT
iajs-3094	311	73	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	311	74	=	=	SYM
iajs-3094	311	75	𝑘𝑝𝑗	𝑘𝑝𝑗	NOUN
iajs-3094	311	76	for	for	ADP
iajs-3094	311	77	all	all	DET
iajs-3094	311	78	𝑘	𝑘	PRON
iajs-3094	311	79	≥	≥	NUM
iajs-3094	311	80	2	2	NUM
iajs-3094	311	81	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	311	82	=	=	SYM
iajs-3094	311	83	3,4,2,5,6,8	3,4,2,5,6,8	NUM
iajs-3094	311	84	,	,	PUNCT
iajs-3094	311	85	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	311	86	=	=	SYM
iajs-3094	311	87	9,12,6,15,18,24	9,12,6,15,18,24	NUM
iajs-3094	311	88	(	(	PUNCT
iajs-3094	311	89	4.1.3	4.1.3	NUM
iajs-3094	311	90	)	)	PUNCT
iajs-3094	311	91	(	(	PUNCT
iajs-3094	311	92	42.3	42.3	NUM
iajs-3094	311	93	)	)	PUNCT
iajs-3094	311	94	267	267	NUM
iajs-3094	311	95	(	(	PUNCT
iajs-3094	311	96	222,2,43	222,2,43	NUM
iajs-3094	311	97	)	)	PUNCT
iajs-3094	311	98	𝑝𝑖	𝑝𝑖	VERB
iajs-3094	311	99	≤	≤	ADJ
iajs-3094	311	100	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	311	101	and	and	CCONJ
iajs-3094	311	102	𝑠𝑖	𝑠𝑖	VERB
iajs-3094	311	103	≤	≤	NUM
iajs-3094	311	104	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	311	105	for	for	ADP
iajs-3094	311	106	all	all	DET
iajs-3094	311	107	𝑗	𝑗	NOUN
iajs-3094	311	108	.	.	PUNCT
iajs-3094	312	1	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	312	2	=	=	SYM
iajs-3094	312	3	6,10,12,14,14,18	6,10,12,14,14,18	PROPN
iajs-3094	312	4	,	,	PUNCT
iajs-3094	312	5	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	312	6	=	=	SYM
iajs-3094	312	7	2,4,8,10,12,13	2,4,8,10,12,13	NUM
iajs-3094	312	8	.	.	PUNCT
iajs-3094	313	1	(	(	PUNCT
iajs-3094	313	2	4.1.4	4.1.4	NUM
iajs-3094	313	3	)	)	PUNCT
iajs-3094	313	4	(	(	PUNCT
iajs-3094	313	5	4.2.4	4.2.4	X
iajs-3094	313	6	)	)	PUNCT
iajs-3094	313	7	72	72	NUM
iajs-3094	313	8	(	(	PUNCT
iajs-3094	313	9	63,0,9	63,0,9	NOUN
iajs-3094	313	10	)	)	PUNCT
iajs-3094	313	11	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	313	12	=	=	SYM
iajs-3094	313	13	𝑝	𝑝	PROPN
iajs-3094	313	14	for	for	ADP
iajs-3094	313	15	all	all	DET
iajs-3094	313	16	𝑗	𝑗	NOUN
iajs-3094	313	17	in	in	ADP
iajs-3094	313	18	a	a	DET
iajs-3094	313	19	schedule	schedule	NOUN
iajs-3094	313	20	edd	edd	PROPN
iajs-3094	313	21	𝛼	𝛼	NOUN
iajs-3094	313	22	.	.	PUNCT
iajs-3094	314	1	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	314	2	=	=	SYM
iajs-3094	314	3	3	3	NUM
iajs-3094	314	4	,	,	PUNCT
iajs-3094	314	5	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	314	6	=	=	SYM
iajs-3094	314	7	3,4,6,7,8,9	3,4,6,7,8,9	NUM
iajs-3094	314	8	(	(	PUNCT
iajs-3094	314	9	4.1.5	4.1.5	NUM
iajs-3094	314	10	)	)	PUNCT
iajs-3094	314	11	(	(	PUNCT
iajs-3094	314	12	4.2.5	4.2.5	X
iajs-3094	314	13	)	)	PUNCT
iajs-3094	314	14	62	62	NUM
iajs-3094	314	15	(	(	PUNCT
iajs-3094	314	16	41,11,10	41,11,10	NUM
iajs-3094	314	17	)	)	PUNCT
iajs-3094	314	18	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	315	1	=	=	SYM
iajs-3094	316	1	𝑑,∀𝑗	𝑑,∀𝑗	NUM
iajs-3094	316	2	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	316	3	=	=	PUNCT
iajs-3094	316	4	5,4,3,2,1,1	5,4,3,2,1,1	NUM
iajs-3094	316	5	,	,	PUNCT
iajs-3094	316	6	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	316	7	=	=	SYM
iajs-3094	316	8	6	6	NUM
iajs-3094	316	9	(	(	PUNCT
iajs-3094	316	10	4.1.6	4.1.6	NUM
iajs-3094	316	11	)	)	PUNCT
iajs-3094	316	12	(	(	PUNCT
iajs-3094	316	13	4.2.6	4.2.6	X
iajs-3094	316	14	)	)	PUNCT
iajs-3094	316	15	123	123	NUM
iajs-3094	316	16	(	(	PUNCT
iajs-3094	316	17	106,0,17	106,0,17	NUM
iajs-3094	316	18	)	)	PUNCT
iajs-3094	316	19	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	316	20	=	=	SYM
iajs-3094	316	21	7,6,5,3,2,1	7,6,5,3,2,1	NUM
iajs-3094	316	22	,	,	PUNCT
iajs-3094	316	23	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	316	24	=	=	SYM
iajs-3094	316	25	7	7	NUM
iajs-3094	316	26	130	130	NUM
iajs-3094	316	27	(	(	PUNCT
iajs-3094	316	28	105,0,25	105,0,25	NUM
iajs-3094	316	29	)	)	PUNCT
iajs-3094	316	30	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	316	31	=	=	SYM
iajs-3094	316	32	𝑝	𝑝	PROPN
iajs-3094	316	33	,	,	PUNCT
iajs-3094	316	34	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	316	35	=	=	SYM
iajs-3094	316	36	𝑑	𝑑	PROPN
iajs-3094	316	37	,	,	PUNCT
iajs-3094	316	38	𝑑	𝑑	PROPN
iajs-3094	316	39	≤	≤	NOUN
iajs-3094	316	40	𝐶𝑗for	𝐶𝑗for	ADP
iajs-3094	316	41	all	all	DET
iajs-3094	316	42	𝑗	𝑗	PRON
iajs-3094	316	43	𝑝	𝑝	NOUN
iajs-3094	316	44	=	=	SYM
iajs-3094	316	45	𝑑	𝑑	NOUN
iajs-3094	316	46	=	=	SYM
iajs-3094	316	47	5	5	NUM
iajs-3094	316	48	(	(	PUNCT
iajs-3094	316	49	4.1.7	4.1.7	NUM
iajs-3094	316	50	)	)	PUNCT
iajs-3094	316	51	(	(	PUNCT
iajs-3094	316	52	4.2.7	4.2.7	X
iajs-3094	316	53	)	)	SYM
iajs-3094	316	54	130	130	NUM
iajs-3094	316	55	(	(	PUNCT
iajs-3094	316	56	105,2,23	105,2,23	NUM
iajs-3094	316	57	)	)	PUNCT
iajs-3094	316	58	𝑝	𝑝	NOUN
iajs-3094	316	59	=	=	SYM
iajs-3094	316	60	5	5	NUM
iajs-3094	316	61	,	,	PUNCT
iajs-3094	316	62	𝑑	𝑑	PROPN
iajs-3094	316	63	=	=	SYM
iajs-3094	316	64	7	7	NUM
iajs-3094	316	65	,	,	PUNCT
iajs-3094	316	66	𝑝	𝑝	NOUN
iajs-3094	316	67	<	<	X
iajs-3094	316	68	𝑑	𝑑	PROPN
iajs-3094	316	69	34	34	NUM
iajs-3094	316	70	(	(	PUNCT
iajs-3094	316	71	34,0,0	34,0,0	NUM
iajs-3094	316	72	)	)	PUNCT
iajs-3094	316	73	𝑑𝑖	𝑑𝑖	PART
iajs-3094	317	1	+	+	CCONJ
iajs-3094	317	2	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	317	3	≤	≤	NOUN
iajs-3094	317	4	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	317	5	for	for	ADP
iajs-3094	317	6	all	all	PRON
iajs-3094	317	7	𝑗	𝑗	ADJ
iajs-3094	317	8	,	,	PUNCT
iajs-3094	317	9	spt	spt	PROPN
iajs-3094	317	10	and	and	CCONJ
iajs-3094	317	11	edd	edd	PROPN
iajs-3094	317	12	rules	rule	NOUN
iajs-3094	317	13	are	be	AUX
iajs-3094	317	14	identical	identical	ADJ
iajs-3094	317	15	.	.	PUNCT
iajs-3094	318	1	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	318	2	=	=	SYM
iajs-3094	318	3	1,1,3,3,2,2	1,1,3,3,2,2	NUM
iajs-3094	318	4	,	,	PUNCT
iajs-3094	318	5	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	318	6	=	=	SYM
iajs-3094	318	7	1,2,9,12,4,6	1,2,9,12,4,6	PROPN
iajs-3094	318	8	(	(	PUNCT
iajs-3094	318	9	4.1.8	4.1.8	NUM
iajs-3094	318	10	)	)	PUNCT
iajs-3094	318	11	(	(	PUNCT
iajs-3094	318	12	4.2.8	4.2.8	NUM
iajs-3094	318	13	)	)	PUNCT
iajs-3094	318	14	73	73	NUM
iajs-3094	318	15	(	(	PUNCT
iajs-3094	318	16	59,0,14	59,0,14	ADV
iajs-3094	318	17	)	)	PUNCT
iajs-3094	318	18	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	319	1	+	+	CCONJ
iajs-3094	319	2	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	319	3	≤	≤	NOUN
iajs-3094	319	4	𝐶𝑗+1	𝐶𝑗+1	ADJ
iajs-3094	319	5	for	for	ADP
iajs-3094	319	6	all	all	PRON
iajs-3094	319	7	𝑗	𝑗	NOUN
iajs-3094	319	8	=	=	SYM
iajs-3094	319	9	2,3	2,3	NUM
iajs-3094	319	10	,	,	PUNCT
iajs-3094	319	11	…	…	PUNCT
iajs-3094	319	12	,	,	PUNCT
iajs-3094	319	13	𝑛	𝑛	DET
iajs-3094	319	14	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	319	15	=	=	NOUN
iajs-3094	319	16	5,4,3,2,4,2	5,4,3,2,4,2	NUM
iajs-3094	319	17	,	,	PUNCT
iajs-3094	319	18	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	319	19	=	=	SYM
iajs-3094	319	20	6,7,4,3,5,2	6,7,4,3,5,2	NUM
iajs-3094	319	21	(	(	PUNCT
iajs-3094	319	22	4.1.9	4.1.9	NUM
iajs-3094	319	23	)	)	PUNCT
iajs-3094	319	24	(	(	PUNCT
iajs-3094	319	25	4.2.9	4.2.9	X
iajs-3094	319	26	)	)	PUNCT
iajs-3094	319	27	39	39	NUM
iajs-3094	319	28	126	126	NUM
iajs-3094	319	29	(	(	PUNCT
iajs-3094	319	30	35,0,4	35,0,4	NUM
iajs-3094	319	31	)	)	PUNCT
iajs-3094	319	32	(	(	PUNCT
iajs-3094	319	33	101,0,25	101,0,25	NUM
iajs-3094	319	34	)	)	PUNCT
iajs-3094	320	1	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	320	2	≥	≥	NUM
iajs-3094	320	3	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	320	4	,	,	PUNCT
iajs-3094	320	5	for	for	ADP
iajs-3094	320	6	all	all	PRON
iajs-3094	320	7	𝑗	𝑗	PRON
iajs-3094	320	8	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	320	9	=	=	SYM
iajs-3094	320	10	4,3,2,2,1,1	4,3,2,2,1,1	NUM
iajs-3094	320	11	,	,	PUNCT
iajs-3094	320	12	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	320	13	=	=	SYM
iajs-3094	320	14	14,9,5,6,2,3	14,9,5,6,2,3	NUM
iajs-3094	320	15	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	320	16	=	=	NOUN
iajs-3094	320	17	3,4,5,6,8,9	3,4,5,6,8,9	NUM
iajs-3094	320	18	,	,	PUNCT
iajs-3094	320	19	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	320	20	=	=	SYM
iajs-3094	320	21	3,5,6,7,9,10	3,5,6,7,9,10	NUM
iajs-3094	320	22	(	(	PUNCT
iajs-3094	320	23	4.1.10	4.1.10	NUM
iajs-3094	320	24	)	)	PUNCT
iajs-3094	320	25	(	(	PUNCT
iajs-3094	320	26	4.2.10	4.2.10	NUM
iajs-3094	320	27	)	)	PUNCT
iajs-3094	320	28	83	83	NUM
iajs-3094	320	29	(	(	PUNCT
iajs-3094	320	30	78,5,0	78,5,0	X
iajs-3094	320	31	)	)	PUNCT
iajs-3094	320	32	𝐶𝑗	𝐶𝑗	NOUN
iajs-3094	320	33	≤	≤	ADJ
iajs-3094	320	34	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	320	35	,	,	PUNCT
iajs-3094	320	36	for	for	ADP
iajs-3094	320	37	all	all	PRON
iajs-3094	320	38	𝑗	𝑗	PRON
iajs-3094	320	39	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	320	40	=	=	SYM
iajs-3094	320	41	8,5,2,6,4,3	8,5,2,6,4,3	NUM
iajs-3094	320	42	,	,	PUNCT
iajs-3094	320	43	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	320	44	=	=	SYM
iajs-3094	320	45	30,14,2,21,10,6	30,14,2,21,10,6	NUM
iajs-3094	320	46	(	(	PUNCT
iajs-3094	320	47	4.1.11	4.1.11	NUM
iajs-3094	320	48	)	)	PUNCT
iajs-3094	320	49	(	(	PUNCT
iajs-3094	320	50	4.2.11	4.2.11	NUM
iajs-3094	320	51	)	)	PUNCT
iajs-3094	320	52	ihjpas	ihjpa	NOUN
iajs-3094	320	53	.	.	PUNCT
iajs-3094	321	1	37	37	NUM
iajs-3094	321	2	(	(	PUNCT
iajs-3094	321	3	1	1	NUM
iajs-3094	321	4	)	)	PUNCT
iajs-3094	321	5	2024	2024	NUM
iajs-3094	321	6	398	398	NUM
iajs-3094	321	7	which	which	PRON
iajs-3094	321	8	is	be	AUX
iajs-3094	321	9	obtained	obtain	VERB
iajs-3094	321	10	by	by	ADP
iajs-3094	321	11	interchanging	interchange	VERB
iajs-3094	321	12	the	the	DET
iajs-3094	321	13	jobs	job	NOUN
iajs-3094	321	14	i	i	PRON
iajs-3094	321	15	and	and	CCONJ
iajs-3094	321	16	j	j	PROPN
iajs-3094	321	17	in	in	ADP
iajs-3094	321	18	σ	σ	PROPN
iajs-3094	321	19	.	.	PUNCT
iajs-3094	322	1	for	for	ADP
iajs-3094	322	2	these	these	DET
iajs-3094	322	3	schedules	schedule	NOUN
iajs-3094	322	4	,	,	PUNCT
iajs-3094	322	5	we	we	PRON
iajs-3094	322	6	study	study	VERB
iajs-3094	322	7	two	two	NUM
iajs-3094	322	8	cases	case	NOUN
iajs-3094	322	9	,	,	PUNCT
iajs-3094	322	10	and	and	CCONJ
iajs-3094	322	11	in	in	ADP
iajs-3094	322	12	every	every	DET
iajs-3094	322	13	case	case	NOUN
iajs-3094	322	14	,	,	PUNCT
iajs-3094	322	15	we	we	PRON
iajs-3094	322	16	will	will	AUX
iajs-3094	322	17	make	make	VERB
iajs-3094	322	18	a	a	DET
iajs-3094	322	19	comparison	comparison	NOUN
iajs-3094	322	20	between	between	ADP
iajs-3094	322	21	them	they	PRON
iajs-3094	322	22	.	.	PUNCT
iajs-3094	323	1	first	first	ADJ
iajs-3094	323	2	case	case	NOUN
iajs-3094	323	3	:	:	PUNCT
iajs-3094	323	4	if	if	SCONJ
iajs-3094	323	5	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	323	6	≤	≤	ADJ
iajs-3094	323	7	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	323	8	,	,	PUNCT
iajs-3094	323	9	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	323	10	≤	≤	NOUN
iajs-3094	323	11	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	323	12	produces	produce	VERB
iajs-3094	323	13	that	that	PRON
iajs-3094	323	14	𝑠𝑖	𝑠𝑖	VERB
iajs-3094	323	15	≤	≤	NOUN
iajs-3094	323	16	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	323	17	in	in	ADP
iajs-3094	323	18	this	this	DET
iajs-3094	323	19	situation	situation	NOUN
iajs-3094	323	20	,	,	PUNCT
iajs-3094	323	21	there	there	PRON
iajs-3094	323	22	are	be	VERB
iajs-3094	323	23	:	:	PUNCT
iajs-3094	323	24	the	the	DET
iajs-3094	323	25	condition	condition	NOUN
iajs-3094	323	26	of	of	ADP
iajs-3094	323	27	the	the	DET
iajs-3094	323	28	processing	processing	NOUN
iajs-3094	323	29	times	time	NOUN
iajs-3094	323	30	ensures	ensure	VERB
iajs-3094	323	31	that	that	SCONJ
iajs-3094	323	32	:	:	PUNCT
iajs-3094	323	33	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	323	34	)	)	PUNCT
iajs-3094	323	35	≤	≤	PUNCT
iajs-3094	323	36	∑𝐶𝒦(	∑𝐶𝒦(	PROPN
iajs-3094	323	37	�	�	PROPN
iajs-3094	323	38	̇	̇	PROPN
iajs-3094	323	39	�	�	PROPN
iajs-3094	323	40	)	)	PUNCT
iajs-3094	323	41	(	(	PUNCT
iajs-3094	323	42	2	2	NUM
iajs-3094	323	43	)	)	PUNCT
iajs-3094	323	44	and	and	CCONJ
iajs-3094	323	45	the	the	DET
iajs-3094	323	46	condition	condition	NOUN
iajs-3094	323	47	of	of	ADP
iajs-3094	323	48	the	the	DET
iajs-3094	323	49	slack	slack	NOUN
iajs-3094	323	50	times	time	NOUN
iajs-3094	323	51	ensures	ensure	VERB
iajs-3094	323	52	that	that	SCONJ
iajs-3094	323	53	:	:	PUNCT
iajs-3094	323	54	𝐸𝑚𝑎𝑥(𝜎	𝐸𝑚𝑎𝑥(𝜎	NOUN
iajs-3094	323	55	)	)	PUNCT
iajs-3094	323	56	≤	≤	NUM
iajs-3094	323	57	𝐸𝑚𝑎𝑥(	𝐸𝑚𝑎𝑥(	ADP
iajs-3094	323	58	�	�	PROPN
iajs-3094	323	59	̇	̇	PROPN
iajs-3094	323	60	�	�	PROPN
iajs-3094	323	61	)	)	PUNCT
iajs-3094	323	62	then	then	ADV
iajs-3094	323	63	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	323	64	)	)	PUNCT
iajs-3094	323	65	≤	≤	NUM
iajs-3094	323	66	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	323	67	�	�	SYM
iajs-3094	323	68	̇	̇	NOUN
iajs-3094	323	69	�	�	PROPN
iajs-3094	323	70	)	)	PUNCT
iajs-3094	323	71	and	and	CCONJ
iajs-3094	323	72	the	the	DET
iajs-3094	323	73	condition	condition	NOUN
iajs-3094	323	74	on	on	ADP
iajs-3094	323	75	the	the	DET
iajs-3094	323	76	due	due	ADJ
iajs-3094	323	77	date	date	NOUN
iajs-3094	323	78	ensures	ensure	VERB
iajs-3094	323	79	that	that	SCONJ
iajs-3094	323	80	:	:	PUNCT
iajs-3094	323	81	𝑇𝑚𝑎𝑥(𝜎	𝑇𝑚𝑎𝑥(𝜎	NUM
iajs-3094	323	82	)	)	PUNCT
iajs-3094	323	83	≤	≤	NUM
iajs-3094	323	84	𝑇𝑚𝑎𝑥(	𝑇𝑚𝑎𝑥(	PROPN
iajs-3094	323	85	�	�	PROPN
iajs-3094	323	86	̇	̇	PROPN
iajs-3094	323	87	�	�	PROPN
iajs-3094	323	88	)	)	PUNCT
iajs-3094	323	89	(	(	PUNCT
iajs-3094	323	90	3	3	X
iajs-3094	323	91	)	)	PUNCT
iajs-3094	323	92	hence	hence	ADV
iajs-3094	323	93	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	NOUN
iajs-3094	323	94	)	)	PUNCT
iajs-3094	323	95	+	+	CCONJ
iajs-3094	323	96	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	323	97	)	)	PUNCT
iajs-3094	323	98	+	+	CCONJ
iajs-3094	323	99	𝑇𝑚𝑎𝑥(𝜎	𝑇𝑚𝑎𝑥(𝜎	PROPN
iajs-3094	323	100	)	)	PUNCT
iajs-3094	323	101	≤	≤	NUM
iajs-3094	323	102	∑𝐶𝒦(	∑𝐶𝒦(	PROPN
iajs-3094	323	103	�	�	PROPN
iajs-3094	323	104	̇	̇	VERB
iajs-3094	323	105	�	�	PROPN
iajs-3094	323	106	)	)	PUNCT
iajs-3094	323	107	+	+	CCONJ
iajs-3094	323	108	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	323	109	�	�	SYM
iajs-3094	323	110	̇	̇	NOUN
iajs-3094	323	111	�	�	PROPN
iajs-3094	323	112	)	)	PUNCT
iajs-3094	323	113	+	+	CCONJ
iajs-3094	323	114	𝑇𝑚𝑎𝑥(	𝑇𝑚𝑎𝑥(	PROPN
iajs-3094	323	115	�	�	PROPN
iajs-3094	323	116	̇	̇	PROPN
iajs-3094	323	117	�	�	PROPN
iajs-3094	323	118	)	)	PUNCT
iajs-3094	323	119	second	second	ADJ
iajs-3094	323	120	case	case	NOUN
iajs-3094	323	121	:	:	PUNCT
iajs-3094	323	122	if	if	SCONJ
iajs-3094	323	123	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	323	124	≤	≤	ADJ
iajs-3094	323	125	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	323	126	,	,	PUNCT
iajs-3094	323	127	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	323	128	≤	≤	NOUN
iajs-3094	323	129	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	323	130	yields	yield	NOUN
iajs-3094	323	131	that	that	PRON
iajs-3094	323	132	𝑠𝑖	𝑠𝑖	VERB
iajs-3094	323	133	≥	≥	NOUN
iajs-3094	323	134	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	323	135	.	.	PUNCT
iajs-3094	324	1	in	in	ADP
iajs-3094	324	2	this	this	DET
iajs-3094	324	3	situation	situation	NOUN
iajs-3094	324	4	,	,	PUNCT
iajs-3094	324	5	the	the	DET
iajs-3094	324	6	condition	condition	NOUN
iajs-3094	324	7	on	on	ADP
iajs-3094	324	8	the	the	DET
iajs-3094	324	9	processing	processing	NOUN
iajs-3094	324	10	times	time	NOUN
iajs-3094	324	11	ensures	ensure	VERB
iajs-3094	324	12	that	that	SCONJ
iajs-3094	324	13	(	(	PUNCT
iajs-3094	324	14	5.1	5.1	NUM
iajs-3094	324	15	)	)	PUNCT
iajs-3094	324	16	is	be	AUX
iajs-3094	324	17	satisfied	satisfied	ADJ
iajs-3094	324	18	,	,	PUNCT
iajs-3094	324	19	and	and	CCONJ
iajs-3094	324	20	the	the	DET
iajs-3094	324	21	cost	cost	NOUN
iajs-3094	324	22	which	which	PRON
iajs-3094	324	23	is	be	AUX
iajs-3094	324	24	obtained	obtain	VERB
iajs-3094	324	25	from	from	ADP
iajs-3094	324	26	equation	equation	NOUN
iajs-3094	324	27	(	(	PUNCT
iajs-3094	324	28	2	2	X
iajs-3094	324	29	)	)	PUNCT
iajs-3094	324	30	is	be	AUX
iajs-3094	324	31	equal	equal	ADJ
iajs-3094	324	32	to	to	ADP
iajs-3094	324	33	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	324	34	−	−	PROPN
iajs-3094	324	35	𝑝𝑖	𝑝𝑖	PROPN
iajs-3094	324	36	i.	i.	PROPN
iajs-3094	324	37	e.	e.	PROPN
iajs-3094	324	38	∑𝐶𝒦(	∑𝐶𝒦(	PROPN
iajs-3094	324	39	�	�	PROPN
iajs-3094	324	40	̇	̇	PROPN
iajs-3094	324	41	�	�	PROPN
iajs-3094	324	42	)	)	PUNCT
iajs-3094	324	43	=	=	SYM
iajs-3094	324	44	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	324	45	)	)	PUNCT
iajs-3094	324	46	+	+	CCONJ
iajs-3094	324	47	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	324	48	−	−	PROPN
iajs-3094	324	49	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	324	50	(	(	PUNCT
iajs-3094	324	51	4	4	NUM
iajs-3094	324	52	)	)	PUNCT
iajs-3094	324	53	,	,	PUNCT
iajs-3094	324	54	then	then	ADV
iajs-3094	324	55	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	324	56	−	−	PROPN
iajs-3094	324	57	𝐶𝑖(𝜎	𝐶𝑖(𝜎	NOUN
iajs-3094	324	58	)	)	PUNCT
iajs-3094	324	59	=	=	PRON
iajs-3094	324	60	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	324	61	−	−	PROPN
iajs-3094	324	62	𝐶𝑗(	𝐶𝑗(	SYM
iajs-3094	324	63	�	�	PROPN
iajs-3094	324	64	̇	̇	PROPN
iajs-3094	324	65	�	�	PROPN
iajs-3094	324	66	)	)	PUNCT
iajs-3094	324	67	+	+	CCONJ
iajs-3094	324	68	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	324	69	−	−	PROPN
iajs-3094	324	70	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	324	71	,	,	PUNCT
iajs-3094	324	72	since	since	SCONJ
iajs-3094	324	73	𝐶𝑖(𝜎	𝐶𝑖(𝜎	NOUN
iajs-3094	324	74	)	)	PUNCT
iajs-3094	324	75	=	=	PUNCT
iajs-3094	324	76	𝐶𝑗(	𝐶𝑗(	PROPN
iajs-3094	324	77	�	�	PROPN
iajs-3094	324	78	̇	̇	PROPN
iajs-3094	324	79	�	�	PROPN
iajs-3094	324	80	)	)	PUNCT
iajs-3094	324	81	−	−	PROPN
iajs-3094	324	82	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	324	83	+	+	NOUN
iajs-3094	324	84	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	324	85	.	.	PUNCT
iajs-3094	325	1	since	since	SCONJ
iajs-3094	325	2	𝑠𝑖	𝑠𝑖	PROPN
iajs-3094	325	3	=	=	PUNCT
iajs-3094	325	4	𝑑𝑖	𝑑𝑖	PROPN
iajs-3094	325	5	−	−	PROPN
iajs-3094	325	6	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	325	7	≥	≥	NOUN
iajs-3094	326	1	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	326	2	=	=	NOUN
iajs-3094	326	3	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	326	4	−	−	PROPN
iajs-3094	326	5	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	326	6	then	then	ADV
iajs-3094	326	7	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	326	8	−	−	PROPN
iajs-3094	326	9	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	326	10	−	−	PROPN
iajs-3094	326	11	𝐶𝑗(	𝐶𝑗(	NOUN
iajs-3094	326	12	�	�	PROPN
iajs-3094	326	13	̇	̇	PROPN
iajs-3094	326	14	�	�	PROPN
iajs-3094	326	15	)	)	PUNCT
iajs-3094	326	16	≥	≥	NOUN
iajs-3094	326	17	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	326	18	−	−	PROPN
iajs-3094	326	19	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	326	20	−	−	PROPN
iajs-3094	326	21	𝐶𝑗(	𝐶𝑗(	NOUN
iajs-3094	326	22	�	�	PROPN
iajs-3094	326	23	̇	̇	PROPN
iajs-3094	326	24	�	�	PROPN
iajs-3094	326	25	)	)	PUNCT
iajs-3094	326	26	hence	hence	ADV
iajs-3094	326	27	𝑑𝑖	𝑑𝑖	PROPN
iajs-3094	326	28	−	−	PROPN
iajs-3094	326	29	𝑝𝑖	𝑝𝑖	PROPN
iajs-3094	326	30	+	+	NOUN
iajs-3094	326	31	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	326	32	−	−	PROPN
iajs-3094	326	33	𝐶𝑗(	𝐶𝑗(	NOUN
iajs-3094	326	34	�	�	PROPN
iajs-3094	326	35	̇	̇	PROPN
iajs-3094	326	36	�	�	PROPN
iajs-3094	326	37	)	)	PUNCT
iajs-3094	326	38	≥	≥	NOUN
iajs-3094	326	39	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	326	40	−	−	PROPN
iajs-3094	326	41	𝒞𝑗(	𝒞𝑗(	ADJ
iajs-3094	326	42	�	�	PROPN
iajs-3094	326	43	̇	̇	NOUN
iajs-3094	326	44	�	�	PROPN
iajs-3094	326	45	)	)	PUNCT
iajs-3094	326	46	,	,	PUNCT
iajs-3094	326	47	from	from	ADP
iajs-3094	326	48	which	which	PRON
iajs-3094	326	49	we	we	PRON
iajs-3094	326	50	deduce	deduce	VERB
iajs-3094	326	51	that	that	PRON
iajs-3094	326	52	𝐸𝑚𝑎𝑥(𝜎	𝐸𝑚𝑎𝑥(𝜎	NOUN
iajs-3094	326	53	)	)	PUNCT
iajs-3094	326	54	≥	≥	NOUN
iajs-3094	326	55	𝐸𝑚𝑎𝑥(	𝐸𝑚𝑎𝑥(	PART
iajs-3094	326	56	�	�	PROPN
iajs-3094	326	57	̇	̇	PROPN
iajs-3094	326	58	�	�	PROPN
iajs-3094	326	59	)	)	PUNCT
iajs-3094	326	60	then	then	ADV
iajs-3094	326	61	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	326	62	)	)	PUNCT
iajs-3094	326	63	≥	≥	NOUN
iajs-3094	326	64	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	326	65	�	�	PROPN
iajs-3094	326	66	̇	̇	PROPN
iajs-3094	326	67	�	�	PROPN
iajs-3094	326	68	)	)	PUNCT
iajs-3094	326	69	the	the	DET
iajs-3094	326	70	addition	addition	NOUN
iajs-3094	326	71	in	in	ADP
iajs-3094	326	72	cost	cost	NOUN
iajs-3094	326	73	which	which	PRON
iajs-3094	326	74	is	be	AUX
iajs-3094	326	75	obtained	obtain	VERB
iajs-3094	326	76	from	from	ADP
iajs-3094	326	77	this	this	DET
iajs-3094	326	78	inequality	inequality	NOUN
iajs-3094	326	79	is	be	AUX
iajs-3094	326	80	equal	equal	ADJ
iajs-3094	326	81	to	to	PART
iajs-3094	326	82	𝑠𝑖	𝑠𝑖	VERB
iajs-3094	326	83	−	−	PROPN
iajs-3094	326	84	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	326	85	,	,	PUNCT
iajs-3094	326	86	i.e.	i.e.	X
iajs-3094	326	87	,	,	PUNCT
iajs-3094	326	88	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	326	89	)	)	PUNCT
iajs-3094	326	90	=	=	SYM
iajs-3094	326	91	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	326	92	�	�	PROPN
iajs-3094	326	93	̇	̇	NOUN
iajs-3094	326	94	�	�	PROPN
iajs-3094	326	95	)	)	PUNCT
iajs-3094	326	96	+	+	CCONJ
iajs-3094	326	97	(	(	PUNCT
iajs-3094	326	98	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	326	99	−	−	NOUN
iajs-3094	326	100	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	326	101	)	)	PUNCT
iajs-3094	326	102	(	(	PUNCT
iajs-3094	326	103	5	5	NUM
iajs-3094	326	104	)	)	PUNCT
iajs-3094	326	105	.	.	PUNCT
iajs-3094	327	1	since	since	SCONJ
iajs-3094	327	2	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	327	3	≤	≤	ADJ
iajs-3094	327	4	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	327	5	then	then	ADV
iajs-3094	327	6	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	327	7	−	−	PROPN
iajs-3094	327	8	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	327	9	≥	≥	NOUN
iajs-3094	327	10	0	0	NUM
iajs-3094	327	11	∀𝑖	∀𝑖	PROPN
iajs-3094	327	12	,	,	PUNCT
iajs-3094	327	13	𝑗	𝑗	VERB
iajs-3094	327	14	since	since	SCONJ
iajs-3094	327	15	𝑑𝑖	𝑑𝑖	PROPN
iajs-3094	327	16	≤	≤	ADV
iajs-3094	327	17	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	327	18	then	then	ADV
iajs-3094	327	19	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	327	20	−	−	PROPN
iajs-3094	327	21	𝑑𝑖	𝑑𝑖	PROPN
iajs-3094	327	22	≥	≥	NOUN
iajs-3094	327	23	0	0	NUM
iajs-3094	328	1	∀𝑖	∀𝑖	PROPN
iajs-3094	328	2	,	,	PUNCT
iajs-3094	328	3	𝑗	𝑗	PROPN
iajs-3094	328	4	from	from	ADP
iajs-3094	328	5	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	328	6	−	−	PROPN
iajs-3094	329	1	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	329	2	≤	≤	NUM
iajs-3094	329	3	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	329	4	−	−	PROPN
iajs-3094	329	5	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	329	6	,	,	PUNCT
iajs-3094	329	7	then	then	ADV
iajs-3094	329	8	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	329	9	�	�	SYM
iajs-3094	329	10	̇	̇	NOUN
iajs-3094	329	11	�	�	PROPN
iajs-3094	329	12	)	)	PUNCT
iajs-3094	329	13	+	+	CCONJ
iajs-3094	329	14	(	(	PUNCT
iajs-3094	329	15	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	329	16	−	−	NOUN
iajs-3094	329	17	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	329	18	)	)	PUNCT
iajs-3094	329	19	≤	≤	NUM
iajs-3094	329	20	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	329	21	�	�	NOUN
iajs-3094	329	22	̇	̇	NOUN
iajs-3094	329	23	�	�	PROPN
iajs-3094	329	24	)	)	PUNCT
iajs-3094	330	1	+	+	CCONJ
iajs-3094	330	2	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	330	3	−	−	PROPN
iajs-3094	330	4	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	330	5	.	.	PUNCT
iajs-3094	331	1	(	(	PUNCT
iajs-3094	331	2	by	by	ADP
iajs-3094	331	3	adding	add	VERB
iajs-3094	331	4	∑𝐸𝑘(	∑𝐸𝑘(	PROPN
iajs-3094	331	5	�	�	PROPN
iajs-3094	331	6	̇	̇	PROPN
iajs-3094	331	7	�	�	PROPN
iajs-3094	331	8	)	)	PUNCT
iajs-3094	331	9	for	for	ADP
iajs-3094	331	10	both	both	DET
iajs-3094	331	11	sides	side	NOUN
iajs-3094	331	12	)	)	PUNCT
iajs-3094	331	13	by	by	ADP
iajs-3094	331	14	equation	equation	NOUN
iajs-3094	331	15	(	(	PUNCT
iajs-3094	331	16	5	5	NUM
iajs-3094	331	17	)	)	PUNCT
iajs-3094	331	18	then	then	ADV
iajs-3094	331	19	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	331	20	)	)	PUNCT
iajs-3094	331	21	+	+	CCONJ
iajs-3094	331	22	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	331	23	)	)	PUNCT
iajs-3094	331	24	≤	≤	NOUN
iajs-3094	331	25	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	NOUN
iajs-3094	331	26	)	)	PUNCT
iajs-3094	331	27	+	+	CCONJ
iajs-3094	331	28	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	331	29	−	−	PROPN
iajs-3094	331	30	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	331	31	+	+	CCONJ
iajs-3094	331	32	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	331	33	�	�	PROPN
iajs-3094	331	34	̇	̇	NOUN
iajs-3094	331	35	�	�	PROPN
iajs-3094	331	36	)	)	PUNCT
iajs-3094	331	37	.	.	PUNCT
iajs-3094	332	1	from	from	ADP
iajs-3094	332	2	equation	equation	NOUN
iajs-3094	332	3	(	(	PUNCT
iajs-3094	332	4	3	3	NUM
iajs-3094	332	5	)	)	PUNCT
iajs-3094	332	6	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	NOUN
iajs-3094	332	7	)	)	PUNCT
iajs-3094	332	8	+	+	CCONJ
iajs-3094	332	9	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	332	10	)	)	PUNCT
iajs-3094	332	11	≤	≤	PUNCT
iajs-3094	332	12	∑𝐶𝒦(	∑𝐶𝒦(	PROPN
iajs-3094	332	13	�	�	PROPN
iajs-3094	332	14	̇	̇	VERB
iajs-3094	332	15	�	�	PROPN
iajs-3094	332	16	)	)	PUNCT
iajs-3094	332	17	+	+	CCONJ
iajs-3094	332	18	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	332	19	�	�	SYM
iajs-3094	332	20	̇	̇	NOUN
iajs-3094	332	21	�	�	NOUN
iajs-3094	332	22	)(by	)(by	NOUN
iajs-3094	332	23	adding	add	VERB
iajs-3094	332	24	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	332	25	for	for	ADP
iajs-3094	332	26	both	both	DET
iajs-3094	332	27	sides	side	NOUN
iajs-3094	332	28	)	)	PUNCT
iajs-3094	332	29	.	.	PUNCT
iajs-3094	333	1	and	and	CCONJ
iajs-3094	333	2	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	333	3	)	)	PUNCT
iajs-3094	333	4	+	+	CCONJ
iajs-3094	333	5	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	333	6	)	)	PUNCT
iajs-3094	333	7	+	+	CCONJ
iajs-3094	333	8	𝑇𝑚𝑎𝑥(𝜎	𝑇𝑚𝑎𝑥(𝜎	PROPN
iajs-3094	333	9	)	)	PUNCT
iajs-3094	333	10	≤	≤	NUM
iajs-3094	333	11	∑𝐶𝒦(	∑𝐶𝒦(	PROPN
iajs-3094	333	12	�	�	PROPN
iajs-3094	333	13	̇	̇	VERB
iajs-3094	333	14	�	�	PROPN
iajs-3094	333	15	)	)	PUNCT
iajs-3094	333	16	+	+	CCONJ
iajs-3094	333	17	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	333	18	�	�	SYM
iajs-3094	333	19	̇	̇	NOUN
iajs-3094	333	20	�	�	PROPN
iajs-3094	333	21	)	)	PUNCT
iajs-3094	333	22	+	+	CCONJ
iajs-3094	333	23	𝑇𝑚𝑎𝑥(	𝑇𝑚𝑎𝑥(	PROPN
iajs-3094	333	24	�	�	PROPN
iajs-3094	333	25	̇	̇	PROPN
iajs-3094	333	26	�	�	PROPN
iajs-3094	333	27	)	)	PUNCT
iajs-3094	333	28	.	.	PUNCT
iajs-3094	334	1	rule	rule	NOUN
iajs-3094	334	2	(	(	PUNCT
iajs-3094	334	3	2	2	NUM
iajs-3094	334	4	):	):	PUNCT
iajs-3094	334	5	the	the	DET
iajs-3094	334	6	schedule	schedule	NOUN
iajs-3094	334	7	σij	σij	NOUN
iajs-3094	334	8	is	be	AUX
iajs-3094	334	9	dominated	dominate	VERB
iajs-3094	334	10	by	by	ADP
iajs-3094	334	11	the	the	DET
iajs-3094	334	12	schedule	schedule	NOUN
iajs-3094	334	13	σji	σji	NOUN
iajs-3094	334	14	if	if	SCONJ
iajs-3094	334	15	the	the	DET
iajs-3094	334	16	following	follow	VERB
iajs-3094	334	17	inequalities	inequality	NOUN
iajs-3094	334	18	hold	hold	VERB
iajs-3094	334	19	:	:	PUNCT
iajs-3094	334	20	(	(	PUNCT
iajs-3094	334	21	1	1	X
iajs-3094	334	22	)	)	PUNCT
iajs-3094	334	23	𝑝𝑖	𝑝𝑖	VERB
iajs-3094	334	24	≤	≤	ADJ
iajs-3094	334	25	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	334	26	(	(	PUNCT
iajs-3094	334	27	2	2	NUM
iajs-3094	334	28	)	)	PUNCT
iajs-3094	334	29	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	334	30	≤	≤	NOUN
iajs-3094	334	31	𝑑𝑖	𝑑𝑖	PROPN
iajs-3094	334	32	(	(	PUNCT
iajs-3094	334	33	3	3	X
iajs-3094	334	34	)	)	PUNCT
iajs-3094	334	35	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	334	36	≥	≥	NOUN
iajs-3094	334	37	𝑠𝑖.	𝑠𝑖.	NOUN
iajs-3094	334	38	proof	proof	NOUN
iajs-3094	334	39	:	:	PUNCT
iajs-3094	334	40	consider	consider	VERB
iajs-3094	334	41	a	a	DET
iajs-3094	334	42	schedule	schedule	NOUN
iajs-3094	334	43	𝜎	𝜎	NOUN
iajs-3094	334	44	=	=	X
iajs-3094	334	45	𝜎1𝑖𝑗𝜎2	𝜎1𝑖𝑗𝜎2	PROPN
iajs-3094	334	46	and	and	CCONJ
iajs-3094	334	47	a	a	DET
iajs-3094	334	48	schedule	schedule	NOUN
iajs-3094	334	49	�	�	NOUN
iajs-3094	334	50	̇	̇	NOUN
iajs-3094	334	51	�	�	PROPN
iajs-3094	334	52	=	=	PUNCT
iajs-3094	334	53	𝜎1𝑗𝑖𝜎2	𝜎1𝑗𝑖𝜎2	NOUN
iajs-3094	334	54	which	which	PRON
iajs-3094	334	55	is	be	AUX
iajs-3094	334	56	obtained	obtain	VERB
iajs-3094	334	57	by	by	ADP
iajs-3094	334	58	interchanging	interchange	VERB
iajs-3094	334	59	the	the	DET
iajs-3094	334	60	jobs	job	NOUN
iajs-3094	334	61	i	i	PRON
iajs-3094	334	62	and	and	CCONJ
iajs-3094	334	63	j	j	PROPN
iajs-3094	334	64	in	in	ADP
iajs-3094	334	65	σ	σ	PROPN
iajs-3094	334	66	.	.	PUNCT
iajs-3094	335	1	the	the	DET
iajs-3094	335	2	condition	condition	NOUN
iajs-3094	335	3	of	of	ADP
iajs-3094	335	4	the	the	DET
iajs-3094	335	5	processing	processing	NOUN
iajs-3094	335	6	times	time	NOUN
iajs-3094	335	7	ensures	ensure	VERB
iajs-3094	335	8	that	that	SCONJ
iajs-3094	335	9	(	(	PUNCT
iajs-3094	335	10	∑c𝒦(σ	∑c𝒦(σ	NOUN
iajs-3094	335	11	)	)	PUNCT
iajs-3094	335	12	≤	≤	NOUN
iajs-3094	335	13	∑c𝒦(σ̇	∑c𝒦(σ̇	NOUN
iajs-3094	335	14	)	)	PUNCT
iajs-3094	335	15	is	be	AUX
iajs-3094	335	16	satisfied	satisfied	ADJ
iajs-3094	335	17	and	and	CCONJ
iajs-3094	335	18	then	then	ADV
iajs-3094	335	19	the	the	DET
iajs-3094	335	20	addition	addition	NOUN
iajs-3094	335	21	in	in	ADP
iajs-3094	335	22	cost	cost	NOUN
iajs-3094	335	23	is	be	AUX
iajs-3094	335	24	obtained	obtain	VERB
iajs-3094	335	25	by	by	ADP
iajs-3094	335	26	(	(	PUNCT
iajs-3094	335	27	∑𝐶𝒦(	∑𝐶𝒦(	PROPN
iajs-3094	335	28	�	�	PROPN
iajs-3094	335	29	̇	̇	VERB
iajs-3094	335	30	�	�	PROPN
iajs-3094	335	31	)	)	PUNCT
iajs-3094	335	32	=	=	SYM
iajs-3094	335	33	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	335	34	)	)	PUNCT
iajs-3094	335	35	+	+	CCONJ
iajs-3094	335	36	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	335	37	−	−	PROPN
iajs-3094	335	38	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	335	39	(	(	PUNCT
iajs-3094	335	40	6	6	NUM
iajs-3094	335	41	)	)	PUNCT
iajs-3094	335	42	since	since	SCONJ
iajs-3094	335	43	𝐶𝑖(𝜎	𝐶𝑖(𝜎	NOUN
iajs-3094	335	44	)	)	PUNCT
iajs-3094	335	45	=	=	PUNCT
iajs-3094	335	46	𝐶𝑗(	𝐶𝑗(	PROPN
iajs-3094	335	47	�	�	PROPN
iajs-3094	335	48	̇	̇	PROPN
iajs-3094	335	49	�	�	PROPN
iajs-3094	335	50	)	)	PUNCT
iajs-3094	335	51	−	−	PROPN
iajs-3094	335	52	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	335	53	+	+	CCONJ
iajs-3094	335	54	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	335	55	then	then	ADV
iajs-3094	335	56	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	335	57	−	−	PROPN
iajs-3094	335	58	𝐶𝑖(𝜎	𝐶𝑖(𝜎	NOUN
iajs-3094	335	59	)	)	PUNCT
iajs-3094	335	60	=	=	PRON
iajs-3094	335	61	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	335	62	−	−	PROPN
iajs-3094	335	63	𝐶𝑗(	𝐶𝑗(	SYM
iajs-3094	335	64	�	�	PROPN
iajs-3094	335	65	̇	̇	PROPN
iajs-3094	335	66	�	�	PROPN
iajs-3094	335	67	)	)	PUNCT
iajs-3094	335	68	+	+	CCONJ
iajs-3094	335	69	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	335	70	−	−	NOUN
iajs-3094	335	71	𝑝𝑖.the	𝑝𝑖.the	PRON
iajs-3094	335	72	condition	condition	NOUN
iajs-3094	335	73	(	(	PUNCT
iajs-3094	335	74	1	1	NUM
iajs-3094	335	75	)	)	PUNCT
iajs-3094	335	76	,	,	PUNCT
iajs-3094	335	77	(	(	PUNCT
iajs-3094	335	78	2	2	X
iajs-3094	335	79	)	)	PUNCT
iajs-3094	335	80	implies	imply	VERB
iajs-3094	335	81	,	,	PUNCT
iajs-3094	335	82	since	since	SCONJ
iajs-3094	335	83	𝑠𝑖	𝑠𝑖	PROPN
iajs-3094	335	84	≥	≥	NOUN
iajs-3094	335	85	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	335	86	then	then	ADV
iajs-3094	335	87	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	335	88	−	−	PROPN
iajs-3094	335	89	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	335	90	−	−	PROPN
iajs-3094	335	91	𝐶𝑗(	𝐶𝑗(	NOUN
iajs-3094	335	92	�	�	PROPN
iajs-3094	335	93	̇	̇	PROPN
iajs-3094	335	94	�	�	PROPN
iajs-3094	335	95	)	)	PUNCT
iajs-3094	335	96	≥	≥	NOUN
iajs-3094	335	97	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	335	98	−	−	PROPN
iajs-3094	335	99	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	335	100	−	−	PROPN
iajs-3094	335	101	𝐶𝑗(	𝐶𝑗(	NOUN
iajs-3094	335	102	�	�	PROPN
iajs-3094	335	103	̇	̇	PROPN
iajs-3094	335	104	�	�	PROPN
iajs-3094	335	105	)	)	PUNCT
iajs-3094	335	106	hence	hence	ADV
iajs-3094	335	107	𝑑𝑖	𝑑𝑖	PROPN
iajs-3094	335	108	−	−	PROPN
iajs-3094	335	109	𝑝𝑖	𝑝𝑖	PROPN
iajs-3094	335	110	+	+	NOUN
iajs-3094	335	111	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	335	112	−	−	PROPN
iajs-3094	335	113	𝐶𝑗(	𝐶𝑗(	NOUN
iajs-3094	335	114	�	�	PROPN
iajs-3094	335	115	̇	̇	PROPN
iajs-3094	335	116	�	�	PROPN
iajs-3094	335	117	)	)	PUNCT
iajs-3094	335	118	≥	≥	NOUN
iajs-3094	335	119	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	335	120	−	−	ADP
iajs-3094	335	121	𝐶𝑗(	𝐶𝑗(	NOUN
iajs-3094	335	122	�	�	PROPN
iajs-3094	335	123	̇	̇	PROPN
iajs-3094	335	124	�	�	PROPN
iajs-3094	335	125	)	)	PUNCT
iajs-3094	335	126	from	from	ADP
iajs-3094	335	127	which	which	PRON
iajs-3094	335	128	we	we	PRON
iajs-3094	335	129	deduce	deduce	VERB
iajs-3094	335	130	that	that	PRON
iajs-3094	335	131	𝐸𝑚𝑎𝑥(𝜎	𝐸𝑚𝑎𝑥(𝜎	NOUN
iajs-3094	335	132	)	)	PUNCT
iajs-3094	335	133	≥	≥	NOUN
iajs-3094	335	134	𝐸𝑚𝑎𝑥(	𝐸𝑚𝑎𝑥(	PART
iajs-3094	335	135	�	�	PROPN
iajs-3094	335	136	̇	̇	PROPN
iajs-3094	335	137	�	�	PROPN
iajs-3094	335	138	)	)	PUNCT
iajs-3094	335	139	then	then	ADV
iajs-3094	335	140	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	335	141	)	)	PUNCT
iajs-3094	336	1	≥	≥	NOUN
iajs-3094	336	2	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	336	3	�	�	PROPN
iajs-3094	336	4	̇	̇	NOUN
iajs-3094	336	5	�	�	PROPN
iajs-3094	336	6	)	)	PUNCT
iajs-3094	336	7	.	.	PUNCT
iajs-3094	337	1	ihjpas	ihjpas	PROPN
iajs-3094	337	2	.	.	PUNCT
iajs-3094	338	1	37	37	NUM
iajs-3094	338	2	(	(	PUNCT
iajs-3094	338	3	1	1	NUM
iajs-3094	338	4	)	)	PUNCT
iajs-3094	338	5	2024	2024	NUM
iajs-3094	338	6	399	399	NUM
iajs-3094	338	7	then	then	ADV
iajs-3094	338	8	the	the	DET
iajs-3094	338	9	addition	addition	NOUN
iajs-3094	338	10	in	in	ADP
iajs-3094	338	11	cost	cost	NOUN
iajs-3094	338	12	from	from	ADP
iajs-3094	338	13	this	this	DET
iajs-3094	338	14	inequality	inequality	NOUN
iajs-3094	338	15	is	be	AUX
iajs-3094	338	16	obtained	obtain	VERB
iajs-3094	338	17	from	from	ADP
iajs-3094	338	18	(	(	PUNCT
iajs-3094	338	19	∑𝐸(𝜎	∑𝐸(𝜎	PROPN
iajs-3094	338	20	)	)	PUNCT
iajs-3094	338	21	=	=	SYM
iajs-3094	338	22	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	338	23	�	�	PROPN
iajs-3094	338	24	̇	̇	NOUN
iajs-3094	338	25	�	�	PROPN
iajs-3094	338	26	)	)	PUNCT
iajs-3094	339	1	+	+	CCONJ
iajs-3094	339	2	(	(	PUNCT
iajs-3094	339	3	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	339	4	−	−	PROPN
iajs-3094	339	5	𝑠𝑗	𝑠𝑗	PROPN
iajs-3094	339	6	)	)	PUNCT
iajs-3094	339	7	𝑑𝑖	𝑑𝑖	PART
iajs-3094	339	8	≥	≥	NUM
iajs-3094	339	9	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	339	10	and	and	CCONJ
iajs-3094	339	11	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	339	12	≥	≥	NOUN
iajs-3094	339	13	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	339	14	this	this	DET
iajs-3094	339	15	mean	mean	INTJ
iajs-3094	339	16	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	339	17	−	−	PROPN
iajs-3094	339	18	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	339	19	≥	≥	NOUN
iajs-3094	339	20	0	0	NUM
iajs-3094	339	21	,	,	PUNCT
iajs-3094	339	22	hence	hence	ADV
iajs-3094	339	23	𝑑𝑖	𝑑𝑖	VERB
iajs-3094	340	1	−	−	PROPN
iajs-3094	340	2	𝑑𝑗	𝑑𝑗	PROPN
iajs-3094	340	3	+	+	CCONJ
iajs-3094	340	4	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	340	5	−	−	PROPN
iajs-3094	340	6	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	340	7	≥	≥	PROPN
iajs-3094	340	8	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	340	9	−	−	PROPN
iajs-3094	340	10	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	340	11	,	,	PUNCT
iajs-3094	340	12	and	and	CCONJ
iajs-3094	340	13	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	340	14	−	−	PROPN
iajs-3094	341	1	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	341	2	≥	≥	NOUN
iajs-3094	341	3	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	341	4	−	−	PROPN
iajs-3094	341	5	𝑝𝑖.	𝑝𝑖.	CCONJ
iajs-3094	341	6	then	then	ADV
iajs-3094	341	7	∑𝐸𝑘(	∑𝐸𝑘(	PROPN
iajs-3094	341	8	�	�	PROPN
iajs-3094	341	9	̇	̇	PROPN
iajs-3094	341	10	�	�	PROPN
iajs-3094	341	11	)	)	PUNCT
iajs-3094	342	1	+	+	CCONJ
iajs-3094	342	2	(	(	PUNCT
iajs-3094	342	3	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	342	4	−	−	PROPN
iajs-3094	342	5	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	342	6	)	)	PUNCT
iajs-3094	342	7	≥	≥	NOUN
iajs-3094	342	8	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	342	9	�	�	PROPN
iajs-3094	342	10	̇	̇	NOUN
iajs-3094	342	11	�	�	PROPN
iajs-3094	342	12	)	)	PUNCT
iajs-3094	343	1	+	+	CCONJ
iajs-3094	343	2	𝑝𝑗	𝑝𝑗	PROPN
iajs-3094	343	3	−	−	PROPN
iajs-3094	343	4	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	343	5	,	,	PUNCT
iajs-3094	343	6	(	(	PUNCT
iajs-3094	343	7	by	by	ADP
iajs-3094	343	8	adding	add	VERB
iajs-3094	343	9	∑e𝒦(σ̇	∑e𝒦(σ̇	PROPN
iajs-3094	343	10	)	)	PUNCT
iajs-3094	343	11	for	for	ADP
iajs-3094	343	12	both	both	DET
iajs-3094	343	13	sides	side	NOUN
iajs-3094	343	14	)	)	PUNCT
iajs-3094	343	15	.	.	PUNCT
iajs-3094	344	1	from	from	ADP
iajs-3094	344	2	(	(	PUNCT
iajs-3094	344	3	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	344	4	)	)	PUNCT
iajs-3094	344	5	=	=	SYM
iajs-3094	344	6	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	344	7	�	�	PROPN
iajs-3094	344	8	̇	̇	NOUN
iajs-3094	344	9	�	�	PROPN
iajs-3094	344	10	)	)	PUNCT
iajs-3094	344	11	+	+	CCONJ
iajs-3094	344	12	(	(	PUNCT
iajs-3094	344	13	𝑠𝑖	𝑠𝑖	NOUN
iajs-3094	344	14	−	−	NOUN
iajs-3094	344	15	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	344	16	)	)	PUNCT
iajs-3094	344	17	and	and	CCONJ
iajs-3094	344	18	then	then	ADV
iajs-3094	344	19	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	344	20	)	)	PUNCT
iajs-3094	344	21	+	+	CCONJ
iajs-3094	344	22	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	344	23	)	)	PUNCT
iajs-3094	344	24	≥	≥	NOUN
iajs-3094	344	25	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	344	26	)	)	PUNCT
iajs-3094	344	27	+	+	CCONJ
iajs-3094	344	28	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	344	29	−	−	PROPN
iajs-3094	344	30	𝑝𝑖	𝑝𝑖	NOUN
iajs-3094	344	31	+	+	CCONJ
iajs-3094	344	32	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	344	33	�	�	PROPN
iajs-3094	344	34	̇	̇	NOUN
iajs-3094	344	35	�	�	PROPN
iajs-3094	344	36	)	)	PUNCT
iajs-3094	344	37	,	,	PUNCT
iajs-3094	344	38	(	(	PUNCT
iajs-3094	344	39	by	by	ADP
iajs-3094	344	40	adding	add	VERB
iajs-3094	344	41	∑𝐶𝑘(𝜎	∑𝐶𝑘(𝜎	PUNCT
iajs-3094	344	42	)	)	PUNCT
iajs-3094	344	43	for	for	ADP
iajs-3094	344	44	both	both	DET
iajs-3094	344	45	sides	side	NOUN
iajs-3094	344	46	)	)	PUNCT
iajs-3094	344	47	.	.	PUNCT
iajs-3094	345	1	from	from	ADP
iajs-3094	345	2	equation	equation	NOUN
iajs-3094	345	3	(	(	PUNCT
iajs-3094	345	4	6	6	NUM
iajs-3094	345	5	)	)	PUNCT
iajs-3094	345	6	there	there	PRON
iajs-3094	345	7	is	be	VERB
iajs-3094	345	8	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	345	9	)	)	PUNCT
iajs-3094	345	10	+	+	CCONJ
iajs-3094	345	11	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	345	12	)	)	PUNCT
iajs-3094	345	13	≤	≤	PUNCT
iajs-3094	345	14	∑𝐶𝒦(	∑𝐶𝒦(	PROPN
iajs-3094	345	15	�	�	PROPN
iajs-3094	345	16	̇	̇	VERB
iajs-3094	345	17	�	�	PROPN
iajs-3094	345	18	)	)	PUNCT
iajs-3094	345	19	+	+	CCONJ
iajs-3094	345	20	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	345	21	�	�	SYM
iajs-3094	345	22	̇	̇	NOUN
iajs-3094	345	23	�	�	PROPN
iajs-3094	345	24	)	)	PUNCT
iajs-3094	345	25	(	(	PUNCT
iajs-3094	345	26	by	by	ADP
iajs-3094	345	27	adding	add	VERB
iajs-3094	345	28	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	345	29	for	for	ADP
iajs-3094	345	30	both	both	DET
iajs-3094	345	31	sides	side	NOUN
iajs-3094	345	32	)	)	PUNCT
iajs-3094	345	33	,	,	PUNCT
iajs-3094	345	34	finally	finally	ADV
iajs-3094	345	35	∑𝐶𝒦(𝜎	∑𝐶𝒦(𝜎	PROPN
iajs-3094	345	36	)	)	PUNCT
iajs-3094	345	37	+	+	CCONJ
iajs-3094	345	38	∑𝐸𝒦(𝜎	∑𝐸𝒦(𝜎	PROPN
iajs-3094	345	39	)	)	PUNCT
iajs-3094	346	1	+	+	CCONJ
iajs-3094	346	2	𝑇𝑚𝑎𝑥(𝜎	𝑇𝑚𝑎𝑥(𝜎	PROPN
iajs-3094	346	3	)	)	PUNCT
iajs-3094	346	4	≤	≤	NUM
iajs-3094	346	5	∑𝐶𝑘(	∑𝐶𝑘(	PROPN
iajs-3094	346	6	�	�	PROPN
iajs-3094	346	7	̇	̇	PROPN
iajs-3094	346	8	�	�	PROPN
iajs-3094	346	9	)	)	PUNCT
iajs-3094	346	10	+	+	CCONJ
iajs-3094	346	11	∑𝐸𝒦(	∑𝐸𝒦(	PROPN
iajs-3094	346	12	�	�	SYM
iajs-3094	346	13	̇	̇	NOUN
iajs-3094	346	14	�	�	PROPN
iajs-3094	346	15	)	)	PUNCT
iajs-3094	347	1	+	+	NUM
iajs-3094	347	2	𝑇(	𝑇(	PROPN
iajs-3094	347	3	�	�	PROPN
iajs-3094	347	4	̇	̇	PROPN
iajs-3094	347	5	�	�	PROPN
iajs-3094	347	6	)	)	PUNCT
iajs-3094	347	7	.	.	PUNCT
iajs-3094	348	1	example	example	NOUN
iajs-3094	348	2	(	(	PUNCT
iajs-3094	348	3	3	3	NUM
iajs-3094	348	4	):	):	PUNCT
iajs-3094	348	5	let	let	VERB
iajs-3094	348	6	’s	’s	PRON
iajs-3094	348	7	use	use	VERB
iajs-3094	348	8	msp	msp	NOUN
iajs-3094	348	9	with	with	ADP
iajs-3094	348	10	5	5	NUM
iajs-3094	348	11	jobs	job	NOUN
iajs-3094	348	12	and	and	CCONJ
iajs-3094	348	13	processing	processing	NOUN
iajs-3094	348	14	time	time	NOUN
iajs-3094	348	15	and	and	CCONJ
iajs-3094	348	16	due	due	ADJ
iajs-3094	348	17	date	date	NOUN
iajs-3094	348	18	as	as	ADP
iajs-3094	348	19	the	the	DET
iajs-3094	348	20	following	follow	VERB
iajs-3094	348	21	table	table	NOUN
iajs-3094	348	22	:	:	PUNCT
iajs-3094	348	23	table	table	NOUN
iajs-3094	348	24	4	4	NUM
iajs-3094	348	25	.	.	PUNCT
iajs-3094	349	1	the	the	DET
iajs-3094	349	2	data	datum	NOUN
iajs-3094	349	3	of	of	ADP
iajs-3094	349	4	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	349	5	,	,	PUNCT
iajs-3094	349	6	𝑑𝑗	𝑑𝑗	NOUN
iajs-3094	349	7	,	,	PUNCT
iajs-3094	349	8	and	and	CCONJ
iajs-3094	349	9	𝑠𝑗	𝑠𝑗	INTJ
iajs-3094	349	10	for	for	ADP
iajs-3094	349	11	problem	problem	NOUN
iajs-3094	349	12	(	(	PUNCT
iajs-3094	349	13	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	349	14	)	)	PUNCT
iajs-3094	349	15	when	when	SCONJ
iajs-3094	349	16	using	use	VERB
iajs-3094	349	17	the	the	DET
iajs-3094	349	18	rule	rule	NOUN
iajs-3094	349	19	(	(	PUNCT
iajs-3094	349	20	1	1	X
iajs-3094	349	21	)	)	PUNCT
iajs-3094	349	22	we	we	PRON
iajs-3094	349	23	obtain	obtain	VERB
iajs-3094	349	24	the	the	DET
iajs-3094	349	25	drs	dr	NOUN
iajs-3094	349	26	mentioned	mention	VERB
iajs-3094	349	27	in	in	ADP
iajs-3094	349	28	figure	figure	NOUN
iajs-3094	349	29	(	(	PUNCT
iajs-3094	349	30	3	3	NUM
iajs-3094	349	31	)	)	PUNCT
iajs-3094	349	32	.	.	PUNCT
iajs-3094	350	1	figure	figure	NOUN
iajs-3094	350	2	(	(	PUNCT
iajs-3094	350	3	3	3	NUM
iajs-3094	350	4	):	):	PUNCT
iajs-3094	350	5	the	the	DET
iajs-3094	350	6	drs	dr	NOUN
iajs-3094	350	7	of	of	ADP
iajs-3094	350	8	the	the	DET
iajs-3094	350	9	example	example	NOUN
iajs-3094	350	10	(	(	PUNCT
iajs-3094	350	11	3	3	NUM
iajs-3094	350	12	)	)	PUNCT
iajs-3094	350	13	.	.	PUNCT
iajs-3094	351	1	from	from	ADP
iajs-3094	351	2	rule	rule	NOUN
iajs-3094	351	3	(	(	PUNCT
iajs-3094	351	4	1	1	X
iajs-3094	351	5	)	)	PUNCT
iajs-3094	351	6	there	there	PRON
iajs-3094	351	7	are	be	VERB
iajs-3094	351	8	(	(	PUNCT
iajs-3094	351	9	6	6	NUM
iajs-3094	351	10	)	)	PUNCT
iajs-3094	351	11	drs	dr	NOUN
iajs-3094	351	12	,	,	PUNCT
iajs-3094	351	13	as	as	SCONJ
iajs-3094	351	14	can	can	AUX
iajs-3094	351	15	see	see	VERB
iajs-3094	351	16	:	:	PUNCT
iajs-3094	351	17	12	12	NUM
iajs-3094	351	18	,	,	PUNCT
iajs-3094	351	19	1	1	NUM
iajs-3094	351	20	3,14	3,14	NUM
iajs-3094	351	21	,	,	PUNCT
iajs-3094	351	22	16	16	NUM
iajs-3094	351	23	,	,	PUNCT
iajs-3094	351	24	2	2	NUM
iajs-3094	351	25	6	6	NUM
iajs-3094	351	26	,	,	PUNCT
iajs-3094	351	27	42	42	NUM
iajs-3094	351	28	,	,	PUNCT
iajs-3094	351	29	4	4	NUM
iajs-3094	351	30	3	3	NUM
iajs-3094	351	31	,	,	PUNCT
iajs-3094	351	32	4	4	NUM
iajs-3094	351	33	6,53	6,53	NOUN
iajs-3094	351	34	.	.	PUNCT
iajs-3094	352	1	in	in	ADP
iajs-3094	352	2	table	table	NOUN
iajs-3094	352	3	5	5	NUM
iajs-3094	352	4	,	,	PUNCT
iajs-3094	352	5	contain	contain	VERB
iajs-3094	352	6	(	(	PUNCT
iajs-3094	352	7	7	7	NUM
iajs-3094	352	8	)	)	PUNCT
iajs-3094	352	9	likely	likely	ADJ
iajs-3094	352	10	sequences	sequence	NOUN
iajs-3094	352	11	some	some	PRON
iajs-3094	352	12	/all	/all	PUNCT
iajs-3094	352	13	are	be	AUX
iajs-3094	352	14	subject	subject	ADJ
iajs-3094	352	15	to	to	ADP
iajs-3094	352	16	the	the	DET
iajs-3094	352	17	aforementioned	aforementioned	ADJ
iajs-3094	352	18	drs	dr	NOUN
iajs-3094	352	19	.	.	PUNCT
iajs-3094	353	1	the	the	DET
iajs-3094	353	2	adjacency	adjacency	PROPN
iajs-3094	353	3	matrix	matrix	NOUN
iajs-3094	353	4	𝐴	𝐴	PROPN
iajs-3094	353	5	is	be	AUX
iajs-3094	353	6	as	as	ADP
iajs-3094	353	7	followings	following	NOUN
iajs-3094	353	8	:	:	PUNCT
iajs-3094	353	9	𝐴(𝐺	𝐴(𝐺	NOUN
iajs-3094	353	10	)	)	PUNCT
iajs-3094	353	11	=	=	PUNCT
iajs-3094	354	1	[	[	PUNCT
iajs-3094	354	2	0	0	NUM
iajs-3094	354	3	1	1	NUM
iajs-3094	354	4	1	1	NUM
iajs-3094	354	5	1	1	NUM
iajs-3094	354	6	𝑎15	𝑎15	NOUN
iajs-3094	354	7	0	0	NUM
iajs-3094	354	8	0	0	NUM
iajs-3094	354	9	𝑎23	𝑎23	NOUN
iajs-3094	354	10	0	0	NUM
iajs-3094	354	11	𝑎25	𝑎25	NOUN
iajs-3094	354	12	0	0	NUM
iajs-3094	354	13	𝑎32	𝑎32	NOUN
iajs-3094	354	14	0	0	NUM
iajs-3094	354	15	0	0	NUM
iajs-3094	354	16	0	0	NUM
iajs-3094	354	17	0	0	NUM
iajs-3094	354	18	1	1	NUM
iajs-3094	354	19	1	1	NUM
iajs-3094	354	20	0	0	NUM
iajs-3094	354	21	𝑎45	𝑎45	PROPN
iajs-3094	354	22	𝑎51	𝑎51	PROPN
iajs-3094	354	23	𝑎52	𝑎52	PROPN
iajs-3094	354	24	1	1	NUM
iajs-3094	354	25	𝑎54	𝑎54	NOUN
iajs-3094	354	26	0	0	NUM
iajs-3094	354	27	]	]	PUNCT
iajs-3094	354	28	.	.	PUNCT
iajs-3094	355	1	where	where	SCONJ
iajs-3094	355	2	𝑎𝑗𝑖	𝑎𝑗𝑖	ADV
iajs-3094	355	3	=	=	PUNCT
iajs-3094	355	4	{	{	PUNCT
iajs-3094	355	5	1	1	NUM
iajs-3094	355	6	,	,	PUNCT
iajs-3094	355	7	if	if	SCONJ
iajs-3094	355	8	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-3094	355	9	=	=	SYM
iajs-3094	355	10	0	0	NUM
iajs-3094	355	11	0	0	NUM
iajs-3094	355	12	,	,	PUNCT
iajs-3094	355	13	if	if	SCONJ
iajs-3094	355	14	𝑎𝑖𝑗	𝑎𝑖𝑗	NOUN
iajs-3094	355	15	=	=	SYM
iajs-3094	355	16	1	1	NUM
iajs-3094	355	17	.	.	NOUN
iajs-3094	355	18	1	1	NUM
iajs-3094	355	19	2	2	NUM
iajs-3094	355	20	3	3	NUM
iajs-3094	355	21	4	4	NUM
iajs-3094	355	22	5	5	NUM
iajs-3094	355	23	𝑝𝑗	𝑝𝑗	NOUN
iajs-3094	355	24	1	1	NUM
iajs-3094	355	25	8	8	NUM
iajs-3094	355	26	10	10	NUM
iajs-3094	355	27	4	4	NUM
iajs-3094	355	28	9	9	NUM
iajs-3094	355	29	𝑑𝑗	𝑑𝑗	ADP
iajs-3094	355	30	14	14	NUM
iajs-3094	355	31	28	28	NUM
iajs-3094	355	32	27	27	NUM
iajs-3094	355	33	23	23	NUM
iajs-3094	355	34	12	12	NUM
iajs-3094	355	35	𝑠𝑗	𝑠𝑗	NOUN
iajs-3094	355	36	13	13	NUM
iajs-3094	355	37	20	20	NUM
iajs-3094	355	38	17	17	NUM
iajs-3094	355	39	19	19	NUM
iajs-3094	355	40	3	3	NUM
iajs-3094	355	41	1	1	NUM
iajs-3094	355	42	4	4	NUM
iajs-3094	355	43	5	5	NUM
iajs-3094	355	44	2	2	NUM
iajs-3094	355	45	3	3	NUM
iajs-3094	355	46	ihjpas	ihjpa	NOUN
iajs-3094	355	47	.	.	PUNCT
iajs-3094	356	1	37	37	NUM
iajs-3094	356	2	(	(	PUNCT
iajs-3094	356	3	1	1	NUM
iajs-3094	356	4	)	)	PUNCT
iajs-3094	356	5	2024	2024	NUM
iajs-3094	356	6	400	400	NUM
iajs-3094	356	7	table	table	NOUN
iajs-3094	356	8	5	5	NUM
iajs-3094	356	9	.	.	PUNCT
iajs-3094	357	1	the	the	DET
iajs-3094	357	2	efficient	efficient	ADJ
iajs-3094	357	3	sequences	sequence	NOUN
iajs-3094	357	4	for	for	ADP
iajs-3094	357	5	example	example	NOUN
iajs-3094	357	6	(	(	PUNCT
iajs-3094	357	7	3	3	X
iajs-3094	357	8	)	)	PUNCT
iajs-3094	357	9	under	under	ADP
iajs-3094	357	10	dr	dr	PROPN
iajs-3094	357	11	ef	ef	PROPN
iajs-3094	357	12	-	-	PROPN
iajs-3094	357	13	sq	sq	INTJ
iajs-3094	357	14	(	(	PUNCT
iajs-3094	357	15	𝑺𝑪𝑺𝑬𝑻	𝑺𝑪𝑺𝑬𝑻	PROPN
iajs-3094	357	16	)	)	PUNCT
iajs-3094	357	17	𝑺₱𝟕	𝑺₱𝟕	NOUN
iajs-3094	357	18	seq	seq	NOUN
iajs-3094	357	19	.	.	PUNCT
iajs-3094	358	1	pos1	pos1	PROPN
iajs-3094	358	2	pos	pos	PROPN
iajs-3094	358	3	2	2	NUM
iajs-3094	358	4	pos	pos	NOUN
iajs-3094	358	5	3	3	NUM
iajs-3094	358	6	pos	pos	NOUN
iajs-3094	358	7	4	4	NUM
iajs-3094	358	8	pos	pos	NOUN
iajs-3094	358	9	5	5	NUM
iajs-3094	358	10	(	(	PUNCT
iajs-3094	358	11	∑𝑪𝒋	∑𝑪𝒋	PROPN
iajs-3094	358	12	,	,	PUNCT
iajs-3094	358	13	∑𝑬𝒋	∑𝑬𝒋	NOUN
iajs-3094	358	14	,	,	PUNCT
iajs-3094	358	15	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	358	16	)	)	PUNCT
iajs-3094	358	17	∑𝑪𝒋	∑𝑪𝒋	X
iajs-3094	359	1	+	+	CCONJ
iajs-3094	359	2	∑𝑬𝒋	∑𝑬𝒋	VERB
iajs-3094	359	3	+	+	CCONJ
iajs-3094	359	4	𝑻𝒎𝒂𝒙	𝑻𝒎𝒂𝒙	PROPN
iajs-3094	359	5	1	1	NUM
iajs-3094	359	6	1	1	NUM
iajs-3094	359	7	4	4	NUM
iajs-3094	359	8	2	2	NUM
iajs-3094	359	9	5	5	NUM
iajs-3094	359	10	3	3	NUM
iajs-3094	359	11	(	(	PUNCT
iajs-3094	359	12	73,46,10	73,46,10	NUM
iajs-3094	359	13	)	)	PUNCT
iajs-3094	359	14	129	129	NUM
iajs-3094	359	15	2	2	NUM
iajs-3094	359	16	1	1	NUM
iajs-3094	359	17	4	4	NUM
iajs-3094	359	18	5	5	NUM
iajs-3094	359	19	2	2	NUM
iajs-3094	359	20	3	3	NUM
iajs-3094	359	21	(	(	PUNCT
iajs-3094	359	22	74,37,5	74,37,5	NUM
iajs-3094	359	23	)	)	PUNCT
iajs-3094	359	24	116	116	NUM
iajs-3094	359	25	3	3	NUM
iajs-3094	359	26	1	1	NUM
iajs-3094	359	27	4	4	NUM
iajs-3094	359	28	5	5	NUM
iajs-3094	359	29	3	3	NUM
iajs-3094	359	30	2	2	NUM
iajs-3094	359	31	(	(	PUNCT
iajs-3094	359	32	76,34,4	76,34,4	NUM
iajs-3094	359	33	)	)	PUNCT
iajs-3094	359	34	114	114	NUM
iajs-3094	359	35	4	4	NUM
iajs-3094	359	36	1	1	NUM
iajs-3094	359	37	5	5	NUM
iajs-3094	359	38	4	4	NUM
iajs-3094	359	39	2	2	NUM
iajs-3094	359	40	3	3	NUM
iajs-3094	359	41	(	(	PUNCT
iajs-3094	359	42	79,30,5	79,30,5	NOUN
iajs-3094	359	43	)	)	PUNCT
iajs-3094	359	44	114	114	NUM
iajs-3094	359	45	5	5	NUM
iajs-3094	359	46	1	1	NUM
iajs-3094	359	47	5	5	NUM
iajs-3094	359	48	4	4	NUM
iajs-3094	359	49	3	3	NUM
iajs-3094	359	50	2	2	NUM
iajs-3094	359	51	(	(	PUNCT
iajs-3094	359	52	81,27,5	81,27,5	NUM
iajs-3094	359	53	)	)	PUNCT
iajs-3094	359	54	113	113	NUM
iajs-3094	359	55	6	6	NUM
iajs-3094	359	56	5	5	NUM
iajs-3094	359	57	1	1	NUM
iajs-3094	359	58	4	4	NUM
iajs-3094	359	59	2	2	NUM
iajs-3094	359	60	3	3	NUM
iajs-3094	359	61	(	(	PUNCT
iajs-3094	359	62	87,22,4	87,22,4	NUM
iajs-3094	359	63	)	)	PUNCT
iajs-3094	359	64	114	114	NUM
iajs-3094	359	65	7	7	NUM
iajs-3094	359	66	5	5	NUM
iajs-3094	359	67	1	1	NUM
iajs-3094	359	68	4	4	NUM
iajs-3094	359	69	3	3	NUM
iajs-3094	359	70	2	2	NUM
iajs-3094	359	71	(	(	PUNCT
iajs-3094	359	72	89,19,4	89,19,4	NUM
iajs-3094	359	73	)	)	PUNCT
iajs-3094	359	74	112	112	NUM
iajs-3094	359	75	where	where	SCONJ
iajs-3094	359	76	ef	ef	VERB
iajs-3094	359	77	-	-	ADJ
iajs-3094	359	78	sq	sq	ADJ
iajs-3094	359	79	=	=	ADJ
iajs-3094	359	80	efficient	efficient	ADJ
iajs-3094	359	81	sequence	sequence	NOUN
iajs-3094	359	82	,	,	PUNCT
iajs-3094	359	83	pos	pos	NOUN
iajs-3094	359	84	=	=	NOUN
iajs-3094	359	85	position	position	NOUN
iajs-3094	359	86	the	the	DET
iajs-3094	359	87	sequences	sequence	NOUN
iajs-3094	359	88	(	(	PUNCT
iajs-3094	359	89	1–7	1–7	NUM
iajs-3094	359	90	)	)	PUNCT
iajs-3094	359	91	provide	provide	VERB
iajs-3094	359	92	the	the	DET
iajs-3094	359	93	problem	problem	NOUN
iajs-3094	359	94	(	(	PUNCT
iajs-3094	359	95	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	359	96	)	)	PUNCT
iajs-3094	359	97	an	an	DET
iajs-3094	359	98	effective	effective	ADJ
iajs-3094	359	99	value	value	NOUN
iajs-3094	359	100	and	and	CCONJ
iajs-3094	359	101	the	the	DET
iajs-3094	359	102	sequence	sequence	NOUN
iajs-3094	359	103	(	(	PUNCT
iajs-3094	359	104	7	7	NUM
iajs-3094	359	105	)	)	PUNCT
iajs-3094	359	106	an	an	DET
iajs-3094	359	107	optimal	optimal	ADJ
iajs-3094	359	108	value	value	NOUN
iajs-3094	359	109	for	for	ADP
iajs-3094	359	110	the	the	DET
iajs-3094	359	111	problem	problem	NOUN
iajs-3094	359	112	(	(	PUNCT
iajs-3094	359	113	s₱7	s₱7	PROPN
iajs-3094	359	114	)	)	PUNCT
iajs-3094	359	115	,	,	PUNCT
iajs-3094	359	116	as	as	SCONJ
iajs-3094	359	117	can	can	AUX
iajs-3094	359	118	be	be	AUX
iajs-3094	359	119	shown	show	VERB
iajs-3094	359	120	in	in	ADP
iajs-3094	359	121	table	table	NOUN
iajs-3094	359	122	5	5	NUM
iajs-3094	359	123	.	.	NOUN
iajs-3094	359	124	6	6	NUM
iajs-3094	359	125	.	.	PUNCT
iajs-3094	360	1	conclusions	conclusion	NOUN
iajs-3094	360	2	in	in	ADP
iajs-3094	360	3	this	this	DET
iajs-3094	360	4	study	study	NOUN
iajs-3094	360	5	,	,	PUNCT
iajs-3094	360	6	a	a	DET
iajs-3094	360	7	mathematical	mathematical	ADJ
iajs-3094	360	8	model	model	NOUN
iajs-3094	360	9	was	be	AUX
iajs-3094	360	10	created	create	VERB
iajs-3094	360	11	to	to	PART
iajs-3094	360	12	address	address	VERB
iajs-3094	360	13	the	the	DET
iajs-3094	360	14	research	research	NOUN
iajs-3094	360	15	problems	problem	NOUN
iajs-3094	360	16	1//𝐹(∑𝐶𝑗	1//𝐹(∑𝐶𝑗	PROPN
iajs-3094	360	17	,	,	PUNCT
iajs-3094	360	18	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	360	19	,	,	PUNCT
iajs-3094	360	20	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	360	21	)	)	PUNCT
iajs-3094	360	22	,	,	PUNCT
iajs-3094	360	23	1//	1//	NUM
iajs-3094	360	24	∑𝐶𝑗	∑𝐶𝑗	NOUN
iajs-3094	360	25	+	+	NUM
iajs-3094	360	26	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	361	1	+	+	PROPN
iajs-3094	361	2	𝑇𝑚𝑎𝑥.	𝑇𝑚𝑎𝑥.	NOUN
iajs-3094	361	3	discovered	discover	VERB
iajs-3094	361	4	a	a	DET
iajs-3094	361	5	straightforward	straightforward	ADJ
iajs-3094	361	6	algorithm	algorithm	NOUN
iajs-3094	361	7	for	for	ADP
iajs-3094	361	8	the	the	DET
iajs-3094	361	9	efficient	efficient	ADJ
iajs-3094	361	10	schedule	schedule	NOUN
iajs-3094	361	11	for	for	ADP
iajs-3094	361	12	sub	sub	NOUN
iajs-3094	361	13	-	-	NOUN
iajs-3094	361	14	problems	problem	NOUN
iajs-3094	361	15	for	for	ADP
iajs-3094	361	16	1//𝐹(∑𝐶𝑗	1//𝐹(∑𝐶𝑗	PROPN
iajs-3094	361	17	,	,	PUNCT
iajs-3094	361	18	∑	∑	PROPN
iajs-3094	361	19	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	361	20	,	,	PUNCT
iajs-3094	361	21	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	361	22	)	)	PUNCT
iajs-3094	361	23	and	and	CCONJ
iajs-3094	361	24	it	it	PRON
iajs-3094	361	25	was	be	AUX
iajs-3094	361	26	proven	prove	VERB
iajs-3094	361	27	that	that	SCONJ
iajs-3094	361	28	some	some	DET
iajs-3094	361	29	rules	rule	NOUN
iajs-3094	361	30	give	give	VERB
iajs-3094	361	31	efficient	efficient	ADJ
iajs-3094	361	32	(	(	PUNCT
iajs-3094	361	33	optimal	optimal	ADJ
iajs-3094	361	34	)	)	PUNCT
iajs-3094	361	35	solutions	solution	NOUN
iajs-3094	361	36	to	to	ADP
iajs-3094	361	37	these	these	DET
iajs-3094	361	38	problems	problem	NOUN
iajs-3094	361	39	(	(	PUNCT
iajs-3094	361	40	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	361	41	)	)	PUNCT
iajs-3094	361	42	and(s₱7	and(s₱7	PROPN
iajs-3094	361	43	)	)	PUNCT
iajs-3094	361	44	,	,	PUNCT
iajs-3094	361	45	finding	find	VERB
iajs-3094	361	46	and	and	CCONJ
iajs-3094	361	47	proving	prove	VERB
iajs-3094	361	48	some	some	DET
iajs-3094	361	49	special	special	ADJ
iajs-3094	361	50	cases	case	NOUN
iajs-3094	361	51	that	that	PRON
iajs-3094	361	52	find	find	VERB
iajs-3094	361	53	some	some	DET
iajs-3094	361	54	efficient	efficient	ADJ
iajs-3094	361	55	(	(	PUNCT
iajs-3094	361	56	optimal	optimal	ADJ
iajs-3094	361	57	)	)	PUNCT
iajs-3094	361	58	solutions	solution	NOUN
iajs-3094	361	59	suitable	suitable	ADJ
iajs-3094	361	60	for	for	ADP
iajs-3094	361	61	the	the	DET
iajs-3094	361	62	problems	problem	NOUN
iajs-3094	361	63	(	(	PUNCT
iajs-3094	361	64	𝑆𝐶𝑆𝐸𝑇	𝑆𝐶𝑆𝐸𝑇	PROPN
iajs-3094	361	65	)	)	PUNCT
iajs-3094	361	66	and(s₱7	and(s₱7	PROPN
iajs-3094	361	67	)	)	PUNCT
iajs-3094	361	68	.	.	PUNCT
iajs-3094	362	1	this	this	DET
iajs-3094	362	2	paper	paper	NOUN
iajs-3094	362	3	has	have	AUX
iajs-3094	362	4	proved	prove	VERB
iajs-3094	362	5	the	the	DET
iajs-3094	362	6	efficacy	efficacy	NOUN
iajs-3094	362	7	of	of	ADP
iajs-3094	362	8	rules	rule	NOUN
iajs-3094	362	9	spt	spt	PROPN
iajs-3094	362	10	and	and	CCONJ
iajs-3094	362	11	edd	edd	PROPN
iajs-3094	362	12	and	and	CCONJ
iajs-3094	362	13	demonstrated	demonstrate	VERB
iajs-3094	362	14	the	the	DET
iajs-3094	362	15	significance	significance	NOUN
iajs-3094	362	16	of	of	ADP
iajs-3094	362	17	the	the	DET
iajs-3094	362	18	dominance	dominance	NOUN
iajs-3094	362	19	rule	rule	NOUN
iajs-3094	362	20	(	(	PUNCT
iajs-3094	362	21	dr	dr	PROPN
iajs-3094	362	22	)	)	PUNCT
iajs-3094	362	23	that	that	PRON
iajs-3094	362	24	can	can	AUX
iajs-3094	362	25	be	be	AUX
iajs-3094	362	26	used	use	VERB
iajs-3094	362	27	in	in	ADP
iajs-3094	362	28	this	this	DET
iajs-3094	362	29	problem	problem	NOUN
iajs-3094	362	30	to	to	PART
iajs-3094	362	31	improve	improve	VERB
iajs-3094	362	32	efficient	efficient	ADJ
iajs-3094	362	33	solutions	solution	NOUN
iajs-3094	362	34	.	.	PUNCT
iajs-3094	363	1	in	in	ADP
iajs-3094	363	2	the	the	DET
iajs-3094	363	3	future	future	NOUN
iajs-3094	363	4	,	,	PUNCT
iajs-3094	363	5	it	it	PRON
iajs-3094	363	6	would	would	AUX
iajs-3094	363	7	be	be	AUX
iajs-3094	363	8	interesting	interesting	ADJ
iajs-3094	363	9	to	to	PART
iajs-3094	363	10	conduct	conduct	VERB
iajs-3094	363	11	a	a	DET
iajs-3094	363	12	study	study	NOUN
iajs-3094	363	13	on	on	ADP
iajs-3094	363	14	the	the	DET
iajs-3094	363	15	following	follow	VERB
iajs-3094	363	16	machine	machine	NOUN
iajs-3094	363	17	scheduling	scheduling	NOUN
iajs-3094	363	18	problems	problem	NOUN
iajs-3094	363	19	(	(	PUNCT
iajs-3094	363	20	msps	msps	PROPN
iajs-3094	363	21	)	)	PUNCT
iajs-3094	363	22	.	.	PUNCT
iajs-3094	364	1	1	1	X
iajs-3094	364	2	)	)	PUNCT
iajs-3094	364	3	1/𝑟𝑗/	1/𝑟𝑗/	NUM
iajs-3094	364	4	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	364	5	,	,	PUNCT
iajs-3094	364	6	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	364	7	,	,	PUNCT
iajs-3094	364	8	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	364	9	)	)	PUNCT
iajs-3094	364	10	.	.	PUNCT
iajs-3094	365	1	2	2	X
iajs-3094	365	2	)	)	PUNCT
iajs-3094	365	3	1/𝑟𝑗/	1/𝑟𝑗/	NUM
iajs-3094	365	4	∑	∑	PUNCT
iajs-3094	366	1	𝐶𝑗	𝐶𝑗	PROPN
iajs-3094	366	2	+	+	NUM
iajs-3094	366	3	∑𝐸𝑗	∑𝐸𝑗	PROPN
iajs-3094	367	1	+	+	ADJ
iajs-3094	367	2	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	367	3	.	.	PUNCT
iajs-3094	368	1	3	3	X
iajs-3094	368	2	)	)	PUNCT
iajs-3094	368	3	1/𝑆𝑓/	1/𝑆𝑓/	NUM
iajs-3094	368	4	𝐹(∑𝐶𝑗	𝐹(∑𝐶𝑗	NOUN
iajs-3094	368	5	,	,	PUNCT
iajs-3094	368	6	∑	∑	PROPN
iajs-3094	368	7	𝐸𝑗	𝐸𝑗	PROPN
iajs-3094	368	8	,	,	PUNCT
iajs-3094	368	9	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-3094	368	10	)	)	PUNCT
iajs-3094	368	11	.	.	PUNCT
iajs-3094	369	1	acknowledgment	acknowledgment	NOUN
iajs-3094	369	2	the	the	DET
iajs-3094	369	3	authors	author	NOUN
iajs-3094	369	4	are	be	AUX
iajs-3094	369	5	greatly	greatly	ADV
iajs-3094	369	6	appreciated	appreciate	VERB
iajs-3094	369	7	the	the	DET
iajs-3094	369	8	referees	referee	NOUN
iajs-3094	369	9	for	for	ADP
iajs-3094	369	10	their	their	PRON
iajs-3094	369	11	valuable	valuable	ADJ
iajs-3094	369	12	comments	comment	NOUN
iajs-3094	369	13	and	and	CCONJ
iajs-3094	369	14	suggestions	suggestion	NOUN
iajs-3094	369	15	for	for	ADP
iajs-3094	369	16	improving	improve	VERB
iajs-3094	369	17	the	the	DET
iajs-3094	369	18	paper	paper	NOUN
iajs-3094	369	19	conflict	conflict	NOUN
iajs-3094	369	20	of	of	ADP
iajs-3094	369	21	interest	interest	NOUN
iajs-3094	369	22	the	the	DET
iajs-3094	369	23	authors	author	NOUN
iajs-3094	369	24	declare	declare	VERB
iajs-3094	369	25	that	that	SCONJ
iajs-3094	369	26	they	they	PRON
iajs-3094	369	27	have	have	VERB
iajs-3094	369	28	no	no	DET
iajs-3094	369	29	conflicts	conflict	NOUN
iajs-3094	369	30	of	of	ADP
iajs-3094	369	31	interest	interest	NOUN
iajs-3094	369	32	.	.	PUNCT
iajs-3094	370	1	funding	funding	NOUN
iajs-3094	370	2	there	there	PRON
iajs-3094	370	3	is	be	VERB
iajs-3094	370	4	no	no	DET
iajs-3094	370	5	financial	financial	ADJ
iajs-3094	370	6	support	support	NOUN
iajs-3094	370	7	in	in	ADP
iajs-3094	370	8	preparation	preparation	NOUN
iajs-3094	370	9	for	for	ADP
iajs-3094	370	10	the	the	DET
iajs-3094	370	11	publication	publication	NOUN
iajs-3094	370	12	.	.	PUNCT
iajs-3094	371	1	references	reference	NOUN
iajs-3094	371	2	1	1	NUM
iajs-3094	371	3	.	.	PUNCT
iajs-3094	371	4	wassenhove	wassenhove	ADJ
iajs-3094	371	5	,	,	PUNCT
iajs-3094	371	6	l.n.v	l.n.v	PROPN
iajs-3094	371	7	.	.	PUNCT
iajs-3094	371	8	single	single	ADJ
iajs-3094	371	9	machine	machine	NOUN
iajs-3094	371	10	scheduling	scheduling	NOUN
iajs-3094	371	11	to	to	PART
iajs-3094	371	12	minimize	minimize	VERB
iajs-3094	371	13	total	total	ADJ
iajs-3094	371	14	late	late	ADJ
iajs-3094	371	15	work	work	NOUN
iajs-3094	371	16	.	.	PUNCT
iajs-3094	372	1	oper	oper	PROPN
iajs-3094	372	2	.	.	PUNCT
iajs-3094	372	3	res	res	PROPN
iajs-3094	372	4	.	.	PROPN
iajs-3094	372	5	1992	1992	NUM
iajs-3094	372	6	,	,	PUNCT
iajs-3094	372	7	40	40	NUM
iajs-3094	372	8	,	,	PUNCT
iajs-3094	372	9	586–595	586–595	NUM
iajs-3094	372	10	.	.	PUNCT
iajs-3094	373	1	https://doi:10.1287	https://doi:10.1287	PROPN
iajs-3094	373	2	/	/	SYM
iajs-3094	373	3	opre.40.3.586	opre.40.3.586	NOUN
iajs-3094	373	4	.	.	X
iajs-3094	374	1	2	2	NUM
iajs-3094	374	2	.	.	X
iajs-3094	374	3	tanaev	tanaev	NOUN
iajs-3094	374	4	,	,	PUNCT
iajs-3094	374	5	v.	v.	PROPN
iajs-3094	374	6	;	;	PUNCT
iajs-3094	374	7	gordon	gordon	PROPN
iajs-3094	374	8	,	,	PUNCT
iajs-3094	374	9	w.	w.	PROPN
iajs-3094	374	10	;	;	PUNCT
iajs-3094	374	11	shafransky	shafransky	ADV
iajs-3094	374	12	,	,	PUNCT
iajs-3094	374	13	y.	y.	PROPN
iajs-3094	374	14	m.	m.	NOUN
iajs-3094	374	15	scheduling	scheduling	NOUN
iajs-3094	374	16	theory	theory	NOUN
iajs-3094	374	17	.	.	PUNCT
iajs-3094	375	1	single	single	ADJ
iajs-3094	375	2	-	-	PUNCT
iajs-3094	375	3	stage	stage	NOUN
iajs-3094	375	4	systems	system	NOUN
iajs-3094	375	5	.	.	PUNCT
iajs-3094	376	1	springer	springer	NOUN
iajs-3094	376	2	science	science	PROPN
iajs-3094	376	3	and	and	CCONJ
iajs-3094	376	4	business	business	NOUN
iajs-3094	376	5	media	medium	NOUN
iajs-3094	376	6	.	.	PUNCT
iajs-3094	377	1	2012	2012	NUM
iajs-3094	377	2	.	.	PUNCT
iajs-3094	378	1	3	3	X
iajs-3094	378	2	.	.	X
iajs-3094	378	3	hoogeveen	hoogeveen	PROPN
iajs-3094	378	4	,	,	PUNCT
iajs-3094	378	5	h.	h.	PROPN
iajs-3094	378	6	multicriteria	multicriteria	PROPN
iajs-3094	378	7	scheduling	scheduling	NOUN
iajs-3094	378	8	.	.	PUNCT
iajs-3094	379	1	eur	eur	PROPN
iajs-3094	379	2	.	.	PUNCT
iajs-3094	380	1	j.	j.	PROPN
iajs-3094	380	2	oper	oper	PROPN
iajs-3094	380	3	.	.	PUNCT
iajs-3094	381	1	res	res	PROPN
iajs-3094	381	2	.	.	PROPN
iajs-3094	381	3	2005	2005	NUM
iajs-3094	381	4	,	,	PUNCT
iajs-3094	381	5	167	167	NUM
iajs-3094	381	6	,	,	PUNCT
iajs-3094	381	7	592–623	592–623	NUM
iajs-3094	381	8	.	.	PUNCT
iajs-3094	382	1	https://doi:10.1016	https://doi:10.1016	PROPN
iajs-3094	382	2	/	/	SYM
iajs-3094	382	3	j.ejor.2004.07.011	j.ejor.2004.07.011	PROPN
iajs-3094	382	4	.	.	PUNCT
iajs-3094	382	5	https://doi:10.1287	https://doi:10.1287	PROPN
iajs-3094	382	6	/	/	SYM
iajs-3094	382	7	opre.40.3.586	opre.40.3.586	ADJ
iajs-3094	382	8	https://doi:10.1016	https://doi:10.1016	PROPN
iajs-3094	382	9	/	/	SYM
iajs-3094	382	10	j.ejor.2004.07.011	j.ejor.2004.07.011	PROPN
iajs-3094	382	11	ihjpas	ihjpas	PROPN
iajs-3094	382	12	.	.	PUNCT
iajs-3094	383	1	37	37	NUM
iajs-3094	383	2	(	(	PUNCT
iajs-3094	383	3	1	1	NUM
iajs-3094	383	4	)	)	PUNCT
iajs-3094	383	5	2024	2024	NUM
iajs-3094	383	6	401	401	NUM
iajs-3094	383	7	4	4	NUM
iajs-3094	383	8	.	.	PUNCT
iajs-3094	383	9	zaidan	zaidan	PROPN
iajs-3094	383	10	,	,	PUNCT
iajs-3094	383	11	a.a	a.a	PROPN
iajs-3094	383	12	.	.	PROPN
iajs-3094	383	13	;	;	PUNCT
iajs-3094	383	14	atiya	atiya	PROPN
iajs-3094	383	15	,	,	PUNCT
iajs-3094	383	16	b.	b.	PROPN
iajs-3094	383	17	;	;	PUNCT
iajs-3094	383	18	abu	abu	PROPN
iajs-3094	383	19	bakar	bakar	PROPN
iajs-3094	383	20	,	,	PUNCT
iajs-3094	383	21	m.r	m.r	PROPN
iajs-3094	383	22	.	.	PROPN
iajs-3094	383	23	;	;	PUNCT
iajs-3094	383	24	zaidan	zaidan	PROPN
iajs-3094	383	25	,	,	PUNCT
iajs-3094	383	26	b.	b.	PROPN
iajs-3094	383	27	b.	b.	PROPN
iajs-3094	384	1	a	a	DET
iajs-3094	384	2	new	new	ADJ
iajs-3094	384	3	hybrid	hybrid	ADJ
iajs-3094	384	4	algorithm	algorithm	NOUN
iajs-3094	384	5	of	of	ADP
iajs-3094	384	6	simulated	simulate	VERB
iajs-3094	384	7	annealing	annealing	NOUN
iajs-3094	384	8	and	and	CCONJ
iajs-3094	384	9	simplex	simplex	NOUN
iajs-3094	384	10	downhill	downhill	ADV
iajs-3094	384	11	for	for	ADP
iajs-3094	384	12	solving	solve	VERB
iajs-3094	384	13	multiple	multiple	ADJ
iajs-3094	384	14	-	-	PUNCT
iajs-3094	384	15	objective	objective	ADJ
iajs-3094	384	16	aggregate	aggregate	ADJ
iajs-3094	384	17	production	production	NOUN
iajs-3094	384	18	planning	planning	NOUN
iajs-3094	384	19	on	on	ADP
iajs-3094	384	20	fuzzy	fuzzy	ADJ
iajs-3094	384	21	environment	environment	NOUN
iajs-3094	384	22	.	.	PUNCT
iajs-3094	385	1	neural	neural	ADJ
iajs-3094	385	2	comput	comput	PROPN
iajs-3094	385	3	&	&	CCONJ
iajs-3094	385	4	applic	applic	PROPN
iajs-3094	385	5	,	,	PUNCT
iajs-3094	385	6	2019	2019	NUM
iajs-3094	385	7	,	,	PUNCT
iajs-3094	385	8	31	31	NUM
iajs-3094	385	9	,	,	PUNCT
iajs-3094	385	10	1823–1834	1823–1834	NUM
iajs-3094	385	11	.	.	PUNCT
iajs-3094	386	1	https://doi.org/10.1007/s00521-017-3159-5	https://doi.org/10.1007/s00521-017-3159-5	PROPN
iajs-3094	386	2	5	5	NUM
iajs-3094	386	3	.	.	PUNCT
iajs-3094	386	4	chachan	chachan	PROPN
iajs-3094	386	5	,	,	PUNCT
iajs-3094	386	6	h.	h.	PROPN
iajs-3094	386	7	a.	a.	PROPN
iajs-3094	386	8	,	,	PUNCT
iajs-3094	386	9	;	;	PUNCT
iajs-3094	386	10	jaafar	jaafar	ADV
iajs-3094	386	11	,	,	PUNCT
iajs-3094	386	12	h.	h.	PROPN
iajs-3094	386	13	a.	a.	PROPN
iajs-3094	386	14	exact	exact	PROPN
iajs-3094	386	15	solutions	solution	NOUN
iajs-3094	386	16	for	for	ADP
iajs-3094	386	17	minimizing	minimize	VERB
iajs-3094	386	18	cost	cost	NOUN
iajs-3094	386	19	function	function	NOUN
iajs-3094	386	20	with	with	ADP
iajs-3094	386	21	five	five	NUM
iajs-3094	386	22	criteria	criterion	NOUN
iajs-3094	386	23	and	and	CCONJ
iajs-3094	386	24	release	release	VERB
iajs-3094	386	25	dates	date	NOUN
iajs-3094	386	26	on	on	ADP
iajs-3094	386	27	single	single	ADJ
iajs-3094	386	28	machine	machine	NOUN
iajs-3094	386	29	.	.	PUNCT
iajs-3094	387	1	ibn	ibn	PROPN
iajs-3094	387	2	al	al	PROPN
iajs-3094	387	3	-	-	PUNCT
iajs-3094	387	4	haitham	haitham	PROPN
iajs-3094	387	5	journal	journal	PROPN
iajs-3094	387	6	for	for	ADP
iajs-3094	387	7	pure	pure	ADJ
iajs-3094	387	8	and	and	CCONJ
iajs-3094	387	9	applied	applied	ADJ
iajs-3094	387	10	sciences	science	NOUN
iajs-3094	387	11	,	,	PUNCT
iajs-3094	387	12	2020	2020	NUM
iajs-3094	387	13	.	.	PUNCT
iajs-3094	388	1	33(3	33(3	NOUN
iajs-3094	388	2	)	)	PUNCT
iajs-3094	388	3	,	,	PUNCT
iajs-3094	388	4	140–157	140–157	NUM
iajs-3094	388	5	.	.	PUNCT
iajs-3094	389	1	https://doi.org/10.30526/33.3.2479	https://doi.org/10.30526/33.3.2479	PROPN
iajs-3094	389	2	6	6	NUM
iajs-3094	389	3	.	.	X
iajs-3094	389	4	ali	ali	PROPN
iajs-3094	389	5	,	,	PUNCT
iajs-3094	389	6	z.m	z.m	PROPN
iajs-3094	389	7	.	.	PROPN
iajs-3094	389	8	;	;	PUNCT
iajs-3094	389	9	abdul	abdul	PROPN
iajs-3094	389	10	razaq	razaq	PROPN
iajs-3094	389	11	,	,	PUNCT
iajs-3094	389	12	t.s	t.s	PROPN
iajs-3094	389	13	.	.	PROPN
iajs-3094	389	14	minimizing	minimize	VERB
iajs-3094	389	15	the	the	DET
iajs-3094	389	16	total	total	ADJ
iajs-3094	389	17	completion	completion	NOUN
iajs-3094	389	18	times	time	NOUN
iajs-3094	389	19	,	,	PUNCT
iajs-3094	389	20	the	the	DET
iajs-3094	389	21	total	total	ADJ
iajs-3094	389	22	tardinessand	tardinessand	VERB
iajs-3094	389	23	the	the	DET
iajs-3094	389	24	maximum	maximum	ADJ
iajs-3094	389	25	tardiness	tardiness	NOUN
iajs-3094	389	26	.	.	PUNCT
iajs-3094	390	1	2015	2015	NUM
iajs-3094	390	2	,	,	PUNCT
iajs-3094	390	3	28	28	NUM
iajs-3094	390	4	,	,	PUNCT
iajs-3094	390	5	155–170	155–170	NUM
iajs-3094	390	6	.	.	PUNCT
iajs-3094	391	1	7	7	NUM
iajs-3094	391	2	.	.	X
iajs-3094	391	3	ahmed	ahmed	PROPN
iajs-3094	391	4	,	,	PUNCT
iajs-3094	391	5	m.g	m.g	PROPN
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iajs-3094	391	7	;	;	PUNCT
iajs-3094	391	8	ali	ali	PROPN
iajs-3094	391	9	,	,	PUNCT
iajs-3094	391	10	f.h	f.h	PROPN
iajs-3094	391	11	.	.	PROPN
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iajs-3094	391	13	method	method	NOUN
iajs-3094	391	14	with	with	ADP
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iajs-3094	391	16	rules	rule	NOUN
iajs-3094	391	17	for	for	ADP
iajs-3094	391	18	solving	solve	VERB
iajs-3094	391	19	scheduling	scheduling	NOUN
iajs-3094	391	20	on	on	ADP
iajs-3094	391	21	a	a	DET
iajs-3094	391	22	single	single	ADJ
iajs-3094	391	23	machine	machine	NOUN
iajs-3094	391	24	problem	problem	NOUN
iajs-3094	391	25	with	with	ADP
iajs-3094	391	26	mult	mult	PROPN
iajs-3094	391	27	iobjective	iobjective	ADJ
iajs-3094	391	28	function	function	NOUN
iajs-3094	391	29	.	.	PUNCT
iajs-3094	392	1	al	al	PROPN
iajs-3094	392	2	-	-	PUNCT
iajs-3094	392	3	mustansiriyah	mustansiriyah	PROPN
iajs-3094	392	4	j.	j.	PROPN
iajs-3094	392	5	sci	sci	PROPN
iajs-3094	392	6	.	.	PROPN
iajs-3094	392	7	2022	2022	NUM
iajs-3094	392	8	,	,	PUNCT
iajs-3094	392	9	33	33	NUM
iajs-3094	392	10	,	,	PUNCT
iajs-3094	392	11	56–63	56–63	NUM
iajs-3094	392	12	.	.	PUNCT
iajs-3094	393	1	https://doi:10.23851	https://doi:10.23851	PROPN
iajs-3094	393	2	/	/	SYM
iajs-3094	393	3	mjs.v33i2.1091	mjs.v33i2.1091	PROPN
iajs-3094	393	4	.	.	PROPN
iajs-3094	393	5	8	8	NUM
iajs-3094	393	6	.	.	X
iajs-3094	393	7	ali	ali	PROPN
iajs-3094	393	8	,	,	PUNCT
iajs-3094	393	9	f.h	f.h	PROPN
iajs-3094	393	10	.	.	PROPN
iajs-3094	393	11	;	;	PUNCT
iajs-3094	393	12	ahmed	ahmed	PROPN
iajs-3094	393	13	,	,	PUNCT
iajs-3094	393	14	m.g	m.g	PROPN
iajs-3094	393	15	.	.	PROPN
iajs-3094	393	16	local	local	ADJ
iajs-3094	393	17	search	search	NOUN
iajs-3094	393	18	methods	method	NOUN
iajs-3094	393	19	for	for	ADP
iajs-3094	393	20	solving	solve	VERB
iajs-3094	393	21	total	total	ADJ
iajs-3094	393	22	completion	completion	NOUN
iajs-3094	393	23	times	time	NOUN
iajs-3094	393	24	,	,	PUNCT
iajs-3094	393	25	range	range	NOUN
iajs-3094	393	26	of	of	ADP
iajs-3094	393	27	lateness	lateness	NOUN
iajs-3094	393	28	and	and	CCONJ
iajs-3094	393	29	maximum	maximum	ADJ
iajs-3094	393	30	tardiness	tardiness	ADJ
iajs-3094	393	31	problem	problem	NOUN
iajs-3094	393	32	.	.	PUNCT
iajs-3094	394	1	proc	proc	NOUN
iajs-3094	394	2	.	.	PUNCT
iajs-3094	395	1	6th	6th	ADJ
iajs-3094	395	2	int	int	NOUN
iajs-3094	395	3	.	.	PUNCT
iajs-3094	396	1	eng	eng	PROPN
iajs-3094	396	2	.	.	PUNCT
iajs-3094	396	3	conf	conf	PROPN
iajs-3094	396	4	.	.	PUNCT
iajs-3094	397	1	sustainable	sustainable	ADJ
iajs-3094	397	2	technol	technol	NOUN
iajs-3094	397	3	.	.	PUNCT
iajs-3094	397	4	dev	dev	PROPN
iajs-3094	397	5	.	.	PUNCT
iajs-3094	398	1	iec	iec	PROPN
iajs-3094	398	2	2020	2020	NUM
iajs-3094	398	3	,	,	PUNCT
iajs-3094	398	4	103	103	NUM
iajs-3094	398	5	–	–	SYM
iajs-3094	398	6	108	108	NUM
iajs-3094	398	7	.	.	PUNCT
iajs-3094	399	1	https://doi:10.1109	https://doi:10.1109	PROPN
iajs-3094	399	2	/	/	SYM
iajs-3094	399	3	iec49899.2020.9122821	iec49899.2020.9122821	NOUN
iajs-3094	399	4	.	.	PUNCT
iajs-3094	400	1	9	9	X
iajs-3094	400	2	.	.	X
iajs-3094	401	1	hassan	hassan	PROPN
iajs-3094	401	2	,	,	PUNCT
iajs-3094	401	3	d.a	d.a	PROPN
iajs-3094	401	4	.	.	PROPN
iajs-3094	401	5	;	;	PUNCT
iajs-3094	401	6	mehdavi	mehdavi	NOUN
iajs-3094	401	7	-	-	PUNCT
iajs-3094	401	8	amiri	amiri	ADV
iajs-3094	401	9	,	,	PUNCT
iajs-3094	401	10	n.	n.	PROPN
iajs-3094	401	11	;	;	PUNCT
iajs-3094	401	12	ramadan	ramadan	PROPN
iajs-3094	401	13	,	,	PUNCT
iajs-3094	401	14	a.m.	a.m.	PROPN
iajs-3094	402	1	a	a	DET
iajs-3094	402	2	heuristic	heuristic	ADJ
iajs-3094	402	3	approach	approach	NOUN
iajs-3094	402	4	to	to	PART
iajs-3094	402	5	minimize	minimize	VERB
iajs-3094	402	6	three	three	NUM
iajs-3094	402	7	criteria	criterion	NOUN
iajs-3094	402	8	using	use	VERB
iajs-3094	402	9	efficient	efficient	ADJ
iajs-3094	402	10	solutions	solution	NOUN
iajs-3094	402	11	.	.	PUNCT
iajs-3094	403	1	indones	indone	NOUN
iajs-3094	403	2	.	.	PUNCT
iajs-3094	404	1	j.	j.	PROPN
iajs-3094	404	2	electr	electr	PROPN
iajs-3094	404	3	.	.	PUNCT
iajs-3094	405	1	eng	eng	PROPN
iajs-3094	405	2	.	.	PUNCT
iajs-3094	406	1	comput	comput	PROPN
iajs-3094	406	2	.	.	PUNCT
iajs-3094	407	1	sci	sci	PROPN
iajs-3094	407	2	.	.	PROPN
iajs-3094	407	3	2022	2022	NUM
iajs-3094	407	4	,	,	PUNCT
iajs-3094	407	5	6	6	NUM
iajs-3094	407	6	,	,	PUNCT
iajs-3094	407	7	334–341	334–341	NUM
iajs-3094	407	8	.	.	PUNCT
iajs-3094	407	9	https://doi:10.11591	https://doi:10.11591	PROPN
iajs-3094	407	10	/	/	SYM
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iajs-3094	407	12	-	-	PUNCT
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iajs-3094	407	16	.	.	PUNCT
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iajs-3094	408	2	,	,	PUNCT
iajs-3094	408	3	h.	h.	PROPN
iajs-3094	408	4	f.	f.	PROPN
iajs-3094	408	5	multicriteria	multicriteria	PROPN
iajs-3094	408	6	scheduling	scheduling	NOUN
iajs-3094	408	7	problems	problem	NOUN
iajs-3094	408	8	to	to	PART
iajs-3094	408	9	minimize	minimize	VERB
iajs-3094	408	10	total	total	ADJ
iajs-3094	408	11	tardiness	tardiness	NOUN
iajs-3094	408	12	subject	subject	NOUN
iajs-3094	408	13	to	to	ADP
iajs-3094	408	14	maximum	maximum	ADJ
iajs-3094	408	15	earliness	earliness	NOUN
iajs-3094	408	16	or	or	CCONJ
iajs-3094	408	17	tardiness	tardiness	NOUN
iajs-3094	408	18	.	.	PUNCT
iajs-3094	409	1	ibn	ibn	PROPN
iajs-3094	409	2	al	al	PROPN
iajs-3094	409	3	-	-	PUNCT
iajs-3094	409	4	haitham	haitham	PROPN
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iajs-3094	409	6	for	for	ADP
iajs-3094	409	7	pure	pure	ADJ
iajs-3094	409	8	and	and	CCONJ
iajs-3094	409	9	applied	applied	ADJ
iajs-3094	409	10	sciences	science	NOUN
iajs-3094	409	11	,	,	PUNCT
iajs-3094	409	12	2017	2017	NUM
iajs-3094	409	13	,	,	PUNCT
iajs-3094	409	14	23(1	23(1	NUM
iajs-3094	409	15	)	)	PUNCT
iajs-3094	409	16	,	,	PUNCT
iajs-3094	409	17	311	311	NUM
iajs-3094	409	18	–	–	PUNCT
iajs-3094	409	19	320	320	NUM
iajs-3094	409	20	.	.	PUNCT
iajs-3094	409	21	https://jih.uobaghdad.edu.iq/index.php/j/article/view/988	https://jih.uobaghdad.edu.iq/index.php/j/article/view/988	NOUN
iajs-3094	410	1	11	11	NUM
iajs-3094	410	2	.	.	PUNCT
iajs-3094	411	1	smith	smith	PROPN
iajs-3094	411	2	,	,	PUNCT
iajs-3094	411	3	w.e	w.e	PROPN
iajs-3094	411	4	.	.	PROPN
iajs-3094	411	5	various	various	ADJ
iajs-3094	411	6	optimizers	optimizer	NOUN
iajs-3094	411	7	for	for	ADP
iajs-3094	411	8	single	single	ADJ
iajs-3094	411	9	-	-	PUNCT
iajs-3094	411	10	stage	stage	NOUN
iajs-3094	411	11	production	production	NOUN
iajs-3094	411	12	.	.	PUNCT
iajs-3094	412	1	nav	nav	NOUN
iajs-3094	412	2	.	.	PUNCT
iajs-3094	413	1	res	re	NOUN
iajs-3094	413	2	.	.	PUNCT
iajs-3094	414	1	logist	logist	PROPN
iajs-3094	414	2	.	.	PUNCT
iajs-3094	415	1	q.	q.	PROPN
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iajs-3094	415	3	,	,	PUNCT
iajs-3094	415	4	3	3	NUM
iajs-3094	415	5	,	,	PUNCT
iajs-3094	415	6	59–66	59–66	NUM
iajs-3094	415	7	,	,	PUNCT
iajs-3094	415	8	https://doi:10.1002	https://doi:10.1002	PROPN
iajs-3094	415	9	/	/	SYM
iajs-3094	415	10	nav.3800030106	nav.3800030106	NUM
iajs-3094	415	11	12	12	NUM
iajs-3094	415	12	.	.	PUNCT
iajs-3094	416	1	abdul	abdul	PROPN
iajs-3094	416	2	-	-	PUNCT
iajs-3094	416	3	razaq	razaq	PROPN
iajs-3094	416	4	,	,	PUNCT
iajs-3094	416	5	t.s	t.s	PROPN
iajs-3094	416	6	.	.	PROPN
iajs-3094	416	7	;	;	PUNCT
iajs-3094	416	8	akram	akram	PROPN
iajs-3094	416	9	,	,	PUNCT
iajs-3094	416	10	a.o	a.o	PROPN
iajs-3094	416	11	.	.	PROPN
iajs-3094	416	12	local	local	ADJ
iajs-3094	416	13	search	search	NOUN
iajs-3094	416	14	algorithms	algorithm	NOUN
iajs-3094	416	15	for	for	ADP
iajs-3094	416	16	multi	multi	ADJ
iajs-3094	416	17	-	-	ADJ
iajs-3094	416	18	criteria	criteria	ADJ
iajs-3094	416	19	single	single	ADJ
iajs-3094	416	20	machine	machine	NOUN
iajs-3094	416	21	scheduling	scheduling	NOUN
iajs-3094	416	22	problem	problem	NOUN
iajs-3094	416	23	.	.	PUNCT
iajs-3094	417	1	ibn	ibn	PROPN
iajs-3094	417	2	al	al	PROPN
iajs-3094	417	3	-	-	PUNCT
iajs-3094	417	4	haitham	haitham	PROPN
iajs-3094	417	5	j.	j.	PROPN
iajs-3094	417	6	pure	pure	PROPN
iajs-3094	417	7	appl	appl	PROPN
iajs-3094	417	8	.	.	PUNCT
iajs-3094	418	1	sci	sci	PROPN
iajs-3094	418	2	.	.	PROPN
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iajs-3094	418	4	,	,	PUNCT
iajs-3094	418	5	436	436	NUM
iajs-3094	418	6	–	–	PUNCT
iajs-3094	418	7	451.https://doi:10.30526/2017.ihsciconf.1817	451.https://doi:10.30526/2017.ihsciconf.1817	NOUN
iajs-3094	418	8	.	.	PUNCT
iajs-3094	419	1	13	13	NUM
iajs-3094	419	2	.	.	PUNCT
iajs-3094	420	1	hoogeveen	hoogeveen	PROPN
iajs-3094	420	2	,	,	PUNCT
iajs-3094	420	3	j.a	j.a	PROPN
iajs-3094	420	4	.	.	PROPN
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iajs-3094	420	7	promptness	promptness	ADJ
iajs-3094	420	8	and	and	CCONJ
iajs-3094	420	9	maximum	maximum	ADJ
iajs-3094	420	10	lateness	lateness	NOUN
iajs-3094	420	11	on	on	ADP
iajs-3094	420	12	a	a	DET
iajs-3094	420	13	single	single	ADJ
iajs-3094	420	14	machine	machine	NOUN
iajs-3094	420	15	.	.	PUNCT
iajs-3094	421	1	math	math	NOUN
iajs-3094	421	2	.	.	PUNCT
iajs-3094	422	1	oper	oper	PROPN
iajs-3094	422	2	.	.	PUNCT
iajs-3094	422	3	res	res	PROPN
iajs-3094	422	4	.	.	PROPN
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iajs-3094	422	6	,	,	PUNCT
iajs-3094	422	7	21	21	NUM
iajs-3094	422	8	,	,	PUNCT
iajs-3094	422	9	100–114	100–114	NUM
iajs-3094	422	10	,	,	PUNCT
iajs-3094	422	11	https://doi:10.1287	https://doi:10.1287	NOUN
iajs-3094	422	12	/	/	SYM
iajs-3094	422	13	moor.21.1.100	moor.21.1.100	NUM
iajs-3094	422	14	.	.	PUNCT
iajs-3094	423	1	14	14	NUM
iajs-3094	423	2	.	.	PUNCT
iajs-3094	424	1	jawad	jawad	PROPN
iajs-3094	424	2	,	,	PUNCT
iajs-3094	424	3	a.a	a.a	PROPN
iajs-3094	424	4	.	.	PROPN
iajs-3094	424	5	;	;	PUNCT
iajs-3094	424	6	ali	ali	PROPN
iajs-3094	424	7	,	,	PUNCT
iajs-3094	424	8	f.h	f.h	PROPN
iajs-3094	424	9	.	.	PROPN
iajs-3094	424	10	;	;	PUNCT
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iajs-3094	424	14	.	.	PUNCT
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iajs-3094	424	19	and	and	CCONJ
iajs-3094	424	20	bound	bind	VERB
iajs-3094	424	21	methods	method	NOUN
iajs-3094	424	22	to	to	PART
iajs-3094	424	23	solve	solve	VERB
iajs-3094	424	24	a	a	DET
iajs-3094	424	25	multi	multi	ADJ
iajs-3094	424	26	-	-	ADJ
iajs-3094	424	27	criteria	criteria	ADJ
iajs-3094	424	28	machine	machine	NOUN
iajs-3094	424	29	scheduling	scheduling	NOUN
iajs-3094	424	30	problem	problem	NOUN
iajs-3094	424	31	.	.	PUNCT
iajs-3094	425	1	iraqi	iraqi	ADJ
iajs-3094	425	2	j.	j.	PROPN
iajs-3094	425	3	sci	sci	PROPN
iajs-3094	425	4	.	.	PROPN
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iajs-3094	425	6	,	,	PUNCT
iajs-3094	425	7	61	61	NUM
iajs-3094	425	8	,	,	PUNCT
iajs-3094	425	9	2055–2069	2055–2069	NUM
iajs-3094	425	10	.	.	PUNCT
iajs-3094	426	1	https://doi:10.24996	https://doi:10.24996	NOUN
iajs-3094	426	2	/	/	SYM
iajs-3094	426	3	ijs.2020.61.8.21	ijs.2020.61.8.21	PROPN
iajs-3094	426	4	15	15	NUM
iajs-3094	426	5	.	.	PUNCT
iajs-3094	427	1	abdul	abdul	PROPN
iajs-3094	427	2	-	-	PUNCT
iajs-3094	427	3	zahra	zahra	PROPN
iajs-3094	427	4	,	,	PUNCT
iajs-3094	427	5	i.	i.	PROPN
iajs-3094	427	6	;	;	PUNCT
iajs-3094	427	7	abbas	abbas	PROPN
iajs-3094	427	8	,	,	PUNCT
iajs-3094	427	9	i.	i.	PROPN
iajs-3094	427	10	t.	t.	PROPN
iajs-3094	427	11	;	;	PUNCT
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iajs-3094	427	13	,	,	PUNCT
iajs-3094	427	14	b.	b.	PROPN
iajs-3094	427	15	a.	a.	PROPN
iajs-3094	427	16	;	;	PUNCT
iajs-3094	427	17	bakar	bakar	PROPN
iajs-3094	427	18	,	,	PUNCT
iajs-3094	427	19	r.	r.	PROPN
iajs-3094	427	20	a.	a.	PROPN
iajs-3094	427	21	;	;	PUNCT
iajs-3094	427	22	june	june	PROPN
iajs-3094	427	23	,	,	PUNCT
iajs-3094	427	24	l.	l.	PROPN
iajs-3094	427	25	w.	w.	PROPN
iajs-3094	427	26	,	,	PUNCT
iajs-3094	427	27	;	;	PUNCT
iajs-3094	427	28	monsi	monsi	PROPN
iajs-3094	427	29	,	,	PUNCT
iajs-3094	427	30	m.	m.	PROPN
iajs-3094	427	31	b.	b.	PROPN
iajs-3094	427	32	.	.	PUNCT
iajs-3094	428	1	the	the	DET
iajs-3094	428	2	role	role	NOUN
iajs-3094	428	3	of	of	ADP
iajs-3094	428	4	dynamic	dynamic	ADJ
iajs-3094	428	5	programming	programming	NOUN
iajs-3094	428	6	in	in	ADP
iajs-3094	428	7	the	the	DET
iajs-3094	428	8	distribution	distribution	NOUN
iajs-3094	428	9	of	of	ADP
iajs-3094	428	10	investment	investment	NOUN
iajs-3094	428	11	allocations	allocation	NOUN
iajs-3094	428	12	between	between	ADP
iajs-3094	428	13	production	production	NOUN
iajs-3094	428	14	lines	line	NOUN
iajs-3094	428	15	with	with	ADP
iajs-3094	428	16	an	an	DET
iajs-3094	428	17	application	application	NOUN
iajs-3094	428	18	.	.	PUNCT
iajs-3094	429	1	international	international	ADJ
iajs-3094	429	2	journal	journal	NOUN
iajs-3094	429	3	of	of	ADP
iajs-3094	429	4	pure	pure	ADJ
iajs-3094	429	5	and	and	CCONJ
iajs-3094	429	6	applied	applied	ADJ
iajs-3094	429	7	mathematics	mathematic	NOUN
iajs-3094	429	8	,	,	PUNCT
iajs-3094	429	9	2016	2016	NUM
iajs-3094	429	10	,	,	PUNCT
iajs-3094	429	11	106(2	106(2	NUM
iajs-3094	429	12	)	)	PUNCT
iajs-3094	429	13	,	,	PUNCT
iajs-3094	429	14	365	365	NUM
iajs-3094	429	15	-	-	SYM
iajs-3094	429	16	380	380	NUM
iajs-3094	429	17	.	.	PUNCT
iajs-3094	430	1	16	16	NUM
iajs-3094	430	2	.	.	PUNCT
iajs-3094	430	3	atiya	atiya	PROPN
iajs-3094	430	4	,	,	PUNCT
iajs-3094	430	5	b.	b.	PROPN
iajs-3094	430	6	;	;	PUNCT
iajs-3094	430	7	bakheet	bakheet	PROPN
iajs-3094	430	8	,	,	PUNCT
iajs-3094	430	9	a.	a.	PROPN
iajs-3094	430	10	j.	j.	PROPN
iajs-3094	430	11	k.	k.	PROPN
iajs-3094	430	12	;	;	PUNCT
iajs-3094	430	13	abbas	abbas	PROPN
iajs-3094	430	14	,	,	PUNCT
iajs-3094	430	15	i.	i.	PROPN
iajs-3094	430	16	t.	t.	PROPN
iajs-3094	430	17	;	;	PUNCT
iajs-3094	430	18	bakar	bakar	PROPN
iajs-3094	430	19	,	,	PUNCT
iajs-3094	430	20	m.	m.	PROPN
iajs-3094	430	21	r.	r.	PROPN
iajs-3094	430	22	a.	a.	PROPN
iajs-3094	430	23	;	;	PUNCT
iajs-3094	430	24	soon	soon	ADV
iajs-3094	430	25	,	,	PUNCT
iajs-3094	430	26	l.	l.	PROPN
iajs-3094	430	27	l.	l.	PROPN
iajs-3094	430	28	,	,	PUNCT
iajs-3094	430	29	;	;	PUNCT
iajs-3094	430	30	monsi	monsi	PROPN
iajs-3094	430	31	,	,	PUNCT
iajs-3094	430	32	m.	m.	PROPN
iajs-3094	430	33	b.	b.	PROPN
iajs-3094	430	34	application	application	NOUN
iajs-3094	430	35	of	of	ADP
iajs-3094	430	36	simulated	simulate	VERB
iajs-3094	430	37	annealing	annealing	NOUN
iajs-3094	430	38	to	to	PART
iajs-3094	430	39	solve	solve	VERB
iajs-3094	430	40	multi	multi	NOUN
iajs-3094	430	41	-	-	NOUN
iajs-3094	430	42	objectives	objective	NOUN
iajs-3094	430	43	for	for	ADP
iajs-3094	430	44	aggregate	aggregate	ADJ
iajs-3094	430	45	production	production	NOUN
iajs-3094	430	46	planning	planning	NOUN
iajs-3094	430	47	.	.	PUNCT
iajs-3094	431	1	aip	aip	PROPN
iajs-3094	431	2	conference	conference	NOUN
iajs-3094	431	3	proceedings	proceeding	NOUN
iajs-3094	431	4	(	(	PUNCT
iajs-3094	431	5	2016	2016	NUM
iajs-3094	431	6	,	,	PUNCT
iajs-3094	431	7	june	june	PROPN
iajs-3094	431	8	)	)	PUNCT
iajs-3094	431	9	.	.	PUNCT
iajs-3094	432	1	1739(1	1739(1	NUM
iajs-3094	432	2	)	)	PUNCT
iajs-3094	432	3	,	,	PUNCT
iajs-3094	432	4	020086	020086	NUM
iajs-3094	432	5	)	)	PUNCT
iajs-3094	432	6	.	.	PUNCT
iajs-3094	433	1	aip	aip	PROPN
iajs-3094	433	2	publishing	publishing	PROPN
iajs-3094	433	3	llc	llc	PROPN
iajs-3094	433	4	.	.	PUNCT
iajs-3094	434	1	https://doi.org/10.1063/1.4952566	https://doi.org/10.1063/1.4952566	PROPN
iajs-3094	434	2	17	17	NUM
iajs-3094	434	3	.	.	PUNCT
iajs-3094	435	1	kalaf	kalaf	PROPN
iajs-3094	435	2	,	,	PUNCT
iajs-3094	435	3	b.	b.	PROPN
iajs-3094	435	4	a.	a.	PROPN
iajs-3094	435	5	,	,	PUNCT
iajs-3094	435	6	mohammed	mohammed	PROPN
iajs-3094	435	7	,	,	PUNCT
iajs-3094	435	8	g.	g.	PROPN
iajs-3094	435	9	j.	j.	PROPN
iajs-3094	435	10	;	;	PUNCT
iajs-3094	435	11	salman	salman	PROPN
iajs-3094	435	12	,	,	PUNCT
iajs-3094	435	13	m.	m.	PROPN
iajs-3094	435	14	d.	d.	PROPN
iajs-3094	436	1	a	a	DET
iajs-3094	436	2	new	new	ADJ
iajs-3094	436	3	hybrid	hybrid	ADJ
iajs-3094	436	4	meta	meta	ADJ
iajs-3094	436	5	-	-	PUNCT
iajs-3094	436	6	heuristics	heuristic	NOUN
iajs-3094	436	7	algorithms	algorithm	NOUN
iajs-3094	436	8	to	to	PART
iajs-3094	436	9	solve	solve	VERB
iajs-3094	436	10	app	app	NOUN
iajs-3094	436	11	problems	problem	NOUN
iajs-3094	436	12	.	.	PUNCT
iajs-3094	437	1	in	in	ADP
iajs-3094	437	2	journal	journal	PROPN
iajs-3094	437	3	of	of	ADP
iajs-3094	437	4	physics	physics	PROPN
iajs-3094	437	5	:	:	PUNCT
iajs-3094	437	6	conference	conference	NOUN
iajs-3094	437	7	series	series	NOUN
iajs-3094	437	8	(	(	PUNCT
iajs-3094	437	9	2021	2021	NUM
iajs-3094	437	10	,	,	PUNCT
iajs-3094	437	11	may	may	AUX
iajs-3094	437	12	)	)	PUNCT
iajs-3094	437	13	.	.	PUNCT
iajs-3094	438	1	1897(1	1897(1	NUM
iajs-3094	438	2	)	)	PUNCT
iajs-3094	438	3	,	,	PUNCT
iajs-3094	438	4	012011	012011	NUM
iajs-3094	438	5	)	)	PUNCT
iajs-3094	438	6	.	.	PUNCT
iajs-3094	439	1	iop	iop	PROPN
iajs-3094	439	2	publishing	publishing	NOUN
iajs-3094	439	3	.	.	PUNCT
iajs-3094	440	1	18	18	NUM
iajs-3094	440	2	.	.	X
iajs-3094	440	3	allahverdi	allahverdi	PROPN
iajs-3094	440	4	,	,	PUNCT
iajs-3094	440	5	a.;ng	a.;ng	NOUN
iajs-3094	440	6	,	,	PUNCT
iajs-3094	440	7	c.	c.	PROPN
iajs-3094	440	8	t.	t.	PROPN
iajs-3094	440	9	;	;	PUNCT
iajs-3094	440	10	cheng	cheng	PROPN
iajs-3094	440	11	,	,	PUNCT
iajs-3094	440	12	t.	t.	PROPN
iajs-3094	440	13	e.	e.	PROPN
iajs-3094	440	14	;	;	PUNCT
iajs-3094	440	15	kovalyov	kovalyov	NOUN
iajs-3094	440	16	,	,	PUNCT
iajs-3094	440	17	m.	m.	NOUN
iajs-3094	440	18	y.	y.	PROPN
iajs-3094	440	19	a	a	DET
iajs-3094	440	20	survey	survey	NOUN
iajs-3094	440	21	of	of	ADP
iajs-3094	440	22	scheduling	scheduling	NOUN
iajs-3094	440	23	problems	problem	NOUN
iajs-3094	440	24	with	with	ADP
iajs-3094	440	25	setup	setup	NOUN
iajs-3094	440	26	times	time	NOUN
iajs-3094	440	27	or	or	CCONJ
iajs-3094	440	28	costs	cost	NOUN
iajs-3094	440	29	,	,	PUNCT
iajs-3094	440	30	european	european	ADJ
iajs-3094	440	31	journal	journal	PROPN
iajs-3094	440	32	of	of	ADP
iajs-3094	440	33	operational	operational	ADJ
iajs-3094	440	34	research	research	NOUN
iajs-3094	440	35	,	,	PUNCT
iajs-3094	440	36	2008	2008	NUM
iajs-3094	440	37	.	.	PUNCT
iajs-3094	441	1	187(3	187(3	NUM
iajs-3094	441	2	)	)	PUNCT
iajs-3094	441	3	,	,	PUNCT
iajs-3094	442	1	985–1032	985–1032	NUM
iajs-3094	442	2	.	.	PUNCT
iajs-3094	443	1	https://doi.org/10.1016/j.ejor.2006.06.060	https://doi.org/10.1016/j.ejor.2006.06.060	PROPN
iajs-3094	443	2	.	.	PROPN
iajs-3094	444	1	19	19	NUM
iajs-3094	444	2	.	.	PUNCT
iajs-3094	444	3	allaoua	allaoua	PROPN
iajs-3094	444	4	,	,	PUNCT
iajs-3094	444	5	h.	h.	PROPN
iajs-3094	444	6	;	;	PUNCT
iajs-3094	444	7	brahim	brahim	PROPN
iajs-3094	444	8	,	,	PUNCT
iajs-3094	444	9	b.	b.	PROPN
iajs-3094	444	10	new	new	ADJ
iajs-3094	444	11	properties	property	NOUN
iajs-3094	444	12	for	for	ADP
iajs-3094	444	13	solving	solve	VERB
iajs-3094	444	14	the	the	DET
iajs-3094	444	15	single	single	ADJ
iajs-3094	444	16	-	-	PUNCT
iajs-3094	444	17	machine	machine	NOUN
iajs-3094	444	18	scheduling	scheduling	NOUN
iajs-3094	444	19	problem	problem	NOUN
iajs-3094	444	20	with	with	ADP
iajs-3094	444	21	early	early	ADJ
iajs-3094	444	22	/	/	SYM
iajs-3094	444	23	tardy	tardy	NOUN
iajs-3094	444	24	jobs	job	NOUN
iajs-3094	444	25	,	,	PUNCT
iajs-3094	444	26	journal	journal	NOUN
iajs-3094	444	27	of	of	ADP
iajs-3094	444	28	intelligent	intelligent	ADJ
iajs-3094	444	29	systems	system	NOUN
iajs-3094	444	30	,	,	PUNCT
iajs-3094	444	31	2017	2017	NUM
iajs-3094	444	32	,	,	PUNCT
iajs-3094	444	33	26(3	26(3	NUM
iajs-3094	444	34	)	)	PUNCT
iajs-3094	444	35	,	,	PUNCT
iajs-3094	444	36	531–543	531–543	NUM
iajs-3094	444	37	.	.	PUNCT
iajs-3094	445	1	https://doi.org/10.1515/jisys2016-0063	https://doi.org/10.1515/jisys2016-0063	ADJ
iajs-3094	445	2	.	.	PUNCT
iajs-3094	446	1	20	20	NUM
iajs-3094	446	2	.	.	X
iajs-3094	447	1	jawad	jawad	PROPN
iajs-3094	447	2	,	,	PUNCT
iajs-3094	447	3	a.a	a.a	PROPN
iajs-3094	447	4	.	.	PROPN
iajs-3094	447	5	;	;	PUNCT
iajs-3094	447	6	ali	ali	PROPN
iajs-3094	447	7	,	,	PUNCT
iajs-3094	447	8	f.h	f.h	PROPN
iajs-3094	447	9	.	.	PROPN
iajs-3094	447	10	;	;	PUNCT
iajs-3094	447	11	hasanain	hasanain	PROPN
iajs-3094	447	12	,	,	PUNCT
iajs-3094	447	13	w.s	w.s	PROPN
iajs-3094	447	14	.	.	PROPN
iajs-3094	447	15	.using	.using	PROPN
iajs-3094	447	16	heuristic	heuristic	NOUN
iajs-3094	447	17	and	and	CCONJ
iajs-3094	447	18	branch	branch	NOUN
iajs-3094	447	19	and	and	CCONJ
iajs-3094	447	20	bound	bind	VERB
iajs-3094	447	21	methods	method	NOUN
iajs-3094	447	22	to	to	PART
iajs-3094	447	23	solve	solve	VERB
iajs-3094	447	24	a	a	DET
iajs-3094	447	25	multi	multi	ADJ
iajs-3094	447	26	-	-	ADJ
iajs-3094	447	27	criteria	criteria	ADJ
iajs-3094	447	28	machine	machine	NOUN
iajs-3094	447	29	scheduling	scheduling	NOUN
iajs-3094	447	30	problem	problem	NOUN
iajs-3094	447	31	,	,	PUNCT
iajs-3094	447	32	iraqi	iraqi	ADJ
iajs-3094	447	33	journal	journal	NOUN
iajs-3094	447	34	of	of	ADP
iajs-3094	447	35	science	science	NOUN
iajs-3094	447	36	,	,	PUNCT
iajs-3094	447	37	2020	2020	NUM
iajs-3094	447	38	,	,	PUNCT
iajs-3094	447	39	61(8	61(8	NUM
iajs-3094	447	40	)	)	PUNCT
iajs-3094	447	41	,	,	PUNCT
iajs-3094	447	42	2055–2069	2055–2069	NUM
iajs-3094	447	43	.	.	PUNCT
iajs-3094	448	1	https://doi.org/10.24996/ijs.2020.61.8.21	https://doi.org/10.24996/ijs.2020.61.8.21	PROPN
iajs-3094	448	2	https://doi.org/10.1007/s00521-017-3159-5	https://doi.org/10.1007/s00521-017-3159-5	PROPN
iajs-3094	448	3	https://doi.org/10.30526/33.3.2479	https://doi.org/10.30526/33.3.2479	PUNCT
iajs-3094	448	4	https://doi:10.23851	https://doi:10.23851	PROPN
iajs-3094	448	5	/	/	SYM
iajs-3094	448	6	mjs.v33i2.1091	mjs.v33i2.1091	PROPN
iajs-3094	448	7	https://doi:10.1109	https://doi:10.1109	PROPN
iajs-3094	448	8	/	/	SYM
iajs-3094	448	9	iec49899.2020.9122821	iec49899.2020.9122821	PROPN
iajs-3094	448	10	https://doi:10.11591	https://doi:10.11591	PROPN
iajs-3094	448	11	/	/	SYM
iajs-3094	448	12	ijeecs.v26.i1.pp334	ijeecs.v26.i1.pp334	NOUN
iajs-3094	448	13	-	-	PUNCT
iajs-3094	448	14	341	341	NUM
iajs-3094	448	15	https://jih.uobaghdad.edu.iq/index.php/j/article/view/988	https://jih.uobaghdad.edu.iq/index.php/j/article/view/988	NOUN
iajs-3094	448	16	https://doi:10.1002	https://doi:10.1002	PROPN
iajs-3094	448	17	/	/	SYM
iajs-3094	448	18	nav.3800030106	nav.3800030106	NUM
iajs-3094	448	19	https://doi:10.30526/2017.ihsciconf.1817	https://doi:10.30526/2017.ihsciconf.1817	PROPN
iajs-3094	448	20	https://doi:10.1287	https://doi:10.1287	NOUN
iajs-3094	448	21	/	/	SYM
iajs-3094	448	22	moor.21.1.100	moor.21.1.100	NUM
iajs-3094	448	23	https://doi:10.24996	https://doi:10.24996	PROPN
iajs-3094	448	24	/	/	SYM
iajs-3094	448	25	ijs.2020.61.8.21	ijs.2020.61.8.21	NOUN
iajs-3094	448	26	https://doi.org/10.1063/1.4952566	https://doi.org/10.1063/1.4952566	PROPN
iajs-3094	449	1	https://doi.org/10.1016/j.ejor.2006.06.060	https://doi.org/10.1016/j.ejor.2006.06.060	NOUN
iajs-3094	449	2	https://doi.org/10.1515/jisys-2016-0063	https://doi.org/10.1515/jisys-2016-0063	PROPN
iajs-3094	449	3	https://doi.org/10.1515/jisys-2016-0063	https://doi.org/10.1515/jisys-2016-0063	PROPN
iajs-3094	449	4	https://doi.org/10.24996/ijs.2020.61.8.21	https://doi.org/10.24996/ijs.2020.61.8.21	PROPN
iajs-3094	449	5	ihjpas	ihjpas	PROPN
iajs-3094	449	6	.	.	PUNCT
iajs-3094	450	1	37	37	NUM
iajs-3094	450	2	(	(	PUNCT
iajs-3094	450	3	1	1	NUM
iajs-3094	450	4	)	)	PUNCT
iajs-3094	450	5	2024	2024	NUM
iajs-3094	450	6	402	402	NUM
iajs-3094	450	7	21	21	NUM
iajs-3094	450	8	.	.	PUNCT
iajs-3094	450	9	mahnam	mahnam	PROPN
iajs-3094	450	10	,	,	PUNCT
iajs-3094	450	11	m.	m.	NOUN
iajs-3094	450	12	;	;	PUNCT
iajs-3094	450	13	moslehi	moslehi	NOUN
iajs-3094	450	14	,	,	PUNCT
iajs-3094	450	15	g.	g.	PROPN
iajs-3094	450	16	;	;	PUNCT
iajs-3094	450	17	fatemi	fatemi	PROPN
iajs-3094	450	18	ghomi	ghomi	PROPN
iajs-3094	450	19	,	,	PUNCT
iajs-3094	450	20	s.m.t	s.m.t	ADJ
iajs-3094	450	21	.	.	PROPN
iajs-3094	450	22	single	single	ADJ
iajs-3094	450	23	machine	machine	NOUN
iajs-3094	450	24	scheduling	scheduling	NOUN
iajs-3094	450	25	with	with	ADP
iajs-3094	450	26	unequal	unequal	ADJ
iajs-3094	450	27	release	release	NOUN
iajs-3094	450	28	times	time	NOUN
iajs-3094	450	29	and	and	CCONJ
iajs-3094	450	30	idle	idle	ADJ
iajs-3094	450	31	insert	insert	NOUN
iajs-3094	450	32	for	for	ADP
iajs-3094	450	33	minimizing	minimize	VERB
iajs-3094	450	34	the	the	DET
iajs-3094	450	35	sum	sum	NOUN
iajs-3094	450	36	of	of	ADP
iajs-3094	450	37	maximum	maximum	ADJ
iajs-3094	450	38	earliness	earliness	NOUN
iajs-3094	450	39	and	and	CCONJ
iajs-3094	450	40	tardiness	tardiness	NOUN
iajs-3094	450	41	,	,	PUNCT
iajs-3094	450	42	mathematical	mathematical	ADJ
iajs-3094	450	43	and	and	CCONJ
iajs-3094	450	44	computer	computer	NOUN
iajs-3094	450	45	modelling	modelling	NOUN
iajs-3094	450	46	,	,	PUNCT
iajs-3094	450	47	2013	2013	NUM
iajs-3094	450	48	,	,	PUNCT
iajs-3094	450	49	57(9–10	57(9–10	NUM
iajs-3094	450	50	)	)	PUNCT
iajs-3094	450	51	,	,	PUNCT
iajs-3094	450	52	2549–2563	2549–2563	NUM
iajs-3094	450	53	https://doi.org/10.1016/j.mcm.2013.01.007	https://doi.org/10.1016/j.mcm.2013.01.007	NOUN
iajs-3094	450	54	.	.	PUNCT
iajs-3094	451	1	22	22	NUM
iajs-3094	451	2	.	.	PUNCT
iajs-3094	451	3	mosheiov	mosheiov	PROPN
iajs-3094	451	4	,	,	PUNCT
iajs-3094	451	5	g.	g.	PROPN
iajs-3094	451	6	;	;	PUNCT
iajs-3094	451	7	oron	oron	PROPN
iajs-3094	451	8	,	,	PUNCT
iajs-3094	451	9	d.	d.	PROPN
iajs-3094	451	10	;	;	PUNCT
iajs-3094	451	11	shabtay	shabtay	PROPN
iajs-3094	451	12	,	,	PUNCT
iajs-3094	451	13	d.	d.	PROPN
iajs-3094	451	14	minimizing	minimize	VERB
iajs-3094	451	15	total	total	ADJ
iajs-3094	451	16	late	late	ADJ
iajs-3094	451	17	work	work	NOUN
iajs-3094	451	18	on	on	ADP
iajs-3094	451	19	a	a	DET
iajs-3094	451	20	single	single	ADJ
iajs-3094	451	21	machine	machine	NOUN
iajs-3094	451	22	with	with	ADP
iajs-3094	451	23	generalized	generalized	ADJ
iajs-3094	451	24	due	due	ADJ
iajs-3094	451	25	-	-	PUNCT
iajs-3094	451	26	dates	date	NOUN
iajs-3094	451	27	,	,	PUNCT
iajs-3094	451	28	european	european	ADJ
iajs-3094	451	29	journal	journal	PROPN
iajs-3094	451	30	of	of	ADP
iajs-3094	451	31	operational	operational	ADJ
iajs-3094	451	32	research	research	NOUN
iajs-3094	451	33	,	,	PUNCT
iajs-3094	451	34	2021	2021	NUM
iajs-3094	451	35	,	,	PUNCT
iajs-3094	451	36	293(3	293(3	NUM
iajs-3094	451	37	)	)	PUNCT
iajs-3094	451	38	,	,	PUNCT
iajs-3094	451	39	837–846	837–846	NUM
iajs-3094	451	40	.	.	PUNCT
iajs-3094	452	1	https://doi.org/10.1016/j.ejor.2020.12.061	https://doi.org/10.1016/j.ejor.2020.12.061	NOUN
iajs-3094	452	2	.	.	PUNCT
iajs-3094	453	1	23	23	NUM
iajs-3094	453	2	.	.	PUNCT
iajs-3094	454	1	neamah	neamah	PROPN
iajs-3094	454	2	,	,	PUNCT
iajs-3094	454	3	n.	n.	NOUN
iajs-3094	454	4	m.	m.	NOUN
iajs-3094	454	5	;	;	PUNCT
iajs-3094	454	6	kalaf	kalaf	PROPN
iajs-3094	454	7	,	,	PUNCT
iajs-3094	454	8	b.	b.	PROPN
iajs-3094	454	9	a.	a.	NOUN
iajs-3094	454	10	solving	solve	VERB
iajs-3094	454	11	the	the	DET
iajs-3094	454	12	multi	multi	NOUN
iajs-3094	454	13	-	-	NOUN
iajs-3094	454	14	criteria	criterion	NOUN
iajs-3094	454	15	:	:	PUNCT
iajs-3094	454	16	total	total	ADJ
iajs-3094	454	17	completion	completion	NOUN
iajs-3094	454	18	time	time	NOUN
iajs-3094	454	19	,	,	PUNCT
iajs-3094	454	20	total	total	ADJ
iajs-3094	454	21	late	late	ADJ
iajs-3094	454	22	work	work	NOUN
iajs-3094	454	23	,	,	PUNCT
iajs-3094	454	24	and	and	CCONJ
iajs-3094	454	25	maximum	maximum	ADJ
iajs-3094	454	26	earliness	earliness	NOUN
iajs-3094	454	27	problem	problem	NOUN
iajs-3094	454	28	.	.	PUNCT
iajs-3094	455	1	periodicals	periodical	NOUN
iajs-3094	455	2	of	of	ADP
iajs-3094	455	3	engineering	engineering	NOUN
iajs-3094	455	4	and	and	CCONJ
iajs-3094	455	5	natural	natural	ADJ
iajs-3094	455	6	sciences	science	NOUN
iajs-3094	455	7	,	,	PUNCT
iajs-3094	455	8	2023	2023	NUM
iajs-3094	455	9	.	.	PUNCT
iajs-3094	456	1	11(3	11(3	NUM
iajs-3094	456	2	)	)	PUNCT
iajs-3094	456	3	,	,	PUNCT
iajs-3094	456	4	46	46	NUM
iajs-3094	456	5	-	-	SYM
iajs-3094	456	6	57	57	NUM
iajs-3094	456	7	.	.	X
iajs-3094	457	1	24	24	NUM
iajs-3094	457	2	.	.	X
iajs-3094	457	3	centinkaya	centinkaya	PROPN
iajs-3094	457	4	,	,	PUNCT
iajs-3094	457	5	m.	m.	NOUN
iajs-3094	457	6	;	;	PUNCT
iajs-3094	457	7	ozyurek	ozyurek	PROPN
iajs-3094	457	8	,	,	PUNCT
iajs-3094	457	9	c.	c.	PROPN
iajs-3094	457	10	,	,	PUNCT
iajs-3094	457	11	the	the	DET
iajs-3094	457	12	effect	effect	NOUN
iajs-3094	457	13	of	of	ADP
iajs-3094	457	14	inquiry	inquiry	NOUN
iajs-3094	457	15	-	-	PUNCT
iajs-3094	457	16	based	base	VERB
iajs-3094	457	17	science	science	NOUN
iajs-3094	457	18	activities	activity	NOUN
iajs-3094	457	19	on	on	ADP
iajs-3094	457	20	prospective	prospective	ADJ
iajs-3094	457	21	science	science	NOUN
iajs-3094	457	22	teachers	teacher	NOUN
iajs-3094	457	23	’	’	PART
iajs-3094	457	24	scientific	scientific	ADJ
iajs-3094	457	25	process	process	NOUN
iajs-3094	457	26	skills	skill	NOUN
iajs-3094	457	27	,	,	PUNCT
iajs-3094	457	28	international	international	ADJ
iajs-3094	457	29	online	online	ADJ
iajs-3094	457	30	journal	journal	NOUN
iajs-3094	457	31	of	of	ADP
iajs-3094	457	32	education	education	NOUN
iajs-3094	457	33	and	and	CCONJ
iajs-3094	457	34	teaching	teaching	NOUN
iajs-3094	457	35	,	,	PUNCT
iajs-3094	457	36	.	.	PUNCT
iajs-3094	458	1	2019	2019	NUM
iajs-3094	458	2	,	,	PUNCT
iajs-3094	458	3	6(1	6(1	NUM
iajs-3094	458	4	)	)	PUNCT
iajs-3094	458	5	,	,	PUNCT
iajs-3094	458	6	56–70	56–70	NUM
iajs-3094	458	7	.	.	PUNCT
iajs-3094	459	1	25	25	NUM
iajs-3094	459	2	.	.	PUNCT
iajs-3094	459	3	chachan	chachan	PROPN
iajs-3094	459	4	,	,	PUNCT
iajs-3094	459	5	h.a	h.a	PROPN
iajs-3094	459	6	.	.	NOUN
iajs-3094	459	7	solving	solve	VERB
iajs-3094	459	8	machine	machine	NOUN
iajs-3094	459	9	scheduling	scheduling	NOUN
iajs-3094	459	10	problem	problem	NOUN
iajs-3094	459	11	using	use	VERB
iajs-3094	459	12	particle	particle	NOUN
iajs-3094	459	13	swarm	swarm	NOUN
iajs-3094	459	14	optimization	optimization	NOUN
iajs-3094	459	15	method	method	NOUN
iajs-3094	459	16	,	,	PUNCT
iajs-3094	459	17	the	the	DET
iajs-3094	459	18	iraqi	iraqi	ADJ
iajs-3094	459	19	magazine	magazine	NOUN
iajs-3094	459	20	for	for	ADP
iajs-3094	459	21	administrative	administrative	ADJ
iajs-3094	459	22	sciences	science	NOUN
iajs-3094	459	23	,	,	PUNCT
iajs-3094	459	24	2012	2012	NUM
iajs-3094	459	25	,	,	PUNCT
iajs-3094	459	26	8(33	8(33	NUM
iajs-3094	459	27	)	)	PUNCT
iajs-3094	459	28	,	,	PUNCT
iajs-3094	459	29	197–213	197–213	NUM
iajs-3094	459	30	.	.	PUNCT
iajs-3094	459	31	26	26	NUM
iajs-3094	459	32	.	.	PUNCT
iajs-3094	460	1	abid	abid	PROPN
iajs-3094	460	2	,	,	PUNCT
iajs-3094	460	3	h.	h.	PROPN
iajs-3094	460	4	;	;	PUNCT
iajs-3094	460	5	mohammed	mohammed	PROPN
iajs-3094	460	6	,	,	PUNCT
iajs-3094	460	7	a.	a.	NOUN
iajs-3094	460	8	scheduling	scheduling	NOUN
iajs-3094	460	9	job	job	NOUN
iajs-3094	460	10	families	family	NOUN
iajs-3094	460	11	with	with	ADP
iajs-3094	460	12	setups	setup	NOUN
iajs-3094	460	13	on	on	ADP
iajs-3094	460	14	a	a	DET
iajs-3094	460	15	single	single	ADJ
iajs-3094	460	16	machine	machine	NOUN
iajs-3094	460	17	,	,	PUNCT
iajs-3094	460	18	journal	journal	NOUN
iajs-3094	460	19	of	of	ADP
iajs-3094	460	20	kerbala	kerbala	PROPN
iajs-3094	460	21	university	university	PROPN
iajs-3094	460	22	,	,	PUNCT
iajs-3094	460	23	2012	2012	NUM
iajs-3094	460	24	,	,	PUNCT
iajs-3094	460	25	10(2	10(2	NUM
iajs-3094	460	26	)	)	PUNCT
iajs-3094	460	27	,	,	PUNCT
iajs-3094	460	28	99–113	99–113	PROPN
iajs-3094	460	29	.	.	PUNCT
iajs-3094	460	30	27	27	NUM
iajs-3094	460	31	.	.	PUNCT
iajs-3094	461	1	adel	adel	PROPN
iajs-3094	461	2	d.	d.	PROPN
iajs-3094	461	3	,	,	PUNCT
iajs-3094	461	4	search	search	NOUN
iajs-3094	461	5	method	method	NOUN
iajs-3094	461	6	for	for	ADP
iajs-3094	461	7	solving	solve	VERB
iajs-3094	461	8	multicriteria	multicriteria	PROPN
iajs-3094	461	9	scheduling	scheduling	NOUN
iajs-3094	461	10	problem	problem	NOUN
iajs-3094	461	11	,	,	PUNCT
iajs-3094	461	12	2022	2022	NUM
iajs-3094	461	13	,	,	PUNCT
iajs-3094	461	14	13(march	13(march	NUM
iajs-3094	461	15	2021	2021	NUM
iajs-3094	461	16	)	)	PUNCT
iajs-3094	461	17	,	,	PUNCT
iajs-3094	461	18	1709	1709	NUM
iajs-3094	461	19	–	–	PUNCT
iajs-3094	461	20	1720	1720	NUM
iajs-3094	461	21	.	.	PUNCT
iajs-3094	462	1	28	28	NUM
iajs-3094	462	2	.	.	X
iajs-3094	463	1	ahmadov	ahmadov	PROPN
iajs-3094	463	2	,	,	PUNCT
iajs-3094	463	3	y.	y.	PROPN
iajs-3094	463	4	;	;	PUNCT
iajs-3094	463	5	helo	helo	PROPN
iajs-3094	463	6	,	,	PUNCT
iajs-3094	463	7	p.	p.	PROPN
iajs-3094	463	8	,	,	PUNCT
iajs-3094	463	9	a	a	DET
iajs-3094	463	10	cloud	cloud	NOUN
iajs-3094	463	11	based	base	VERB
iajs-3094	463	12	job	job	NOUN
iajs-3094	463	13	sequencing	sequence	VERB
iajs-3094	463	14	with	with	ADP
iajs-3094	463	15	sequence	sequence	NOUN
iajs-3094	463	16	-	-	PUNCT
iajs-3094	463	17	dependent	dependent	ADJ
iajs-3094	463	18	setup	setup	NOUN
iajs-3094	463	19	for	for	ADP
iajs-3094	463	20	sheet	sheet	NOUN
iajs-3094	463	21	metal	metal	NOUN
iajs-3094	463	22	manufacturing	manufacturing	NOUN
iajs-3094	463	23	’	'	PUNCT
iajs-3094	463	24	,	,	PUNCT
iajs-3094	463	25	annals	annal	NOUN
iajs-3094	463	26	of	of	ADP
iajs-3094	463	27	operations	operation	NOUN
iajs-3094	463	28	research	research	NOUN
iajs-3094	463	29	,	,	PUNCT
iajs-3094	463	30	2018	2018	NUM
iajs-3094	463	31	,	,	PUNCT
iajs-3094	463	32	270(1–2),5–24	270(1–2),5–24	NUM
iajs-3094	463	33	.	.	PUNCT
iajs-3094	464	1	https://doi.org/10.1007/s10479-016-2304-3	https://doi.org/10.1007/s10479-016-2304-3	NUM
iajs-3094	464	2	.	.	PROPN
iajs-3094	464	3	29	29	NUM
iajs-3094	464	4	.	.	PUNCT
iajs-3094	465	1	ahmed	ahmed	PROPN
iajs-3094	465	2	,	,	PUNCT
iajs-3094	465	3	m.	m.	NOUN
iajs-3094	465	4	;	;	PUNCT
iajs-3094	465	5	ali	ali	PROPN
iajs-3094	465	6	,	,	PUNCT
iajs-3094	465	7	f.	f.	PROPN
iajs-3094	465	8	efficient	efficient	ADJ
iajs-3094	465	9	algorithms	algorithm	NOUN
iajs-3094	465	10	to	to	PART
iajs-3094	465	11	solve	solve	VERB
iajs-3094	465	12	tricriteria	tricriteria	NOUN
iajs-3094	465	13	machine	machine	NOUN
iajs-3094	465	14	scheduling	scheduling	NOUN
iajs-3094	465	15	problem	problem	NOUN
iajs-3094	465	16	.	.	PUNCT
iajs-3094	466	1	journal	journal	PROPN
iajs-3094	466	2	of	of	ADP
iajs-3094	466	3	al	al	PROPN
iajs-3094	466	4	-	-	PUNCT
iajs-3094	466	5	rafidain	rafidain	PROPN
iajs-3094	466	6	university	university	PROPN
iajs-3094	466	7	college	college	NOUN
iajs-3094	466	8	for	for	ADP
iajs-3094	466	9	sciences	science	NOUN
iajs-3094	466	10	,	,	PUNCT
iajs-3094	466	11	2020	2020	NUM
iajs-3094	466	12	,	,	PUNCT
iajs-3094	466	13	(	(	PUNCT
iajs-3094	466	14	1	1	NUM
iajs-3094	466	15	)	)	PUNCT
iajs-3094	466	16	,	,	PUNCT
iajs-3094	466	17	485	485	NUM
iajs-3094	466	18	-	-	SYM
iajs-3094	466	19	493	493	NUM
iajs-3094	466	20	.	.	PUNCT
iajs-3094	466	21	30	30	NUM
iajs-3094	466	22	.	.	PUNCT
iajs-3094	467	1	ahmed	ahmed	PROPN
iajs-3094	467	2	,	,	PUNCT
iajs-3094	467	3	m.g	m.g	PROPN
iajs-3094	467	4	.	.	PROPN
iajs-3094	467	5	and	and	CCONJ
iajs-3094	467	6	ali	ali	PROPN
iajs-3094	467	7	,	,	PUNCT
iajs-3094	467	8	f.h	f.h	PROPN
iajs-3094	467	9	.	.	PROPN
iajs-3094	467	10	exact	exact	ADJ
iajs-3094	467	11	method	method	NOUN
iajs-3094	467	12	with	with	ADP
iajs-3094	467	13	dominance	dominance	NOUN
iajs-3094	467	14	rules	rule	NOUN
iajs-3094	467	15	for	for	ADP
iajs-3094	467	16	solving	solve	VERB
iajs-3094	467	17	scheduling	scheduling	NOUN
iajs-3094	467	18	on	on	ADP
iajs-3094	467	19	a	a	DET
iajs-3094	467	20	single	single	ADJ
iajs-3094	467	21	machine	machine	NOUN
iajs-3094	467	22	problem	problem	NOUN
iajs-3094	467	23	with	with	ADP
iajs-3094	467	24	multi	multi	ADJ
iajs-3094	467	25	objective	objective	ADJ
iajs-3094	467	26	function	function	NOUN
iajs-3094	467	27	’	'	PUNCT
iajs-3094	467	28	,	,	PUNCT
iajs-3094	467	29	al	al	PROPN
iajs-3094	467	30	-	-	PUNCT
iajs-3094	467	31	mustansiriyah	mustansiriyah	PROPN
iajs-3094	467	32	journal	journal	NOUN
iajs-3094	467	33	of	of	ADP
iajs-3094	467	34	science	science	NOUN
iajs-3094	467	35	,	,	PUNCT
iajs-3094	467	36	2022	2022	NUM
iajs-3094	467	37	,	,	PUNCT
iajs-3094	467	38	33(2	33(2	NUM
iajs-3094	467	39	)	)	PUNCT
iajs-3094	467	40	,	,	PUNCT
iajs-3094	467	41	56–63	56–63	NUM
iajs-3094	467	42	.	.	PUNCT
iajs-3094	467	43	available	available	ADJ
iajs-3094	467	44	at	at	ADP
iajs-3094	467	45	:	:	PUNCT
iajs-3094	467	46	https://doi.org/10.23851/mjs.v33i2.1091	https://doi.org/10.23851/mjs.v33i2.1091	PROPN
iajs-3094	467	47	.	.	PUNCT
iajs-3094	468	1	https://doi.org/10.1016/j.mcm.2013.01.007	https://doi.org/10.1016/j.mcm.2013.01.007	PROPN
iajs-3094	468	2	https://doi.org/10.1016/j.ejor.2020.12.061	https://doi.org/10.1016/j.ejor.2020.12.061	PROPN
iajs-3094	468	3	https://doi.org/10.1007/s10479-016-2304-3	https://doi.org/10.1007/s10479-016-2304-3	NUM