id	sid	tid	token	lemma	pos
iajs-2677	1	1	50	50	NUM
iajs-2677	1	2	novel	novel	ADJ
iajs-2677	1	3	heuristic	heuristic	ADJ
iajs-2677	1	4	approach	approach	NOUN
iajs-2677	1	5	for	for	ADP
iajs-2677	1	6	solving	solve	VERB
iajs-2677	1	7	multi	multi	ADJ
iajs-2677	1	8	-	-	ADJ
iajs-2677	1	9	objective	objective	ADJ
iajs-2677	1	10	scheduling	scheduling	NOUN
iajs-2677	1	11	problems	problem	NOUN
iajs-2677	1	12	begard	begard	VERB
iajs-2677	2	1	a.	a.	PROPN
iajs-2677	2	2	amin	amin	PROPN
iajs-2677	2	3	ayad	ayad	PROPN
iajs-2677	2	4	m.	m.	PROPN
iajs-2677	2	5	ramadan	ramadan	PROPN
iajs-2677	2	6	begardamin1976@gmail.com	begardamin1976@gmail.com	PROPN
iajs-2677	3	1	mathematics	mathematics	PROPN
iajs-2677	3	2	department	department	PROPN
iajs-2677	3	3	,	,	PUNCT
iajs-2677	3	4	college	college	NOUN
iajs-2677	3	5	of	of	ADP
iajs-2677	3	6	science	science	NOUN
iajs-2677	3	7	,	,	PUNCT
iajs-2677	3	8	sulaimani	sulaimani	PROPN
iajs-2677	3	9	university	university	PROPN
iajs-2677	3	10	abstract	abstract	NOUN
iajs-2677	3	11	in	in	ADP
iajs-2677	3	12	this	this	DET
iajs-2677	3	13	paper	paper	NOUN
iajs-2677	3	14	,	,	PUNCT
iajs-2677	3	15	we	we	PRON
iajs-2677	3	16	studied	study	VERB
iajs-2677	3	17	the	the	DET
iajs-2677	3	18	scheduling	scheduling	NOUN
iajs-2677	3	19	of	of	ADP
iajs-2677	3	20	𝑛	𝑛	DET
iajs-2677	3	21	jobs	job	NOUN
iajs-2677	3	22	on	on	ADP
iajs-2677	3	23	a	a	DET
iajs-2677	3	24	single	single	ADJ
iajs-2677	3	25	machine	machine	NOUN
iajs-2677	3	26	.	.	PUNCT
iajs-2677	4	1	each	each	DET
iajs-2677	4	2	of	of	ADP
iajs-2677	4	3	n	n	PRON
iajs-2677	4	4	jobs	job	NOUN
iajs-2677	4	5	is	be	AUX
iajs-2677	4	6	to	to	PART
iajs-2677	4	7	be	be	AUX
iajs-2677	4	8	processed	process	VERB
iajs-2677	4	9	without	without	ADP
iajs-2677	4	10	interruption	interruption	NOUN
iajs-2677	4	11	and	and	CCONJ
iajs-2677	4	12	becomes	become	VERB
iajs-2677	4	13	available	available	ADJ
iajs-2677	4	14	for	for	ADP
iajs-2677	4	15	processing	processing	NOUN
iajs-2677	4	16	at	at	ADP
iajs-2677	4	17	time	time	NOUN
iajs-2677	4	18	zero	zero	NUM
iajs-2677	4	19	.	.	PUNCT
iajs-2677	5	1	the	the	DET
iajs-2677	5	2	objective	objective	NOUN
iajs-2677	5	3	is	be	AUX
iajs-2677	5	4	to	to	PART
iajs-2677	5	5	find	find	VERB
iajs-2677	5	6	a	a	DET
iajs-2677	5	7	processing	processing	NOUN
iajs-2677	5	8	order	order	NOUN
iajs-2677	5	9	of	of	ADP
iajs-2677	5	10	the	the	DET
iajs-2677	5	11	jobs	job	NOUN
iajs-2677	5	12	,	,	PUNCT
iajs-2677	5	13	minimizing	minimize	VERB
iajs-2677	5	14	the	the	DET
iajs-2677	5	15	sum	sum	NOUN
iajs-2677	5	16	of	of	ADP
iajs-2677	5	17	maximum	maximum	ADJ
iajs-2677	5	18	earliness	earliness	NOUN
iajs-2677	5	19	and	and	CCONJ
iajs-2677	5	20	maximum	maximum	ADJ
iajs-2677	5	21	tardiness	tardiness	NOUN
iajs-2677	5	22	.	.	PUNCT
iajs-2677	6	1	this	this	DET
iajs-2677	6	2	problem	problem	NOUN
iajs-2677	6	3	is	be	AUX
iajs-2677	6	4	to	to	PART
iajs-2677	6	5	minimize	minimize	VERB
iajs-2677	6	6	the	the	DET
iajs-2677	6	7	earliness	earliness	NOUN
iajs-2677	6	8	and	and	CCONJ
iajs-2677	6	9	tardiness	tardiness	NOUN
iajs-2677	6	10	values	value	NOUN
iajs-2677	6	11	,	,	PUNCT
iajs-2677	6	12	so	so	SCONJ
iajs-2677	6	13	this	this	DET
iajs-2677	6	14	model	model	NOUN
iajs-2677	6	15	is	be	AUX
iajs-2677	6	16	equivalent	equivalent	ADJ
iajs-2677	6	17	to	to	ADP
iajs-2677	6	18	the	the	DET
iajs-2677	6	19	just	just	ADV
iajs-2677	6	20	-	-	PUNCT
iajs-2677	6	21	in	in	ADP
iajs-2677	6	22	-	-	PUNCT
iajs-2677	6	23	time	time	NOUN
iajs-2677	6	24	production	production	NOUN
iajs-2677	6	25	system	system	NOUN
iajs-2677	6	26	.	.	PUNCT
iajs-2677	7	1	our	our	PRON
iajs-2677	7	2	lower	low	ADJ
iajs-2677	7	3	bound	bind	VERB
iajs-2677	7	4	depended	depend	VERB
iajs-2677	7	5	on	on	ADP
iajs-2677	7	6	the	the	DET
iajs-2677	7	7	decomposition	decomposition	NOUN
iajs-2677	7	8	of	of	ADP
iajs-2677	7	9	the	the	DET
iajs-2677	7	10	problem	problem	NOUN
iajs-2677	7	11	into	into	ADP
iajs-2677	7	12	two	two	NUM
iajs-2677	7	13	subprograms	subprogram	NOUN
iajs-2677	7	14	.	.	PUNCT
iajs-2677	8	1	we	we	PRON
iajs-2677	8	2	presented	present	VERB
iajs-2677	8	3	a	a	DET
iajs-2677	8	4	novel	novel	ADJ
iajs-2677	8	5	heuristic	heuristic	ADJ
iajs-2677	8	6	approach	approach	NOUN
iajs-2677	8	7	to	to	PART
iajs-2677	8	8	find	find	VERB
iajs-2677	8	9	a	a	DET
iajs-2677	8	10	near	near	ADV
iajs-2677	8	11	-	-	PUNCT
iajs-2677	8	12	optimal	optimal	ADJ
iajs-2677	8	13	solution	solution	NOUN
iajs-2677	8	14	for	for	ADP
iajs-2677	8	15	the	the	DET
iajs-2677	8	16	problem	problem	NOUN
iajs-2677	8	17	.	.	PUNCT
iajs-2677	9	1	this	this	DET
iajs-2677	9	2	approach	approach	NOUN
iajs-2677	9	3	depends	depend	VERB
iajs-2677	9	4	on	on	ADP
iajs-2677	9	5	finding	find	VERB
iajs-2677	9	6	efficient	efficient	ADJ
iajs-2677	9	7	solutions	solution	NOUN
iajs-2677	9	8	for	for	ADP
iajs-2677	9	9	two	two	NUM
iajs-2677	9	10	problems	problem	NOUN
iajs-2677	9	11	.	.	PUNCT
iajs-2677	10	1	the	the	DET
iajs-2677	10	2	first	first	ADJ
iajs-2677	10	3	problem	problem	NOUN
iajs-2677	10	4	is	be	AUX
iajs-2677	10	5	minimizing	minimize	VERB
iajs-2677	10	6	total	total	ADJ
iajs-2677	10	7	completion	completion	NOUN
iajs-2677	10	8	time	time	NOUN
iajs-2677	10	9	and	and	CCONJ
iajs-2677	10	10	maximum	maximum	ADJ
iajs-2677	10	11	tardiness	tardiness	NOUN
iajs-2677	10	12	.	.	PUNCT
iajs-2677	11	1	the	the	DET
iajs-2677	11	2	second	second	NOUN
iajs-2677	11	3	is	be	AUX
iajs-2677	11	4	minimizing	minimize	VERB
iajs-2677	11	5	total	total	ADJ
iajs-2677	11	6	completion	completion	NOUN
iajs-2677	11	7	time	time	NOUN
iajs-2677	11	8	and	and	CCONJ
iajs-2677	11	9	maximum	maximum	ADJ
iajs-2677	11	10	earliness	earliness	NOUN
iajs-2677	11	11	.	.	PUNCT
iajs-2677	12	1	we	we	PRON
iajs-2677	12	2	used	use	VERB
iajs-2677	12	3	these	these	DET
iajs-2677	12	4	efficient	efficient	ADJ
iajs-2677	12	5	solutions	solution	NOUN
iajs-2677	12	6	to	to	PART
iajs-2677	12	7	find	find	VERB
iajs-2677	12	8	a	a	DET
iajs-2677	12	9	near	near	ADV
iajs-2677	12	10	-	-	PUNCT
iajs-2677	12	11	optimal	optimal	ADJ
iajs-2677	12	12	solution	solution	NOUN
iajs-2677	12	13	for	for	ADP
iajs-2677	12	14	another	another	DET
iajs-2677	12	15	problem	problem	NOUN
iajs-2677	12	16	which	which	PRON
iajs-2677	12	17	is	be	AUX
iajs-2677	12	18	a	a	DET
iajs-2677	12	19	sum	sum	NOUN
iajs-2677	12	20	of	of	ADP
iajs-2677	12	21	maximum	maximum	ADJ
iajs-2677	12	22	earliness	earliness	NOUN
iajs-2677	12	23	and	and	CCONJ
iajs-2677	12	24	maximum	maximum	ADJ
iajs-2677	12	25	tardiness	tardiness	NOUN
iajs-2677	12	26	.	.	PUNCT
iajs-2677	13	1	this	this	PRON
iajs-2677	13	2	means	mean	VERB
iajs-2677	13	3	we	we	PRON
iajs-2677	13	4	eliminate	eliminate	VERB
iajs-2677	13	5	the	the	DET
iajs-2677	13	6	total	total	ADJ
iajs-2677	13	7	completion	completion	NOUN
iajs-2677	13	8	time	time	NOUN
iajs-2677	13	9	from	from	ADP
iajs-2677	13	10	the	the	DET
iajs-2677	13	11	two	two	NUM
iajs-2677	13	12	problems	problem	NOUN
iajs-2677	13	13	.	.	PUNCT
iajs-2677	14	1	the	the	DET
iajs-2677	14	2	algorithm	algorithm	NOUN
iajs-2677	14	3	was	be	AUX
iajs-2677	14	4	tested	test	VERB
iajs-2677	14	5	on	on	ADP
iajs-2677	14	6	a	a	DET
iajs-2677	14	7	set	set	NOUN
iajs-2677	14	8	of	of	ADP
iajs-2677	14	9	problems	problem	NOUN
iajs-2677	14	10	of	of	ADP
iajs-2677	14	11	different	different	ADJ
iajs-2677	14	12	n.	n.	NOUN
iajs-2677	14	13	computational	computational	ADJ
iajs-2677	14	14	results	result	NOUN
iajs-2677	14	15	demonstrate	demonstrate	VERB
iajs-2677	14	16	the	the	DET
iajs-2677	14	17	efficiency	efficiency	NOUN
iajs-2677	14	18	of	of	ADP
iajs-2677	14	19	the	the	DET
iajs-2677	14	20	proposed	propose	VERB
iajs-2677	14	21	method	method	NOUN
iajs-2677	14	22	.	.	PUNCT
iajs-2677	15	1	keywords	keyword	NOUN
iajs-2677	15	2	:	:	PUNCT
iajs-2677	15	3	scheduling	scheduling	NOUN
iajs-2677	15	4	problems	problem	NOUN
iajs-2677	15	5	,	,	PUNCT
iajs-2677	15	6	multi	multi	ADJ
iajs-2677	15	7	-	-	ADJ
iajs-2677	15	8	objective	objective	ADJ
iajs-2677	15	9	function	function	NOUN
iajs-2677	15	10	,	,	PUNCT
iajs-2677	15	11	maximum	maximum	ADJ
iajs-2677	15	12	tardiness	tardiness	NOUN
iajs-2677	15	13	,	,	PUNCT
iajs-2677	15	14	maximum	maximum	ADJ
iajs-2677	15	15	earliness	earliness	NOUN
iajs-2677	15	16	,	,	PUNCT
iajs-2677	15	17	heuristic	heuristic	ADJ
iajs-2677	15	18	method	method	NOUN
iajs-2677	15	19	.	.	PUNCT
iajs-2677	16	1	1	1	X
iajs-2677	16	2	.	.	X
iajs-2677	16	3	introduction	introduction	NOUN
iajs-2677	16	4	since	since	SCONJ
iajs-2677	16	5	1954	1954	NUM
iajs-2677	16	6	,	,	PUNCT
iajs-2677	16	7	scheduling	scheduling	NOUN
iajs-2677	16	8	problems	problem	NOUN
iajs-2677	16	9	have	have	AUX
iajs-2677	16	10	received	receive	VERB
iajs-2677	16	11	much	much	ADJ
iajs-2677	16	12	attention	attention	NOUN
iajs-2677	16	13	in	in	ADP
iajs-2677	16	14	the	the	DET
iajs-2677	16	15	literature	literature	NOUN
iajs-2677	16	16	.	.	PUNCT
iajs-2677	17	1	at	at	ADP
iajs-2677	17	2	first	first	ADV
iajs-2677	17	3	,	,	PUNCT
iajs-2677	17	4	the	the	DET
iajs-2677	17	5	researchers	researcher	NOUN
iajs-2677	17	6	considered	consider	VERB
iajs-2677	17	7	only	only	ADV
iajs-2677	17	8	one	one	NUM
iajs-2677	17	9	objective	objective	ADJ
iajs-2677	17	10	function	function	NOUN
iajs-2677	17	11	.	.	PUNCT
iajs-2677	18	1	in	in	ADP
iajs-2677	18	2	practical	practical	ADJ
iajs-2677	18	3	cases	case	NOUN
iajs-2677	18	4	,	,	PUNCT
iajs-2677	18	5	the	the	DET
iajs-2677	18	6	decision	decision	NOUN
iajs-2677	18	7	-	-	PUNCT
iajs-2677	18	8	maker	maker	NOUN
iajs-2677	18	9	is	be	AUX
iajs-2677	18	10	obligated	obligate	VERB
iajs-2677	18	11	to	to	PART
iajs-2677	18	12	choose	choose	VERB
iajs-2677	18	13	only	only	ADV
iajs-2677	18	14	one	one	NUM
iajs-2677	18	15	objective	objective	NOUN
iajs-2677	18	16	from	from	ADP
iajs-2677	18	17	some	some	DET
iajs-2677	18	18	objectives	objective	NOUN
iajs-2677	18	19	[	[	X
iajs-2677	18	20	1	1	NUM
iajs-2677	18	21	]	]	PUNCT
iajs-2677	18	22	.	.	PUNCT
iajs-2677	19	1	nowadays	nowadays	ADV
iajs-2677	19	2	,	,	PUNCT
iajs-2677	19	3	research	research	NOUN
iajs-2677	19	4	on	on	ADP
iajs-2677	19	5	multi	multi	ADJ
iajs-2677	19	6	-	-	ADJ
iajs-2677	19	7	criteria	criteria	ADJ
iajs-2677	19	8	scheduling	scheduling	NOUN
iajs-2677	19	9	problems	problem	NOUN
iajs-2677	19	10	has	have	AUX
iajs-2677	19	11	increased	increase	VERB
iajs-2677	19	12	.	.	PUNCT
iajs-2677	20	1	nagar	nagar	NOUN
iajs-2677	20	2	et	et	PROPN
iajs-2677	20	3	al	al	PROPN
iajs-2677	20	4	.	.	PUNCT
iajs-2677	21	1	[	[	X
iajs-2677	21	2	2	2	X
iajs-2677	21	3	]	]	PUNCT
iajs-2677	21	4	introduced	introduce	VERB
iajs-2677	21	5	a	a	DET
iajs-2677	21	6	survey	survey	NOUN
iajs-2677	21	7	of	of	ADP
iajs-2677	21	8	multiple	multiple	ADJ
iajs-2677	21	9	and	and	CCONJ
iajs-2677	21	10	bicriteria	bicriteria	NOUN
iajs-2677	21	11	problems	problem	NOUN
iajs-2677	21	12	in	in	ADP
iajs-2677	21	13	scheduling	scheduling	NOUN
iajs-2677	21	14	.	.	PUNCT
iajs-2677	22	1	in	in	ADP
iajs-2677	22	2	general	general	ADJ
iajs-2677	22	3	,	,	PUNCT
iajs-2677	22	4	we	we	PRON
iajs-2677	22	5	have	have	VERB
iajs-2677	22	6	two	two	NUM
iajs-2677	22	7	structures	structure	NOUN
iajs-2677	22	8	to	to	PART
iajs-2677	22	9	deal	deal	VERB
iajs-2677	22	10	ibn	ibn	PROPN
iajs-2677	22	11	al	al	PROPN
iajs-2677	22	12	haitham	haitham	PROPN
iajs-2677	22	13	journal	journal	PROPN
iajs-2677	22	14	for	for	ADP
iajs-2677	22	15	pure	pure	ADJ
iajs-2677	22	16	and	and	CCONJ
iajs-2677	22	17	applied	apply	VERB
iajs-2677	22	18	science	science	NOUN
iajs-2677	22	19	journal	journal	PROPN
iajs-2677	22	20	homepage	homepage	NOUN
iajs-2677	22	21	:	:	PUNCT
iajs-2677	22	22	http://jih.uobaghdad.edu.iq/index.php/j/index	http://jih.uobaghdad.edu.iq/index.php/j/index	NOUN
iajs-2677	22	23	doi	doi	NOUN
iajs-2677	22	24	:	:	PUNCT
iajs-2677	22	25	10.30526/34.3.2677	10.30526/34.3.2677	PROPN
iajs-2677	22	26	article	article	NOUN
iajs-2677	22	27	history	history	NOUN
iajs-2677	22	28	:	:	PUNCT
iajs-2677	22	29	received	receive	VERB
iajs-2677	22	30	20	20	NUM
iajs-2677	22	31	december	december	PROPN
iajs-2677	22	32	,	,	PUNCT
iajs-2677	22	33	2020	2020	NUM
iajs-2677	22	34	,	,	PUNCT
iajs-2677	22	35	accepted	accept	VERB
iajs-2677	22	36	16,febeuary,20	16,febeuary,20	NUM
iajs-2677	22	37	12	12	NUM
iajs-2677	22	38	,	,	PUNCT
iajs-2677	22	39	published	publish	VERB
iajs-2677	22	40	in	in	ADP
iajs-2677	22	41	july	july	PROPN
iajs-2677	22	42	2021	2021	NUM
iajs-2677	22	43	.	.	PUNCT
iajs-2677	23	1	ayad.ramadan@univsul.edu.iq	ayad.ramadan@univsul.edu.iq	PROPN
iajs-2677	23	2	mailto:begardamin1976@gmail.com	mailto:begardamin1976@gmail.com	PROPN
iajs-2677	23	3	mailto:ayad.ramadan@univsul.edu.iq	mailto:ayad.ramadan@univsul.edu.iq	PROPN
iajs-2677	23	4	ibn	ibn	PROPN
iajs-2677	23	5	al	al	PROPN
iajs-2677	23	6	-	-	PUNCT
iajs-2677	23	7	haitham	haitham	PROPN
iajs-2677	23	8	jour	jour	X
iajs-2677	23	9	.	.	PROPN
iajs-2677	24	1	for	for	ADP
iajs-2677	24	2	pure	pure	ADJ
iajs-2677	24	3	&	&	CCONJ
iajs-2677	24	4	appl	appl	PROPN
iajs-2677	24	5	.	.	PUNCT
iajs-2677	25	1	sci	sci	PROPN
iajs-2677	25	2	.	.	PROPN
iajs-2677	26	1	34(3)2021	34(3)2021	NUM
iajs-2677	26	2	51	51	NUM
iajs-2677	26	3	with	with	ADP
iajs-2677	26	4	conflicting	conflicting	ADJ
iajs-2677	26	5	criteria	criterion	NOUN
iajs-2677	26	6	:	:	PUNCT
iajs-2677	26	7	the	the	DET
iajs-2677	26	8	hierarchical	hierarchical	ADJ
iajs-2677	26	9	minimization	minimization	NOUN
iajs-2677	26	10	and	and	CCONJ
iajs-2677	26	11	the	the	DET
iajs-2677	26	12	simultaneous	simultaneous	ADJ
iajs-2677	26	13	minimization	minimization	NOUN
iajs-2677	27	1	[	[	X
iajs-2677	27	2	3	3	NUM
iajs-2677	27	3	]	]	PUNCT
iajs-2677	27	4	.	.	PUNCT
iajs-2677	28	1	the	the	DET
iajs-2677	28	2	first	first	ADJ
iajs-2677	28	3	one	one	NOUN
iajs-2677	28	4	is	be	AUX
iajs-2677	28	5	the	the	DET
iajs-2677	28	6	primary	primary	ADJ
iajs-2677	28	7	criterion	criterion	NOUN
iajs-2677	28	8	,	,	PUNCT
iajs-2677	28	9	and	and	CCONJ
iajs-2677	28	10	the	the	DET
iajs-2677	28	11	other	other	ADJ
iajs-2677	28	12	is	be	AUX
iajs-2677	28	13	the	the	DET
iajs-2677	28	14	secondary	secondary	ADJ
iajs-2677	28	15	criterion	criterion	NOUN
iajs-2677	28	16	.	.	PUNCT
iajs-2677	29	1	in	in	ADP
iajs-2677	29	2	this	this	DET
iajs-2677	29	3	case	case	NOUN
iajs-2677	29	4	,	,	PUNCT
iajs-2677	29	5	one	one	PRON
iajs-2677	29	6	minimizes	minimize	VERB
iajs-2677	29	7	the	the	DET
iajs-2677	29	8	primary	primary	ADJ
iajs-2677	29	9	criterion	criterion	NOUN
iajs-2677	29	10	and	and	CCONJ
iajs-2677	29	11	chooses	choose	VERB
iajs-2677	29	12	a	a	DET
iajs-2677	29	13	schedule	schedule	NOUN
iajs-2677	29	14	with	with	ADP
iajs-2677	29	15	a	a	DET
iajs-2677	29	16	minimum	minimum	ADJ
iajs-2677	29	17	secondary	secondary	ADJ
iajs-2677	29	18	criterion	criterion	NOUN
iajs-2677	29	19	value	value	NOUN
iajs-2677	29	20	.	.	PUNCT
iajs-2677	30	1	in	in	ADP
iajs-2677	30	2	the	the	DET
iajs-2677	30	3	second	second	ADJ
iajs-2677	30	4	approach	approach	NOUN
iajs-2677	30	5	,	,	PUNCT
iajs-2677	30	6	the	the	DET
iajs-2677	30	7	efficient	efficient	ADJ
iajs-2677	30	8	solutions	solution	NOUN
iajs-2677	30	9	(	(	PUNCT
iajs-2677	30	10	pareto	pareto	ADJ
iajs-2677	30	11	set	set	NOUN
iajs-2677	30	12	)	)	PUNCT
iajs-2677	30	13	will	will	AUX
iajs-2677	30	14	be	be	AUX
iajs-2677	30	15	generated	generate	VERB
iajs-2677	30	16	,	,	PUNCT
iajs-2677	30	17	and	and	CCONJ
iajs-2677	30	18	the	the	DET
iajs-2677	30	19	decision	decision	NOUN
iajs-2677	30	20	-	-	PUNCT
iajs-2677	30	21	maker	maker	NOUN
iajs-2677	30	22	the	the	DET
iajs-2677	30	23	one	one	NOUN
iajs-2677	30	24	with	with	ADP
iajs-2677	30	25	the	the	DET
iajs-2677	30	26	best	good	ADJ
iajs-2677	30	27	composite	composite	ADJ
iajs-2677	30	28	objective	objective	ADJ
iajs-2677	30	29	function	function	NOUN
iajs-2677	30	30	[	[	X
iajs-2677	30	31	4	4	NUM
iajs-2677	30	32	]	]	PUNCT
iajs-2677	30	33	.	.	PUNCT
iajs-2677	31	1	the	the	DET
iajs-2677	31	2	first	first	ADJ
iajs-2677	31	3	paper	paper	NOUN
iajs-2677	31	4	on	on	ADP
iajs-2677	31	5	a	a	DET
iajs-2677	31	6	problem	problem	NOUN
iajs-2677	31	7	of	of	ADP
iajs-2677	31	8	this	this	DET
iajs-2677	31	9	type	type	NOUN
iajs-2677	31	10	was	be	AUX
iajs-2677	31	11	presented	present	VERB
iajs-2677	31	12	by	by	ADP
iajs-2677	31	13	smith	smith	PROPN
iajs-2677	32	1	[	[	X
iajs-2677	32	2	5	5	NUM
iajs-2677	32	3	]	]	PUNCT
iajs-2677	32	4	.	.	PUNCT
iajs-2677	33	1	in	in	ADP
iajs-2677	33	2	this	this	DET
iajs-2677	33	3	work	work	NOUN
iajs-2677	33	4	,	,	PUNCT
iajs-2677	33	5	the	the	DET
iajs-2677	33	6	problem	problem	NOUN
iajs-2677	33	7	of	of	ADP
iajs-2677	33	8	scheduling	scheduling	NOUN
iajs-2677	33	9	n	n	CCONJ
iajs-2677	33	10	jobs	job	NOUN
iajs-2677	33	11	on	on	ADP
iajs-2677	33	12	one	one	NUM
iajs-2677	33	13	machine	machine	NOUN
iajs-2677	33	14	can	can	AUX
iajs-2677	33	15	be	be	AUX
iajs-2677	33	16	processed	process	VERB
iajs-2677	33	17	at	at	ADP
iajs-2677	33	18	most	most	ADV
iajs-2677	33	19	one	one	NUM
iajs-2677	33	20	job	job	NOUN
iajs-2677	33	21	at	at	ADP
iajs-2677	33	22	a	a	DET
iajs-2677	33	23	time	time	NOUN
iajs-2677	33	24	and	and	CCONJ
iajs-2677	33	25	without	without	ADP
iajs-2677	33	26	interruption	interruption	NOUN
iajs-2677	33	27	.	.	PUNCT
iajs-2677	34	1	each	each	DET
iajs-2677	34	2	job	job	NOUN
iajs-2677	34	3	becomes	become	VERB
iajs-2677	34	4	available	available	ADJ
iajs-2677	34	5	for	for	ADP
iajs-2677	34	6	processing	processing	NOUN
iajs-2677	34	7	at	at	ADP
iajs-2677	34	8	time	time	NOUN
iajs-2677	34	9	zero	zero	NUM
iajs-2677	34	10	,	,	PUNCT
iajs-2677	34	11	which	which	PRON
iajs-2677	34	12	requires	require	VERB
iajs-2677	34	13	a	a	DET
iajs-2677	34	14	positive	positive	ADJ
iajs-2677	34	15	processing	processing	NOUN
iajs-2677	34	16	time	time	NOUN
iajs-2677	34	17	.	.	PUNCT
iajs-2677	35	1	the	the	DET
iajs-2677	35	2	objective	objective	ADJ
iajs-2677	35	3	function	function	NOUN
iajs-2677	35	4	is	be	AUX
iajs-2677	35	5	to	to	PART
iajs-2677	35	6	minimize	minimize	VERB
iajs-2677	35	7	the	the	DET
iajs-2677	35	8	sum	sum	NOUN
iajs-2677	35	9	of	of	ADP
iajs-2677	35	10	maximum	maximum	ADJ
iajs-2677	35	11	earliness	earliness	NOUN
iajs-2677	35	12	and	and	CCONJ
iajs-2677	35	13	maximum	maximum	ADJ
iajs-2677	35	14	tardiness	tardiness	NOUN
iajs-2677	35	15	etmax	etmax	ADV
iajs-2677	35	16	.	.	PUNCT
iajs-2677	36	1	this	this	DET
iajs-2677	36	2	problem	problem	NOUN
iajs-2677	36	3	was	be	AUX
iajs-2677	36	4	first	first	ADV
iajs-2677	36	5	introduced	introduce	VERB
iajs-2677	36	6	by	by	ADP
iajs-2677	36	7	amin	amin	NOUN
iajs-2677	36	8	-	-	PROPN
iajs-2677	36	9	nayeri	nayeri	PROPN
iajs-2677	36	10	and	and	CCONJ
iajs-2677	36	11	moslehi	moslehi	NOUN
iajs-2677	37	1	[	[	X
iajs-2677	37	2	6	6	NUM
iajs-2677	37	3	]	]	PUNCT
iajs-2677	37	4	.	.	PUNCT
iajs-2677	38	1	we	we	PRON
iajs-2677	38	2	shall	shall	AUX
iajs-2677	38	3	use	use	VERB
iajs-2677	38	4	a	a	DET
iajs-2677	38	5	novel	novel	ADJ
iajs-2677	38	6	heuristic	heuristic	ADJ
iajs-2677	38	7	method	method	NOUN
iajs-2677	38	8	to	to	PART
iajs-2677	38	9	find	find	VERB
iajs-2677	38	10	the	the	DET
iajs-2677	38	11	best	good	ADJ
iajs-2677	38	12	solution	solution	NOUN
iajs-2677	38	13	for	for	ADP
iajs-2677	38	14	the	the	DET
iajs-2677	38	15	problem	problem	NOUN
iajs-2677	38	16	and	and	CCONJ
iajs-2677	38	17	drive	drive	VERB
iajs-2677	38	18	a	a	DET
iajs-2677	38	19	lower	lower	ADV
iajs-2677	38	20	bound	bind	VERB
iajs-2677	38	21	which	which	PRON
iajs-2677	38	22	depends	depend	VERB
iajs-2677	38	23	on	on	ADP
iajs-2677	38	24	a	a	DET
iajs-2677	38	25	decomposition	decomposition	NOUN
iajs-2677	38	26	of	of	ADP
iajs-2677	38	27	the	the	DET
iajs-2677	38	28	problem	problem	NOUN
iajs-2677	38	29	into	into	ADP
iajs-2677	38	30	two	two	NUM
iajs-2677	38	31	subprograms	subprogram	NOUN
iajs-2677	38	32	.	.	PUNCT
iajs-2677	39	1	we	we	PRON
iajs-2677	39	2	present	present	VERB
iajs-2677	39	3	a	a	DET
iajs-2677	39	4	novel	novel	ADJ
iajs-2677	39	5	heuristic	heuristic	ADJ
iajs-2677	39	6	method	method	NOUN
iajs-2677	39	7	to	to	PART
iajs-2677	39	8	find	find	VERB
iajs-2677	39	9	a	a	DET
iajs-2677	39	10	best	good	ADJ
iajs-2677	39	11	solution	solution	NOUN
iajs-2677	39	12	depending	depend	VERB
iajs-2677	39	13	on	on	ADP
iajs-2677	39	14	a	a	DET
iajs-2677	39	15	new	new	ADJ
iajs-2677	39	16	idea	idea	NOUN
iajs-2677	39	17	that	that	PRON
iajs-2677	39	18	is	be	AUX
iajs-2677	39	19	inserting	insert	VERB
iajs-2677	39	20	an	an	DET
iajs-2677	39	21	objective	objective	ADJ
iajs-2677	39	22	function	function	NOUN
iajs-2677	39	23	to	to	ADP
iajs-2677	39	24	our	our	PRON
iajs-2677	39	25	problem	problem	NOUN
iajs-2677	39	26	,	,	PUNCT
iajs-2677	39	27	and	and	CCONJ
iajs-2677	39	28	then	then	ADV
iajs-2677	39	29	find	find	VERB
iajs-2677	39	30	efficient	efficient	ADJ
iajs-2677	39	31	solutions	solution	NOUN
iajs-2677	39	32	for	for	ADP
iajs-2677	39	33	the	the	DET
iajs-2677	39	34	two	two	NUM
iajs-2677	39	35	problems	problem	NOUN
iajs-2677	39	36	.	.	PUNCT
iajs-2677	40	1	2	2	X
iajs-2677	40	2	.	.	NUM
iajs-2677	40	3	notations	notation	NOUN
iajs-2677	40	4	and	and	CCONJ
iajs-2677	40	5	definitions	definition	NOUN
iajs-2677	40	6	in	in	ADP
iajs-2677	40	7	this	this	DET
iajs-2677	40	8	section	section	NOUN
iajs-2677	40	9	,	,	PUNCT
iajs-2677	40	10	we	we	PRON
iajs-2677	40	11	give	give	VERB
iajs-2677	40	12	some	some	DET
iajs-2677	40	13	notations	notation	NOUN
iajs-2677	40	14	and	and	CCONJ
iajs-2677	40	15	definitions	definition	NOUN
iajs-2677	40	16	n	n	NOUN
iajs-2677	40	17	=	=	SYM
iajs-2677	40	18	the	the	DET
iajs-2677	40	19	set	set	NOUN
iajs-2677	40	20	{	{	PUNCT
iajs-2677	40	21	1	1	NUM
iajs-2677	40	22	,	,	PUNCT
iajs-2677	40	23	2	2	NUM
iajs-2677	40	24	,	,	PUNCT
iajs-2677	40	25	3	3	NUM
iajs-2677	40	26	,	,	PUNCT
iajs-2677	40	27	…	…	PUNCT
iajs-2677	40	28	,	,	PUNCT
iajs-2677	40	29	n	n	CCONJ
iajs-2677	40	30	}	}	PUNCT
iajs-2677	40	31	.	.	PUNCT
iajs-2677	41	1			NOUN
iajs-2677	41	2	=	=	PRON
iajs-2677	41	3	the	the	DET
iajs-2677	41	4	set	set	NOUN
iajs-2677	41	5	of	of	ADP
iajs-2677	41	6	permutation	permutation	NOUN
iajs-2677	41	7	schedules	schedule	NOUN
iajs-2677	41	8	.	.	PUNCT
iajs-2677	42	1			NOUN
iajs-2677	42	2	=	=	PUNCT
iajs-2677	42	3	a	a	DET
iajs-2677	42	4	permutation	permutation	NOUN
iajs-2677	42	5	schedule	schedule	NOUN
iajs-2677	42	6	.	.	PUNCT
iajs-2677	43	1	pj	pj	NOUN
iajs-2677	43	2	=	=	PUNCT
iajs-2677	43	3	processing	processing	NOUN
iajs-2677	43	4	time	time	NOUN
iajs-2677	43	5	for	for	ADP
iajs-2677	43	6	job	job	NOUN
iajs-2677	44	1	j.	j.	PROPN
iajs-2677	44	2	dj	dj	PROPN
iajs-2677	45	1	=	=	PUNCT
iajs-2677	45	2	due	due	ADJ
iajs-2677	45	3	date	date	NOUN
iajs-2677	45	4	for	for	ADP
iajs-2677	45	5	job	job	NOUN
iajs-2677	45	6	j.	j.	PROPN
iajs-2677	45	7	cj	cj	PROPN
iajs-2677	45	8	=	=	PUNCT
iajs-2677	45	9	completion	completion	NOUN
iajs-2677	45	10	time	time	NOUN
iajs-2677	45	11	for	for	ADP
iajs-2677	45	12	job	job	NOUN
iajs-2677	45	13	j.	j.	PROPN
iajs-2677	45	14	ei	ei	PROPN
iajs-2677	45	15	=	=	PROPN
iajs-2677	45	16	max	max	PROPN
iajs-2677	45	17	{	{	PUNCT
iajs-2677	45	18	di	di	INTJ
iajs-2677	45	19	–	–	PUNCT
iajs-2677	45	20	ci	ci	NOUN
iajs-2677	45	21	,	,	PUNCT
iajs-2677	45	22	0	0	NUM
iajs-2677	45	23	}	}	PUNCT
iajs-2677	45	24	;	;	PUNCT
iajs-2677	45	25	the	the	DET
iajs-2677	45	26	earliness	earliness	NOUN
iajs-2677	45	27	of	of	ADP
iajs-2677	45	28	job	job	NOUN
iajs-2677	45	29	i.	i.	NOUN
iajs-2677	45	30	emax	emax	PROPN
iajs-2677	45	31	=	=	SYM
iajs-2677	45	32	max	max	PROPN
iajs-2677	45	33	{	{	PUNCT
iajs-2677	45	34	ei	ei	PROPN
iajs-2677	45	35	}	}	PUNCT
iajs-2677	45	36	;	;	PUNCT
iajs-2677	45	37	the	the	DET
iajs-2677	45	38	maximum	maximum	ADJ
iajs-2677	45	39	earliness	earliness	NOUN
iajs-2677	45	40	.	.	PUNCT
iajs-2677	46	1	ti	ti	X
iajs-2677	46	2	=	=	SYM
iajs-2677	46	3	max	max	PROPN
iajs-2677	46	4	{	{	PUNCT
iajs-2677	46	5	ci	ci	PROPN
iajs-2677	46	6	–	–	PUNCT
iajs-2677	46	7	di	di	NOUN
iajs-2677	46	8	,	,	PUNCT
iajs-2677	46	9	0	0	NUM
iajs-2677	46	10	}	}	PUNCT
iajs-2677	46	11	;	;	PUNCT
iajs-2677	46	12	the	the	DET
iajs-2677	46	13	tardiness	tardiness	NOUN
iajs-2677	46	14	of	of	ADP
iajs-2677	46	15	job	job	NOUN
iajs-2677	46	16	i.	i.	NOUN
iajs-2677	46	17	tmax	tmax	PROPN
iajs-2677	46	18	=	=	SYM
iajs-2677	46	19	max	max	X
iajs-2677	46	20	{	{	PUNCT
iajs-2677	46	21	ti	ti	NOUN
iajs-2677	46	22	}	}	PUNCT
iajs-2677	46	23	;	;	PUNCT
iajs-2677	46	24	the	the	DET
iajs-2677	46	25	maximum	maximum	ADJ
iajs-2677	46	26	tardiness	tardiness	NOUN
iajs-2677	46	27	.	.	PUNCT
iajs-2677	47	1	mst	mst	PROPN
iajs-2677	47	2	:	:	PUNCT
iajs-2677	47	3	(	(	PUNCT
iajs-2677	47	4	minimum	minimum	ADJ
iajs-2677	47	5	slack	slack	NOUN
iajs-2677	47	6	times	time	NOUN
iajs-2677	47	7	)	)	PUNCT
iajs-2677	47	8	jobs	job	NOUN
iajs-2677	47	9	are	be	AUX
iajs-2677	47	10	sequenced	sequence	VERB
iajs-2677	47	11	in	in	ADP
iajs-2677	47	12	non	non	ADJ
iajs-2677	47	13	-	-	ADJ
iajs-2677	47	14	decreasing	decrease	VERB
iajs-2677	47	15	order	order	NOUN
iajs-2677	47	16	of	of	ADP
iajs-2677	47	17	minimum	minimum	ADJ
iajs-2677	47	18	slack	slack	NOUN
iajs-2677	47	19	times	time	NOUN
iajs-2677	47	20	sj	sj	INTJ
iajs-2677	47	21	,	,	PUNCT
iajs-2677	48	1	where	where	SCONJ
iajs-2677	48	2	sj	sj	INTJ
iajs-2677	48	3	=	=	NOUN
iajs-2677	48	4	dj	dj	PROPN
iajs-2677	48	5	pj	pj	PROPN
iajs-2677	48	6	.	.	PUNCT
iajs-2677	48	7	spt	spt	PROPN
iajs-2677	48	8	:	:	PUNCT
iajs-2677	48	9	(	(	PUNCT
iajs-2677	48	10	shortest	short	ADJ
iajs-2677	48	11	processing	processing	NOUN
iajs-2677	48	12	time	time	NOUN
iajs-2677	48	13	)	)	PUNCT
iajs-2677	49	1	they	they	PRON
iajs-2677	49	2	are	be	AUX
iajs-2677	49	3	in	in	ADP
iajs-2677	49	4	non	non	ADJ
iajs-2677	49	5	-	-	ADJ
iajs-2677	49	6	decreasing	decrease	VERB
iajs-2677	49	7	order	order	NOUN
iajs-2677	49	8	of	of	ADP
iajs-2677	49	9	pj	pj	PROPN
iajs-2677	49	10	.	.	PUNCT
iajs-2677	49	11	eddrule	eddrule	PROPN
iajs-2677	49	12	:	:	PUNCT
iajs-2677	49	13	(	(	PUNCT
iajs-2677	49	14	early	early	ADJ
iajs-2677	49	15	due	due	ADJ
iajs-2677	49	16	date	date	NOUN
iajs-2677	49	17	)	)	PUNCT
iajs-2677	49	18	they	they	PRON
iajs-2677	49	19	are	be	AUX
iajs-2677	49	20	sequenced	sequence	VERB
iajs-2677	49	21	in	in	ADP
iajs-2677	49	22	non	non	ADJ
iajs-2677	49	23	-	-	ADJ
iajs-2677	49	24	decreasing	decrease	VERB
iajs-2677	49	25	order	order	NOUN
iajs-2677	49	26	of	of	ADP
iajs-2677	49	27	dj	dj	NOUN
iajs-2677	49	28	.	.	PUNCT
iajs-2677	50	1	lb	lb	X
iajs-2677	50	2	:	:	PUNCT
iajs-2677	50	3	lower	low	ADJ
iajs-2677	50	4	bound	bind	VERB
iajs-2677	50	5	.	.	PUNCT
iajs-2677	51	1	ub	ub	ADP
iajs-2677	51	2	:	:	PUNCT
iajs-2677	51	3	upper	upper	ADJ
iajs-2677	51	4	bound	bind	VERB
iajs-2677	51	5	.	.	PUNCT
iajs-2677	52	1	definition	definition	NOUN
iajs-2677	52	2	(	(	PUNCT
iajs-2677	52	3	1	1	X
iajs-2677	52	4	)	)	PUNCT
iajs-2677	53	1	[	[	X
iajs-2677	53	2	7	7	NUM
iajs-2677	53	3	]	]	PUNCT
iajs-2677	53	4	:	:	PUNCT
iajs-2677	53	5	consider	consider	VERB
iajs-2677	53	6	a	a	DET
iajs-2677	53	7	problem	problem	NOUN
iajs-2677	53	8	p	p	NOUN
iajs-2677	53	9	,	,	PUNCT
iajs-2677	53	10	a	a	DET
iajs-2677	53	11	schedule	schedule	NOUN
iajs-2677	53	12			X
iajs-2677	53	13	(	(	PUNCT
iajs-2677	53	14	where	where	SCONJ
iajs-2677	53	15			NOUN
iajs-2677	53	16	is	be	AUX
iajs-2677	53	17	the	the	DET
iajs-2677	53	18	set	set	NOUN
iajs-2677	53	19	of	of	ADP
iajs-2677	53	20	all	all	DET
iajs-2677	53	21	schedules	schedule	NOUN
iajs-2677	53	22	)	)	PUNCT
iajs-2677	53	23	is	be	AUX
iajs-2677	53	24	said	say	VERB
iajs-2677	53	25	to	to	PART
iajs-2677	53	26	be	be	AUX
iajs-2677	53	27	feasible	feasible	ADJ
iajs-2677	53	28	,	,	PUNCT
iajs-2677	53	29	if	if	SCONJ
iajs-2677	53	30	it	it	PRON
iajs-2677	53	31	satisfies	satisfy	VERB
iajs-2677	53	32	the	the	DET
iajs-2677	53	33	constraints	constraint	NOUN
iajs-2677	53	34	of	of	ADP
iajs-2677	53	35	p.	p.	NOUN
iajs-2677	53	36	definition	definition	NOUN
iajs-2677	53	37	(	(	PUNCT
iajs-2677	53	38	2	2	X
iajs-2677	53	39	)	)	PUNCT
iajs-2677	54	1	[	[	X
iajs-2677	54	2	8	8	NUM
iajs-2677	54	3	]	]	X
iajs-2677	54	4	:	:	PUNCT
iajs-2677	54	5	a	a	DET
iajs-2677	54	6	feasible	feasible	ADJ
iajs-2677	54	7	schedule	schedule	NOUN
iajs-2677	54	8	𝜋∗	𝜋∗	NOUN
iajs-2677	54	9	is	be	AUX
iajs-2677	54	10	efficient	efficient	ADJ
iajs-2677	54	11	,	,	PUNCT
iajs-2677	54	12	with	with	ADP
iajs-2677	54	13	respect	respect	NOUN
iajs-2677	54	14	to	to	ADP
iajs-2677	54	15	the	the	DET
iajs-2677	54	16	criteria	criterion	NOUN
iajs-2677	54	17	(	(	PUNCT
iajs-2677	54	18	and	and	CCONJ
iajs-2677	54	19	)	)	PUNCT
iajs-2677	54	20	if	if	SCONJ
iajs-2677	54	21	there	there	PRON
iajs-2677	54	22	is	be	VERB
iajs-2677	54	23	no	no	DET
iajs-2677	54	24	any	any	DET
iajs-2677	54	25	feasible	feasible	ADJ
iajs-2677	54	26	schedule	schedule	NOUN
iajs-2677	54	27	π	π	PROPN
iajs-2677	54	28	such	such	ADJ
iajs-2677	54	29	f(	f(	NOUN
iajs-2677	54	30	)	)	PUNCT
iajs-2677	54	31	≤	≤	NUM
iajs-2677	54	32	f(	f(	PROPN
iajs-2677	54	33	*	*	PUNCT
iajs-2677	54	34	)	)	PUNCT
iajs-2677	54	35	and	and	CCONJ
iajs-2677	54	36	g(	g(	PROPN
iajs-2677	54	37	)	)	PUNCT
iajs-2677	54	38	≤	≤	NUM
iajs-2677	54	39	g(	g(	NOUN
iajs-2677	54	40	*	*	PROPN
iajs-2677	54	41	)	)	PUNCT
iajs-2677	54	42	,	,	PUNCT
iajs-2677	54	43	and	and	CCONJ
iajs-2677	54	44	at	at	ADV
iajs-2677	54	45	least	least	ADJ
iajs-2677	54	46	one	one	NUM
iajs-2677	54	47	of	of	ADP
iajs-2677	54	48	the	the	DET
iajs-2677	54	49	inequalities	inequality	NOUN
iajs-2677	54	50	is	be	AUX
iajs-2677	54	51	strict	strict	ADJ
iajs-2677	54	52	.	.	PUNCT
iajs-2677	55	1	ibn	ibn	PROPN
iajs-2677	55	2	al	al	PROPN
iajs-2677	55	3	-	-	PUNCT
iajs-2677	55	4	haitham	haitham	PROPN
iajs-2677	55	5	jour	jour	X
iajs-2677	55	6	.	.	PROPN
iajs-2677	55	7	for	for	ADP
iajs-2677	55	8	pure	pure	ADJ
iajs-2677	55	9	&	&	CCONJ
iajs-2677	55	10	appl	appl	PROPN
iajs-2677	55	11	.	.	PUNCT
iajs-2677	56	1	sci	sci	PROPN
iajs-2677	56	2	.	.	PROPN
iajs-2677	57	1	34(3)2021	34(3)2021	NUM
iajs-2677	57	2	52	52	NUM
iajs-2677	57	3	3	3	NUM
iajs-2677	57	4	.	.	PUNCT
iajs-2677	58	1	problem	problem	NOUN
iajs-2677	58	2	formulation	formulation	NOUN
iajs-2677	58	3	in	in	ADP
iajs-2677	58	4	this	this	DET
iajs-2677	58	5	study	study	NOUN
iajs-2677	58	6	,	,	PUNCT
iajs-2677	58	7	we	we	PRON
iajs-2677	58	8	consider	consider	VERB
iajs-2677	58	9	the	the	DET
iajs-2677	58	10	one	one	NUM
iajs-2677	58	11	machine	machine	NOUN
iajs-2677	58	12	scheduling	scheduling	NOUN
iajs-2677	58	13	problem	problem	NOUN
iajs-2677	58	14	with	with	ADP
iajs-2677	58	15	multi	multi	ADJ
iajs-2677	58	16	-	-	ADJ
iajs-2677	58	17	objective	objective	ADJ
iajs-2677	58	18	function	function	NOUN
iajs-2677	58	19	which	which	PRON
iajs-2677	58	20	is	be	AUX
iajs-2677	58	21	minimizing	minimize	VERB
iajs-2677	58	22	the	the	DET
iajs-2677	58	23	sum	sum	NOUN
iajs-2677	58	24	of	of	ADP
iajs-2677	58	25	the	the	DET
iajs-2677	58	26	maximum	maximum	ADJ
iajs-2677	58	27	earliness	earliness	NOUN
iajs-2677	58	28	and	and	CCONJ
iajs-2677	58	29	tardiness	tardiness	NOUN
iajs-2677	58	30	,	,	PUNCT
iajs-2677	58	31	denoted	denote	VERB
iajs-2677	58	32	by	by	ADP
iajs-2677	58	33	1	1	NUM
iajs-2677	58	34			PROPN
iajs-2677	58	35			PROPN
iajs-2677	58	36	emax	emax	X
iajs-2677	58	37	+	+	CCONJ
iajs-2677	58	38	tmax	tmax	ADV
iajs-2677	58	39	,	,	PUNCT
iajs-2677	58	40	for	for	ADP
iajs-2677	58	41	simplicity	simplicity	NOUN
iajs-2677	58	42	it	it	PRON
iajs-2677	58	43	is	be	AUX
iajs-2677	58	44	1	1	NUM
iajs-2677	58	45			PROPN
iajs-2677	58	46			PROPN
iajs-2677	58	47	etmax	etmax	ADV
iajs-2677	58	48	.	.	PUNCT
iajs-2677	59	1	a	a	DET
iajs-2677	59	2	set	set	NOUN
iajs-2677	59	3	n	n	NOUN
iajs-2677	59	4	=	=	SYM
iajs-2677	59	5	{	{	PUNCT
iajs-2677	59	6	1	1	NUM
iajs-2677	59	7	,	,	PUNCT
iajs-2677	59	8	2	2	NUM
iajs-2677	59	9	,	,	PUNCT
iajs-2677	59	10	…	…	PUNCT
iajs-2677	59	11	,	,	PUNCT
iajs-2677	59	12	n	n	CCONJ
iajs-2677	59	13	}	}	PUNCT
iajs-2677	59	14	of	of	ADP
iajs-2677	59	15	n	n	PRON
iajs-2677	59	16	independent	independent	ADJ
iajs-2677	59	17	jobs	job	NOUN
iajs-2677	59	18	that	that	PRON
iajs-2677	59	19	has	have	VERB
iajs-2677	59	20	to	to	PART
iajs-2677	59	21	be	be	AUX
iajs-2677	59	22	scheduled	schedule	VERB
iajs-2677	59	23	on	on	ADP
iajs-2677	59	24	a	a	DET
iajs-2677	59	25	single	single	ADJ
iajs-2677	59	26	machine	machine	NOUN
iajs-2677	59	27	to	to	PART
iajs-2677	59	28	minimize	minimize	VERB
iajs-2677	59	29	a	a	DET
iajs-2677	59	30	criterion	criterion	NOUN
iajs-2677	59	31	.	.	PUNCT
iajs-2677	60	1	job	job	NOUN
iajs-2677	60	2	j	j	PROPN
iajs-2677	60	3	(	(	PUNCT
iajs-2677	60	4	j	j	PROPN
iajs-2677	60	5	=	=	SYM
iajs-2677	60	6	1	1	NUM
iajs-2677	60	7	,	,	PUNCT
iajs-2677	60	8	2	2	NUM
iajs-2677	60	9	,	,	PUNCT
iajs-2677	60	10	…	…	PUNCT
iajs-2677	60	11	,	,	PUNCT
iajs-2677	60	12	n	n	CCONJ
iajs-2677	60	13	)	)	PUNCT
iajs-2677	60	14	is	be	AUX
iajs-2677	60	15	to	to	PART
iajs-2677	60	16	be	be	AUX
iajs-2677	60	17	processed	process	VERB
iajs-2677	60	18	on	on	ADP
iajs-2677	60	19	a	a	DET
iajs-2677	60	20	single	single	ADJ
iajs-2677	60	21	machine	machine	NOUN
iajs-2677	60	22	without	without	ADP
iajs-2677	60	23	interruption	interruption	NOUN
iajs-2677	60	24	that	that	PRON
iajs-2677	60	25	handles	handle	VERB
iajs-2677	60	26	only	only	ADV
iajs-2677	60	27	one	one	NUM
iajs-2677	60	28	job	job	NOUN
iajs-2677	60	29	at	at	ADP
iajs-2677	60	30	a	a	DET
iajs-2677	60	31	time	time	NOUN
iajs-2677	60	32	,	,	PUNCT
iajs-2677	60	33	requires	require	VERB
iajs-2677	60	34	processing	processing	NOUN
iajs-2677	60	35	time	time	NOUN
iajs-2677	60	36	pj	pj	PROPN
iajs-2677	60	37	,	,	PUNCT
iajs-2677	60	38	and	and	CCONJ
iajs-2677	60	39	due	due	ADJ
iajs-2677	60	40	date	date	NOUN
iajs-2677	60	41	dj	dj	NOUN
iajs-2677	60	42	.	.	PUNCT
iajs-2677	61	1	for	for	ADP
iajs-2677	61	2	a	a	DET
iajs-2677	61	3	sequence	sequence	NOUN
iajs-2677	61	4	π	π	NOUN
iajs-2677	61	5	of	of	ADP
iajs-2677	61	6	the	the	DET
iajs-2677	61	7	jobs	job	NOUN
iajs-2677	61	8	,	,	PUNCT
iajs-2677	61	9	earliness	earliness	NOUN
iajs-2677	61	10	eπ(j	eπ(j	NOUN
iajs-2677	61	11	)	)	PUNCT
iajs-2677	61	12	,	,	PUNCT
iajs-2677	61	13	and	and	CCONJ
iajs-2677	61	14	the	the	DET
iajs-2677	61	15	tardiness	tardiness	NOUN
iajs-2677	61	16	tπ(j	tπ(j	PUNCT
iajs-2677	61	17	)	)	PUNCT
iajs-2677	61	18	are	be	AUX
iajs-2677	61	19	given	give	VERB
iajs-2677	61	20	by	by	ADP
iajs-2677	61	21	:	:	PUNCT
iajs-2677	61	22	eπ(j)=	eπ(j)=	PRON
iajs-2677	61	23	max	max	PROPN
iajs-2677	61	24	{	{	PUNCT
iajs-2677	61	25	dπ(j	dπ(j	PROPN
iajs-2677	61	26	)	)	PUNCT
iajs-2677	61	27	−	−	NOUN
iajs-2677	61	28	cπ(j	cπ(j	NOUN
iajs-2677	61	29	)	)	PUNCT
iajs-2677	61	30	,	,	PUNCT
iajs-2677	61	31	0	0	NUM
iajs-2677	61	32	}	}	PUNCT
iajs-2677	61	33	,	,	PUNCT
iajs-2677	61	34	j	j	PROPN
iajs-2677	61	35	=	=	SYM
iajs-2677	61	36	1	1	NUM
iajs-2677	61	37	,	,	PUNCT
iajs-2677	61	38	2	2	NUM
iajs-2677	61	39	,	,	PUNCT
iajs-2677	61	40	…	…	PUNCT
iajs-2677	61	41	,	,	PUNCT
iajs-2677	61	42	n.	n.	PROPN
iajs-2677	61	43	tπ(j)=	tπ(j)=	PROPN
iajs-2677	61	44	max	max	PROPN
iajs-2677	61	45	{	{	PUNCT
iajs-2677	61	46	cπ(j	cπ(j	NOUN
iajs-2677	61	47	)	)	PUNCT
iajs-2677	61	48	−	−	NOUN
iajs-2677	61	49	dπ(j	dπ(j	NOUN
iajs-2677	61	50	)	)	PUNCT
iajs-2677	61	51	,	,	PUNCT
iajs-2677	61	52	0	0	NUM
iajs-2677	61	53	}	}	PUNCT
iajs-2677	61	54	,	,	PUNCT
iajs-2677	61	55	j	j	PROPN
iajs-2677	61	56	=	=	SYM
iajs-2677	61	57	1	1	NUM
iajs-2677	61	58	,	,	PUNCT
iajs-2677	61	59	2	2	NUM
iajs-2677	61	60	,	,	PUNCT
iajs-2677	61	61	…	…	PUNCT
iajs-2677	61	62	,	,	PUNCT
iajs-2677	61	63	n.	n.	PROPN
iajs-2677	61	64	so	so	SCONJ
iajs-2677	61	65	the	the	DET
iajs-2677	61	66	mathematical	mathematical	ADJ
iajs-2677	61	67	form	form	NOUN
iajs-2677	61	68	of	of	ADP
iajs-2677	61	69	this	this	DET
iajs-2677	61	70	problem	problem	NOUN
iajs-2677	61	71	can	can	AUX
iajs-2677	61	72	be	be	AUX
iajs-2677	61	73	formulated	formulate	VERB
iajs-2677	61	74	as	as	ADP
iajs-2677	61	75	:	:	PUNCT
iajs-2677	61	76	z	z	NOUN
iajs-2677	61	77	=	=	SYM
iajs-2677	61	78	min{emax(π	min{emax(π	PROPN
iajs-2677	61	79	)	)	PUNCT
iajs-2677	61	80	+	+	NUM
iajs-2677	61	81	tmax(π	tmax(π	NOUN
iajs-2677	61	82	)	)	PUNCT
iajs-2677	61	83	}	}	PUNCT
iajs-2677	61	84	s.	s.	PROPN
iajs-2677	61	85	t.	t.	PROPN
iajs-2677	61	86	eπ(j	eπ(j	PROPN
iajs-2677	61	87	)	)	PUNCT
iajs-2677	61	88	≥	≥	NOUN
iajs-2677	61	89	0	0	NUM
iajs-2677	61	90	,	,	PUNCT
iajs-2677	61	91	j	j	PROPN
iajs-2677	61	92	=	=	SYM
iajs-2677	61	93	1	1	NUM
iajs-2677	61	94	,	,	PUNCT
iajs-2677	61	95	2	2	NUM
iajs-2677	61	96	,	,	PUNCT
iajs-2677	61	97	…	…	PUNCT
iajs-2677	61	98	,	,	PUNCT
iajs-2677	61	99	n.	n.	NOUN
iajs-2677	61	100	tπ(j	tπ(j	NUM
iajs-2677	61	101	)	)	PUNCT
iajs-2677	61	102	≥	≥	NOUN
iajs-2677	61	103	0	0	NUM
iajs-2677	61	104	,	,	PUNCT
iajs-2677	61	105	j	j	PROPN
iajs-2677	61	106	=	=	SYM
iajs-2677	61	107	1	1	NUM
iajs-2677	61	108	,	,	PUNCT
iajs-2677	61	109	2	2	NUM
iajs-2677	61	110	,	,	PUNCT
iajs-2677	61	111	…	…	PUNCT
iajs-2677	61	112	,	,	PUNCT
iajs-2677	61	113	n.	n.	NOUN
iajs-2677	61	114	...	...	PUNCT
iajs-2677	61	115	(	(	PUNCT
iajs-2677	61	116	p1	p1	NOUN
iajs-2677	61	117	)	)	PUNCT
iajs-2677	61	118	eπ(j	eπ(j	NOUN
iajs-2677	61	119	)	)	PUNCT
iajs-2677	61	120	≥	≥	NOUN
iajs-2677	61	121	dπ(j	dπ(j	NOUN
iajs-2677	61	122	)	)	PUNCT
iajs-2677	61	123	−	−	NOUN
iajs-2677	61	124	cπ(j	cπ(j	NOUN
iajs-2677	61	125	)	)	PUNCT
iajs-2677	61	126	,	,	PUNCT
iajs-2677	61	127	j	j	PROPN
iajs-2677	61	128	=	=	SYM
iajs-2677	61	129	1	1	NUM
iajs-2677	61	130	,	,	PUNCT
iajs-2677	61	131	2	2	NUM
iajs-2677	61	132	,	,	PUNCT
iajs-2677	61	133	…	…	PUNCT
iajs-2677	61	134	,	,	PUNCT
iajs-2677	61	135	n.	n.	NOUN
iajs-2677	61	136	tπ(j	tπ(j	NUM
iajs-2677	61	137	)	)	PUNCT
iajs-2677	61	138	≥	≥	NOUN
iajs-2677	61	139	cπ(j	cπ(j	NOUN
iajs-2677	61	140	)	)	PUNCT
iajs-2677	61	141	−	−	NOUN
iajs-2677	61	142	dπ(j	dπ(j	NOUN
iajs-2677	61	143	)	)	PUNCT
iajs-2677	61	144	,	,	PUNCT
iajs-2677	61	145	j	j	PROPN
iajs-2677	61	146	=	=	SYM
iajs-2677	61	147	1	1	NUM
iajs-2677	61	148	,	,	PUNCT
iajs-2677	61	149	2	2	NUM
iajs-2677	61	150	,	,	PUNCT
iajs-2677	61	151	…	…	PUNCT
iajs-2677	61	152	,	,	PUNCT
iajs-2677	61	153	n.	n.	NOUN
iajs-2677	61	154	to	to	PART
iajs-2677	61	155	find	find	VERB
iajs-2677	61	156	a	a	DET
iajs-2677	61	157	sequence	sequence	NOUN
iajs-2677	61	158	π	π	NOUN
iajs-2677	61	159	that	that	PRON
iajs-2677	61	160	minimizes	minimize	VERB
iajs-2677	61	161	z	z	PROPN
iajs-2677	61	162	,	,	PUNCT
iajs-2677	61	163	the	the	DET
iajs-2677	61	164	schedules	schedule	NOUN
iajs-2677	61	165	that	that	PRON
iajs-2677	61	166	minimize	minimize	VERB
iajs-2677	61	167	emax	emax	NOUN
iajs-2677	61	168	and	and	CCONJ
iajs-2677	61	169	tmax	tmax	ADV
iajs-2677	61	170	are	be	AUX
iajs-2677	61	171	referred	refer	VERB
iajs-2677	61	172	to	to	ADP
iajs-2677	61	173	as	as	ADP
iajs-2677	61	174	edd	edd	PROPN
iajs-2677	61	175	and	and	CCONJ
iajs-2677	61	176	mst	mst	PROPN
iajs-2677	61	177	rules	rule	NOUN
iajs-2677	61	178	respectively	respectively	ADV
iajs-2677	61	179	[	[	X
iajs-2677	61	180	9	9	NUM
iajs-2677	61	181	]	]	PUNCT
iajs-2677	61	182	.	.	PUNCT
iajs-2677	62	1	for	for	ADP
iajs-2677	62	2	the	the	DET
iajs-2677	62	3	composition	composition	NOUN
iajs-2677	62	4	of	of	ADP
iajs-2677	62	5	these	these	DET
iajs-2677	62	6	two	two	NUM
iajs-2677	62	7	functions	function	NOUN
iajs-2677	62	8	,	,	PUNCT
iajs-2677	62	9	we	we	PRON
iajs-2677	62	10	can	can	AUX
iajs-2677	62	11	not	not	PART
iajs-2677	62	12	find	find	VERB
iajs-2677	62	13	optimal	optimal	ADJ
iajs-2677	62	14	solution	solution	NOUN
iajs-2677	62	15	by	by	ADP
iajs-2677	62	16	any	any	DET
iajs-2677	62	17	direct	direct	ADJ
iajs-2677	62	18	rule	rule	NOUN
iajs-2677	62	19	.	.	PUNCT
iajs-2677	63	1	4	4	X
iajs-2677	63	2	.	.	X
iajs-2677	63	3	analysis	analysis	NOUN
iajs-2677	63	4	of	of	ADP
iajs-2677	63	5	the	the	DET
iajs-2677	63	6	problem	problem	NOUN
iajs-2677	63	7	with	with	ADP
iajs-2677	63	8	special	special	ADJ
iajs-2677	63	9	cases	case	NOUN
iajs-2677	63	10	this	this	DET
iajs-2677	63	11	problem	problem	NOUN
iajs-2677	63	12	has	have	AUX
iajs-2677	63	13	been	be	AUX
iajs-2677	63	14	studied	study	VERB
iajs-2677	63	15	in	in	ADP
iajs-2677	63	16	various	various	ADJ
iajs-2677	63	17	conditions	condition	NOUN
iajs-2677	63	18	and	and	CCONJ
iajs-2677	63	19	compositions	composition	NOUN
iajs-2677	63	20	.	.	PUNCT
iajs-2677	64	1	the	the	DET
iajs-2677	64	2	problem	problem	NOUN
iajs-2677	64	3	was	be	AUX
iajs-2677	64	4	studied	study	VERB
iajs-2677	64	5	at	at	ADP
iajs-2677	64	6	first	first	ADV
iajs-2677	64	7	by	by	ADP
iajs-2677	64	8	amin	amin	NOUN
iajs-2677	64	9	and	and	CCONJ
iajs-2677	64	10	moslehi	moslehi	NOUN
iajs-2677	64	11	[	[	X
iajs-2677	64	12	6	6	NUM
iajs-2677	64	13	]	]	PUNCT
iajs-2677	64	14	,	,	PUNCT
iajs-2677	64	15	they	they	PRON
iajs-2677	64	16	studied	study	VERB
iajs-2677	64	17	the	the	DET
iajs-2677	64	18	problem	problem	NOUN
iajs-2677	64	19	of	of	ADP
iajs-2677	64	20	sequencing	sequence	VERB
iajs-2677	64	21	a	a	DET
iajs-2677	64	22	single	single	ADJ
iajs-2677	64	23	machine	machine	NOUN
iajs-2677	64	24	to	to	PART
iajs-2677	64	25	find	find	VERB
iajs-2677	64	26	an	an	DET
iajs-2677	64	27	optimal	optimal	ADJ
iajs-2677	64	28	sequence	sequence	NOUN
iajs-2677	64	29	of	of	ADP
iajs-2677	64	30	jobs	job	NOUN
iajs-2677	64	31	,	,	PUNCT
iajs-2677	64	32	also	also	ADV
iajs-2677	64	33	they	they	PRON
iajs-2677	64	34	showed	show	VERB
iajs-2677	64	35	that	that	SCONJ
iajs-2677	64	36	the	the	DET
iajs-2677	64	37	algorithm	algorithm	NOUN
iajs-2677	64	38	solved	solve	VERB
iajs-2677	64	39	100	100	NUM
iajs-2677	64	40	%	%	NOUN
iajs-2677	64	41	of	of	ADP
iajs-2677	64	42	the	the	DET
iajs-2677	64	43	examples	example	NOUN
iajs-2677	64	44	.	.	PUNCT
iajs-2677	65	1	since	since	SCONJ
iajs-2677	65	2	the	the	DET
iajs-2677	65	3	problem	problem	NOUN
iajs-2677	65	4	is	be	AUX
iajs-2677	65	5	np	np	INTJ
iajs-2677	65	6	-	-	ADJ
iajs-2677	65	7	hard	hard	ADJ
iajs-2677	65	8	(	(	PUNCT
iajs-2677	65	9	no	no	DET
iajs-2677	65	10	bounded	bounded	ADJ
iajs-2677	65	11	polynomial	polynomial	ADJ
iajs-2677	65	12	exists	exist	VERB
iajs-2677	65	13	)	)	PUNCT
iajs-2677	66	1	[	[	X
iajs-2677	66	2	10	10	NUM
iajs-2677	66	3	]	]	PUNCT
iajs-2677	66	4	,	,	PUNCT
iajs-2677	66	5	several	several	ADJ
iajs-2677	66	6	heuristic	heuristic	ADJ
iajs-2677	66	7	approaches	approach	NOUN
iajs-2677	66	8	have	have	AUX
iajs-2677	66	9	been	be	AUX
iajs-2677	66	10	developed	develop	VERB
iajs-2677	66	11	for	for	ADP
iajs-2677	66	12	the	the	DET
iajs-2677	66	13	problem	problem	NOUN
iajs-2677	66	14	.	.	PUNCT
iajs-2677	67	1	abdul	abdul	PROPN
iajs-2677	67	2	-	-	PUNCT
iajs-2677	67	3	razaq	razaq	PROPN
iajs-2677	67	4	and	and	CCONJ
iajs-2677	67	5	akram	akram	NOUN
iajs-2677	67	6	used	use	VERB
iajs-2677	67	7	local	local	ADJ
iajs-2677	67	8	search	search	NOUN
iajs-2677	67	9	algorithm	algorithm	NOUN
iajs-2677	67	10	to	to	PART
iajs-2677	67	11	solve	solve	VERB
iajs-2677	67	12	a	a	DET
iajs-2677	67	13	multi	multi	ADJ
iajs-2677	67	14	-	-	ADJ
iajs-2677	67	15	criteria	criteria	ADJ
iajs-2677	67	16	function	function	NOUN
iajs-2677	67	17	of	of	ADP
iajs-2677	67	18	five	five	NUM
iajs-2677	67	19	objectives	objective	NOUN
iajs-2677	67	20	included	include	VERB
iajs-2677	67	21	maximum	maximum	ADJ
iajs-2677	67	22	earliness	earliness	NOUN
iajs-2677	67	23	and	and	CCONJ
iajs-2677	67	24	maximum	maximum	ADJ
iajs-2677	67	25	tardiness	tardiness	NOUN
iajs-2677	68	1	[	[	X
iajs-2677	68	2	11	11	NUM
iajs-2677	68	3	]	]	PUNCT
iajs-2677	68	4	.	.	PUNCT
iajs-2677	69	1	abdullah	abdullah	PROPN
iajs-2677	69	2	considered	consider	VERB
iajs-2677	69	3	maximum	maximum	ADJ
iajs-2677	69	4	earliness	earliness	NOUN
iajs-2677	69	5	and	and	CCONJ
iajs-2677	69	6	maximum	maximum	ADJ
iajs-2677	69	7	tardiness	tardiness	NOUN
iajs-2677	69	8	as	as	ADP
iajs-2677	69	9	primary	primary	ADJ
iajs-2677	69	10	criteria	criterion	NOUN
iajs-2677	69	11	[	[	X
iajs-2677	69	12	12	12	NUM
iajs-2677	69	13	]	]	PUNCT
iajs-2677	69	14	.	.	PUNCT
iajs-2677	70	1	the	the	DET
iajs-2677	70	2	problem	problem	NOUN
iajs-2677	70	3	is	be	AUX
iajs-2677	70	4	also	also	ADV
iajs-2677	70	5	considered	consider	VERB
iajs-2677	70	6	with	with	ADP
iajs-2677	70	7	a	a	DET
iajs-2677	70	8	common	common	ADJ
iajs-2677	70	9	due	due	ADJ
iajs-2677	70	10	date	date	NOUN
iajs-2677	70	11	.	.	PUNCT
iajs-2677	71	1	in	in	ADP
iajs-2677	71	2	a	a	DET
iajs-2677	71	3	known	know	VERB
iajs-2677	71	4	sequence	sequence	NOUN
iajs-2677	71	5	,	,	PUNCT
iajs-2677	71	6	tavakkoli	tavakkoli	NOUN
iajs-2677	71	7	-	-	PUNCT
iajs-2677	71	8	moghaddam	moghaddam	NOUN
iajs-2677	71	9	et	et	PROPN
iajs-2677	71	10	al	al	PROPN
iajs-2677	71	11	.	.	PUNCT
iajs-2677	72	1	[	[	X
iajs-2677	72	2	10	10	NUM
iajs-2677	72	3	]	]	PUNCT
iajs-2677	72	4	found	find	VERB
iajs-2677	72	5	the	the	DET
iajs-2677	72	6	best	good	ADJ
iajs-2677	72	7	value	value	NOUN
iajs-2677	72	8	of	of	ADP
iajs-2677	72	9	an	an	DET
iajs-2677	72	10	idle	idle	ADJ
iajs-2677	72	11	insert	insert	NOUN
iajs-2677	72	12	.	.	PUNCT
iajs-2677	73	1	tavakkolimoghaddam	tavakkolimoghaddam	PROPN
iajs-2677	73	2	et	et	PROPN
iajs-2677	73	3	al	al	PROPN
iajs-2677	73	4	.	.	PROPN
iajs-2677	73	5	presented	present	VERB
iajs-2677	73	6	also	also	ADV
iajs-2677	73	7	a	a	DET
iajs-2677	73	8	branch	branch	NOUN
iajs-2677	73	9	-	-	PUNCT
iajs-2677	73	10	and	and	CCONJ
iajs-2677	73	11	-	-	PUNCT
iajs-2677	73	12	bound	bind	VERB
iajs-2677	73	13	algorithm	algorithm	NOUN
iajs-2677	73	14	to	to	PART
iajs-2677	73	15	solve	solve	VERB
iajs-2677	73	16	the	the	DET
iajs-2677	73	17	problem	problem	NOUN
iajs-2677	73	18	,	,	PUNCT
iajs-2677	73	19	with	with	ADP
iajs-2677	73	20	an	an	DET
iajs-2677	73	21	idle	idle	ADJ
iajs-2677	73	22	insert	insert	NOUN
iajs-2677	73	23	[	[	X
iajs-2677	73	24	13	13	NUM
iajs-2677	73	25	]	]	PUNCT
iajs-2677	73	26	.	.	PUNCT
iajs-2677	74	1	mahnam	mahnam	PROPN
iajs-2677	74	2	and	and	CCONJ
iajs-2677	74	3	moslehi	moslehi	NOUN
iajs-2677	74	4	presented	present	VERB
iajs-2677	74	5	an	an	DET
iajs-2677	74	6	efficient	efficient	ADJ
iajs-2677	74	7	branch	branch	NOUN
iajs-2677	74	8	-	-	PUNCT
iajs-2677	74	9	and	and	CCONJ
iajs-2677	74	10	-	-	PUNCT
iajs-2677	74	11	bound	bind	VERB
iajs-2677	74	12	algorithm	algorithm	NOUN
iajs-2677	74	13	to	to	PART
iajs-2677	74	14	minimize	minimize	VERB
iajs-2677	74	15	the	the	DET
iajs-2677	74	16	problem	problem	NOUN
iajs-2677	74	17	on	on	ADP
iajs-2677	74	18	a	a	DET
iajs-2677	74	19	single	single	ADJ
iajs-2677	74	20	machine	machine	NOUN
iajs-2677	74	21	with	with	ADP
iajs-2677	74	22	unequal	unequal	ADJ
iajs-2677	74	23	release	release	NOUN
iajs-2677	74	24	times	time	NOUN
iajs-2677	74	25	and	and	CCONJ
iajs-2677	74	26	no	no	DET
iajs-2677	74	27	unforced	unforced	ADJ
iajs-2677	74	28	idle	idle	ADJ
iajs-2677	74	29	time	time	NOUN
iajs-2677	74	30	[	[	X
iajs-2677	74	31	14	14	NUM
iajs-2677	74	32	]	]	SYM
iajs-2677	74	33	.	.	PUNCT
iajs-2677	75	1	moslehi	moslehi	NOUN
iajs-2677	75	2	,	,	PUNCT
iajs-2677	75	3	et	et	PROPN
iajs-2677	75	4	al	al	PROPN
iajs-2677	75	5	.	.	PROPN
iajs-2677	75	6	,	,	PUNCT
iajs-2677	75	7	showed	show	VERB
iajs-2677	75	8	that	that	SCONJ
iajs-2677	75	9	the	the	DET
iajs-2677	75	10	problem	problem	NOUN
iajs-2677	75	11	is	be	AUX
iajs-2677	75	12	irregular	irregular	ADJ
iajs-2677	75	13	;	;	PUNCT
iajs-2677	75	14	so	so	CCONJ
iajs-2677	75	15	many	many	ADJ
iajs-2677	75	16	properties	property	NOUN
iajs-2677	75	17	of	of	ADP
iajs-2677	75	18	regular	regular	ADJ
iajs-2677	75	19	will	will	AUX
iajs-2677	75	20	be	be	AUX
iajs-2677	75	21	missed	miss	VERB
iajs-2677	75	22	for	for	ADP
iajs-2677	75	23	the	the	DET
iajs-2677	75	24	present	present	ADJ
iajs-2677	75	25	objective	objective	ADJ
iajs-2677	75	26	function	function	NOUN
iajs-2677	75	27	.	.	PUNCT
iajs-2677	76	1	they	they	PRON
iajs-2677	76	2	presented	present	VERB
iajs-2677	76	3	a	a	DET
iajs-2677	76	4	heuristic	heuristic	ADJ
iajs-2677	76	5	method	method	NOUN
iajs-2677	76	6	using	use	VERB
iajs-2677	76	7	a	a	DET
iajs-2677	76	8	novel	novel	ADJ
iajs-2677	76	9	branch	branch	NOUN
iajs-2677	76	10	-	-	PUNCT
iajs-2677	76	11	and	and	CCONJ
iajs-2677	76	12	-	-	PUNCT
iajs-2677	76	13	bound	bind	VERB
iajs-2677	76	14	algorithm	algorithm	NOUN
iajs-2677	76	15	to	to	PART
iajs-2677	76	16	minimize	minimize	VERB
iajs-2677	76	17	the	the	DET
iajs-2677	76	18	sum	sum	NOUN
iajs-2677	76	19	of	of	ADP
iajs-2677	76	20	maximum	maximum	ADJ
iajs-2677	76	21	earliness	earliness	NOUN
iajs-2677	76	22	and	and	CCONJ
iajs-2677	76	23	tardiness	tardiness	NOUN
iajs-2677	76	24	on	on	ADP
iajs-2677	76	25	a	a	DET
iajs-2677	76	26	single	single	ADJ
iajs-2677	76	27	-	-	PUNCT
iajs-2677	76	28	machine	machine	NOUN
iajs-2677	76	29	scheduling	scheduling	NOUN
iajs-2677	76	30	problem	problem	NOUN
iajs-2677	76	31	where	where	SCONJ
iajs-2677	76	32	the	the	DET
iajs-2677	76	33	due	due	ADJ
iajs-2677	76	34	dates	date	NOUN
iajs-2677	76	35	were	be	AUX
iajs-2677	76	36	distinct	distinct	ADJ
iajs-2677	76	37	[	[	X
iajs-2677	76	38	15	15	NUM
iajs-2677	76	39	]	]	PUNCT
iajs-2677	76	40	.	.	PUNCT
iajs-2677	77	1	ibn	ibn	PROPN
iajs-2677	77	2	al	al	PROPN
iajs-2677	77	3	-	-	PUNCT
iajs-2677	77	4	haitham	haitham	PROPN
iajs-2677	77	5	jour	jour	X
iajs-2677	77	6	.	.	PROPN
iajs-2677	77	7	for	for	ADP
iajs-2677	77	8	pure	pure	ADJ
iajs-2677	77	9	&	&	CCONJ
iajs-2677	77	10	appl	appl	PROPN
iajs-2677	77	11	.	.	PUNCT
iajs-2677	78	1	sci	sci	PROPN
iajs-2677	78	2	.	.	PROPN
iajs-2677	79	1	34(3)2021	34(3)2021	NUM
iajs-2677	79	2	53	53	NUM
iajs-2677	79	3	5	5	NUM
iajs-2677	79	4	.	.	PUNCT
iajs-2677	80	1	algorithms	algorithm	NOUN
iajs-2677	80	2	for	for	ADP
iajs-2677	80	3	solving	solve	VERB
iajs-2677	80	4	multi	multi	ADJ
iajs-2677	80	5	-	-	ADJ
iajs-2677	80	6	objective	objective	ADJ
iajs-2677	80	7	problems	problem	NOUN
iajs-2677	80	8	in	in	ADP
iajs-2677	80	9	this	this	DET
iajs-2677	80	10	section	section	NOUN
iajs-2677	80	11	,	,	PUNCT
iajs-2677	80	12	we	we	PRON
iajs-2677	80	13	introduce	introduce	VERB
iajs-2677	80	14	two	two	NUM
iajs-2677	80	15	problems	problem	NOUN
iajs-2677	80	16	that	that	SCONJ
iajs-2677	80	17	concerning	concern	VERB
iajs-2677	80	18	our	our	PRON
iajs-2677	80	19	problem	problem	NOUN
iajs-2677	80	20	.	.	PUNCT
iajs-2677	81	1	they	they	PRON
iajs-2677	81	2	have	have	VERB
iajs-2677	81	3	three	three	NUM
iajs-2677	81	4	criteria	criterion	NOUN
iajs-2677	81	5	,	,	PUNCT
iajs-2677	81	6	namely	namely	ADV
iajs-2677	81	7	∑	∑	PUNCT
iajs-2677	81	8	∁j	∁j	PROPN
iajs-2677	81	9	n	n	PRON
iajs-2677	81	10	j=1	j=1	NOUN
iajs-2677	81	11	,	,	PUNCT
iajs-2677	81	12	tmax	tmax	ADV
iajs-2677	81	13	and	and	CCONJ
iajs-2677	81	14	emax	emax	NOUN
iajs-2677	81	15	.	.	PUNCT
iajs-2677	82	1	5.1	5.1	NUM
iajs-2677	82	2	1/	1/	NUM
iajs-2677	82	3	/	/	SYM
iajs-2677	82	4	f	f	PROPN
iajs-2677	82	5	(	(	PUNCT
iajs-2677	82	6	∑	∑	PROPN
iajs-2677	82	7	∁j	∁j	PROPN
iajs-2677	82	8	n	n	PRON
iajs-2677	82	9	j=1	j=1	NOUN
iajs-2677	82	10	,	,	PUNCT
iajs-2677	82	11	tmax	tmax	ADV
iajs-2677	82	12	)	)	PUNCT
iajs-2677	82	13	(	(	PUNCT
iajs-2677	82	14	total	total	ADJ
iajs-2677	82	15	completion	completion	NOUN
iajs-2677	82	16	time	time	NOUN
iajs-2677	82	17	and	and	CCONJ
iajs-2677	82	18	maximum	maximum	ADJ
iajs-2677	82	19	tardiness	tardiness	NOUN
iajs-2677	82	20	)	)	PUNCT
iajs-2677	82	21	this	this	DET
iajs-2677	82	22	problem	problem	NOUN
iajs-2677	82	23	can	can	AUX
iajs-2677	82	24	be	be	AUX
iajs-2677	82	25	written	write	VERB
iajs-2677	82	26	as	as	ADP
iajs-2677	82	27	:	:	PUNCT
iajs-2677	82	28	min	min	NOUN
iajs-2677	82	29	∑	∑	PUNCT
iajs-2677	82	30	∁j	∁j	PROPN
iajs-2677	82	31	n	n	CCONJ
iajs-2677	82	32	j=1	j=1	NOUN
iajs-2677	82	33	and	and	CCONJ
iajs-2677	82	34	...	...	PUNCT
iajs-2677	82	35	(	(	PUNCT
iajs-2677	82	36	p2	p2	PROPN
iajs-2677	82	37	)	)	PUNCT
iajs-2677	82	38	min	min	NOUN
iajs-2677	82	39	tmax	tmax	ADV
iajs-2677	82	40	v.	v.	CCONJ
iajs-2677	82	41	wassenhove	wassenhove	NOUN
iajs-2677	82	42	and	and	CCONJ
iajs-2677	82	43	gelders	gelder	NOUN
iajs-2677	83	1	[	[	X
iajs-2677	83	2	8	8	NUM
iajs-2677	83	3	]	]	PUNCT
iajs-2677	83	4	found	find	VERB
iajs-2677	83	5	all	all	DET
iajs-2677	83	6	efficient	efficient	ADJ
iajs-2677	83	7	solutions	solution	NOUN
iajs-2677	83	8	for	for	ADP
iajs-2677	83	9	(	(	PUNCT
iajs-2677	83	10	p2	p2	NOUN
iajs-2677	83	11	)	)	PUNCT
iajs-2677	83	12	.	.	PUNCT
iajs-2677	84	1	5.2	5.2	NUM
iajs-2677	84	2	1/	1/	NUM
iajs-2677	84	3	/	/	SYM
iajs-2677	84	4	f	f	PROPN
iajs-2677	84	5	(	(	PUNCT
iajs-2677	84	6	∑	∑	PROPN
iajs-2677	84	7	∁j	∁j	PROPN
iajs-2677	84	8	n	n	PRON
iajs-2677	84	9	j=1	j=1	NOUN
iajs-2677	84	10	,	,	PUNCT
iajs-2677	84	11	emax	emax	X
iajs-2677	84	12	)	)	PUNCT
iajs-2677	84	13	(	(	PUNCT
iajs-2677	84	14	total	total	ADJ
iajs-2677	84	15	completion	completion	NOUN
iajs-2677	84	16	time	time	NOUN
iajs-2677	84	17	and	and	CCONJ
iajs-2677	84	18	maximum	maximum	ADJ
iajs-2677	84	19	earliness	earliness	NOUN
iajs-2677	84	20	)	)	PUNCT
iajs-2677	84	21	this	this	DET
iajs-2677	84	22	problem	problem	NOUN
iajs-2677	84	23	can	can	AUX
iajs-2677	84	24	be	be	AUX
iajs-2677	84	25	written	write	VERB
iajs-2677	84	26	as	as	ADP
iajs-2677	84	27	:	:	PUNCT
iajs-2677	84	28	min	min	NOUN
iajs-2677	84	29	∑	∑	PUNCT
iajs-2677	84	30	∁j	∁j	PROPN
iajs-2677	84	31	n	n	CCONJ
iajs-2677	84	32	j=1	j=1	NOUN
iajs-2677	84	33	and	and	CCONJ
iajs-2677	84	34	...	...	PUNCT
iajs-2677	84	35	(	(	PUNCT
iajs-2677	84	36	p3	p3	NOUN
iajs-2677	84	37	)	)	PUNCT
iajs-2677	84	38	min	min	PROPN
iajs-2677	84	39	emax	emax	X
iajs-2677	84	40	.	.	PUNCT
iajs-2677	85	1	hoogeveen	hoogeveen	PROPN
iajs-2677	85	2	and	and	CCONJ
iajs-2677	85	3	van	van	PROPN
iajs-2677	85	4	de	de	PROPN
iajs-2677	85	5	velde	velde	PROPN
iajs-2677	85	6	[	[	X
iajs-2677	85	7	16	16	NUM
iajs-2677	85	8	]	]	PUNCT
iajs-2677	85	9	presented	present	VERB
iajs-2677	85	10	an	an	DET
iajs-2677	85	11	algorithm	algorithm	NOUN
iajs-2677	85	12	in	in	ADP
iajs-2677	85	13	which	which	PRON
iajs-2677	85	14	they	they	PRON
iajs-2677	85	15	found	find	VERB
iajs-2677	85	16	all	all	DET
iajs-2677	85	17	the	the	DET
iajs-2677	85	18	efficient	efficient	ADJ
iajs-2677	85	19	solutions	solution	NOUN
iajs-2677	85	20	(	(	PUNCT
iajs-2677	85	21	pareto	pareto	ADJ
iajs-2677	85	22	set	set	NOUN
iajs-2677	85	23	)	)	PUNCT
iajs-2677	85	24	for	for	ADP
iajs-2677	85	25	(	(	PUNCT
iajs-2677	85	26	p3	p3	PROPN
iajs-2677	85	27	)	)	PUNCT
iajs-2677	85	28	.	.	PUNCT
iajs-2677	86	1	6	6	X
iajs-2677	86	2	.	.	X
iajs-2677	86	3	a	a	DET
iajs-2677	86	4	novel	novel	ADJ
iajs-2677	86	5	heuristic	heuristic	ADJ
iajs-2677	86	6	approach	approach	NOUN
iajs-2677	86	7	two	two	NUM
iajs-2677	86	8	methods	method	NOUN
iajs-2677	86	9	have	have	AUX
iajs-2677	86	10	been	be	AUX
iajs-2677	86	11	used	use	VERB
iajs-2677	86	12	to	to	PART
iajs-2677	86	13	solve	solve	VERB
iajs-2677	86	14	multi	multi	ADJ
iajs-2677	86	15	-	-	ADJ
iajs-2677	86	16	objective	objective	ADJ
iajs-2677	86	17	scheduling	scheduling	NOUN
iajs-2677	86	18	problem	problem	NOUN
iajs-2677	86	19	exact	exact	ADJ
iajs-2677	86	20	and	and	CCONJ
iajs-2677	86	21	approximation	approximation	NOUN
iajs-2677	86	22	method	method	NOUN
iajs-2677	86	23	.	.	PUNCT
iajs-2677	87	1	the	the	DET
iajs-2677	87	2	exact	exact	ADJ
iajs-2677	87	3	solutions	solution	NOUN
iajs-2677	87	4	are	be	AUX
iajs-2677	87	5	obtained	obtain	VERB
iajs-2677	87	6	by	by	ADP
iajs-2677	87	7	enumeration	enumeration	NOUN
iajs-2677	87	8	method	method	NOUN
iajs-2677	87	9	,	,	PUNCT
iajs-2677	87	10	branch	branch	NOUN
iajs-2677	87	11	and	and	CCONJ
iajs-2677	87	12	bound	bind	VERB
iajs-2677	87	13	method	method	NOUN
iajs-2677	87	14	,	,	PUNCT
iajs-2677	87	15	and	and	CCONJ
iajs-2677	87	16	dynamic	dynamic	ADJ
iajs-2677	87	17	programming	programming	NOUN
iajs-2677	87	18	method	method	NOUN
iajs-2677	87	19	.	.	PUNCT
iajs-2677	88	1	the	the	DET
iajs-2677	88	2	approximate	approximate	ADJ
iajs-2677	88	3	solutions	solution	NOUN
iajs-2677	88	4	are	be	AUX
iajs-2677	88	5	obtained	obtain	VERB
iajs-2677	88	6	by	by	ADP
iajs-2677	88	7	local	local	ADJ
iajs-2677	88	8	search	search	NOUN
iajs-2677	88	9	methods	method	NOUN
iajs-2677	88	10	which	which	PRON
iajs-2677	88	11	form	form	VERB
iajs-2677	88	12	a	a	DET
iajs-2677	88	13	very	very	ADV
iajs-2677	88	14	general	general	ADJ
iajs-2677	88	15	class	class	NOUN
iajs-2677	88	16	of	of	ADP
iajs-2677	88	17	heuristic	heuristic	ADJ
iajs-2677	88	18	methods	method	NOUN
iajs-2677	88	19	[	[	X
iajs-2677	88	20	9	9	NUM
iajs-2677	88	21	]	]	PUNCT
iajs-2677	88	22	.	.	PUNCT
iajs-2677	89	1	here	here	ADV
iajs-2677	89	2	we	we	PRON
iajs-2677	89	3	will	will	AUX
iajs-2677	89	4	give	give	VERB
iajs-2677	89	5	a	a	DET
iajs-2677	89	6	novel	novel	ADJ
iajs-2677	89	7	heuristic	heuristic	ADJ
iajs-2677	89	8	method	method	NOUN
iajs-2677	89	9	to	to	PART
iajs-2677	89	10	find	find	VERB
iajs-2677	89	11	a	a	DET
iajs-2677	89	12	best	good	ADJ
iajs-2677	89	13	solution	solution	NOUN
iajs-2677	89	14	for	for	ADP
iajs-2677	89	15	the	the	DET
iajs-2677	89	16	(	(	PUNCT
iajs-2677	89	17	p1	p1	NOUN
iajs-2677	89	18	)	)	PUNCT
iajs-2677	89	19	problem	problem	NOUN
iajs-2677	89	20	.	.	PUNCT
iajs-2677	90	1	let	let	VERB
iajs-2677	90	2	s	s	PRON
iajs-2677	90	3	be	be	AUX
iajs-2677	90	4	a	a	DET
iajs-2677	90	5	set	set	NOUN
iajs-2677	90	6	of	of	ADP
iajs-2677	90	7	all	all	DET
iajs-2677	90	8	efficient	efficient	ADJ
iajs-2677	90	9	solutions	solution	NOUN
iajs-2677	90	10	for	for	ADP
iajs-2677	90	11	the	the	DET
iajs-2677	90	12	problem	problem	NOUN
iajs-2677	90	13	(	(	PUNCT
iajs-2677	90	14	p2	p2	NOUN
iajs-2677	90	15	)	)	PUNCT
iajs-2677	90	16	,	,	PUNCT
iajs-2677	90	17	and	and	CCONJ
iajs-2677	90	18	let	let	VERB
iajs-2677	90	19	s1	s1	NOUN
iajs-2677	90	20	be	be	AUX
iajs-2677	90	21	a	a	DET
iajs-2677	90	22	set	set	NOUN
iajs-2677	90	23	of	of	ADP
iajs-2677	90	24	all	all	DET
iajs-2677	90	25	efficient	efficient	ADJ
iajs-2677	90	26	solutions	solution	NOUN
iajs-2677	90	27	for	for	ADP
iajs-2677	90	28	the	the	DET
iajs-2677	90	29	problem	problem	NOUN
iajs-2677	90	30	(	(	PUNCT
iajs-2677	90	31	p3	p3	PROPN
iajs-2677	90	32	)	)	PUNCT
iajs-2677	90	33	.	.	PUNCT
iajs-2677	91	1	proposition	proposition	NOUN
iajs-2677	91	2	(	(	PUNCT
iajs-2677	91	3	1	1	NUM
iajs-2677	91	4	):	):	PUNCT
iajs-2677	91	5	s	s	VERB
iajs-2677	91	6	∩	∩	ADJ
iajs-2677	91	7	s1	s1	NOUN
iajs-2677	91	8	≠	≠	PROPN
iajs-2677	91	9	φ	φ	NOUN
iajs-2677	91	10	.	.	PUNCT
iajs-2677	92	1	proof	proof	NOUN
iajs-2677	92	2	:	:	PUNCT
iajs-2677	92	3	since	since	SCONJ
iajs-2677	92	4	spt	spt	NOUN
iajs-2677	92	5	-	-	PUNCT
iajs-2677	92	6	rule	rule	NOUN
iajs-2677	92	7	is	be	AUX
iajs-2677	92	8	one	one	NUM
iajs-2677	92	9	of	of	ADP
iajs-2677	92	10	the	the	DET
iajs-2677	92	11	efficient	efficient	ADJ
iajs-2677	92	12	solutions	solution	NOUN
iajs-2677	92	13	for	for	ADP
iajs-2677	92	14	(	(	PUNCT
iajs-2677	92	15	p2	p2	NOUN
iajs-2677	92	16	)	)	PUNCT
iajs-2677	92	17	,	,	PUNCT
iajs-2677	92	18	and	and	CCONJ
iajs-2677	92	19	also	also	ADV
iajs-2677	92	20	,	,	PUNCT
iajs-2677	92	21	spt	spt	ADJ
iajs-2677	92	22	-	-	PUNCT
iajs-2677	92	23	rule	rule	NOUN
iajs-2677	92	24	is	be	AUX
iajs-2677	92	25	one	one	NUM
iajs-2677	92	26	of	of	ADP
iajs-2677	92	27	the	the	DET
iajs-2677	92	28	efficient	efficient	ADJ
iajs-2677	92	29	solutions	solution	NOUN
iajs-2677	92	30	for	for	ADP
iajs-2677	92	31	(	(	PUNCT
iajs-2677	92	32	p4	p4	ADJ
iajs-2677	92	33	)	)	PUNCT
iajs-2677	92	34	,	,	PUNCT
iajs-2677	92	35	so	so	ADV
iajs-2677	92	36	spt	spt	ADJ
iajs-2677	92	37	-	-	PUNCT
iajs-2677	92	38	rule	rule	NOUN
iajs-2677	92	39	is	be	AUX
iajs-2677	92	40	one	one	NUM
iajs-2677	92	41	of	of	ADP
iajs-2677	92	42	the	the	DET
iajs-2677	92	43	common	common	ADJ
iajs-2677	92	44	sequences	sequence	NOUN
iajs-2677	92	45	of	of	ADP
iajs-2677	92	46	(	(	PUNCT
iajs-2677	92	47	s	s	X
iajs-2677	92	48	∩	∩	ADJ
iajs-2677	92	49	s1	s1	NOUN
iajs-2677	92	50	)	)	PUNCT
iajs-2677	92	51	.	.	PUNCT
iajs-2677	93	1	∎	∎	PROPN
iajs-2677	93	2	for	for	ADP
iajs-2677	93	3	each	each	DET
iajs-2677	93	4	π	π	PROPN
iajs-2677	93	5	∈	∈	PROPN
iajs-2677	93	6	(	(	PUNCT
iajs-2677	93	7	s	s	NOUN
iajs-2677	93	8	∪	∪	ADJ
iajs-2677	93	9	s1	s1	NOUN
iajs-2677	93	10	)	)	PUNCT
iajs-2677	93	11	,	,	PUNCT
iajs-2677	93	12	find	find	VERB
iajs-2677	93	13	(	(	PUNCT
iajs-2677	93	14	emax	emax	X
iajs-2677	93	15	(	(	PUNCT
iajs-2677	93	16	π)+tmax(π	π)+tmax(π	NOUN
iajs-2677	93	17	)	)	PUNCT
iajs-2677	93	18	)	)	PUNCT
iajs-2677	93	19	.	.	PUNCT
iajs-2677	94	1	this	this	PRON
iajs-2677	94	2	construct	construct	VERB
iajs-2677	94	3	a	a	DET
iajs-2677	94	4	set	set	NOUN
iajs-2677	94	5	of	of	ADP
iajs-2677	94	6	solutions	solution	NOUN
iajs-2677	94	7	,	,	PUNCT
iajs-2677	94	8	and	and	CCONJ
iajs-2677	94	9	one	one	NUM
iajs-2677	94	10	of	of	ADP
iajs-2677	94	11	them	they	PRON
iajs-2677	94	12	may	may	AUX
iajs-2677	94	13	be	be	AUX
iajs-2677	94	14	an	an	DET
iajs-2677	94	15	optimal	optimal	ADJ
iajs-2677	94	16	solution	solution	NOUN
iajs-2677	94	17	for	for	ADP
iajs-2677	94	18	problem	problem	NOUN
iajs-2677	94	19	(	(	PUNCT
iajs-2677	94	20	p1	p1	NOUN
iajs-2677	94	21	)	)	PUNCT
iajs-2677	94	22	.	.	PUNCT
iajs-2677	95	1	in	in	ADP
iajs-2677	95	2	general	general	ADJ
iajs-2677	95	3	,	,	PUNCT
iajs-2677	95	4	one	one	PRON
iajs-2677	95	5	can	can	AUX
iajs-2677	95	6	not	not	PART
iajs-2677	95	7	guarantee	guarantee	VERB
iajs-2677	95	8	to	to	PART
iajs-2677	95	9	find	find	VERB
iajs-2677	95	10	finding	find	VERB
iajs-2677	95	11	an	an	DET
iajs-2677	95	12	optimal	optimal	ADJ
iajs-2677	95	13	solution	solution	NOUN
iajs-2677	95	14	form	form	VERB
iajs-2677	95	15	the	the	DET
iajs-2677	95	16	set	set	NOUN
iajs-2677	95	17	.	.	PUNCT
iajs-2677	96	1	6.1	6.1	NUM
iajs-2677	96	2	special	special	ADJ
iajs-2677	96	3	cases	case	NOUN
iajs-2677	96	4	of	of	ADP
iajs-2677	96	5	the	the	DET
iajs-2677	96	6	problem	problem	NOUN
iajs-2677	96	7	(	(	PUNCT
iajs-2677	96	8	𝐩𝟏	𝐩𝟏	NOUN
iajs-2677	96	9	)	)	PUNCT
iajs-2677	96	10	case	case	NOUN
iajs-2677	96	11	(	(	PUNCT
iajs-2677	96	12	1	1	NUM
iajs-2677	96	13	):	):	PUNCT
iajs-2677	96	14	if	if	SCONJ
iajs-2677	96	15	a	a	DET
iajs-2677	96	16	schedule	schedule	NOUN
iajs-2677	96	17	π	π	PROPN
iajs-2677	96	18	gives	give	VERB
iajs-2677	96	19	spt	spt	NOUN
iajs-2677	96	20	-	-	PUNCT
iajs-2677	96	21	rule	rule	NOUN
iajs-2677	96	22	and	and	CCONJ
iajs-2677	96	23	edd	edd	PROPN
iajs-2677	96	24	-	-	PUNCT
iajs-2677	96	25	rule	rule	NOUN
iajs-2677	96	26	at	at	ADP
iajs-2677	96	27	the	the	DET
iajs-2677	96	28	same	same	ADJ
iajs-2677	96	29	,	,	PUNCT
iajs-2677	96	30	then	then	ADV
iajs-2677	96	31	π	π	PROPN
iajs-2677	96	32	is	be	AUX
iajs-2677	96	33	optimal	optimal	ADJ
iajs-2677	96	34	schedule	schedule	NOUN
iajs-2677	96	35	for	for	ADP
iajs-2677	96	36	(	(	PUNCT
iajs-2677	96	37	p2	p2	NOUN
iajs-2677	96	38	)	)	PUNCT
iajs-2677	96	39	,	,	PUNCT
iajs-2677	96	40	and	and	CCONJ
iajs-2677	96	41	produces	produce	VERB
iajs-2677	96	42	one	one	NUM
iajs-2677	96	43	efficient	efficient	ADJ
iajs-2677	96	44	solution	solution	NOUN
iajs-2677	96	45	.	.	PUNCT
iajs-2677	97	1	proof	proof	NOUN
iajs-2677	97	2	:	:	PUNCT
iajs-2677	97	3	directly	directly	ADV
iajs-2677	97	4	from	from	ADP
iajs-2677	97	5	the	the	DET
iajs-2677	97	6	definition	definition	NOUN
iajs-2677	97	7	of	of	ADP
iajs-2677	97	8	spt	spt	NOUN
iajs-2677	97	9	-	-	PUNCT
iajs-2677	97	10	rule	rule	NOUN
iajs-2677	97	11	and	and	CCONJ
iajs-2677	97	12	edd	edd	PROPN
iajs-2677	97	13	-	-	PUNCT
iajs-2677	97	14	rule	rule	NOUN
iajs-2677	97	15	.	.	PUNCT
iajs-2677	98	1	■	■	PUNCT
iajs-2677	98	2	ibn	ibn	PROPN
iajs-2677	98	3	al	al	PROPN
iajs-2677	98	4	-	-	PUNCT
iajs-2677	98	5	haitham	haitham	PROPN
iajs-2677	98	6	jour	jour	X
iajs-2677	98	7	.	.	PROPN
iajs-2677	98	8	for	for	ADP
iajs-2677	98	9	pure	pure	ADJ
iajs-2677	98	10	&	&	CCONJ
iajs-2677	98	11	appl	appl	PROPN
iajs-2677	98	12	.	.	PUNCT
iajs-2677	99	1	sci	sci	PROPN
iajs-2677	99	2	.	.	PROPN
iajs-2677	100	1	34(3)2021	34(3)2021	NUM
iajs-2677	100	2	54	54	NUM
iajs-2677	100	3	case	case	NOUN
iajs-2677	100	4	(	(	PUNCT
iajs-2677	100	5	2	2	NUM
iajs-2677	100	6	):	):	PUNCT
iajs-2677	100	7	if	if	SCONJ
iajs-2677	100	8	a	a	DET
iajs-2677	100	9	schedule	schedule	NOUN
iajs-2677	100	10	π	π	PROPN
iajs-2677	100	11	gives	give	VERB
iajs-2677	100	12	spt	spt	NOUN
iajs-2677	100	13	-	-	PUNCT
iajs-2677	100	14	rule	rule	NOUN
iajs-2677	100	15	and	and	CCONJ
iajs-2677	100	16	mst	mst	NOUN
iajs-2677	100	17	-	-	PUNCT
iajs-2677	100	18	rule	rule	NOUN
iajs-2677	100	19	at	at	ADP
iajs-2677	100	20	the	the	DET
iajs-2677	100	21	same	same	ADJ
iajs-2677	100	22	,	,	PUNCT
iajs-2677	100	23	then	then	ADV
iajs-2677	100	24	π	π	PROPN
iajs-2677	100	25	is	be	AUX
iajs-2677	100	26	optimal	optimal	ADJ
iajs-2677	100	27	schedule	schedule	NOUN
iajs-2677	100	28	for	for	ADP
iajs-2677	100	29	(	(	PUNCT
iajs-2677	100	30	p3	p3	PROPN
iajs-2677	100	31	)	)	PUNCT
iajs-2677	100	32	,	,	PUNCT
iajs-2677	100	33	and	and	CCONJ
iajs-2677	100	34	produces	produce	VERB
iajs-2677	100	35	one	one	NUM
iajs-2677	100	36	efficient	efficient	ADJ
iajs-2677	100	37	solution	solution	NOUN
iajs-2677	100	38	.	.	PUNCT
iajs-2677	101	1	proof	proof	NOUN
iajs-2677	101	2	:	:	PUNCT
iajs-2677	101	3	directly	directly	ADV
iajs-2677	101	4	from	from	ADP
iajs-2677	101	5	the	the	DET
iajs-2677	101	6	definition	definition	NOUN
iajs-2677	101	7	of	of	ADP
iajs-2677	101	8	spt	spt	NOUN
iajs-2677	101	9	-	-	PUNCT
iajs-2677	101	10	rule	rule	NOUN
iajs-2677	101	11	and	and	CCONJ
iajs-2677	101	12	mst	mst	NOUN
iajs-2677	101	13	-	-	PUNCT
iajs-2677	101	14	rule	rule	NOUN
iajs-2677	101	15	.	.	PUNCT
iajs-2677	102	1	■	■	PUNCT
iajs-2677	102	2	case	case	NOUN
iajs-2677	102	3	(	(	PUNCT
iajs-2677	102	4	3	3	NUM
iajs-2677	102	5	):	):	PUNCT
iajs-2677	102	6	if	if	SCONJ
iajs-2677	102	7	a	a	DET
iajs-2677	102	8	schedule	schedule	NOUN
iajs-2677	102	9	π	π	PROPN
iajs-2677	102	10	gives	give	VERB
iajs-2677	102	11	edd	edd	PROPN
iajs-2677	102	12	-	-	PUNCT
iajs-2677	102	13	rule	rule	NOUN
iajs-2677	102	14	and	and	CCONJ
iajs-2677	102	15	mst	mst	NOUN
iajs-2677	102	16	-	-	PUNCT
iajs-2677	102	17	rule	rule	NOUN
iajs-2677	102	18	at	at	ADP
iajs-2677	102	19	the	the	DET
iajs-2677	102	20	same	same	ADJ
iajs-2677	102	21	time	time	NOUN
iajs-2677	102	22	,	,	PUNCT
iajs-2677	102	23	then	then	ADV
iajs-2677	102	24	π	π	PROPN
iajs-2677	102	25	is	be	AUX
iajs-2677	102	26	optimal	optimal	ADJ
iajs-2677	102	27	schedule	schedule	NOUN
iajs-2677	102	28	for	for	ADP
iajs-2677	102	29	(	(	PUNCT
iajs-2677	102	30	p1	p1	NOUN
iajs-2677	102	31	)	)	PUNCT
iajs-2677	102	32	,	,	PUNCT
iajs-2677	102	33	and	and	CCONJ
iajs-2677	102	34	produces	produce	VERB
iajs-2677	102	35	the	the	DET
iajs-2677	102	36	only	only	ADJ
iajs-2677	102	37	efficient	efficient	ADJ
iajs-2677	102	38	solution	solution	NOUN
iajs-2677	102	39	for	for	ADP
iajs-2677	102	40	(	(	PUNCT
iajs-2677	102	41	p1	p1	NOUN
iajs-2677	102	42	)	)	PUNCT
iajs-2677	102	43	.	.	PUNCT
iajs-2677	103	1	proof	proof	NOUN
iajs-2677	103	2	:	:	PUNCT
iajs-2677	103	3	directly	directly	ADV
iajs-2677	103	4	from	from	ADP
iajs-2677	103	5	the	the	DET
iajs-2677	103	6	definition	definition	NOUN
iajs-2677	103	7	of	of	ADP
iajs-2677	103	8	edd	edd	PROPN
iajs-2677	103	9	-	-	PUNCT
iajs-2677	103	10	rule	rule	NOUN
iajs-2677	103	11	and	and	CCONJ
iajs-2677	103	12	mst	mst	NOUN
iajs-2677	103	13	-	-	PUNCT
iajs-2677	103	14	rule	rule	NOUN
iajs-2677	103	15	.	.	PUNCT
iajs-2677	104	1	■	■	PUNCT
iajs-2677	104	2	preposition	preposition	NOUN
iajs-2677	104	3	(	(	PUNCT
iajs-2677	104	4	2	2	NUM
iajs-2677	104	5	):	):	PUNCT
iajs-2677	104	6	there	there	PRON
iajs-2677	104	7	exists	exist	VERB
iajs-2677	104	8	an	an	DET
iajs-2677	104	9	optimal	optimal	ADJ
iajs-2677	104	10	solution	solution	NOUN
iajs-2677	104	11	π	π	NOUN
iajs-2677	104	12	such	such	ADJ
iajs-2677	104	13	that	that	SCONJ
iajs-2677	104	14	π	π	PROPN
iajs-2677	104	15	(	(	PUNCT
iajs-2677	104	16	s	s	NOUN
iajs-2677	104	17	∪	∪	ADJ
iajs-2677	104	18	s1	s1	NOUN
iajs-2677	104	19	)	)	PUNCT
iajs-2677	104	20	.	.	PUNCT
iajs-2677	105	1	proof	proof	NOUN
iajs-2677	105	2	:	:	PUNCT
iajs-2677	105	3	since	since	SCONJ
iajs-2677	105	4	in	in	ADP
iajs-2677	105	5	general	general	ADJ
iajs-2677	105	6	edd	edd	PROPN
iajs-2677	105	7	-	-	PUNCT
iajs-2677	105	8	rule	rule	NOUN
iajs-2677	105	9	and	and	CCONJ
iajs-2677	105	10	mstrule	mstrule	NOUN
iajs-2677	105	11	are	be	AUX
iajs-2677	105	12	not	not	PART
iajs-2677	105	13	efficient	efficient	ADJ
iajs-2677	105	14	solutions	solution	NOUN
iajs-2677	105	15	for	for	ADP
iajs-2677	105	16	the	the	DET
iajs-2677	105	17	problems	problem	NOUN
iajs-2677	105	18	(	(	PUNCT
iajs-2677	105	19	p2	p2	PROPN
iajs-2677	105	20	)	)	PUNCT
iajs-2677	105	21	and	and	CCONJ
iajs-2677	105	22	(	(	PUNCT
iajs-2677	105	23	p3	p3	PROPN
iajs-2677	105	24	)	)	PUNCT
iajs-2677	105	25	respectively	respectively	ADV
iajs-2677	105	26	.	.	PUNCT
iajs-2677	106	1	let	let	VERB
iajs-2677	106	2	π	π	PRON
iajs-2677	106	3	be	be	AUX
iajs-2677	106	4	the	the	DET
iajs-2677	106	5	edd	edd	NOUN
iajs-2677	106	6	-	-	PUNCT
iajs-2677	106	7	rule	rule	NOUN
iajs-2677	106	8	,	,	PUNCT
iajs-2677	106	9	and	and	CCONJ
iajs-2677	106	10	let	let	VERB
iajs-2677	106	11	π∗	π∗	PROPN
iajs-2677	106	12	be	be	AUX
iajs-2677	106	13	another	another	DET
iajs-2677	106	14	schedule	schedule	NOUN
iajs-2677	106	15	with	with	ADP
iajs-2677	106	16	tmax	tmax	PROPN
iajs-2677	106	17	(	(	PUNCT
iajs-2677	106	18	π∗	π∗	PROPN
iajs-2677	106	19	)	)	PUNCT
iajs-2677	106	20	=	=	SYM
iajs-2677	107	1	tmax	tmax	X
iajs-2677	107	2	(	(	PUNCT
iajs-2677	107	3	edd	edd	PROPN
iajs-2677	107	4	)	)	PUNCT
iajs-2677	107	5	.	.	PUNCT
iajs-2677	108	1	if	if	SCONJ
iajs-2677	108	2	π∗	π∗	PROPN
iajs-2677	108	3	is	be	AUX
iajs-2677	108	4	an	an	DET
iajs-2677	108	5	efficient	efficient	ADJ
iajs-2677	108	6	solution	solution	NOUN
iajs-2677	108	7	for	for	ADP
iajs-2677	108	8	(	(	PUNCT
iajs-2677	108	9	p2	p2	NOUN
iajs-2677	108	10	)	)	PUNCT
iajs-2677	108	11	,	,	PUNCT
iajs-2677	108	12	this	this	PRON
iajs-2677	108	13	means	mean	VERB
iajs-2677	108	14	π∗	π∗	PROPN
iajs-2677	108	15	∈	∈	PROPN
iajs-2677	108	16	s	s	PROPN
iajs-2677	108	17	,	,	PUNCT
iajs-2677	108	18	and	and	CCONJ
iajs-2677	108	19	dominates	dominate	VERB
iajs-2677	108	20	π	π	PROPN
iajs-2677	108	21	,	,	PUNCT
iajs-2677	108	22	because	because	SCONJ
iajs-2677	108	23	∑	∑	PROPN
iajs-2677	108	24	cj	cj	PROPN
iajs-2677	108	25	n	n	PRON
iajs-2677	108	26	j=1	j=1	PROPN
iajs-2677	108	27	(	(	PUNCT
iajs-2677	108	28	π∗	π∗	PROPN
iajs-2677	108	29	)	)	PUNCT
iajs-2677	108	30	<	<	X
iajs-2677	108	31	∑	∑	PUNCT
iajs-2677	108	32	cj	cj	PROPN
iajs-2677	108	33	n	n	PRON
iajs-2677	108	34	j=1	j=1	NOUN
iajs-2677	108	35	(	(	PUNCT
iajs-2677	108	36	π	π	NOUN
iajs-2677	108	37	)	)	PUNCT
iajs-2677	108	38	.	.	PUNCT
iajs-2677	109	1	at	at	ADP
iajs-2677	109	2	the	the	DET
iajs-2677	109	3	same	same	ADJ
iajs-2677	109	4	time	time	NOUN
iajs-2677	109	5	,	,	PUNCT
iajs-2677	109	6	it	it	PRON
iajs-2677	109	7	is	be	AUX
iajs-2677	109	8	possible	possible	ADJ
iajs-2677	109	9	that	that	SCONJ
iajs-2677	109	10	emax(π∗	emax(π∗	NOUN
iajs-2677	109	11	)	)	PUNCT
iajs-2677	109	12	>	>	X
iajs-2677	110	1	emax(π	emax(π	PROPN
iajs-2677	110	2	)	)	PUNCT
iajs-2677	110	3	,	,	PUNCT
iajs-2677	110	4	so	so	ADV
iajs-2677	110	5	π	π	PROPN
iajs-2677	110	6	is	be	AUX
iajs-2677	110	7	an	an	DET
iajs-2677	110	8	efficient	efficient	ADJ
iajs-2677	110	9	solution	solution	NOUN
iajs-2677	110	10	for	for	ADP
iajs-2677	110	11	(	(	PUNCT
iajs-2677	110	12	p1	p1	PROPN
iajs-2677	110	13	)	)	PUNCT
iajs-2677	110	14	(	(	PUNCT
iajs-2677	110	15	optimal	optimal	ADJ
iajs-2677	110	16	)	)	PUNCT
iajs-2677	110	17	and	and	CCONJ
iajs-2677	110	18	dominates	dominate	VERB
iajs-2677	110	19	π∗.	π∗.	ADJ
iajs-2677	110	20	■	■	PUNCT
iajs-2677	110	21	6.2	6.2	NUM
iajs-2677	110	22	lower	lower	ADV
iajs-2677	110	23	bound	bind	VERB
iajs-2677	110	24	(	(	PUNCT
iajs-2677	110	25	lb	lb	NOUN
iajs-2677	110	26	)	)	PUNCT
iajs-2677	110	27	deriving	derive	VERB
iajs-2677	110	28	lower	low	ADJ
iajs-2677	110	29	bounds	bound	NOUN
iajs-2677	110	30	for	for	ADP
iajs-2677	110	31	a	a	DET
iajs-2677	110	32	multiple	multiple	ADJ
iajs-2677	110	33	objective	objective	ADJ
iajs-2677	110	34	function	function	NOUN
iajs-2677	110	35	is	be	AUX
iajs-2677	110	36	difficult	difficult	ADJ
iajs-2677	110	37	,	,	PUNCT
iajs-2677	110	38	because	because	SCONJ
iajs-2677	110	39	we	we	PRON
iajs-2677	110	40	have	have	VERB
iajs-2677	110	41	to	to	PART
iajs-2677	110	42	minimize	minimize	VERB
iajs-2677	110	43	the	the	DET
iajs-2677	110	44	objectives	objective	NOUN
iajs-2677	110	45	at	at	ADP
iajs-2677	110	46	the	the	DET
iajs-2677	110	47	same	same	ADJ
iajs-2677	110	48	time	time	NOUN
iajs-2677	110	49	,	,	PUNCT
iajs-2677	110	50	so	so	ADV
iajs-2677	110	51	we	we	PRON
iajs-2677	110	52	introduce	introduce	VERB
iajs-2677	110	53	here	here	ADV
iajs-2677	110	54	a	a	DET
iajs-2677	110	55	lower	lower	ADV
iajs-2677	110	56	bound	bind	VERB
iajs-2677	110	57	for	for	ADP
iajs-2677	110	58	our	our	PRON
iajs-2677	110	59	problem	problem	NOUN
iajs-2677	110	60	as	as	SCONJ
iajs-2677	110	61	follows	follow	VERB
iajs-2677	110	62	6.2.1	6.2.1	NUM
iajs-2677	110	63	derive	derive	VERB
iajs-2677	110	64	a	a	DET
iajs-2677	110	65	lower	lower	ADV
iajs-2677	110	66	bound	bind	VERB
iajs-2677	110	67	(	(	PUNCT
iajs-2677	110	68	lb	lb	X
iajs-2677	110	69	)	)	PUNCT
iajs-2677	110	70	consider	consider	VERB
iajs-2677	110	71	again	again	ADV
iajs-2677	110	72	the	the	DET
iajs-2677	110	73	problem	problem	NOUN
iajs-2677	110	74	(	(	PUNCT
iajs-2677	110	75	p1	p1	NOUN
iajs-2677	110	76	)	)	PUNCT
iajs-2677	110	77	.	.	PUNCT
iajs-2677	111	1	if	if	SCONJ
iajs-2677	111	2	we	we	PRON
iajs-2677	111	3	have	have	VERB
iajs-2677	111	4	only	only	ADV
iajs-2677	111	5	one	one	NUM
iajs-2677	111	6	objective	objective	ADJ
iajs-2677	111	7	function	function	NOUN
iajs-2677	111	8	,	,	PUNCT
iajs-2677	111	9	𝐸𝑚𝑎𝑥	𝐸𝑚𝑎𝑥	PROPN
iajs-2677	111	10	problem	problem	NOUN
iajs-2677	111	11	,	,	PUNCT
iajs-2677	111	12	or	or	CCONJ
iajs-2677	111	13	𝑇𝑚𝑎𝑥	𝑇𝑚𝑎𝑥	PROPN
iajs-2677	111	14	problem	problem	NOUN
iajs-2677	111	15	,	,	PUNCT
iajs-2677	111	16	then	then	ADV
iajs-2677	111	17	we	we	PRON
iajs-2677	111	18	can	can	AUX
iajs-2677	111	19	solve	solve	VERB
iajs-2677	111	20	the	the	DET
iajs-2677	111	21	problems	problem	NOUN
iajs-2677	111	22	by	by	ADP
iajs-2677	111	23	mst	mst	PROPN
iajs-2677	111	24	-	-	PUNCT
iajs-2677	111	25	rule	rule	NOUN
iajs-2677	111	26	and	and	CCONJ
iajs-2677	111	27	eddrule	eddrule	NOUN
iajs-2677	111	28	respectively	respectively	ADV
iajs-2677	111	29	.	.	PUNCT
iajs-2677	112	1	this	this	DET
iajs-2677	112	2	technique	technique	NOUN
iajs-2677	112	3	is	be	AUX
iajs-2677	112	4	called	call	VERB
iajs-2677	112	5	the	the	DET
iajs-2677	112	6	decomposition	decomposition	NOUN
iajs-2677	112	7	of	of	ADP
iajs-2677	112	8	the	the	DET
iajs-2677	112	9	problem	problem	NOUN
iajs-2677	112	10	[	[	X
iajs-2677	112	11	13	13	NUM
iajs-2677	112	12	]	]	PUNCT
iajs-2677	112	13	.	.	PUNCT
iajs-2677	113	1	so	so	ADV
iajs-2677	113	2	lb	lb	ADV
iajs-2677	113	3	=	=	PROPN
iajs-2677	113	4	emax	emax	X
iajs-2677	113	5	(	(	PUNCT
iajs-2677	113	6	mst	mst	PROPN
iajs-2677	113	7	)	)	PUNCT
iajs-2677	114	1	+	+	CCONJ
iajs-2677	114	2	tmax	tmax	PROPN
iajs-2677	114	3	(	(	PUNCT
iajs-2677	114	4	edd	edd	PROPN
iajs-2677	114	5	)	)	PUNCT
iajs-2677	114	6	.	.	PUNCT
iajs-2677	115	1	6.3	6.3	NUM
iajs-2677	115	2	optimal	optimal	ADJ
iajs-2677	115	3	solution	solution	NOUN
iajs-2677	115	4	and	and	CCONJ
iajs-2677	115	5	efficient	efficient	ADJ
iajs-2677	115	6	solutions	solution	NOUN
iajs-2677	115	7	it	it	PRON
iajs-2677	115	8	is	be	AUX
iajs-2677	115	9	clear	clear	ADJ
iajs-2677	115	10	that	that	SCONJ
iajs-2677	115	11	the	the	DET
iajs-2677	115	12	optimal	optimal	ADJ
iajs-2677	115	13	solution	solution	NOUN
iajs-2677	115	14	is	be	AUX
iajs-2677	115	15	greater	great	ADJ
iajs-2677	115	16	than	than	ADP
iajs-2677	115	17	or	or	CCONJ
iajs-2677	115	18	equal	equal	ADJ
iajs-2677	115	19	to	to	ADP
iajs-2677	115	20	the	the	DET
iajs-2677	115	21	lower	lower	ADV
iajs-2677	115	22	bound	bind	VERB
iajs-2677	115	23	.	.	PUNCT
iajs-2677	116	1	define	define	VERB
iajs-2677	116	2	the	the	DET
iajs-2677	116	3	upper	upper	ADJ
iajs-2677	116	4	bound	bind	VERB
iajs-2677	116	5	by	by	ADP
iajs-2677	116	6	ub	ub	NOUN
iajs-2677	116	7	=	=	SYM
iajs-2677	116	8	emax(mst	emax(mst	PROPN
iajs-2677	116	9	)	)	PUNCT
iajs-2677	117	1	+	+	CCONJ
iajs-2677	117	2	tmax(mst	tmax(mst	NOUN
iajs-2677	117	3	)	)	PUNCT
iajs-2677	117	4	.	.	PUNCT
iajs-2677	118	1	the	the	DET
iajs-2677	118	2	relation	relation	NOUN
iajs-2677	118	3	between	between	ADP
iajs-2677	118	4	the	the	DET
iajs-2677	118	5	optimal	optimal	ADJ
iajs-2677	118	6	value	value	NOUN
iajs-2677	118	7	(	(	PUNCT
iajs-2677	118	8	opt	opt	PROPN
iajs-2677	118	9	.	.	PUNCT
iajs-2677	118	10	)	)	PUNCT
iajs-2677	118	11	,	,	PUNCT
iajs-2677	118	12	lower	lower	ADV
iajs-2677	118	13	bound	bind	VERB
iajs-2677	118	14	(	(	PUNCT
iajs-2677	118	15	lb	lb	NOUN
iajs-2677	118	16	)	)	PUNCT
iajs-2677	118	17	and	and	CCONJ
iajs-2677	118	18	efficient	efficient	ADJ
iajs-2677	118	19	solutions	solution	NOUN
iajs-2677	118	20	for	for	ADP
iajs-2677	118	21	(	(	PUNCT
iajs-2677	118	22	p1	p1	PROPN
iajs-2677	118	23	)	)	PUNCT
iajs-2677	118	24	is	be	AUX
iajs-2677	118	25	presented	present	VERB
iajs-2677	118	26	below	below	ADV
iajs-2677	118	27	.	.	PUNCT
iajs-2677	119	1	theorem	theorem	VERB
iajs-2677	119	2	:	:	PUNCT
iajs-2677	119	3	there	there	PRON
iajs-2677	119	4	exists	exist	VERB
iajs-2677	119	5	an	an	DET
iajs-2677	119	6	integer	integer	NOUN
iajs-2677	119	7	r	r	NOUN
iajs-2677	119	8	≥	≥	NOUN
iajs-2677	119	9	0	0	NUM
iajs-2677	120	1	such	such	ADJ
iajs-2677	120	2	that	that	SCONJ
iajs-2677	120	3	lb	lb	X
iajs-2677	120	4	+	+	NUM
iajs-2677	120	5	r	r	NOUN
iajs-2677	120	6	=	=	NOUN
iajs-2677	120	7	opt	opt	NOUN
iajs-2677	120	8	.	.	PUNCT
iajs-2677	120	9	,	,	PUNCT
iajs-2677	120	10	and	and	CCONJ
iajs-2677	120	11	r	r	NOUN
iajs-2677	120	12	∈	∈	PROPN
iajs-2677	121	1	[	[	X
iajs-2677	121	2	n1	n1	NOUN
iajs-2677	121	3	−	−	PROPN
iajs-2677	121	4	1	1	NUM
iajs-2677	121	5	,	,	PUNCT
iajs-2677	121	6	n2	n2	ADJ
iajs-2677	121	7	+	+	CCONJ
iajs-2677	121	8	1	1	NUM
iajs-2677	121	9	]	]	PUNCT
iajs-2677	121	10	,	,	PUNCT
iajs-2677	121	11	where	where	SCONJ
iajs-2677	121	12	,	,	PUNCT
iajs-2677	121	13	n1=	n1=	ADJ
iajs-2677	121	14	number	number	NOUN
iajs-2677	121	15	of	of	ADP
iajs-2677	121	16	efficient	efficient	ADJ
iajs-2677	121	17	solutions	solution	NOUN
iajs-2677	121	18	,	,	PUNCT
iajs-2677	121	19	n2	n2	NOUN
iajs-2677	121	20	=	=	SYM
iajs-2677	121	21	tmax	tmax	PROPN
iajs-2677	121	22	(	(	PUNCT
iajs-2677	121	23	mst	mst	PROPN
iajs-2677	121	24	)	)	PUNCT
iajs-2677	121	25	−	−	PROPN
iajs-2677	121	26	tmax	tmax	PROPN
iajs-2677	121	27	(	(	PUNCT
iajs-2677	121	28	edd	edd	PROPN
iajs-2677	121	29	)	)	PUNCT
iajs-2677	121	30	.	.	PUNCT
iajs-2677	122	1	proof	proof	NOUN
iajs-2677	122	2	:	:	PUNCT
iajs-2677	122	3	since	since	SCONJ
iajs-2677	122	4	lb	lb	NUM
iajs-2677	122	5			NOUN
iajs-2677	122	6	opt	opt	VERB
iajs-2677	122	7	.	.	PUNCT
iajs-2677	123	1	,	,	PUNCT
iajs-2677	123	2	so	so	ADV
iajs-2677	123	3	there	there	PRON
iajs-2677	123	4	exists	exist	VERB
iajs-2677	123	5	an	an	DET
iajs-2677	123	6	integer	integer	NOUN
iajs-2677	123	7	r	r	NOUN
iajs-2677	123	8	≥	≥	NOUN
iajs-2677	123	9	0	0	NUM
iajs-2677	123	10	such	such	ADJ
iajs-2677	123	11	that	that	SCONJ
iajs-2677	123	12	lb	lb	X
iajs-2677	123	13	+	+	NUM
iajs-2677	123	14	r	r	NOUN
iajs-2677	123	15	=	=	NOUN
iajs-2677	123	16	opt	opt	NOUN
iajs-2677	123	17	.	.	PUNCT
iajs-2677	124	1	,	,	PUNCT
iajs-2677	124	2	so	so	ADV
iajs-2677	124	3	the	the	DET
iajs-2677	124	4	first	first	ADJ
iajs-2677	124	5	part	part	NOUN
iajs-2677	124	6	of	of	ADP
iajs-2677	124	7	the	the	DET
iajs-2677	124	8	theorem	theorem	NOUN
iajs-2677	124	9	is	be	AUX
iajs-2677	124	10	proved	prove	VERB
iajs-2677	124	11	.	.	PUNCT
iajs-2677	125	1	now	now	ADV
iajs-2677	125	2	,	,	PUNCT
iajs-2677	125	3	we	we	PRON
iajs-2677	125	4	show	show	VERB
iajs-2677	125	5	that	that	SCONJ
iajs-2677	125	6	r	r	NOUN
iajs-2677	125	7	∈	∈	PROPN
iajs-2677	125	8	[	[	X
iajs-2677	125	9	n1	n1	NOUN
iajs-2677	125	10	−	−	PROPN
iajs-2677	125	11	1	1	NUM
iajs-2677	125	12	,	,	PUNCT
iajs-2677	125	13	n2	n2	ADJ
iajs-2677	125	14	+	+	CCONJ
iajs-2677	125	15	1	1	NUM
iajs-2677	125	16	]	]	PUNCT
iajs-2677	125	17	or	or	CCONJ
iajs-2677	125	18	that	that	SCONJ
iajs-2677	125	19	n1	n1	NOUN
iajs-2677	125	20	−	−	PROPN
iajs-2677	125	21	1	1	NUM
iajs-2677	125	22			NOUN
iajs-2677	125	23	r	r	NOUN
iajs-2677	125	24			NOUN
iajs-2677	125	25	n2	n2	NOUN
iajs-2677	125	26	+	+	CCONJ
iajs-2677	125	27	1	1	X
iajs-2677	125	28	.	.	PUNCT
iajs-2677	126	1	now	now	ADV
iajs-2677	126	2	lb	lb	X
iajs-2677	126	3	+	+	CCONJ
iajs-2677	126	4	r	r	NOUN
iajs-2677	126	5	=	=	NOUN
iajs-2677	126	6	opt	opt	NOUN
iajs-2677	126	7	.	.	PUNCT
iajs-2677	126	8	,	,	PUNCT
iajs-2677	126	9	thus	thus	ADV
iajs-2677	126	10	r	r	NOUN
iajs-2677	126	11	=	=	SYM
iajs-2677	126	12	opt	opt	NOUN
iajs-2677	126	13	.	.	PUNCT
iajs-2677	127	1	–	–	PUNCT
iajs-2677	127	2	lb	lb	NUM
iajs-2677	127	3	≤	≤	NUM
iajs-2677	127	4	ub	ub	ADP
iajs-2677	127	5	−	−	PROPN
iajs-2677	127	6	lb	lb	PROPN
iajs-2677	127	7	=	=	PUNCT
iajs-2677	127	8	emax(mst	emax(mst	PROPN
iajs-2677	127	9	)	)	PUNCT
iajs-2677	128	1	+	+	CCONJ
iajs-2677	128	2	tmax(mst	tmax(mst	NOUN
iajs-2677	128	3	)	)	PUNCT
iajs-2677	129	1	−	−	PROPN
iajs-2677	129	2	emax(mst	emax(mst	PROPN
iajs-2677	129	3	)	)	PUNCT
iajs-2677	129	4	−	−	PROPN
iajs-2677	129	5	tmax(edd	tmax(edd	NOUN
iajs-2677	129	6	)	)	PUNCT
iajs-2677	129	7	.	.	PUNCT
iajs-2677	130	1	=	=	PRON
iajs-2677	130	2	tmax	tmax	X
iajs-2677	130	3	(	(	PUNCT
iajs-2677	130	4	mst	mst	PROPN
iajs-2677	130	5	)	)	PUNCT
iajs-2677	130	6	−	−	PROPN
iajs-2677	130	7	tmax(edd	tmax(edd	NOUN
iajs-2677	130	8	)	)	PUNCT
iajs-2677	130	9	=	=	PUNCT
iajs-2677	130	10	n2	n2	ADJ
iajs-2677	130	11	≤	≤	PROPN
iajs-2677	130	12	n2	n2	NOUN
iajs-2677	130	13	+	+	CCONJ
iajs-2677	130	14	1	1	X
iajs-2677	130	15	.	.	X
iajs-2677	131	1	hence	hence	ADV
iajs-2677	131	2	,	,	PUNCT
iajs-2677	131	3	r	r	NOUN
iajs-2677	131	4			NUM
iajs-2677	131	5	n2	n2	NOUN
iajs-2677	131	6	+	+	CCONJ
iajs-2677	131	7	1	1	X
iajs-2677	131	8	.	.	X
iajs-2677	131	9	we	we	PRON
iajs-2677	131	10	will	will	AUX
iajs-2677	131	11	prove	prove	VERB
iajs-2677	131	12	n1	n1	ADJ
iajs-2677	131	13	−	−	PROPN
iajs-2677	131	14	1	1	NUM
iajs-2677	131	15			NOUN
iajs-2677	131	16	r	r	NOUN
iajs-2677	131	17	by	by	ADP
iajs-2677	131	18	mathematical	mathematical	ADJ
iajs-2677	131	19	induction	induction	NOUN
iajs-2677	131	20	on	on	ADP
iajs-2677	131	21	n1	n1	PROPN
iajs-2677	131	22	.	.	PUNCT
iajs-2677	132	1	note	note	VERB
iajs-2677	132	2	that	that	SCONJ
iajs-2677	132	3	n1	n1	NOUN
iajs-2677	132	4	is	be	AUX
iajs-2677	132	5	not	not	PART
iajs-2677	132	6	known	know	VERB
iajs-2677	132	7	.	.	PUNCT
iajs-2677	133	1	if	if	SCONJ
iajs-2677	133	2	𝐍𝟏	𝐍𝟏	NOUN
iajs-2677	133	3	=	=	SYM
iajs-2677	133	4	𝟏	𝟏	PROPN
iajs-2677	133	5	,	,	PUNCT
iajs-2677	133	6	that	that	ADV
iajs-2677	133	7	is	is	ADV
iajs-2677	133	8	,	,	PUNCT
iajs-2677	133	9	there	there	PRON
iajs-2677	133	10	is	be	VERB
iajs-2677	133	11	only	only	ADV
iajs-2677	133	12	one	one	NUM
iajs-2677	133	13	efficient	efficient	ADJ
iajs-2677	133	14	solution	solution	NOUN
iajs-2677	133	15	which	which	PRON
iajs-2677	133	16	is	be	AUX
iajs-2677	133	17	edd	edd	PROPN
iajs-2677	133	18	(	(	PUNCT
iajs-2677	133	19	not	not	PART
iajs-2677	133	20	edd	edd	PROPN
iajs-2677	133	21	-	-	PUNCT
iajs-2677	133	22	rule	rule	NOUN
iajs-2677	133	23	)	)	PUNCT
iajs-2677	133	24	as	as	ADV
iajs-2677	133	25	well	well	ADV
iajs-2677	133	26	as	as	ADP
iajs-2677	133	27	mst	mst	PROPN
iajs-2677	133	28	(	(	PUNCT
iajs-2677	133	29	not	not	PART
iajs-2677	133	30	mst	mst	NOUN
iajs-2677	133	31	-	-	PUNCT
iajs-2677	133	32	rule	rule	NOUN
iajs-2677	133	33	)	)	PUNCT
iajs-2677	133	34	,	,	PUNCT
iajs-2677	133	35	then	then	ADV
iajs-2677	133	36	r	r	NOUN
iajs-2677	133	37	=	=	PUNCT
iajs-2677	133	38	0pt	0pt	NOUN
iajs-2677	133	39	.	.	PUNCT
iajs-2677	134	1	–	–	PUNCT
iajs-2677	134	2	lb	lb	X
iajs-2677	134	3	=	=	NOUN
iajs-2677	134	4	emax(opt	emax(opt	VERB
iajs-2677	134	5	.	.	PUNCT
iajs-2677	134	6	)	)	PUNCT
iajs-2677	135	1	+	+	CCONJ
iajs-2677	135	2	tmax(opt	tmax(opt	ADJ
iajs-2677	135	3	.	.	PUNCT
iajs-2677	135	4	)	)	PUNCT
iajs-2677	136	1	−	−	PROPN
iajs-2677	136	2	emax(mst	emax(mst	PROPN
iajs-2677	136	3	)	)	PUNCT
iajs-2677	136	4	−	−	PROPN
iajs-2677	136	5	tmax(edd	tmax(edd	NOUN
iajs-2677	136	6	)	)	PUNCT
iajs-2677	136	7	=	=	SYM
iajs-2677	136	8	emax(mst	emax(mst	PROPN
iajs-2677	136	9	)	)	PUNCT
iajs-2677	137	1	+	+	NUM
iajs-2677	137	2	tmax(edd	tmax(edd	NOUN
iajs-2677	137	3	)	)	PUNCT
iajs-2677	138	1	−	−	PROPN
iajs-2677	138	2	emax(mst	emax(mst	PROPN
iajs-2677	138	3	)	)	PUNCT
iajs-2677	138	4	−	−	PROPN
iajs-2677	138	5	tmax(edd	tmax(edd	NOUN
iajs-2677	138	6	)	)	PUNCT
iajs-2677	138	7	=	=	SYM
iajs-2677	139	1	0	0	X
iajs-2677	139	2	.	.	PUNCT
iajs-2677	139	3	thus	thus	ADV
iajs-2677	139	4	n1	n1	ADJ
iajs-2677	139	5	−	−	PROPN
iajs-2677	139	6	1	1	NUM
iajs-2677	139	7			NUM
iajs-2677	139	8	r	r	NOUN
iajs-2677	139	9	≤	≤	NOUN
iajs-2677	139	10	n2	n2	NOUN
iajs-2677	139	11	+	+	CCONJ
iajs-2677	139	12	1	1	X
iajs-2677	139	13	.	.	X
iajs-2677	140	1	that	that	PRON
iajs-2677	140	2	is	be	AUX
iajs-2677	140	3	r	r	NOUN
iajs-2677	140	4	ϵ	ϵ	X
iajs-2677	141	1	[	[	X
iajs-2677	141	2	n1	n1	ADJ
iajs-2677	141	3	−	−	PROPN
iajs-2677	141	4	1	1	NUM
iajs-2677	141	5	,	,	PUNCT
iajs-2677	141	6	n2	n2	ADJ
iajs-2677	141	7	+	+	CCONJ
iajs-2677	141	8	1	1	NUM
iajs-2677	141	9	]	]	PUNCT
iajs-2677	141	10	,	,	PUNCT
iajs-2677	141	11	and	and	CCONJ
iajs-2677	141	12	so	so	ADV
iajs-2677	141	13	the	the	DET
iajs-2677	141	14	theorem	theorem	NOUN
iajs-2677	141	15	is	be	AUX
iajs-2677	141	16	true	true	ADJ
iajs-2677	141	17	for	for	ADP
iajs-2677	141	18	n1	n1	NOUN
iajs-2677	141	19	=	=	SYM
iajs-2677	141	20	1	1	X
iajs-2677	141	21	.	.	X
iajs-2677	142	1	ibn	ibn	PROPN
iajs-2677	142	2	al	al	PROPN
iajs-2677	142	3	-	-	PUNCT
iajs-2677	142	4	haitham	haitham	PROPN
iajs-2677	142	5	jour	jour	X
iajs-2677	142	6	.	.	PROPN
iajs-2677	142	7	for	for	ADP
iajs-2677	142	8	pure	pure	ADJ
iajs-2677	142	9	&	&	CCONJ
iajs-2677	142	10	appl	appl	PROPN
iajs-2677	142	11	.	.	PUNCT
iajs-2677	143	1	sci	sci	PROPN
iajs-2677	143	2	.	.	PROPN
iajs-2677	144	1	34(3)2021	34(3)2021	NUM
iajs-2677	144	2	55	55	NUM
iajs-2677	144	3	if	if	SCONJ
iajs-2677	144	4	𝐍𝟏	𝐍𝟏	NOUN
iajs-2677	144	5	=	=	SYM
iajs-2677	144	6	𝟐	𝟐	NUM
iajs-2677	144	7	,	,	PUNCT
iajs-2677	144	8	i.e.	i.e.	X
iajs-2677	144	9	,	,	PUNCT
iajs-2677	144	10	the	the	DET
iajs-2677	144	11	number	number	NOUN
iajs-2677	144	12	of	of	ADP
iajs-2677	144	13	efficient	efficient	ADJ
iajs-2677	144	14	solutions	solution	NOUN
iajs-2677	144	15	is	be	AUX
iajs-2677	144	16	two	two	NUM
iajs-2677	144	17	which	which	PRON
iajs-2677	144	18	are	be	AUX
iajs-2677	144	19	(	(	PUNCT
iajs-2677	144	20	σ	σ	NOUN
iajs-2677	144	21	)	)	PUNCT
iajs-2677	144	22	and	and	CCONJ
iajs-2677	144	23	(	(	PUNCT
iajs-2677	144	24	σ1	σ1	PROPN
iajs-2677	144	25	)	)	PUNCT
iajs-2677	144	26	such	such	ADJ
iajs-2677	144	27	that	that	SCONJ
iajs-2677	144	28	emax	emax	X
iajs-2677	144	29	(	(	PUNCT
iajs-2677	144	30	σ	σ	NOUN
iajs-2677	144	31	)	)	PUNCT
iajs-2677	144	32	=	=	SYM
iajs-2677	144	33	emax	emax	X
iajs-2677	144	34	(	(	PUNCT
iajs-2677	144	35	mst	mst	PROPN
iajs-2677	144	36	)	)	PUNCT
iajs-2677	144	37	and	and	CCONJ
iajs-2677	144	38	tmax	tmax	PROPN
iajs-2677	144	39	(	(	PUNCT
iajs-2677	144	40	σ1	σ1	PROPN
iajs-2677	144	41	)	)	PUNCT
iajs-2677	144	42	=	=	SYM
iajs-2677	145	1	tmax	tmax	X
iajs-2677	145	2	(	(	PUNCT
iajs-2677	145	3	edd	edd	PROPN
iajs-2677	145	4	)	)	PUNCT
iajs-2677	145	5	,	,	PUNCT
iajs-2677	145	6	since	since	SCONJ
iajs-2677	145	7	n1	n1	PROPN
iajs-2677	145	8	=	=	SYM
iajs-2677	145	9	2	2	NUM
iajs-2677	145	10	implies	imply	VERB
iajs-2677	145	11	that	that	SCONJ
iajs-2677	145	12	n1	n1	NOUN
iajs-2677	145	13	−	−	PROPN
iajs-2677	145	14	1	1	NUM
iajs-2677	145	15	=	=	SYM
iajs-2677	145	16	1	1	NUM
iajs-2677	145	17	.	.	PUNCT
iajs-2677	146	1	now	now	ADV
iajs-2677	146	2	if	if	SCONJ
iajs-2677	146	3	(	(	PUNCT
iajs-2677	146	4	σ	σ	NOUN
iajs-2677	146	5	)	)	PUNCT
iajs-2677	146	6	is	be	AUX
iajs-2677	146	7	optimal	optimal	ADJ
iajs-2677	146	8	then	then	ADV
iajs-2677	146	9	:	:	PUNCT
iajs-2677	146	10	r	r	NOUN
iajs-2677	146	11	=	=	SYM
iajs-2677	146	12	emax(σ	emax(σ	NOUN
iajs-2677	146	13	)	)	PUNCT
iajs-2677	147	1	+	+	CCONJ
iajs-2677	147	2	tmax	tmax	PROPN
iajs-2677	147	3	(	(	PUNCT
iajs-2677	147	4	σ	σ	NOUN
iajs-2677	147	5	)	)	PUNCT
iajs-2677	147	6	−	−	PROPN
iajs-2677	147	7	emax(mst	emax(mst	NOUN
iajs-2677	147	8	)	)	PUNCT
iajs-2677	147	9	−	−	PROPN
iajs-2677	148	1	tmax	tmax	PROPN
iajs-2677	148	2	(	(	PUNCT
iajs-2677	148	3	edd	edd	PROPN
iajs-2677	148	4	)	)	PUNCT
iajs-2677	148	5	=	=	SYM
iajs-2677	148	6	emax(mst	emax(mst	PROPN
iajs-2677	148	7	)	)	PUNCT
iajs-2677	149	1	+	+	CCONJ
iajs-2677	149	2	tmax	tmax	ADP
iajs-2677	149	3	(	(	PUNCT
iajs-2677	149	4	σ)−	σ)−	PROPN
iajs-2677	149	5	emax(mst	emax(mst	PROPN
iajs-2677	149	6	)	)	PUNCT
iajs-2677	149	7	−	−	PROPN
iajs-2677	149	8	tmax(edd	tmax(edd	NOUN
iajs-2677	149	9	)	)	PUNCT
iajs-2677	150	1	=	=	SYM
iajs-2677	150	2	tmax	tmax	X
iajs-2677	150	3	(	(	PUNCT
iajs-2677	150	4	σ	σ	NOUN
iajs-2677	150	5	)	)	PUNCT
iajs-2677	150	6	−	−	PROPN
iajs-2677	150	7	tmax(edd	tmax(edd	PROPN
iajs-2677	150	8	)	)	PUNCT
iajs-2677	150	9	≥	≥	NOUN
iajs-2677	150	10	1	1	NUM
iajs-2677	150	11	=	=	SYM
iajs-2677	150	12	n1	n1	NOUN
iajs-2677	150	13	−	−	NOUN
iajs-2677	150	14	1	1	NUM
iajs-2677	150	15	.	.	X
iajs-2677	151	1	hence	hence	ADV
iajs-2677	151	2	n1	n1	ADJ
iajs-2677	151	3	−	−	PROPN
iajs-2677	151	4	1	1	NUM
iajs-2677	151	5			NOUN
iajs-2677	151	6	r	r	NOUN
iajs-2677	151	7			NOUN
iajs-2677	151	8	n2	n2	NOUN
iajs-2677	151	9	+	+	CCONJ
iajs-2677	151	10	1	1	X
iajs-2677	151	11	.	.	PUNCT
iajs-2677	152	1	now	now	ADV
iajs-2677	152	2	if	if	SCONJ
iajs-2677	152	3	(	(	PUNCT
iajs-2677	152	4	σ1	σ1	NOUN
iajs-2677	152	5	)	)	PUNCT
iajs-2677	152	6	is	be	AUX
iajs-2677	152	7	optimal	optimal	ADJ
iajs-2677	152	8	then	then	ADV
iajs-2677	152	9	:	:	PUNCT
iajs-2677	152	10	r	r	NOUN
iajs-2677	152	11	=	=	SYM
iajs-2677	152	12	emax(σ1	emax(σ1	X
iajs-2677	152	13	)	)	PUNCT
iajs-2677	153	1	+	+	CCONJ
iajs-2677	153	2	tmax	tmax	PROPN
iajs-2677	153	3	(	(	PUNCT
iajs-2677	153	4	σ1	σ1	PROPN
iajs-2677	153	5	)	)	PUNCT
iajs-2677	153	6	−	−	PROPN
iajs-2677	153	7	emax(mst	emax(mst	PROPN
iajs-2677	153	8	)	)	PUNCT
iajs-2677	154	1	−	−	PROPN
iajs-2677	154	2	tmax	tmax	PROPN
iajs-2677	154	3	(	(	PUNCT
iajs-2677	154	4	edd	edd	PROPN
iajs-2677	154	5	)	)	PUNCT
iajs-2677	154	6	=	=	SYM
iajs-2677	154	7	emax(σ1	emax(σ1	NOUN
iajs-2677	154	8	)	)	PUNCT
iajs-2677	155	1	+	+	CCONJ
iajs-2677	155	2	tmax	tmax	X
iajs-2677	155	3	(	(	PUNCT
iajs-2677	155	4	edd	edd	PROPN
iajs-2677	155	5	)	)	PUNCT
iajs-2677	155	6	–	–	PUNCT
iajs-2677	155	7	emax(mst	emax(mst	PROPN
iajs-2677	155	8	)	)	PUNCT
iajs-2677	155	9	−	−	PROPN
iajs-2677	155	10	tmax(edd	tmax(edd	NOUN
iajs-2677	155	11	)	)	PUNCT
iajs-2677	155	12	=	=	SYM
iajs-2677	155	13	emax(σ1	emax(σ1	NOUN
iajs-2677	155	14	)	)	PUNCT
iajs-2677	155	15	–	–	PUNCT
iajs-2677	155	16	emax(mst	emax(mst	PROPN
iajs-2677	155	17	)	)	PUNCT
iajs-2677	155	18	≥	≥	NOUN
iajs-2677	155	19	1	1	NUM
iajs-2677	155	20	=	=	SYM
iajs-2677	155	21	n1	n1	NOUN
iajs-2677	155	22	−	−	NOUN
iajs-2677	155	23	1	1	NUM
iajs-2677	155	24	.	.	X
iajs-2677	155	25	hence	hence	ADV
iajs-2677	155	26	n1	n1	ADJ
iajs-2677	155	27	−	−	PROPN
iajs-2677	155	28	1	1	NUM
iajs-2677	155	29			NOUN
iajs-2677	155	30	r	r	NOUN
iajs-2677	155	31			NOUN
iajs-2677	155	32	n2	n2	NOUN
iajs-2677	155	33	+	+	CCONJ
iajs-2677	155	34	1	1	X
iajs-2677	155	35	.	.	PUNCT
iajs-2677	156	1	so	so	ADV
iajs-2677	156	2	,	,	PUNCT
iajs-2677	157	1	r	r	NOUN
iajs-2677	157	2	ϵ	ϵ	X
iajs-2677	158	1	[	[	X
iajs-2677	158	2	n1	n1	ADJ
iajs-2677	158	3	−	−	PROPN
iajs-2677	158	4	1	1	NUM
iajs-2677	158	5	,	,	PUNCT
iajs-2677	158	6	n2	n2	NOUN
iajs-2677	158	7	+	+	CCONJ
iajs-2677	158	8	1	1	NUM
iajs-2677	158	9	]	]	PUNCT
iajs-2677	158	10	and	and	CCONJ
iajs-2677	158	11	the	the	DET
iajs-2677	158	12	theorem	theorem	NOUN
iajs-2677	158	13	is	be	AUX
iajs-2677	158	14	true	true	ADJ
iajs-2677	158	15	for	for	ADP
iajs-2677	158	16	n1	n1	NOUN
iajs-2677	158	17	=	=	SYM
iajs-2677	158	18	2	2	X
iajs-2677	158	19	.	.	X
iajs-2677	159	1	if	if	SCONJ
iajs-2677	159	2	𝐍𝟏	𝐍𝟏	NOUN
iajs-2677	159	3	=	=	SYM
iajs-2677	159	4	𝟑	𝟑	PROPN
iajs-2677	159	5	,	,	PUNCT
iajs-2677	159	6	i.e.	i.e.	X
iajs-2677	159	7	,	,	PUNCT
iajs-2677	159	8	there	there	PRON
iajs-2677	159	9	are	be	VERB
iajs-2677	159	10	three	three	NUM
iajs-2677	159	11	efficient	efficient	ADJ
iajs-2677	159	12	solutions	solution	NOUN
iajs-2677	159	13	(	(	PUNCT
iajs-2677	159	14	σ	σ	NOUN
iajs-2677	159	15	)	)	PUNCT
iajs-2677	159	16	,	,	PUNCT
iajs-2677	159	17	(	(	PUNCT
iajs-2677	159	18	σ1	σ1	PROPN
iajs-2677	159	19	)	)	PUNCT
iajs-2677	159	20	and	and	CCONJ
iajs-2677	159	21	(	(	PUNCT
iajs-2677	159	22	σ2	σ2	NOUN
iajs-2677	159	23	)	)	PUNCT
iajs-2677	159	24	such	such	ADJ
iajs-2677	159	25	that	that	SCONJ
iajs-2677	159	26	emax	emax	X
iajs-2677	159	27	(	(	PUNCT
iajs-2677	159	28	σ	σ	NOUN
iajs-2677	159	29	)	)	PUNCT
iajs-2677	159	30	=	=	SYM
iajs-2677	159	31	emax	emax	X
iajs-2677	159	32	(	(	PUNCT
iajs-2677	159	33	mst	mst	PROPN
iajs-2677	159	34	)	)	PUNCT
iajs-2677	159	35	and	and	CCONJ
iajs-2677	159	36	tmax	tmax	ADV
iajs-2677	159	37	(	(	PUNCT
iajs-2677	159	38	σ2	σ2	NOUN
iajs-2677	159	39	)	)	PUNCT
iajs-2677	159	40	=	=	SYM
iajs-2677	159	41	tmax	tmax	X
iajs-2677	159	42	(	(	PUNCT
iajs-2677	159	43	edd	edd	PROPN
iajs-2677	159	44	)	)	PUNCT
iajs-2677	159	45	.	.	PUNCT
iajs-2677	160	1	since	since	SCONJ
iajs-2677	160	2	n1	n1	PROPN
iajs-2677	160	3	=	=	SYM
iajs-2677	160	4	3	3	NUM
iajs-2677	160	5	implies	imply	VERB
iajs-2677	160	6	that	that	SCONJ
iajs-2677	160	7	n1	n1	NOUN
iajs-2677	160	8	−	−	PROPN
iajs-2677	160	9	1	1	NUM
iajs-2677	160	10	=	=	SYM
iajs-2677	160	11	2	2	NUM
iajs-2677	160	12	.	.	PUNCT
iajs-2677	161	1	now	now	ADV
iajs-2677	161	2	if	if	SCONJ
iajs-2677	161	3	(	(	PUNCT
iajs-2677	161	4	σ	σ	NOUN
iajs-2677	161	5	)	)	PUNCT
iajs-2677	161	6	is	be	AUX
iajs-2677	161	7	optimal	optimal	ADJ
iajs-2677	161	8	then	then	ADV
iajs-2677	161	9	:	:	PUNCT
iajs-2677	161	10	r	r	NOUN
iajs-2677	161	11	=	=	SYM
iajs-2677	161	12	emax(σ	emax(σ	NOUN
iajs-2677	161	13	)	)	PUNCT
iajs-2677	162	1	+	+	CCONJ
iajs-2677	162	2	tmax	tmax	PROPN
iajs-2677	162	3	(	(	PUNCT
iajs-2677	162	4	σ	σ	NOUN
iajs-2677	162	5	)	)	PUNCT
iajs-2677	162	6	−	−	PROPN
iajs-2677	162	7	emax(mst	emax(mst	NOUN
iajs-2677	162	8	)	)	PUNCT
iajs-2677	162	9	−	−	PROPN
iajs-2677	163	1	tmax	tmax	PROPN
iajs-2677	163	2	(	(	PUNCT
iajs-2677	163	3	edd	edd	PROPN
iajs-2677	163	4	)	)	PUNCT
iajs-2677	163	5	=	=	SYM
iajs-2677	163	6	emax(mst	emax(mst	PROPN
iajs-2677	163	7	)	)	PUNCT
iajs-2677	164	1	+	+	CCONJ
iajs-2677	164	2	tmax	tmax	PROPN
iajs-2677	164	3	(	(	PUNCT
iajs-2677	164	4	σ	σ	NOUN
iajs-2677	164	5	)	)	PUNCT
iajs-2677	164	6	−	−	PROPN
iajs-2677	164	7	emax(mst	emax(mst	PROPN
iajs-2677	164	8	)	)	PUNCT
iajs-2677	164	9	−	−	PROPN
iajs-2677	164	10	tmax(edd	tmax(edd	NOUN
iajs-2677	164	11	)	)	PUNCT
iajs-2677	164	12	=	=	SYM
iajs-2677	165	1	tmax	tmax	X
iajs-2677	165	2	(	(	PUNCT
iajs-2677	165	3	σ	σ	NOUN
iajs-2677	165	4	)	)	PUNCT
iajs-2677	165	5	−	−	PROPN
iajs-2677	165	6	tmax(edd	tmax(edd	PROPN
iajs-2677	165	7	)	)	PUNCT
iajs-2677	165	8	≥	≥	NOUN
iajs-2677	165	9	2	2	NUM
iajs-2677	165	10	=	=	SYM
iajs-2677	165	11	n1	n1	NOUN
iajs-2677	165	12	−	−	NOUN
iajs-2677	165	13	1	1	NUM
iajs-2677	165	14	.	.	X
iajs-2677	166	1	hence	hence	ADV
iajs-2677	166	2	n1	n1	ADJ
iajs-2677	166	3	−	−	PROPN
iajs-2677	166	4	1	1	NUM
iajs-2677	166	5			NOUN
iajs-2677	166	6	r	r	NOUN
iajs-2677	166	7			NOUN
iajs-2677	166	8	n2	n2	NOUN
iajs-2677	166	9	+	+	CCONJ
iajs-2677	166	10	1	1	X
iajs-2677	166	11	.	.	PUNCT
iajs-2677	167	1	now	now	ADV
iajs-2677	167	2	if	if	SCONJ
iajs-2677	167	3	(	(	PUNCT
iajs-2677	167	4	σ1	σ1	NOUN
iajs-2677	167	5	)	)	PUNCT
iajs-2677	167	6	is	be	AUX
iajs-2677	167	7	optimal	optimal	ADJ
iajs-2677	167	8	then	then	ADV
iajs-2677	167	9	:	:	PUNCT
iajs-2677	167	10	r	r	NOUN
iajs-2677	167	11	=	=	SYM
iajs-2677	167	12	emax(σ1	emax(σ1	X
iajs-2677	167	13	)	)	PUNCT
iajs-2677	168	1	+	+	CCONJ
iajs-2677	168	2	tmax	tmax	PROPN
iajs-2677	168	3	(	(	PUNCT
iajs-2677	168	4	σ1	σ1	PROPN
iajs-2677	168	5	)	)	PUNCT
iajs-2677	168	6	−	−	PROPN
iajs-2677	168	7	emax(mst	emax(mst	PROPN
iajs-2677	168	8	)	)	PUNCT
iajs-2677	169	1	−	−	PROPN
iajs-2677	169	2	tmax	tmax	PROPN
iajs-2677	169	3	(	(	PUNCT
iajs-2677	169	4	edd	edd	PROPN
iajs-2677	169	5	)	)	PUNCT
iajs-2677	169	6	=	=	SYM
iajs-2677	169	7	emax(σ1	emax(σ1	NOUN
iajs-2677	169	8	)	)	PUNCT
iajs-2677	169	9	−	−	PROPN
iajs-2677	169	10	emax	emax	X
iajs-2677	169	11	(	(	PUNCT
iajs-2677	169	12	mst	mst	PROPN
iajs-2677	169	13	)	)	PUNCT
iajs-2677	169	14	+	+	NUM
iajs-2677	169	15	tmax(σ1	tmax(σ1	ADJ
iajs-2677	169	16	)	)	PUNCT
iajs-2677	169	17	−	−	PROPN
iajs-2677	169	18	tmax(edd	tmax(edd	PROPN
iajs-2677	169	19	)	)	PUNCT
iajs-2677	169	20	≥	≥	NOUN
iajs-2677	169	21	1	1	NUM
iajs-2677	170	1	+	+	CCONJ
iajs-2677	170	2	1	1	NUM
iajs-2677	170	3	=	=	SYM
iajs-2677	170	4	2	2	NUM
iajs-2677	170	5	=	=	SYM
iajs-2677	170	6	n1	n1	NOUN
iajs-2677	170	7	−	−	NOUN
iajs-2677	170	8	1	1	NUM
iajs-2677	170	9	.	.	X
iajs-2677	170	10	hence	hence	ADV
iajs-2677	170	11	n1	n1	ADJ
iajs-2677	170	12	−	−	PROPN
iajs-2677	170	13	1	1	NUM
iajs-2677	170	14			NOUN
iajs-2677	170	15	r	r	NOUN
iajs-2677	170	16			NOUN
iajs-2677	170	17	n2	n2	NOUN
iajs-2677	170	18	+	+	CCONJ
iajs-2677	170	19	1	1	X
iajs-2677	170	20	.	.	PUNCT
iajs-2677	171	1	finally	finally	ADV
iajs-2677	171	2	if	if	SCONJ
iajs-2677	171	3	(	(	PUNCT
iajs-2677	171	4	σ2	σ2	NOUN
iajs-2677	171	5	)	)	PUNCT
iajs-2677	171	6	is	be	AUX
iajs-2677	171	7	optimal	optimal	ADJ
iajs-2677	171	8	,	,	PUNCT
iajs-2677	171	9	then	then	ADV
iajs-2677	171	10	:	:	PUNCT
iajs-2677	171	11	r	r	NOUN
iajs-2677	171	12	=	=	PUNCT
iajs-2677	171	13	emax(σ2	emax(σ2	ADJ
iajs-2677	171	14	)	)	PUNCT
iajs-2677	171	15	+	+	CCONJ
iajs-2677	171	16	tmax	tmax	PROPN
iajs-2677	171	17	(	(	PUNCT
iajs-2677	171	18	σ2	σ2	NOUN
iajs-2677	171	19	)	)	PUNCT
iajs-2677	171	20	−	−	PROPN
iajs-2677	171	21	emax(mst	emax(mst	NOUN
iajs-2677	171	22	)	)	PUNCT
iajs-2677	172	1	−	−	PROPN
iajs-2677	172	2	tmax	tmax	PROPN
iajs-2677	172	3	(	(	PUNCT
iajs-2677	172	4	edd	edd	PROPN
iajs-2677	172	5	)	)	PUNCT
iajs-2677	172	6	=	=	PUNCT
iajs-2677	172	7	emax(σ2	emax(σ2	ADJ
iajs-2677	172	8	)	)	PUNCT
iajs-2677	172	9	−	−	PROPN
iajs-2677	172	10	emax	emax	X
iajs-2677	172	11	(	(	PUNCT
iajs-2677	172	12	mst	mst	PROPN
iajs-2677	172	13	)	)	PUNCT
iajs-2677	172	14	+	+	NUM
iajs-2677	172	15	tmax(edd	tmax(edd	NOUN
iajs-2677	172	16	)	)	PUNCT
iajs-2677	172	17	−	−	PROPN
iajs-2677	172	18	tmax(edd	tmax(edd	PROPN
iajs-2677	172	19	)	)	PUNCT
iajs-2677	172	20	≥	≥	NOUN
iajs-2677	172	21	1	1	NUM
iajs-2677	172	22	+	+	CCONJ
iajs-2677	172	23	1	1	NUM
iajs-2677	172	24	=	=	SYM
iajs-2677	172	25	2	2	NUM
iajs-2677	172	26	=	=	SYM
iajs-2677	172	27	n1	n1	NOUN
iajs-2677	172	28	−	−	NOUN
iajs-2677	172	29	1	1	NUM
iajs-2677	172	30	.	.	X
iajs-2677	172	31	hence	hence	ADV
iajs-2677	172	32	n1	n1	ADJ
iajs-2677	172	33	−	−	PROPN
iajs-2677	172	34	1	1	NUM
iajs-2677	172	35			NOUN
iajs-2677	172	36	r	r	NOUN
iajs-2677	172	37			NOUN
iajs-2677	172	38	n2	n2	NOUN
iajs-2677	172	39	+	+	CCONJ
iajs-2677	172	40	1	1	X
iajs-2677	172	41	.	.	PUNCT
iajs-2677	173	1	so	so	ADV
iajs-2677	173	2	r	r	NOUN
iajs-2677	173	3	ϵ	ϵ	X
iajs-2677	174	1	[	[	X
iajs-2677	174	2	n1	n1	ADJ
iajs-2677	174	3	−	−	PROPN
iajs-2677	174	4	1	1	NUM
iajs-2677	174	5	,	,	PUNCT
iajs-2677	174	6	n2	n2	NOUN
iajs-2677	174	7	+	+	CCONJ
iajs-2677	174	8	1	1	NUM
iajs-2677	174	9	]	]	PUNCT
iajs-2677	174	10	and	and	CCONJ
iajs-2677	174	11	it	it	PRON
iajs-2677	174	12	is	be	AUX
iajs-2677	174	13	true	true	ADJ
iajs-2677	174	14	for	for	ADP
iajs-2677	174	15	n1	n1	NOUN
iajs-2677	174	16	=	=	SYM
iajs-2677	174	17	3	3	X
iajs-2677	174	18	.	.	PUNCT
iajs-2677	174	19	suppose	suppose	VERB
iajs-2677	174	20	the	the	DET
iajs-2677	174	21	theorem	theorem	NOUN
iajs-2677	174	22	is	be	AUX
iajs-2677	174	23	true	true	ADJ
iajs-2677	174	24	for	for	ADP
iajs-2677	174	25	n1	n1	PROPN
iajs-2677	174	26	=	=	SYM
iajs-2677	174	27	k	k	PROPN
iajs-2677	174	28	,	,	PUNCT
iajs-2677	174	29	i.e.	i.e.	X
iajs-2677	174	30	,	,	PUNCT
iajs-2677	174	31	the	the	DET
iajs-2677	174	32	theorem	theorem	NOUN
iajs-2677	174	33	is	be	AUX
iajs-2677	174	34	true	true	ADJ
iajs-2677	174	35	for	for	ADP
iajs-2677	174	36	the	the	DET
iajs-2677	174	37	k	k	PROPN
iajs-2677	174	38	efficient	efficient	ADJ
iajs-2677	174	39	solutions	solution	NOUN
iajs-2677	174	40	(	(	PUNCT
iajs-2677	174	41	σ	σ	NOUN
iajs-2677	174	42	)	)	PUNCT
iajs-2677	174	43	,	,	PUNCT
iajs-2677	174	44	(	(	PUNCT
iajs-2677	174	45	σ1	σ1	PROPN
iajs-2677	174	46	)	)	PUNCT
iajs-2677	174	47	,	,	PUNCT
iajs-2677	174	48	…	…	PUNCT
iajs-2677	174	49	,	,	PUNCT
iajs-2677	174	50	(	(	PUNCT
iajs-2677	174	51	σk−1	σk−1	NOUN
iajs-2677	174	52	)	)	PUNCT
iajs-2677	174	53	,	,	PUNCT
iajs-2677	174	54	that	that	ADV
iajs-2677	174	55	is	is	ADV
iajs-2677	174	56	,	,	PUNCT
iajs-2677	174	57	for	for	ADP
iajs-2677	174	58	these	these	DET
iajs-2677	174	59	k	k	PROPN
iajs-2677	174	60	efficient	efficient	ADJ
iajs-2677	174	61	solutions	solution	NOUN
iajs-2677	174	62	n1	n1	NOUN
iajs-2677	174	63	−	−	PROPN
iajs-2677	174	64	1	1	NUM
iajs-2677	174	65			NOUN
iajs-2677	174	66	r	r	NOUN
iajs-2677	174	67			NOUN
iajs-2677	174	68	n2	n2	NOUN
iajs-2677	174	69	+	+	CCONJ
iajs-2677	174	70	1	1	X
iajs-2677	174	71	.	.	X
iajs-2677	174	72	let	let	VERB
iajs-2677	174	73	n1	n1	PROPN
iajs-2677	174	74	=	=	SYM
iajs-2677	174	75	k	k	PROPN
iajs-2677	175	1	+	+	PROPN
iajs-2677	175	2	1	1	NUM
iajs-2677	175	3	,	,	PUNCT
iajs-2677	175	4	that	that	ADV
iajs-2677	175	5	is	is	ADV
iajs-2677	175	6	,	,	PUNCT
iajs-2677	175	7	there	there	PRON
iajs-2677	175	8	is	be	VERB
iajs-2677	175	9	k	k	PROPN
iajs-2677	175	10	+	+	CCONJ
iajs-2677	175	11	1	1	NUM
iajs-2677	175	12	efficient	efficient	ADJ
iajs-2677	175	13	solutions	solution	NOUN
iajs-2677	175	14	(	(	PUNCT
iajs-2677	175	15	σ	σ	NOUN
iajs-2677	175	16	)	)	PUNCT
iajs-2677	175	17	,	,	PUNCT
iajs-2677	175	18	(	(	PUNCT
iajs-2677	175	19	σ1	σ1	NOUN
iajs-2677	175	20	)	)	PUNCT
iajs-2677	175	21	,	,	PUNCT
iajs-2677	175	22	…	…	PUNCT
iajs-2677	175	23	,	,	PUNCT
iajs-2677	175	24	(	(	PUNCT
iajs-2677	175	25	σk−1	σk−1	NOUN
iajs-2677	175	26	)	)	PUNCT
iajs-2677	175	27	,	,	PUNCT
iajs-2677	175	28	(	(	PUNCT
iajs-2677	175	29	σk	σk	PROPN
iajs-2677	175	30	)	)	PUNCT
iajs-2677	175	31	,	,	PUNCT
iajs-2677	175	32	if	if	SCONJ
iajs-2677	175	33	any	any	DET
iajs-2677	175	34	one	one	NUM
iajs-2677	175	35	of	of	ADP
iajs-2677	175	36	the	the	DET
iajs-2677	175	37	first	first	ADJ
iajs-2677	175	38	k	k	PROPN
iajs-2677	175	39	efficient	efficient	ADJ
iajs-2677	175	40	solutions	solution	NOUN
iajs-2677	175	41	(	(	PUNCT
iajs-2677	175	42	σ	σ	NOUN
iajs-2677	175	43	)	)	PUNCT
iajs-2677	175	44	,	,	PUNCT
iajs-2677	175	45	(	(	PUNCT
iajs-2677	175	46	σ1	σ1	PROPN
iajs-2677	175	47	)	)	PUNCT
iajs-2677	175	48	,	,	PUNCT
iajs-2677	175	49	...	...	PUNCT
iajs-2677	175	50	,	,	PUNCT
iajs-2677	175	51	(	(	PUNCT
iajs-2677	175	52	σk−1	σk−1	NOUN
iajs-2677	175	53	)	)	PUNCT
iajs-2677	175	54	,	,	PUNCT
iajs-2677	175	55	is	be	AUX
iajs-2677	175	56	optimal	optimal	ADJ
iajs-2677	175	57	then	then	ADV
iajs-2677	175	58	since	since	SCONJ
iajs-2677	175	59	it	it	PRON
iajs-2677	175	60	is	be	AUX
iajs-2677	175	61	true	true	ADJ
iajs-2677	175	62	for	for	ADP
iajs-2677	175	63	n1	n1	PROPN
iajs-2677	175	64	=	=	SYM
iajs-2677	175	65	k	k	PROPN
iajs-2677	175	66	,	,	PUNCT
iajs-2677	175	67	we	we	PRON
iajs-2677	175	68	get	get	VERB
iajs-2677	175	69	n1	n1	ADJ
iajs-2677	175	70	−	−	NUM
iajs-2677	175	71	1	1	NUM
iajs-2677	175	72	≤	≤	NOUN
iajs-2677	175	73	r	r	NOUN
iajs-2677	175	74	,	,	PUNCT
iajs-2677	175	75	and	and	CCONJ
iajs-2677	175	76	hence	hence	ADV
iajs-2677	175	77	,	,	PUNCT
iajs-2677	175	78	n1	n1	ADJ
iajs-2677	175	79	−	−	PROPN
iajs-2677	175	80	1	1	NUM
iajs-2677	175	81			NOUN
iajs-2677	175	82	r	r	NOUN
iajs-2677	175	83			NOUN
iajs-2677	175	84	n2	n2	NOUN
iajs-2677	175	85	+	+	CCONJ
iajs-2677	175	86	1	1	NUM
iajs-2677	175	87	,	,	PUNCT
iajs-2677	175	88	and	and	CCONJ
iajs-2677	175	89	if	if	SCONJ
iajs-2677	175	90	the	the	DET
iajs-2677	175	91	last	last	ADJ
iajs-2677	175	92	efficient	efficient	ADJ
iajs-2677	175	93	solution	solution	NOUN
iajs-2677	175	94	(	(	PUNCT
iajs-2677	175	95	σk	σk	CCONJ
iajs-2677	175	96	)	)	PUNCT
iajs-2677	175	97	is	be	AUX
iajs-2677	175	98	optimal	optimal	ADJ
iajs-2677	175	99	,	,	PUNCT
iajs-2677	175	100	then	then	ADV
iajs-2677	175	101	:	:	PUNCT
iajs-2677	175	102	r	r	NOUN
iajs-2677	175	103	=	=	SYM
iajs-2677	175	104	emax(σk	emax(σk	PROPN
iajs-2677	175	105	)	)	PUNCT
iajs-2677	176	1	+	+	CCONJ
iajs-2677	176	2	tmax(σk	tmax(σk	VERB
iajs-2677	176	3	)	)	PUNCT
iajs-2677	176	4	–	–	PUNCT
iajs-2677	176	5	emax(mst	emax(mst	NOUN
iajs-2677	176	6	)	)	PUNCT
iajs-2677	176	7	−	−	PROPN
iajs-2677	176	8	tmax(edd	tmax(edd	NOUN
iajs-2677	176	9	)	)	PUNCT
iajs-2677	177	1	=	=	SYM
iajs-2677	177	2	emax(σk	emax(σk	PROPN
iajs-2677	177	3	)	)	PUNCT
iajs-2677	177	4	−	−	PROPN
iajs-2677	177	5	emax(mst	emax(mst	PROPN
iajs-2677	177	6	)	)	PUNCT
iajs-2677	177	7	≥	≥	NOUN
iajs-2677	178	1	k	k	NOUN
iajs-2677	178	2	=	=	PUNCT
iajs-2677	179	1	k	k	PROPN
iajs-2677	179	2	+	+	CCONJ
iajs-2677	179	3	1	1	NUM
iajs-2677	179	4	=	=	SYM
iajs-2677	179	5	1	1	NUM
iajs-2677	179	6	=	=	SYM
iajs-2677	179	7	n1	n1	NOUN
iajs-2677	179	8	−	−	NOUN
iajs-2677	179	9	1	1	NUM
iajs-2677	179	10	,	,	PUNCT
iajs-2677	179	11	thus	thus	ADV
iajs-2677	179	12	n1	n1	ADJ
iajs-2677	179	13	−	−	PROPN
iajs-2677	179	14	1	1	NUM
iajs-2677	179	15			NOUN
iajs-2677	179	16	r	r	NOUN
iajs-2677	179	17			NOUN
iajs-2677	179	18	n2	n2	NOUN
iajs-2677	179	19	+	+	CCONJ
iajs-2677	179	20	1	1	X
iajs-2677	179	21	.	.	PUNCT
iajs-2677	180	1	thus	thus	ADV
iajs-2677	180	2	it	it	PRON
iajs-2677	180	3	is	be	AUX
iajs-2677	180	4	true	true	ADJ
iajs-2677	180	5	for	for	ADP
iajs-2677	180	6	n1	n1	NOUN
iajs-2677	180	7	=	=	SYM
iajs-2677	180	8	k	k	PROPN
iajs-2677	181	1	+	+	PROPN
iajs-2677	181	2	1	1	NUM
iajs-2677	181	3	which	which	PRON
iajs-2677	181	4	completes	complete	VERB
iajs-2677	181	5	the	the	DET
iajs-2677	181	6	proof	proof	NOUN
iajs-2677	181	7	.	.	PUNCT
iajs-2677	182	1	∎	∎	PROPN
iajs-2677	182	2	corollary	corollary	NOUN
iajs-2677	182	3	:	:	PUNCT
iajs-2677	182	4	if	if	SCONJ
iajs-2677	182	5	tmax(mst	tmax(mst	ADJ
iajs-2677	182	6	)	)	PUNCT
iajs-2677	182	7	=	=	SYM
iajs-2677	182	8	tmax(edd	tmax(edd	PROPN
iajs-2677	182	9	)	)	PUNCT
iajs-2677	182	10	,	,	PUNCT
iajs-2677	182	11	then	then	ADV
iajs-2677	182	12	r	r	NOUN
iajs-2677	182	13	=	=	SYM
iajs-2677	182	14	0	0	X
iajs-2677	182	15	.	.	PUNCT
iajs-2677	183	1	proof	proof	NOUN
iajs-2677	183	2	:	:	PUNCT
iajs-2677	183	3	since	since	SCONJ
iajs-2677	183	4	tmax(mst	tmax(mst	VERB
iajs-2677	183	5	)	)	PUNCT
iajs-2677	183	6	=	=	SYM
iajs-2677	183	7	tmax(edd	tmax(edd	NOUN
iajs-2677	183	8	)	)	PUNCT
iajs-2677	184	1	so	so	ADV
iajs-2677	184	2	,	,	PUNCT
iajs-2677	184	3	we	we	PRON
iajs-2677	184	4	have	have	VERB
iajs-2677	184	5	a	a	DET
iajs-2677	184	6	schedule	schedule	NOUN
iajs-2677	184	7	π	π	NOUN
iajs-2677	184	8	(	(	PUNCT
iajs-2677	184	9	say	say	PROPN
iajs-2677	184	10	)	)	PUNCT
iajs-2677	184	11	which	which	PRON
iajs-2677	184	12	gives	give	VERB
iajs-2677	184	13	edd	edd	PROPN
iajs-2677	184	14	-	-	PUNCT
iajs-2677	184	15	rule	rule	NOUN
iajs-2677	184	16	and	and	CCONJ
iajs-2677	184	17	mst	mst	NOUN
iajs-2677	184	18	-	-	PUNCT
iajs-2677	184	19	rule	rule	NOUN
iajs-2677	184	20	at	at	ADP
iajs-2677	184	21	the	the	DET
iajs-2677	184	22	same	same	ADJ
iajs-2677	184	23	time	time	NOUN
iajs-2677	184	24	,	,	PUNCT
iajs-2677	184	25	and	and	CCONJ
iajs-2677	184	26	π	π	PROPN
iajs-2677	184	27	is	be	AUX
iajs-2677	184	28	also	also	ADV
iajs-2677	184	29	optimal	optimal	ADJ
iajs-2677	184	30	schedule	schedule	NOUN
iajs-2677	184	31	.	.	PUNCT
iajs-2677	185	1	the	the	DET
iajs-2677	185	2	lower	lower	ADV
iajs-2677	185	3	bound	bind	VERB
iajs-2677	185	4	is	be	AUX
iajs-2677	185	5	defined	define	VERB
iajs-2677	185	6	as	as	ADP
iajs-2677	185	7	:	:	PUNCT
iajs-2677	185	8	lb	lb	PROPN
iajs-2677	185	9	=	=	PROPN
iajs-2677	185	10	emax	emax	X
iajs-2677	185	11	(	(	PUNCT
iajs-2677	185	12	mst	mst	PROPN
iajs-2677	185	13	)	)	PUNCT
iajs-2677	185	14	+	+	CCONJ
iajs-2677	185	15	tmax	tmax	PROPN
iajs-2677	185	16	(	(	PUNCT
iajs-2677	185	17	edd	edd	PROPN
iajs-2677	185	18	)	)	PUNCT
iajs-2677	185	19	.	.	PUNCT
iajs-2677	186	1	therefore	therefore	ADV
iajs-2677	186	2	,	,	PUNCT
iajs-2677	186	3	lb	lb	PRON
iajs-2677	186	4	=	=	NOUN
iajs-2677	186	5	opt	opt	PROPN
iajs-2677	186	6	.	.	PUNCT
iajs-2677	187	1	this	this	PRON
iajs-2677	187	2	implies	imply	VERB
iajs-2677	187	3	that	that	SCONJ
iajs-2677	187	4	r	r	NOUN
iajs-2677	187	5	=	=	NOUN
iajs-2677	187	6	0	0	NUM
iajs-2677	187	7	.	.	PUNCT
iajs-2677	188	1	∎	∎	NOUN
iajs-2677	188	2	6.4	6.4	NUM
iajs-2677	188	3	modified	modify	VERB
iajs-2677	188	4	smith	smith	PROPN
iajs-2677	188	5	’s	’s	PART
iajs-2677	188	6	algorithm	algorithm	PROPN
iajs-2677	188	7	ibn	ibn	PROPN
iajs-2677	188	8	al	al	PROPN
iajs-2677	188	9	-	-	PUNCT
iajs-2677	188	10	haitham	haitham	PROPN
iajs-2677	188	11	jour	jour	X
iajs-2677	188	12	.	.	PROPN
iajs-2677	189	1	for	for	ADP
iajs-2677	189	2	pure	pure	ADJ
iajs-2677	189	3	&	&	CCONJ
iajs-2677	189	4	appl	appl	PROPN
iajs-2677	189	5	.	.	PUNCT
iajs-2677	190	1	sci	sci	PROPN
iajs-2677	190	2	.	.	PROPN
iajs-2677	191	1	34(3)2021	34(3)2021	NUM
iajs-2677	191	2	56	56	NUM
iajs-2677	191	3	smith	smith	NOUN
iajs-2677	191	4	presented	present	VERB
iajs-2677	191	5	an	an	DET
iajs-2677	191	6	algorithm	algorithm	NOUN
iajs-2677	191	7	to	to	PART
iajs-2677	191	8	solve	solve	VERB
iajs-2677	191	9	a	a	DET
iajs-2677	191	10	multi	multi	ADJ
iajs-2677	191	11	-	-	ADJ
iajs-2677	191	12	criteria	criteria	ADJ
iajs-2677	191	13	problem	problem	NOUN
iajs-2677	191	14	[	[	X
iajs-2677	191	15	5	5	NUM
iajs-2677	191	16	]	]	PUNCT
iajs-2677	191	17	.	.	PUNCT
iajs-2677	192	1	we	we	PRON
iajs-2677	192	2	modify	modify	VERB
iajs-2677	192	3	it	it	PRON
iajs-2677	192	4	to	to	PART
iajs-2677	192	5	find	find	VERB
iajs-2677	192	6	an	an	DET
iajs-2677	192	7	optimal	optimal	ADJ
iajs-2677	192	8	solution	solution	NOUN
iajs-2677	192	9	for	for	ADP
iajs-2677	192	10	a	a	DET
iajs-2677	192	11	given	give	VERB
iajs-2677	192	12	tmax	tmax	NOUN
iajs-2677	192	13	.	.	PUNCT
iajs-2677	193	1	step	step	NOUN
iajs-2677	193	2	(	(	PUNCT
iajs-2677	193	3	1	1	NUM
iajs-2677	193	4	):	):	PUNCT
iajs-2677	193	5	set	set	VERB
iajs-2677	193	6	r	r	NOUN
iajs-2677	193	7	=	=	PUNCT
iajs-2677	193	8	∑	∑	PROPN
iajs-2677	193	9	pj	pj	PROPN
iajs-2677	193	10	n	n	CCONJ
iajs-2677	193	11	j=1	j=1	PROPN
iajs-2677	193	12	,	,	PUNCT
iajs-2677	193	13	n	n	NOUN
iajs-2677	193	14	=	=	SYM
iajs-2677	193	15	{	{	PUNCT
iajs-2677	193	16	1	1	NUM
iajs-2677	193	17	,	,	PUNCT
iajs-2677	193	18	2	2	NUM
iajs-2677	193	19	,	,	PUNCT
iajs-2677	193	20	…	…	PUNCT
iajs-2677	193	21	,	,	PUNCT
iajs-2677	193	22	n	n	CCONJ
iajs-2677	193	23	}	}	PUNCT
iajs-2677	193	24	,	,	PUNCT
iajs-2677	193	25	k	k	PROPN
iajs-2677	193	26	=	=	PUNCT
iajs-2677	193	27	n.	n.	NOUN
iajs-2677	193	28	step	step	NOUN
iajs-2677	193	29	(	(	PUNCT
iajs-2677	193	30	2	2	NUM
iajs-2677	193	31	):	):	PUNCT
iajs-2677	193	32	find	find	VERB
iajs-2677	193	33	a	a	DET
iajs-2677	193	34	job	job	NOUN
iajs-2677	193	35	j	j	NOUN
iajs-2677	193	36	*	*	PUNCT
iajs-2677	193	37	such	such	ADJ
iajs-2677	193	38	that	that	SCONJ
iajs-2677	193	39	pj∗	pj∗	PROPN
iajs-2677	193	40	≥	≥	PROPN
iajs-2677	193	41	pj	pj	PROPN
iajs-2677	193	42	,	,	PUNCT
iajs-2677	193	43	dj	dj	PROPN
iajs-2677	193	44	*	*	PUNCT
iajs-2677	193	45	,	,	PUNCT
iajs-2677	193	46	dj	dj	X
iajs-2677	193	47	≥	≥	NOUN
iajs-2677	193	48	r	r	NOUN
iajs-2677	193	49	,	,	PUNCT
iajs-2677	193	50	and	and	CCONJ
iajs-2677	194	1	r	r	NOUN
iajs-2677	194	2	−	−	PROPN
iajs-2677	194	3	dj	dj	NOUN
iajs-2677	194	4	≤	≤	ADJ
iajs-2677	194	5	tmax	tmax	PROPN
iajs-2677	194	6	(	(	PUNCT
iajs-2677	194	7	edd	edd	PROPN
iajs-2677	194	8	)	)	PUNCT
iajs-2677	194	9	,	,	PUNCT
iajs-2677	194	10	j	j	PROPN
iajs-2677	194	11	and	and	CCONJ
iajs-2677	194	12	j∗	j∗	PROPN
iajs-2677	194	13	∈	∈	PROPN
iajs-2677	194	14	n.	n.	NOUN
iajs-2677	194	15	(	(	PUNCT
iajs-2677	194	16	break	break	VERB
iajs-2677	194	17	ties	tie	NOUN
iajs-2677	194	18	arbitrarily	arbitrarily	ADV
iajs-2677	194	19	)	)	PUNCT
iajs-2677	194	20	.	.	PUNCT
iajs-2677	195	1	assign	assign	VERB
iajs-2677	195	2	job	job	PROPN
iajs-2677	195	3	j	j	PROPN
iajs-2677	195	4	*	*	PUNCT
iajs-2677	195	5	to	to	PART
iajs-2677	195	6	position	position	VERB
iajs-2677	195	7	k	k	PROPN
iajs-2677	195	8	.	.	PUNCT
iajs-2677	196	1	step	step	NOUN
iajs-2677	196	2	(	(	PUNCT
iajs-2677	196	3	3	3	NUM
iajs-2677	196	4	):	):	PUNCT
iajs-2677	196	5	set	set	VERB
iajs-2677	196	6	r	r	NOUN
iajs-2677	196	7	=	=	SYM
iajs-2677	196	8	r	r	NOUN
iajs-2677	196	9	−	−	PROPN
iajs-2677	196	10	pj	pj	PROPN
iajs-2677	196	11	,	,	PUNCT
iajs-2677	196	12	n	n	CCONJ
iajs-2677	196	13	=	=	SYM
iajs-2677	196	14	n{j	n{j	NOUN
iajs-2677	196	15	*	*	PUNCT
iajs-2677	196	16	}	}	PUNCT
iajs-2677	196	17	,	,	PUNCT
iajs-2677	196	18	k	k	PROPN
iajs-2677	196	19	=	=	PUNCT
iajs-2677	197	1	k	k	PROPN
iajs-2677	198	1	−	−	PROPN
iajs-2677	198	2	1	1	X
iajs-2677	198	3	.	.	PUNCT
iajs-2677	199	1	if	if	SCONJ
iajs-2677	199	2	k	k	PROPN
iajs-2677	199	3	=	=	SYM
iajs-2677	199	4	0	0	PROPN
iajs-2677	199	5	,	,	PUNCT
iajs-2677	199	6	stop	stop	VERB
iajs-2677	199	7	.	.	PUNCT
iajs-2677	200	1	else	else	ADV
iajs-2677	200	2	,	,	PUNCT
iajs-2677	200	3	go	go	VERB
iajs-2677	200	4	to	to	PART
iajs-2677	200	5	step	step	VERB
iajs-2677	200	6	(	(	PUNCT
iajs-2677	200	7	2	2	NUM
iajs-2677	200	8	)	)	PUNCT
iajs-2677	200	9	.	.	PUNCT
iajs-2677	201	1	this	this	DET
iajs-2677	201	2	theorem	theorem	NOUN
iajs-2677	201	3	finds	find	VERB
iajs-2677	201	4	the	the	DET
iajs-2677	201	5	difference	difference	NOUN
iajs-2677	201	6	between	between	ADP
iajs-2677	201	7	the	the	DET
iajs-2677	201	8	lb	lb	NOUN
iajs-2677	201	9	and	and	CCONJ
iajs-2677	201	10	the	the	DET
iajs-2677	201	11	opt	opt	NOUN
iajs-2677	201	12	.	.	PUNCT
iajs-2677	202	1	solution	solution	NOUN
iajs-2677	202	2	.	.	PUNCT
iajs-2677	203	1	we	we	PRON
iajs-2677	203	2	use	use	VERB
iajs-2677	203	3	this	this	DET
iajs-2677	203	4	theorem	theorem	NOUN
iajs-2677	203	5	to	to	PART
iajs-2677	203	6	find	find	VERB
iajs-2677	203	7	a	a	DET
iajs-2677	203	8	heuristic	heuristic	ADJ
iajs-2677	203	9	method	method	NOUN
iajs-2677	203	10	and	and	CCONJ
iajs-2677	203	11	then	then	ADV
iajs-2677	203	12	the	the	DET
iajs-2677	203	13	near	near	ADJ
iajs-2677	203	14	optimal	optimal	ADJ
iajs-2677	203	15	solution	solution	NOUN
iajs-2677	203	16	for	for	ADP
iajs-2677	203	17	(	(	PUNCT
iajs-2677	203	18	p1	p1	NOUN
iajs-2677	203	19	)	)	PUNCT
iajs-2677	203	20	.	.	PUNCT
iajs-2677	204	1	let	let	VERB
iajs-2677	204	2	s1=	s1=	PROPN
iajs-2677	204	3	{	{	PUNCT
iajs-2677	204	4	σ1	σ1	PROPN
iajs-2677	204	5	,	,	PUNCT
iajs-2677	204	6	σ2	σ2	PROPN
iajs-2677	204	7	,	,	PUNCT
iajs-2677	204	8	…	…	PUNCT
iajs-2677	204	9	,	,	PUNCT
iajs-2677	204	10	σk	σk	ADP
iajs-2677	204	11	}	}	PUNCT
iajs-2677	204	12	which	which	PRON
iajs-2677	204	13	means	mean	VERB
iajs-2677	204	14	that	that	SCONJ
iajs-2677	204	15	there	there	PRON
iajs-2677	204	16	are	be	VERB
iajs-2677	204	17	k	k	PROPN
iajs-2677	204	18	efficient	efficient	ADJ
iajs-2677	204	19	solutions	solution	NOUN
iajs-2677	204	20	for	for	ADP
iajs-2677	204	21	the	the	DET
iajs-2677	204	22	problem	problem	NOUN
iajs-2677	204	23	(	(	PUNCT
iajs-2677	204	24	p3	p3	PROPN
iajs-2677	204	25	)	)	PUNCT
iajs-2677	204	26	.	.	PUNCT
iajs-2677	205	1	also	also	ADV
iajs-2677	205	2	let	let	VERB
iajs-2677	205	3	s	s	PRON
iajs-2677	205	4	=	=	NOUN
iajs-2677	205	5	{	{	PUNCT
iajs-2677	205	6	σ∗	σ∗	NOUN
iajs-2677	205	7	1	1	NUM
iajs-2677	205	8	,	,	PUNCT
iajs-2677	205	9	σ∗	σ∗	X
iajs-2677	205	10	2	2	NUM
iajs-2677	205	11	,	,	PUNCT
iajs-2677	205	12	…	…	PUNCT
iajs-2677	205	13	,	,	PUNCT
iajs-2677	205	14	σk1	σk1	NOUN
iajs-2677	205	15	∗	∗	NOUN
iajs-2677	205	16	}	}	PUNCT
iajs-2677	205	17	which	which	PRON
iajs-2677	205	18	means	mean	VERB
iajs-2677	205	19	that	that	SCONJ
iajs-2677	205	20	there	there	PRON
iajs-2677	205	21	are	be	VERB
iajs-2677	205	22	k1	k1	ADJ
iajs-2677	205	23	efficient	efficient	ADJ
iajs-2677	205	24	solutions	solution	NOUN
iajs-2677	205	25	for	for	ADP
iajs-2677	205	26	the	the	DET
iajs-2677	205	27	problem	problem	NOUN
iajs-2677	205	28	(	(	PUNCT
iajs-2677	205	29	p2	p2	PROPN
iajs-2677	205	30	)	)	PUNCT
iajs-2677	205	31	.	.	PUNCT
iajs-2677	206	1	in	in	ADP
iajs-2677	206	2	s1	s1	NOUN
iajs-2677	206	3	,	,	PUNCT
iajs-2677	206	4	there	there	PRON
iajs-2677	206	5	exists	exist	VERB
iajs-2677	206	6	i	i	PRON
iajs-2677	206	7	(	(	PUNCT
iajs-2677	206	8	i	i	NOUN
iajs-2677	206	9	=	=	NOUN
iajs-2677	206	10	1	1	NUM
iajs-2677	206	11	,	,	PUNCT
iajs-2677	206	12	.	.	PUNCT
iajs-2677	206	13	.	.	PUNCT
iajs-2677	207	1	.	.	PUNCT
iajs-2677	208	1	,	,	PUNCT
iajs-2677	208	2	k	k	X
iajs-2677	208	3	)	)	PUNCT
iajs-2677	208	4	such	such	ADJ
iajs-2677	208	5	that	that	SCONJ
iajs-2677	208	6	emax	emax	X
iajs-2677	208	7	(	(	PUNCT
iajs-2677	208	8	σi	σi	NOUN
iajs-2677	208	9	)	)	PUNCT
iajs-2677	208	10	=	=	SYM
iajs-2677	208	11	emax(mst	emax(mst	PROPN
iajs-2677	208	12	)	)	PUNCT
iajs-2677	208	13	,	,	PUNCT
iajs-2677	208	14	and	and	CCONJ
iajs-2677	208	15	there	there	PRON
iajs-2677	208	16	exists	exist	VERB
iajs-2677	208	17	also	also	ADV
iajs-2677	208	18	in	in	ADP
iajs-2677	208	19	s	s	PROPN
iajs-2677	208	20	j	j	PROPN
iajs-2677	208	21	(	(	PUNCT
iajs-2677	208	22	j	j	PROPN
iajs-2677	208	23	=	=	SYM
iajs-2677	208	24	1	1	NUM
iajs-2677	208	25	,	,	PUNCT
iajs-2677	208	26	.	.	PUNCT
iajs-2677	208	27	.	.	PUNCT
iajs-2677	208	28	.	.	PUNCT
iajs-2677	209	1	,	,	PUNCT
iajs-2677	209	2	k1	k1	PROPN
iajs-2677	209	3	)	)	PUNCT
iajs-2677	209	4	such	such	ADJ
iajs-2677	209	5	that	that	PRON
iajs-2677	209	6	tmax	tmax	NOUN
iajs-2677	209	7	(	(	PUNCT
iajs-2677	209	8	σ∗	σ∗	PROPN
iajs-2677	209	9	j	j	PROPN
iajs-2677	209	10	)	)	PUNCT
iajs-2677	210	1	=	=	SYM
iajs-2677	210	2	tmax(edd	tmax(edd	PROPN
iajs-2677	210	3	)	)	PUNCT
iajs-2677	210	4	.	.	PUNCT
iajs-2677	211	1	compute	compute	PROPN
iajs-2677	211	2	zi	zi	NOUN
iajs-2677	211	3	=	=	PUNCT
iajs-2677	211	4	emax	emax	X
iajs-2677	211	5	(	(	PUNCT
iajs-2677	211	6	σi	σi	NOUN
iajs-2677	211	7	)	)	PUNCT
iajs-2677	211	8	+	+	CCONJ
iajs-2677	211	9	tmax(σi	tmax(σi	NOUN
iajs-2677	211	10	)	)	PUNCT
iajs-2677	211	11	∀i	∀i	NOUN
iajs-2677	211	12	,	,	PUNCT
iajs-2677	211	13	i	i	PRON
iajs-2677	211	14	=	=	NOUN
iajs-2677	211	15	1	1	NUM
iajs-2677	211	16	,	,	PUNCT
iajs-2677	211	17	…	…	PUNCT
iajs-2677	211	18	,	,	PUNCT
iajs-2677	211	19	k	k	X
iajs-2677	211	20	.	.	PUNCT
iajs-2677	212	1	also	also	ADV
iajs-2677	212	2	compute	compute	VERB
iajs-2677	212	3	:	:	PUNCT
iajs-2677	212	4	zj	zj	PROPN
iajs-2677	212	5	=	=	PUNCT
iajs-2677	212	6	emax	emax	X
iajs-2677	212	7	(	(	PUNCT
iajs-2677	212	8	σ∗	σ∗	PROPN
iajs-2677	212	9	j	j	PROPN
iajs-2677	212	10	)	)	PUNCT
iajs-2677	213	1	+	+	CCONJ
iajs-2677	213	2	tmax(σ∗	tmax(σ∗	PROPN
iajs-2677	213	3	j	j	PROPN
iajs-2677	213	4	)	)	PUNCT
iajs-2677	213	5	∀j	∀j	PROPN
iajs-2677	213	6	,	,	PUNCT
iajs-2677	213	7	j	j	NOUN
iajs-2677	213	8	=	=	SYM
iajs-2677	213	9	1	1	NUM
iajs-2677	213	10	,	,	PUNCT
iajs-2677	213	11	…	…	PUNCT
iajs-2677	213	12	,	,	PUNCT
iajs-2677	213	13	k1	k1	PROPN
iajs-2677	213	14	.	.	PUNCT
iajs-2677	214	1	we	we	PRON
iajs-2677	214	2	get	get	VERB
iajs-2677	214	3	a	a	DET
iajs-2677	214	4	set	set	NOUN
iajs-2677	214	5	of	of	ADP
iajs-2677	214	6	solutions	solution	NOUN
iajs-2677	214	7	zi	zi	PROPN
iajs-2677	214	8	and	and	CCONJ
iajs-2677	214	9	zj	zj	PROPN
iajs-2677	214	10	which	which	PRON
iajs-2677	214	11	are	be	AUX
iajs-2677	214	12	upper	upper	ADJ
iajs-2677	214	13	bounds	bound	NOUN
iajs-2677	214	14	of	of	ADP
iajs-2677	214	15	the	the	DET
iajs-2677	214	16	problem	problem	NOUN
iajs-2677	214	17	(	(	PUNCT
iajs-2677	214	18	p1	p1	NOUN
iajs-2677	214	19	)	)	PUNCT
iajs-2677	214	20	.	.	PUNCT
iajs-2677	215	1	this	this	PRON
iajs-2677	215	2	means	mean	VERB
iajs-2677	215	3	that	that	SCONJ
iajs-2677	215	4	they	they	PRON
iajs-2677	215	5	are	be	AUX
iajs-2677	215	6	greater	great	ADJ
iajs-2677	215	7	than	than	ADP
iajs-2677	215	8	or	or	CCONJ
iajs-2677	215	9	equal	equal	ADJ
iajs-2677	215	10	to	to	ADP
iajs-2677	215	11	the	the	DET
iajs-2677	215	12	optimal	optimal	ADJ
iajs-2677	215	13	solution	solution	NOUN
iajs-2677	215	14	.	.	PUNCT
iajs-2677	216	1	let	let	VERB
iajs-2677	216	2	z∗	z∗	PROPN
iajs-2677	216	3	be	be	AUX
iajs-2677	216	4	the	the	DET
iajs-2677	216	5	minimum	minimum	ADJ
iajs-2677	216	6	one	one	NUM
iajs-2677	216	7	of	of	ADP
iajs-2677	216	8	zi	zi	PROPN
iajs-2677	216	9	and	and	CCONJ
iajs-2677	216	10	zj	zj	PROPN
iajs-2677	216	11	.	.	PROPN
iajs-2677	216	12	from	from	ADP
iajs-2677	216	13	the	the	DET
iajs-2677	216	14	theorem	theorem	NOUN
iajs-2677	216	15	,	,	PUNCT
iajs-2677	216	16	we	we	PRON
iajs-2677	216	17	have	have	AUX
iajs-2677	216	18	opt	opt	VERB
iajs-2677	216	19	.	.	PUNCT
iajs-2677	217	1	=	=	PUNCT
iajs-2677	218	1	lb	lb	X
iajs-2677	218	2	+	+	CCONJ
iajs-2677	218	3	r	r	NOUN
iajs-2677	218	4	,	,	PUNCT
iajs-2677	218	5	where	where	SCONJ
iajs-2677	218	6	r	r	NOUN
iajs-2677	218	7	∈	∈	PROPN
iajs-2677	219	1	[	[	X
iajs-2677	219	2	n1	n1	NOUN
iajs-2677	219	3	−	−	PROPN
iajs-2677	219	4	1	1	NUM
iajs-2677	219	5	,	,	PUNCT
iajs-2677	219	6	n2	n2	ADJ
iajs-2677	219	7	+	+	CCONJ
iajs-2677	219	8	1	1	NUM
iajs-2677	219	9	]	]	PUNCT
iajs-2677	219	10	.	.	PUNCT
iajs-2677	220	1	now	now	ADV
iajs-2677	220	2	we	we	PRON
iajs-2677	220	3	have	have	VERB
iajs-2677	220	4	the	the	DET
iajs-2677	220	5	possible	possible	ADJ
iajs-2677	220	6	cases	case	NOUN
iajs-2677	220	7	for	for	ADP
iajs-2677	220	8	the	the	DET
iajs-2677	220	9	optimal	optimal	ADJ
iajs-2677	220	10	.	.	PUNCT
iajs-2677	221	1	if	if	SCONJ
iajs-2677	221	2	n1	n1	PROPN
iajs-2677	221	3	=	=	SYM
iajs-2677	221	4	1	1	NUM
iajs-2677	221	5	,	,	PUNCT
iajs-2677	221	6	implies	imply	VERB
iajs-2677	221	7	that	that	SCONJ
iajs-2677	221	8	r	r	NOUN
iajs-2677	221	9	∈	∈	PROPN
iajs-2677	221	10	[	[	X
iajs-2677	221	11	0	0	NUM
iajs-2677	221	12	,	,	PUNCT
iajs-2677	221	13	n2	n2	ADJ
iajs-2677	221	14	+	+	CCONJ
iajs-2677	221	15	1	1	NUM
iajs-2677	221	16	]	]	PUNCT
iajs-2677	221	17	,	,	PUNCT
iajs-2677	221	18	opt	opt	PROPN
iajs-2677	221	19	.	.	PUNCT
iajs-2677	222	1	=	=	PUNCT
iajs-2677	223	1	lb	lb	X
iajs-2677	223	2	+	+	NOUN
iajs-2677	223	3	0	0	NUM
iajs-2677	223	4	.	.	PUNCT
iajs-2677	224	1	if	if	SCONJ
iajs-2677	224	2	n1	n1	PROPN
iajs-2677	224	3	=	=	SYM
iajs-2677	224	4	2	2	NUM
iajs-2677	224	5	,	,	PUNCT
iajs-2677	224	6	implies	imply	VERB
iajs-2677	224	7	that	that	SCONJ
iajs-2677	224	8	r	r	NOUN
iajs-2677	224	9	∈	∈	PROPN
iajs-2677	224	10	[	[	X
iajs-2677	224	11	1	1	NUM
iajs-2677	224	12	,	,	PUNCT
iajs-2677	224	13	n2	n2	ADJ
iajs-2677	224	14	+	+	CCONJ
iajs-2677	224	15	1	1	NUM
iajs-2677	224	16	]	]	PUNCT
iajs-2677	224	17	,	,	PUNCT
iajs-2677	224	18	opt	opt	PROPN
iajs-2677	224	19	.	.	PUNCT
iajs-2677	225	1	=	=	PUNCT
iajs-2677	226	1	lb	lb	X
iajs-2677	226	2	+	+	NUM
iajs-2677	226	3	1	1	NUM
iajs-2677	226	4	,	,	PUNCT
iajs-2677	226	5	and	and	CCONJ
iajs-2677	226	6	so	so	ADV
iajs-2677	226	7	on	on	ADV
iajs-2677	226	8	.	.	PUNCT
iajs-2677	227	1	since	since	SCONJ
iajs-2677	227	2	we	we	PRON
iajs-2677	227	3	have	have	VERB
iajs-2677	227	4	z∗	z∗	NOUN
iajs-2677	227	5	as	as	ADP
iajs-2677	227	6	the	the	DET
iajs-2677	227	7	minimum	minimum	ADJ
iajs-2677	227	8	upper	upper	ADJ
iajs-2677	227	9	bound	bind	VERB
iajs-2677	227	10	,	,	PUNCT
iajs-2677	227	11	so	so	CCONJ
iajs-2677	227	12	if	if	SCONJ
iajs-2677	227	13	opt	opt	VERB
iajs-2677	227	14	.	.	PUNCT
iajs-2677	228	1	=	=	PUNCT
iajs-2677	229	1	lb	lb	X
iajs-2677	229	2	+	+	NUM
iajs-2677	229	3	1	1	NUM
iajs-2677	229	4	>	>	X
iajs-2677	229	5	z∗	z∗	NOUN
iajs-2677	229	6	stop	stop	VERB
iajs-2677	229	7	the	the	DET
iajs-2677	229	8	process	process	NOUN
iajs-2677	229	9	.	.	PUNCT
iajs-2677	230	1	for	for	ADP
iajs-2677	230	2	the	the	DET
iajs-2677	230	3	acceptable	acceptable	ADJ
iajs-2677	230	4	values	value	NOUN
iajs-2677	230	5	of	of	ADP
iajs-2677	230	6	r	r	NOUN
iajs-2677	230	7	we	we	PRON
iajs-2677	230	8	start	start	VERB
iajs-2677	230	9	with	with	ADP
iajs-2677	230	10	r	r	NOUN
iajs-2677	230	11	=	=	SYM
iajs-2677	230	12	0	0	NUM
iajs-2677	230	13	.	.	PUNCT
iajs-2677	231	1	it	it	PRON
iajs-2677	231	2	is	be	AUX
iajs-2677	231	3	a	a	DET
iajs-2677	231	4	special	special	ADJ
iajs-2677	231	5	case	case	NOUN
iajs-2677	231	6	where	where	SCONJ
iajs-2677	231	7	tmax(mst	tmax(mst	VERB
iajs-2677	231	8	)	)	PUNCT
iajs-2677	231	9	=	=	SYM
iajs-2677	231	10	tmax(edd	tmax(edd	NOUN
iajs-2677	231	11	)	)	PUNCT
iajs-2677	231	12	,	,	PUNCT
iajs-2677	231	13	in	in	ADP
iajs-2677	231	14	this	this	DET
iajs-2677	231	15	case	case	NOUN
iajs-2677	231	16	,	,	PUNCT
iajs-2677	231	17	one	one	PRON
iajs-2677	231	18	can	can	AUX
iajs-2677	231	19	find	find	VERB
iajs-2677	231	20	the	the	DET
iajs-2677	231	21	optimal	optimal	ADJ
iajs-2677	231	22	solution	solution	NOUN
iajs-2677	231	23	directly	directly	ADV
iajs-2677	231	24	.	.	PUNCT
iajs-2677	232	1	if	if	SCONJ
iajs-2677	232	2	not	not	PART
iajs-2677	232	3	.	.	PUNCT
iajs-2677	233	1	we	we	PRON
iajs-2677	233	2	check	check	VERB
iajs-2677	233	3	for	for	ADP
iajs-2677	233	4	r	r	NOUN
iajs-2677	233	5	=	=	SYM
iajs-2677	233	6	1	1	NUM
iajs-2677	233	7	.	.	PUNCT
iajs-2677	234	1	if	if	SCONJ
iajs-2677	234	2	there	there	PRON
iajs-2677	234	3	exists	exist	VERB
iajs-2677	234	4	a	a	DET
iajs-2677	234	5	sequence	sequence	NOUN
iajs-2677	234	6	π∗	π∗	PROPN
iajs-2677	234	7	∈	∈	PROPN
iajs-2677	234	8	s1	s1	PROPN
iajs-2677	234	9	∪	∪	NOUN
iajs-2677	234	10	s	s	PRON
iajs-2677	234	11	such	such	ADJ
iajs-2677	234	12	that	that	DET
iajs-2677	234	13	emax(π∗	emax(π∗	NOUN
iajs-2677	234	14	)	)	PUNCT
iajs-2677	235	1	+	+	CCONJ
iajs-2677	235	2	tmax(π∗	tmax(π∗	ADJ
iajs-2677	235	3	)	)	PUNCT
iajs-2677	235	4	=	=	SYM
iajs-2677	236	1	lb	lb	NUM
iajs-2677	237	1	+	+	NUM
iajs-2677	237	2	1	1	NUM
iajs-2677	237	3	,	,	PUNCT
iajs-2677	237	4	so	so	SCONJ
iajs-2677	237	5	it	it	PRON
iajs-2677	237	6	is	be	AUX
iajs-2677	237	7	optimal	optimal	ADJ
iajs-2677	237	8	,	,	PUNCT
iajs-2677	237	9	otherwise	otherwise	ADV
iajs-2677	237	10	solve	solve	VERB
iajs-2677	237	11	(	(	PUNCT
iajs-2677	237	12	p1	p1	NOUN
iajs-2677	237	13	)	)	PUNCT
iajs-2677	237	14	using	use	VERB
iajs-2677	237	15	modified	modified	ADJ
iajs-2677	237	16	smith	smith	PROPN
iajs-2677	237	17	’s	’s	PART
iajs-2677	237	18	algorithm	algorithm	NOUN
iajs-2677	237	19	with	with	ADP
iajs-2677	237	20	given	give	VERB
iajs-2677	237	21	tmax(edd	tmax(edd	NOUN
iajs-2677	237	22	)	)	PUNCT
iajs-2677	237	23	.	.	PUNCT
iajs-2677	238	1	if	if	SCONJ
iajs-2677	238	2	a	a	DET
iajs-2677	238	3	solution	solution	NOUN
iajs-2677	238	4	exists	exist	VERB
iajs-2677	238	5	,	,	PUNCT
iajs-2677	238	6	it	it	PRON
iajs-2677	238	7	is	be	AUX
iajs-2677	238	8	optimal	optimal	ADJ
iajs-2677	238	9	otherwise	otherwise	ADV
iajs-2677	238	10	check	check	NOUN
iajs-2677	238	11	for	for	ADP
iajs-2677	238	12	r	r	NOUN
iajs-2677	238	13	=	=	SYM
iajs-2677	238	14	2	2	NUM
iajs-2677	238	15	.	.	PUNCT
iajs-2677	239	1	the	the	DET
iajs-2677	239	2	proposed	propose	VERB
iajs-2677	239	3	algorithm	algorithm	NOUN
iajs-2677	239	4	:	:	PUNCT
iajs-2677	239	5	step	step	NOUN
iajs-2677	239	6	(	(	PUNCT
iajs-2677	239	7	1	1	NUM
iajs-2677	239	8	):	):	PUNCT
iajs-2677	239	9	find	find	VERB
iajs-2677	239	10	efficient	efficient	ADJ
iajs-2677	239	11	solutions	solution	NOUN
iajs-2677	239	12	for	for	ADP
iajs-2677	239	13	(	(	PUNCT
iajs-2677	239	14	p3	p3	PROPN
iajs-2677	239	15	)	)	PUNCT
iajs-2677	239	16	,	,	PUNCT
iajs-2677	239	17	say	say	VERB
iajs-2677	239	18	s1=	s1=	PROPN
iajs-2677	239	19	{	{	PUNCT
iajs-2677	239	20	σ1	σ1	PROPN
iajs-2677	239	21	,	,	PUNCT
iajs-2677	239	22	σ2	σ2	PROPN
iajs-2677	239	23	,	,	PUNCT
iajs-2677	239	24	…	…	PUNCT
iajs-2677	239	25	,	,	PUNCT
iajs-2677	239	26	σk	σk	ADP
iajs-2677	239	27	}	}	PUNCT
iajs-2677	239	28	and	and	CCONJ
iajs-2677	239	29	for	for	ADP
iajs-2677	239	30	(	(	PUNCT
iajs-2677	239	31	p2	p2	NOUN
iajs-2677	239	32	)	)	PUNCT
iajs-2677	239	33	,	,	PUNCT
iajs-2677	239	34	say	say	VERB
iajs-2677	239	35	s	s	X
iajs-2677	239	36	=	=	PUNCT
iajs-2677	239	37	{	{	PUNCT
iajs-2677	239	38	σ∗	σ∗	NOUN
iajs-2677	239	39	1	1	NUM
iajs-2677	239	40	,	,	PUNCT
iajs-2677	239	41	σ∗	σ∗	X
iajs-2677	239	42	2	2	NUM
iajs-2677	239	43	,	,	PUNCT
iajs-2677	239	44	…	…	PUNCT
iajs-2677	239	45	,	,	PUNCT
iajs-2677	239	46	σk1	σk1	NOUN
iajs-2677	239	47	∗	∗	NOUN
iajs-2677	239	48	}	}	PUNCT
iajs-2677	239	49	.	.	PUNCT
iajs-2677	240	1	n1	n1	PROPN
iajs-2677	240	2	is	be	AUX
iajs-2677	240	3	the	the	DET
iajs-2677	240	4	number	number	NOUN
iajs-2677	240	5	of	of	ADP
iajs-2677	240	6	efficient	efficient	ADJ
iajs-2677	240	7	solutions	solution	NOUN
iajs-2677	240	8	of	of	ADP
iajs-2677	240	9	(	(	PUNCT
iajs-2677	240	10	p1	p1	PROPN
iajs-2677	240	11	)	)	PUNCT
iajs-2677	240	12	,	,	PUNCT
iajs-2677	240	13	n2	n2	NOUN
iajs-2677	240	14	=	=	SYM
iajs-2677	240	15	tmax(mst	tmax(mst	NOUN
iajs-2677	240	16	)	)	PUNCT
iajs-2677	240	17	−	−	PROPN
iajs-2677	241	1	tmax	tmax	PROPN
iajs-2677	241	2	(	(	PUNCT
iajs-2677	241	3	edd	edd	PROPN
iajs-2677	241	4	)	)	PUNCT
iajs-2677	241	5	and	and	CCONJ
iajs-2677	241	6	lb	lb	X
iajs-2677	241	7	=	=	PUNCT
iajs-2677	241	8	emax(mst	emax(mst	PROPN
iajs-2677	241	9	)	)	PUNCT
iajs-2677	242	1	+	+	CCONJ
iajs-2677	242	2	tmax	tmax	PROPN
iajs-2677	242	3	(	(	PUNCT
iajs-2677	242	4	edd	edd	PROPN
iajs-2677	242	5	)	)	PUNCT
iajs-2677	242	6	.	.	PUNCT
iajs-2677	243	1	step	step	NOUN
iajs-2677	243	2	(	(	PUNCT
iajs-2677	243	3	2	2	NUM
iajs-2677	243	4	):	):	PUNCT
iajs-2677	243	5	compute	compute	NOUN
iajs-2677	243	6	zi	zi	NOUN
iajs-2677	243	7	=	=	PUNCT
iajs-2677	243	8	emax	emax	X
iajs-2677	243	9	(	(	PUNCT
iajs-2677	243	10	σi	σi	NOUN
iajs-2677	243	11	)	)	PUNCT
iajs-2677	243	12	+	+	CCONJ
iajs-2677	243	13	tmax(σi	tmax(σi	NOUN
iajs-2677	243	14	)	)	PUNCT
iajs-2677	243	15	∀i	∀i	NOUN
iajs-2677	243	16	,	,	PUNCT
iajs-2677	243	17	i	i	PRON
iajs-2677	243	18	=	=	NOUN
iajs-2677	243	19	1	1	NUM
iajs-2677	243	20	,	,	PUNCT
iajs-2677	243	21	…	…	PUNCT
iajs-2677	243	22	,	,	PUNCT
iajs-2677	243	23	k	k	NOUN
iajs-2677	243	24	,	,	PUNCT
iajs-2677	243	25	and	and	CCONJ
iajs-2677	243	26	compute	compute	PROPN
iajs-2677	243	27	zj	zj	PROPN
iajs-2677	243	28	=	=	PROPN
iajs-2677	243	29	emax	emax	X
iajs-2677	243	30	(	(	PUNCT
iajs-2677	243	31	σ∗	σ∗	PROPN
iajs-2677	243	32	j	j	PROPN
iajs-2677	243	33	)	)	PUNCT
iajs-2677	244	1	+	+	CCONJ
iajs-2677	244	2	tmax(σ∗	tmax(σ∗	PROPN
iajs-2677	244	3	j	j	PROPN
iajs-2677	244	4	)	)	PUNCT
iajs-2677	244	5	∀j	∀j	PROPN
iajs-2677	244	6	,	,	PUNCT
iajs-2677	244	7	j	j	NOUN
iajs-2677	244	8	=	=	SYM
iajs-2677	244	9	1	1	NUM
iajs-2677	244	10	,	,	PUNCT
iajs-2677	244	11	…	…	PUNCT
iajs-2677	244	12	,	,	PUNCT
iajs-2677	244	13	k1	k1	X
iajs-2677	244	14	.	.	PUNCT
iajs-2677	244	15	z∗	z∗	PROPN
iajs-2677	244	16	is	be	AUX
iajs-2677	244	17	minimum	minimum	NOUN
iajs-2677	244	18	of	of	ADP
iajs-2677	244	19	zi	zi	PROPN
iajs-2677	244	20	and	and	CCONJ
iajs-2677	244	21	zj	zj	PROPN
iajs-2677	244	22	.	.	PROPN
iajs-2677	244	23	step	step	NOUN
iajs-2677	244	24	(	(	PUNCT
iajs-2677	244	25	3	3	NUM
iajs-2677	244	26	):	):	PUNCT
iajs-2677	244	27	if	if	SCONJ
iajs-2677	244	28	tmax(mst	tmax(mst	ADJ
iajs-2677	244	29	)	)	PUNCT
iajs-2677	244	30	=	=	SYM
iajs-2677	244	31	tmax(edd	tmax(edd	PROPN
iajs-2677	244	32	)	)	PUNCT
iajs-2677	244	33	,	,	PUNCT
iajs-2677	244	34	then	then	ADV
iajs-2677	244	35	edd	edd	PROPN
iajs-2677	244	36	-	-	PUNCT
iajs-2677	244	37	rule	rule	NOUN
iajs-2677	244	38	as	as	ADV
iajs-2677	244	39	well	well	ADV
iajs-2677	244	40	mst	mst	NOUN
iajs-2677	244	41	-	-	PUNCT
iajs-2677	244	42	rule	rule	NOUN
iajs-2677	244	43	give	give	VERB
iajs-2677	244	44	optimal	optimal	ADJ
iajs-2677	244	45	solution	solution	NOUN
iajs-2677	244	46	.	.	PUNCT
iajs-2677	245	1	go	go	VERB
iajs-2677	245	2	to	to	PART
iajs-2677	245	3	step	step	VERB
iajs-2677	245	4	(	(	PUNCT
iajs-2677	245	5	7	7	NUM
iajs-2677	245	6	)	)	PUNCT
iajs-2677	245	7	.	.	PUNCT
iajs-2677	246	1	else	else	ADV
iajs-2677	246	2	,	,	PUNCT
iajs-2677	246	3	go	go	VERB
iajs-2677	246	4	to	to	PART
iajs-2677	246	5	step	step	VERB
iajs-2677	246	6	(	(	PUNCT
iajs-2677	246	7	4	4	NUM
iajs-2677	246	8	)	)	PUNCT
iajs-2677	246	9	.	.	PUNCT
iajs-2677	247	1	step	step	NOUN
iajs-2677	247	2	(	(	PUNCT
iajs-2677	247	3	4	4	NUM
iajs-2677	247	4	):	):	PUNCT
iajs-2677	247	5	find	find	VERB
iajs-2677	247	6	values	value	NOUN
iajs-2677	247	7	of	of	ADP
iajs-2677	247	8	r	r	NOUN
iajs-2677	247	9	such	such	ADJ
iajs-2677	247	10	that	that	SCONJ
iajs-2677	247	11	r	r	NOUN
iajs-2677	247	12	∈	∈	PROPN
iajs-2677	248	1	[	[	X
iajs-2677	248	2	n1	n1	NOUN
iajs-2677	248	3	−	−	PROPN
iajs-2677	248	4	1	1	NUM
iajs-2677	248	5	,	,	PUNCT
iajs-2677	248	6	n2	n2	ADJ
iajs-2677	248	7	+	+	CCONJ
iajs-2677	248	8	1	1	NUM
iajs-2677	248	9	]	]	PUNCT
iajs-2677	248	10	,	,	PUNCT
iajs-2677	248	11	stop	stop	VERB
iajs-2677	248	12	if	if	SCONJ
iajs-2677	248	13	r	r	NOUN
iajs-2677	248	14	>	>	X
iajs-2677	248	15	n2	n2	NOUN
iajs-2677	248	16	+	+	CCONJ
iajs-2677	248	17	1	1	NUM
iajs-2677	248	18	or	or	CCONJ
iajs-2677	248	19	r	r	X
iajs-2677	248	20	>	>	X
iajs-2677	248	21	z∗	z∗	NOUN
iajs-2677	248	22	,	,	PUNCT
iajs-2677	248	23	r	r	NOUN
iajs-2677	248	24	=	=	SYM
iajs-2677	248	25	1	1	X
iajs-2677	248	26	.	.	X
iajs-2677	248	27	step	step	NOUN
iajs-2677	248	28	(	(	PUNCT
iajs-2677	248	29	5	5	NUM
iajs-2677	248	30	):	):	PUNCT
iajs-2677	248	31	if	if	SCONJ
iajs-2677	248	32	there	there	PRON
iajs-2677	248	33	exists	exist	VERB
iajs-2677	248	34	a	a	DET
iajs-2677	248	35	sequence	sequence	NOUN
iajs-2677	248	36	π∗	π∗	PROPN
iajs-2677	248	37	∈	∈	PROPN
iajs-2677	248	38	s1	s1	PROPN
iajs-2677	248	39	∪	∪	NOUN
iajs-2677	248	40	s	s	PRON
iajs-2677	248	41	such	such	ADJ
iajs-2677	248	42	that	that	DET
iajs-2677	248	43	emax(π∗	emax(π∗	NOUN
iajs-2677	248	44	)	)	PUNCT
iajs-2677	249	1	+	+	CCONJ
iajs-2677	249	2	tmax(π∗	tmax(π∗	ADJ
iajs-2677	249	3	)	)	PUNCT
iajs-2677	249	4	=	=	SYM
iajs-2677	250	1	lb	lb	X
iajs-2677	250	2	+	+	CCONJ
iajs-2677	250	3	r	r	NOUN
iajs-2677	250	4	,	,	PUNCT
iajs-2677	250	5	so	so	SCONJ
iajs-2677	250	6	it	it	PRON
iajs-2677	250	7	is	be	AUX
iajs-2677	250	8	optimal	optimal	ADJ
iajs-2677	250	9	and	and	CCONJ
iajs-2677	250	10	go	go	VERB
iajs-2677	250	11	to	to	PART
iajs-2677	250	12	step	step	VERB
iajs-2677	250	13	(	(	PUNCT
iajs-2677	250	14	7	7	NUM
iajs-2677	250	15	)	)	PUNCT
iajs-2677	250	16	.	.	PUNCT
iajs-2677	251	1	else	else	ADV
iajs-2677	251	2	,	,	PUNCT
iajs-2677	251	3	go	go	VERB
iajs-2677	251	4	to	to	PART
iajs-2677	251	5	step	step	VERB
iajs-2677	251	6	(	(	PUNCT
iajs-2677	251	7	6	6	NUM
iajs-2677	251	8	)	)	PUNCT
iajs-2677	251	9	.	.	PUNCT
iajs-2677	252	1	ibn	ibn	PROPN
iajs-2677	252	2	al	al	PROPN
iajs-2677	252	3	-	-	PUNCT
iajs-2677	252	4	haitham	haitham	PROPN
iajs-2677	252	5	jour	jour	X
iajs-2677	252	6	.	.	PROPN
iajs-2677	252	7	for	for	ADP
iajs-2677	252	8	pure	pure	ADJ
iajs-2677	252	9	&	&	CCONJ
iajs-2677	252	10	appl	appl	PROPN
iajs-2677	252	11	.	.	PUNCT
iajs-2677	253	1	sci	sci	PROPN
iajs-2677	253	2	.	.	PROPN
iajs-2677	254	1	34(3)2021	34(3)2021	NUM
iajs-2677	254	2	57	57	NUM
iajs-2677	254	3	step	step	NOUN
iajs-2677	254	4	(	(	PUNCT
iajs-2677	254	5	6	6	NUM
iajs-2677	254	6	):	):	PUNCT
iajs-2677	254	7	use	use	VERB
iajs-2677	254	8	modified	modify	VERB
iajs-2677	254	9	smith	smith	PROPN
iajs-2677	254	10	’s	’s	PART
iajs-2677	254	11	algorithm	algorithm	NOUN
iajs-2677	254	12	for	for	ADP
iajs-2677	254	13	given	give	VERB
iajs-2677	254	14	tmax(edd	tmax(edd	NOUN
iajs-2677	254	15	)	)	PUNCT
iajs-2677	254	16	.	.	PUNCT
iajs-2677	255	1	if	if	SCONJ
iajs-2677	255	2	a	a	DET
iajs-2677	255	3	solution	solution	NOUN
iajs-2677	255	4	exists	exist	VERB
iajs-2677	255	5	,	,	PUNCT
iajs-2677	255	6	it	it	PRON
iajs-2677	255	7	is	be	AUX
iajs-2677	255	8	optimal	optimal	ADJ
iajs-2677	255	9	.	.	PUNCT
iajs-2677	256	1	go	go	VERB
iajs-2677	256	2	to	to	PART
iajs-2677	256	3	step	step	VERB
iajs-2677	256	4	(	(	PUNCT
iajs-2677	256	5	7	7	NUM
iajs-2677	256	6	)	)	PUNCT
iajs-2677	256	7	.	.	PUNCT
iajs-2677	257	1	else	else	ADV
iajs-2677	257	2	,	,	PUNCT
iajs-2677	257	3	r	r	NOUN
iajs-2677	257	4	=	=	SYM
iajs-2677	257	5	r	r	NOUN
iajs-2677	257	6	+	+	NOUN
iajs-2677	257	7	1	1	X
iajs-2677	257	8	.	.	X
iajs-2677	257	9	go	go	VERB
iajs-2677	257	10	to	to	PART
iajs-2677	257	11	step	step	VERB
iajs-2677	257	12	(	(	PUNCT
iajs-2677	257	13	5	5	NUM
iajs-2677	257	14	)	)	PUNCT
iajs-2677	257	15	.	.	PUNCT
iajs-2677	258	1	step	step	NOUN
iajs-2677	258	2	(	(	PUNCT
iajs-2677	258	3	7	7	NUM
iajs-2677	258	4	):	):	PUNCT
iajs-2677	258	5	stop	stop	NOUN
iajs-2677	258	6	.	.	PUNCT
iajs-2677	259	1	example	example	NOUN
iajs-2677	259	2	:	:	PUNCT
iajs-2677	259	3	consider	consider	VERB
iajs-2677	259	4	a	a	DET
iajs-2677	259	5	4	4	NUM
iajs-2677	259	6	job	job	NOUN
iajs-2677	259	7	problem	problem	NOUN
iajs-2677	259	8	with	with	ADP
iajs-2677	259	9	the	the	DET
iajs-2677	259	10	following	follow	VERB
iajs-2677	259	11	given	give	VERB
iajs-2677	259	12	data	datum	NOUN
iajs-2677	259	13	j	j	PROPN
iajs-2677	259	14	1	1	NUM
iajs-2677	259	15	2	2	NUM
iajs-2677	259	16	3	3	NUM
iajs-2677	259	17	4	4	NUM
iajs-2677	259	18	pj	pj	PROPN
iajs-2677	259	19	5	5	NUM
iajs-2677	259	20	3	3	NUM
iajs-2677	259	21	2	2	NUM
iajs-2677	259	22	7	7	NUM
iajs-2677	259	23	dj	dj	NOUN
iajs-2677	259	24	8	8	NUM
iajs-2677	259	25	6	6	NUM
iajs-2677	259	26	11	11	NUM
iajs-2677	259	27	7	7	NUM
iajs-2677	259	28	at	at	ADP
iajs-2677	259	29	first	first	ADV
iajs-2677	259	30	,	,	PUNCT
iajs-2677	259	31	we	we	PRON
iajs-2677	259	32	find	find	VERB
iajs-2677	259	33	efficient	efficient	ADJ
iajs-2677	259	34	solutions	solution	NOUN
iajs-2677	259	35	for	for	ADP
iajs-2677	259	36	the	the	DET
iajs-2677	259	37	problems	problem	NOUN
iajs-2677	259	38	(	(	PUNCT
iajs-2677	259	39	p2	p2	PROPN
iajs-2677	259	40	)	)	PUNCT
iajs-2677	259	41	and	and	CCONJ
iajs-2677	259	42	(	(	PUNCT
iajs-2677	259	43	p3	p3	PROPN
iajs-2677	259	44	)	)	PUNCT
iajs-2677	259	45	by	by	ADP
iajs-2677	259	46	suitable	suitable	ADJ
iajs-2677	259	47	algorithms	algorithm	NOUN
iajs-2677	259	48	.	.	PUNCT
iajs-2677	260	1	the	the	DET
iajs-2677	260	2	results	result	NOUN
iajs-2677	260	3	are	be	AUX
iajs-2677	260	4	in	in	ADP
iajs-2677	260	5	the	the	DET
iajs-2677	260	6	following	follow	VERB
iajs-2677	260	7	table	table	NOUN
iajs-2677	260	8	.	.	PUNCT
iajs-2677	261	1	we	we	PRON
iajs-2677	261	2	characterize	characterize	VERB
iajs-2677	261	3	each	each	DET
iajs-2677	261	4	efficient	efficient	ADJ
iajs-2677	261	5	solution	solution	NOUN
iajs-2677	261	6	for	for	ADP
iajs-2677	261	7	each	each	DET
iajs-2677	261	8	problem	problem	NOUN
iajs-2677	261	9	by	by	ADP
iajs-2677	261	10			NOUN
iajs-2677	261	11	,	,	PUNCT
iajs-2677	261	12	and	and	CCONJ
iajs-2677	261	13	the	the	DET
iajs-2677	261	14	other	other	ADJ
iajs-2677	261	15	solutions	solution	NOUN
iajs-2677	261	16	are	be	AUX
iajs-2677	261	17	the	the	DET
iajs-2677	261	18	corresponding	corresponding	ADJ
iajs-2677	261	19	solutions	solution	NOUN
iajs-2677	261	20	.	.	PUNCT
iajs-2677	262	1	s1	s1	NOUN
iajs-2677	262	2	=	=	PUNCT
iajs-2677	262	3	{	{	PUNCT
iajs-2677	262	4	(	(	PUNCT
iajs-2677	262	5	3	3	NUM
iajs-2677	262	6	,	,	PUNCT
iajs-2677	262	7	2	2	NUM
iajs-2677	262	8	,	,	PUNCT
iajs-2677	262	9	1	1	NUM
iajs-2677	262	10	,	,	PUNCT
iajs-2677	262	11	4	4	NUM
iajs-2677	262	12	)	)	PUNCT
iajs-2677	262	13	,	,	PUNCT
iajs-2677	262	14	(	(	PUNCT
iajs-2677	262	15	2	2	NUM
iajs-2677	262	16	,	,	PUNCT
iajs-2677	262	17	3	3	NUM
iajs-2677	262	18	,	,	PUNCT
iajs-2677	262	19	1	1	NUM
iajs-2677	262	20	,	,	PUNCT
iajs-2677	262	21	4	4	NUM
iajs-2677	262	22	)	)	PUNCT
iajs-2677	262	23	,	,	PUNCT
iajs-2677	262	24	(	(	PUNCT
iajs-2677	262	25	2	2	NUM
iajs-2677	262	26	,	,	PUNCT
iajs-2677	262	27	1	1	NUM
iajs-2677	262	28	,	,	PUNCT
iajs-2677	262	29	3	3	NUM
iajs-2677	262	30	,	,	PUNCT
iajs-2677	262	31	4	4	NUM
iajs-2677	262	32	)	)	PUNCT
iajs-2677	262	33	,	,	PUNCT
iajs-2677	262	34	(	(	PUNCT
iajs-2677	262	35	4	4	NUM
iajs-2677	262	36	,	,	PUNCT
iajs-2677	262	37	2	2	NUM
iajs-2677	262	38	,	,	PUNCT
iajs-2677	262	39	3	3	NUM
iajs-2677	262	40	,	,	PUNCT
iajs-2677	262	41	1	1	NUM
iajs-2677	262	42	)	)	PUNCT
iajs-2677	262	43	}	}	PUNCT
iajs-2677	262	44	,	,	PUNCT
iajs-2677	262	45	s	s	X
iajs-2677	262	46	=	=	PUNCT
iajs-2677	262	47	{	{	PUNCT
iajs-2677	262	48	(	(	PUNCT
iajs-2677	262	49	3	3	NUM
iajs-2677	262	50	,	,	PUNCT
iajs-2677	262	51	2	2	NUM
iajs-2677	262	52	,	,	PUNCT
iajs-2677	262	53	1	1	NUM
iajs-2677	262	54	,	,	PUNCT
iajs-2677	262	55	4	4	NUM
iajs-2677	262	56	)	)	PUNCT
iajs-2677	262	57	,	,	PUNCT
iajs-2677	262	58	(	(	PUNCT
iajs-2677	262	59	3	3	NUM
iajs-2677	262	60	,	,	PUNCT
iajs-2677	262	61	1	1	NUM
iajs-2677	262	62	,	,	PUNCT
iajs-2677	262	63	2	2	NUM
iajs-2677	262	64	,	,	PUNCT
iajs-2677	262	65	4	4	NUM
iajs-2677	262	66	)	)	PUNCT
iajs-2677	262	67	,	,	PUNCT
iajs-2677	262	68	(	(	PUNCT
iajs-2677	262	69	2	2	NUM
iajs-2677	262	70	,	,	PUNCT
iajs-2677	262	71	1	1	NUM
iajs-2677	262	72	,	,	PUNCT
iajs-2677	262	73	4	4	NUM
iajs-2677	262	74	,	,	PUNCT
iajs-2677	262	75	3	3	NUM
iajs-2677	262	76	)	)	PUNCT
iajs-2677	262	77	,	,	PUNCT
iajs-2677	262	78	(	(	PUNCT
iajs-2677	262	79	2	2	NUM
iajs-2677	262	80	,	,	PUNCT
iajs-2677	262	81	4	4	NUM
iajs-2677	262	82	,	,	PUNCT
iajs-2677	262	83	1	1	NUM
iajs-2677	262	84	,	,	PUNCT
iajs-2677	262	85	3	3	NUM
iajs-2677	262	86	)	)	PUNCT
iajs-2677	262	87	}	}	PUNCT
iajs-2677	262	88	,	,	PUNCT
iajs-2677	262	89	k	k	PROPN
iajs-2677	262	90	=	=	PUNCT
iajs-2677	262	91	4	4	NUM
iajs-2677	262	92	and	and	CCONJ
iajs-2677	262	93	k1=	k1=	PROPN
iajs-2677	262	94	4	4	NUM
iajs-2677	262	95	.	.	PUNCT
iajs-2677	263	1	in	in	ADP
iajs-2677	263	2	s1	s1	NOUN
iajs-2677	263	3	schedule	schedule	NOUN
iajs-2677	263	4	number	number	NOUN
iajs-2677	263	5	7	7	NUM
iajs-2677	263	6	gives	give	VERB
iajs-2677	263	7	emax	emax	NOUN
iajs-2677	263	8	(	(	PUNCT
iajs-2677	263	9	7	7	NUM
iajs-2677	263	10	)	)	PUNCT
iajs-2677	263	11	=	=	SYM
iajs-2677	263	12	emax(mst	emax(mst	PROPN
iajs-2677	263	13	)	)	PUNCT
iajs-2677	264	1	=	=	SYM
iajs-2677	264	2	0	0	NUM
iajs-2677	264	3	,	,	PUNCT
iajs-2677	264	4	and	and	CCONJ
iajs-2677	264	5	in	in	ADP
iajs-2677	264	6	s	s	NOUN
iajs-2677	264	7	schedule	schedule	NOUN
iajs-2677	264	8	number	number	NOUN
iajs-2677	264	9	6	6	NUM
iajs-2677	264	10	gives	give	VERB
iajs-2677	264	11	tmax	tmax	ADP
iajs-2677	264	12	(	(	PUNCT
iajs-2677	264	13	6	6	NUM
iajs-2677	264	14	)	)	PUNCT
iajs-2677	264	15	=	=	NOUN
iajs-2677	264	16	tmax(edd	tmax(edd	NOUN
iajs-2677	264	17	)	)	PUNCT
iajs-2677	264	18	=	=	SYM
iajs-2677	265	1	7	7	NUM
iajs-2677	265	2	(	(	PUNCT
iajs-2677	265	3	in	in	ADP
iajs-2677	265	4	this	this	DET
iajs-2677	265	5	example	example	NOUN
iajs-2677	265	6	it	it	PRON
iajs-2677	265	7	is	be	AUX
iajs-2677	265	8	edd	edd	PROPN
iajs-2677	265	9	-	-	PUNCT
iajs-2677	265	10	rule	rule	NOUN
iajs-2677	265	11	)	)	PUNCT
iajs-2677	265	12	.	.	PUNCT
iajs-2677	266	1	now	now	ADV
iajs-2677	266	2	find	find	VERB
iajs-2677	266	3	the	the	DET
iajs-2677	266	4	set	set	NOUN
iajs-2677	266	5	of	of	ADP
iajs-2677	266	6	solutions	solution	NOUN
iajs-2677	266	7	zi	zi	PROPN
iajs-2677	266	8	and	and	CCONJ
iajs-2677	266	9	zj	zj	PROPN
iajs-2677	266	10	which	which	PRON
iajs-2677	266	11	are	be	AUX
iajs-2677	266	12	in	in	ADP
iajs-2677	266	13	column	column	NOUN
iajs-2677	266	14	5	5	NUM
iajs-2677	266	15	.	.	PUNCT
iajs-2677	266	16	z∗	z∗	NOUN
iajs-2677	266	17	=	=	SYM
iajs-2677	266	18	9	9	NUM
iajs-2677	266	19	to	to	PART
iajs-2677	266	20	apply	apply	VERB
iajs-2677	266	21	the	the	DET
iajs-2677	266	22	theorem	theorem	NOUN
iajs-2677	266	23	lb	lb	X
iajs-2677	266	24	=	=	SYM
iajs-2677	266	25	7	7	NUM
iajs-2677	266	26	+	+	SYM
iajs-2677	266	27	0	0	NUM
iajs-2677	266	28	=	=	SYM
iajs-2677	266	29	7	7	NUM
iajs-2677	266	30	,	,	PUNCT
iajs-2677	266	31	n2	n2	NOUN
iajs-2677	266	32	=	=	NOUN
iajs-2677	266	33	7	7	NUM
iajs-2677	266	34	−	−	PROPN
iajs-2677	266	35	7	7	NUM
iajs-2677	266	36	=	=	SYM
iajs-2677	266	37	0	0	NUM
iajs-2677	266	38	,	,	PUNCT
iajs-2677	266	39	so	so	SCONJ
iajs-2677	266	40	r	r	NOUN
iajs-2677	266	41	∈	∈	PROPN
iajs-2677	267	1	[	[	X
iajs-2677	267	2	n1	n1	NOUN
iajs-2677	267	3	−	−	PROPN
iajs-2677	267	4	1	1	NUM
iajs-2677	267	5	,	,	PUNCT
iajs-2677	267	6	1	1	NUM
iajs-2677	267	7	]	]	PUNCT
iajs-2677	267	8	.	.	PUNCT
iajs-2677	268	1	if	if	SCONJ
iajs-2677	268	2	n1	n1	PROPN
iajs-2677	268	3	=	=	SYM
iajs-2677	268	4	1	1	NUM
iajs-2677	268	5	,	,	PUNCT
iajs-2677	268	6	implies	imply	VERB
iajs-2677	268	7	that	that	SCONJ
iajs-2677	268	8	r	r	NOUN
iajs-2677	268	9	∈	∈	PROPN
iajs-2677	269	1	[	[	X
iajs-2677	269	2	0,1	0,1	NUM
iajs-2677	269	3	]	]	PUNCT
iajs-2677	269	4	,	,	PUNCT
iajs-2677	269	5	opt	opt	PROPN
iajs-2677	269	6	.	.	PUNCT
iajs-2677	270	1	=	=	PUNCT
iajs-2677	271	1	lb	lb	X
iajs-2677	271	2	+	+	NOUN
iajs-2677	271	3	0	0	NUM
iajs-2677	271	4	=	=	SYM
iajs-2677	271	5	7	7	X
iajs-2677	271	6	.	.	PUNCT
iajs-2677	272	1	if	if	SCONJ
iajs-2677	272	2	n1	n1	PROPN
iajs-2677	272	3	=	=	SYM
iajs-2677	272	4	2	2	NUM
iajs-2677	272	5	,	,	PUNCT
iajs-2677	272	6	implies	imply	VERB
iajs-2677	272	7	that	that	SCONJ
iajs-2677	272	8	r	r	NOUN
iajs-2677	272	9	∈	∈	PROPN
iajs-2677	272	10	[	[	X
iajs-2677	272	11	1	1	NUM
iajs-2677	272	12	,	,	PUNCT
iajs-2677	272	13	1	1	NUM
iajs-2677	272	14	]	]	PUNCT
iajs-2677	272	15	,	,	PUNCT
iajs-2677	272	16	opt	opt	PROPN
iajs-2677	272	17	.	.	PUNCT
iajs-2677	273	1	=	=	PUNCT
iajs-2677	274	1	lb	lb	X
iajs-2677	274	2	+	+	NOUN
iajs-2677	274	3	1	1	NUM
iajs-2677	274	4	=	=	SYM
iajs-2677	274	5	8	8	NUM
iajs-2677	274	6	.	.	PUNCT
iajs-2677	275	1	the	the	DET
iajs-2677	275	2	possible	possible	ADJ
iajs-2677	275	3	cases	case	NOUN
iajs-2677	275	4	for	for	ADP
iajs-2677	275	5	the	the	DET
iajs-2677	275	6	optimal	optimal	ADJ
iajs-2677	275	7	value	value	NOUN
iajs-2677	275	8	are	be	AUX
iajs-2677	275	9	7	7	NUM
iajs-2677	275	10	,	,	PUNCT
iajs-2677	275	11	8	8	NUM
iajs-2677	275	12	,	,	PUNCT
iajs-2677	275	13	and	and	CCONJ
iajs-2677	275	14	9	9	X
iajs-2677	275	15	.	.	X
iajs-2677	275	16	start	start	VERB
iajs-2677	275	17	with	with	ADP
iajs-2677	275	18	r	r	NOUN
iajs-2677	275	19	=	=	SYM
iajs-2677	275	20	0	0	NUM
iajs-2677	275	21	.	.	PUNCT
iajs-2677	276	1	since	since	SCONJ
iajs-2677	276	2	there	there	PRON
iajs-2677	276	3	exists	exist	VERB
iajs-2677	276	4	no	no	DET
iajs-2677	276	5	π∗	π∗	PROPN
iajs-2677	276	6	∈	∈	PROPN
iajs-2677	276	7	s1	s1	PROPN
iajs-2677	276	8	∪	∪	NOUN
iajs-2677	276	9	s	s	PRON
iajs-2677	276	10	such	such	ADJ
iajs-2677	276	11	that	that	DET
iajs-2677	276	12	emax(π∗	emax(π∗	NOUN
iajs-2677	276	13	)	)	PUNCT
iajs-2677	277	1	+	+	CCONJ
iajs-2677	277	2	tmax(π∗	tmax(π∗	ADJ
iajs-2677	277	3	)	)	PUNCT
iajs-2677	277	4	=	=	SYM
iajs-2677	278	1	lb	lb	X
iajs-2677	278	2	+	+	NOUN
iajs-2677	278	3	0	0	NUM
iajs-2677	278	4	=	=	SYM
iajs-2677	278	5	7	7	NUM
iajs-2677	278	6	,	,	PUNCT
iajs-2677	278	7	use	use	VERB
iajs-2677	278	8	the	the	DET
iajs-2677	278	9	modified	modify	VERB
iajs-2677	278	10	smith	smith	PROPN
iajs-2677	278	11	’s	’s	PART
iajs-2677	278	12	algorithm	algorithm	NOUN
iajs-2677	278	13	,	,	PUNCT
iajs-2677	278	14	where	where	SCONJ
iajs-2677	278	15	tmax	tmax	ADV
iajs-2677	278	16	=	=	SYM
iajs-2677	278	17	tmax	tmax	X
iajs-2677	278	18	(	(	PUNCT
iajs-2677	278	19	edd	edd	PROPN
iajs-2677	278	20	)	)	PUNCT
iajs-2677	278	21	.	.	PUNCT
iajs-2677	279	1	the	the	DET
iajs-2677	279	2	solution	solution	NOUN
iajs-2677	279	3	is	be	AUX
iajs-2677	279	4	(	(	PUNCT
iajs-2677	279	5	4	4	NUM
iajs-2677	279	6	,	,	PUNCT
iajs-2677	279	7	2	2	NUM
iajs-2677	279	8	,	,	PUNCT
iajs-2677	279	9	1	1	NUM
iajs-2677	279	10	,	,	PUNCT
iajs-2677	279	11	3	3	NUM
iajs-2677	279	12	)	)	PUNCT
iajs-2677	279	13	with	with	ADP
iajs-2677	279	14	tmax	tmax	NOUN
iajs-2677	279	15	=	=	SYM
iajs-2677	279	16	7	7	NUM
iajs-2677	279	17	and	and	CCONJ
iajs-2677	279	18	emax	emax	X
iajs-2677	279	19	=	=	SYM
iajs-2677	279	20	0	0	NUM
iajs-2677	279	21	.	.	NOUN
iajs-2677	280	1	7	7	X
iajs-2677	280	2	.	.	PUNCT
iajs-2677	280	3	computational	computational	ADJ
iajs-2677	280	4	results	result	NOUN
iajs-2677	280	5	here	here	ADV
iajs-2677	280	6	,	,	PUNCT
iajs-2677	280	7	we	we	PRON
iajs-2677	280	8	will	will	AUX
iajs-2677	280	9	introduce	introduce	VERB
iajs-2677	280	10	our	our	PRON
iajs-2677	280	11	results	result	NOUN
iajs-2677	280	12	via	via	ADP
iajs-2677	280	13	computational	computational	ADJ
iajs-2677	280	14	tests	test	NOUN
iajs-2677	280	15	to	to	PART
iajs-2677	280	16	show	show	VERB
iajs-2677	280	17	the	the	DET
iajs-2677	280	18	efficiency	efficiency	NOUN
iajs-2677	280	19	of	of	ADP
iajs-2677	280	20	the	the	DET
iajs-2677	280	21	proposed	propose	VERB
iajs-2677	280	22	algorithm	algorithm	NOUN
iajs-2677	280	23	.	.	PUNCT
iajs-2677	281	1	the	the	DET
iajs-2677	281	2	problems	problem	NOUN
iajs-2677	281	3	are	be	AUX
iajs-2677	281	4	generated	generate	VERB
iajs-2677	281	5	as	as	SCONJ
iajs-2677	281	6	follows	follow	VERB
iajs-2677	281	7	:	:	PUNCT
iajs-2677	281	8	an	an	DET
iajs-2677	281	9	integer	integer	NOUN
iajs-2677	281	10	processing	processing	NOUN
iajs-2677	281	11	time	time	NOUN
iajs-2677	281	12	pj	pj	PROPN
iajs-2677	281	13	generated	generate	VERB
iajs-2677	281	14	from	from	ADP
iajs-2677	281	15	the	the	DET
iajs-2677	281	16	uniform	uniform	ADJ
iajs-2677	281	17	distribution	distribution	NOUN
iajs-2677	281	18	[	[	X
iajs-2677	281	19	1	1	NUM
iajs-2677	281	20	,	,	PUNCT
iajs-2677	281	21	10	10	NUM
iajs-2677	281	22	]	]	PUNCT
iajs-2677	281	23	.	.	PUNCT
iajs-2677	282	1	also	also	ADV
iajs-2677	282	2	,	,	PUNCT
iajs-2677	282	3	an	an	DET
iajs-2677	282	4	integer	integer	NOUN
iajs-2677	282	5	due	due	ADJ
iajs-2677	282	6	date	date	NOUN
iajs-2677	282	7	dj	dj	NOUN
iajs-2677	282	8	is	be	AUX
iajs-2677	282	9	generated	generate	VERB
iajs-2677	282	10	from	from	ADP
iajs-2677	282	11	the	the	DET
iajs-2677	282	12	uniform	uniform	ADJ
iajs-2677	282	13	distribution	distribution	NOUN
iajs-2677	282	14	[	[	X
iajs-2677	282	15	0	0	NUM
iajs-2677	282	16	,	,	PUNCT
iajs-2677	282	17	∑	∑	PUNCT
iajs-2677	282	18	pj	pj	PROPN
iajs-2677	282	19	n	n	PRON
iajs-2677	282	20	j=1	j=1	NOUN
iajs-2677	282	21	]	]	PUNCT
iajs-2677	282	22	.	.	PUNCT
iajs-2677	283	1	numbers	number	NOUN
iajs-2677	283	2	schedules	schedule	NOUN
iajs-2677	283	3	(	(	PUNCT
iajs-2677	283	4	∑	∑	PROPN
iajs-2677	283	5	cj	cj	PROPN
iajs-2677	283	6	4	4	NUM
iajs-2677	283	7	j=1	j=1	NOUN
iajs-2677	283	8	,	,	PUNCT
iajs-2677	283	9	emax	emax	X
iajs-2677	283	10	)	)	PUNCT
iajs-2677	283	11	(	(	PUNCT
iajs-2677	283	12	∑	∑	PROPN
iajs-2677	283	13	cj	cj	PROPN
iajs-2677	283	14	4	4	NUM
iajs-2677	283	15	j=1	j=1	NOUN
iajs-2677	283	16	,	,	PUNCT
iajs-2677	283	17	tmax	tmax	PROPN
iajs-2677	283	18	)	)	PUNCT
iajs-2677	283	19	(	(	PUNCT
iajs-2677	283	20	emax	emax	X
iajs-2677	283	21	+	+	X
iajs-2677	283	22	tmax	tmax	NUM
iajs-2677	283	23	)	)	PUNCT
iajs-2677	283	24	1	1	NUM
iajs-2677	283	25	(	(	PUNCT
iajs-2677	283	26	3	3	NUM
iajs-2677	283	27	,	,	PUNCT
iajs-2677	283	28	2	2	NUM
iajs-2677	283	29	,	,	PUNCT
iajs-2677	283	30	1	1	NUM
iajs-2677	283	31	,	,	PUNCT
iajs-2677	283	32	4	4	NUM
iajs-2677	283	33	)	)	PUNCT
iajs-2677	283	34			NOUN
iajs-2677	284	1	(	(	PUNCT
iajs-2677	284	2	34	34	NUM
iajs-2677	284	3	,	,	PUNCT
iajs-2677	284	4	9	9	NUM
iajs-2677	284	5	)	)	PUNCT
iajs-2677	284	6			NOUN
iajs-2677	284	7	(	(	PUNCT
iajs-2677	284	8	34	34	NUM
iajs-2677	284	9	,	,	PUNCT
iajs-2677	284	10	10	10	NUM
iajs-2677	284	11	)	)	PUNCT
iajs-2677	284	12	19	19	NUM
iajs-2677	284	13	2	2	NUM
iajs-2677	284	14	(	(	PUNCT
iajs-2677	284	15	2	2	NUM
iajs-2677	284	16	,	,	PUNCT
iajs-2677	284	17	3	3	NUM
iajs-2677	284	18	,	,	PUNCT
iajs-2677	284	19	1	1	NUM
iajs-2677	284	20	,	,	PUNCT
iajs-2677	284	21	4	4	NUM
iajs-2677	284	22	)	)	PUNCT
iajs-2677	284	23			NOUN
iajs-2677	285	1	(	(	PUNCT
iajs-2677	285	2	35	35	NUM
iajs-2677	285	3	,	,	PUNCT
iajs-2677	285	4	6	6	NUM
iajs-2677	285	5	)	)	PUNCT
iajs-2677	285	6	(	(	PUNCT
iajs-2677	285	7	35	35	NUM
iajs-2677	285	8	,	,	PUNCT
iajs-2677	285	9	10	10	NUM
iajs-2677	285	10	)	)	PUNCT
iajs-2677	285	11	16	16	NUM
iajs-2677	285	12	3	3	NUM
iajs-2677	285	13	(	(	PUNCT
iajs-2677	285	14	3	3	NUM
iajs-2677	285	15	,	,	PUNCT
iajs-2677	285	16	1	1	NUM
iajs-2677	285	17	,	,	PUNCT
iajs-2677	285	18	2	2	NUM
iajs-2677	285	19	,	,	PUNCT
iajs-2677	285	20	4	4	NUM
iajs-2677	285	21	)	)	PUNCT
iajs-2677	285	22	(	(	PUNCT
iajs-2677	285	23	36	36	NUM
iajs-2677	285	24	,	,	PUNCT
iajs-2677	285	25	9	9	NUM
iajs-2677	285	26	)	)	PUNCT
iajs-2677	285	27			NOUN
iajs-2677	286	1	(	(	PUNCT
iajs-2677	286	2	36	36	NUM
iajs-2677	286	3	,	,	PUNCT
iajs-2677	286	4	9	9	NUM
iajs-2677	286	5	)	)	PUNCT
iajs-2677	286	6	18	18	NUM
iajs-2677	286	7	4	4	NUM
iajs-2677	286	8	(	(	PUNCT
iajs-2677	286	9	2	2	NUM
iajs-2677	286	10	,	,	PUNCT
iajs-2677	286	11	1	1	NUM
iajs-2677	286	12	,	,	PUNCT
iajs-2677	286	13	3	3	NUM
iajs-2677	286	14	,	,	PUNCT
iajs-2677	286	15	4	4	NUM
iajs-2677	286	16	)	)	PUNCT
iajs-2677	286	17			NOUN
iajs-2677	286	18	(	(	PUNCT
iajs-2677	286	19	38	38	NUM
iajs-2677	286	20	,	,	PUNCT
iajs-2677	286	21	3	3	NUM
iajs-2677	286	22	)	)	PUNCT
iajs-2677	286	23	(	(	PUNCT
iajs-2677	286	24	38	38	NUM
iajs-2677	286	25	,	,	PUNCT
iajs-2677	286	26	10	10	NUM
iajs-2677	286	27	)	)	PUNCT
iajs-2677	286	28	13	13	NUM
iajs-2677	286	29	5	5	NUM
iajs-2677	286	30	(	(	PUNCT
iajs-2677	286	31	2	2	NUM
iajs-2677	286	32	,	,	PUNCT
iajs-2677	286	33	1	1	NUM
iajs-2677	286	34	,	,	PUNCT
iajs-2677	286	35	4	4	NUM
iajs-2677	286	36	,	,	PUNCT
iajs-2677	286	37	3	3	NUM
iajs-2677	286	38	)	)	PUNCT
iajs-2677	286	39	(	(	PUNCT
iajs-2677	286	40	43	43	NUM
iajs-2677	286	41	,	,	PUNCT
iajs-2677	286	42	3	3	NUM
iajs-2677	286	43	)	)	PUNCT
iajs-2677	286	44			NOUN
iajs-2677	287	1	(	(	PUNCT
iajs-2677	287	2	43	43	NUM
iajs-2677	287	3	,	,	PUNCT
iajs-2677	287	4	8)	8)	NUM
iajs-2677	287	5	11	11	NUM
iajs-2677	287	6	6	6	NUM
iajs-2677	287	7	(	(	PUNCT
iajs-2677	287	8	2	2	NUM
iajs-2677	287	9	,	,	PUNCT
iajs-2677	287	10	4	4	NUM
iajs-2677	287	11	,	,	PUNCT
iajs-2677	287	12	1	1	NUM
iajs-2677	287	13	,	,	PUNCT
iajs-2677	287	14	3	3	NUM
iajs-2677	287	15	)	)	PUNCT
iajs-2677	287	16	(	(	PUNCT
iajs-2677	287	17	45	45	NUM
iajs-2677	287	18	,	,	PUNCT
iajs-2677	287	19	3	3	NUM
iajs-2677	287	20	)	)	PUNCT
iajs-2677	287	21			NOUN
iajs-2677	287	22	(	(	PUNCT
iajs-2677	287	23	45	45	NUM
iajs-2677	287	24	,	,	PUNCT
iajs-2677	287	25	7	7	NUM
iajs-2677	287	26	)	)	PUNCT
iajs-2677	287	27	10	10	NUM
iajs-2677	287	28	7	7	NUM
iajs-2677	287	29	(	(	PUNCT
iajs-2677	287	30	4	4	NUM
iajs-2677	287	31	,	,	PUNCT
iajs-2677	287	32	2	2	NUM
iajs-2677	287	33	,	,	PUNCT
iajs-2677	287	34	3	3	NUM
iajs-2677	287	35	,	,	PUNCT
iajs-2677	287	36	1	1	NUM
iajs-2677	287	37	)	)	PUNCT
iajs-2677	287	38			NOUN
iajs-2677	288	1	(	(	PUNCT
iajs-2677	288	2	46	46	NUM
iajs-2677	288	3	,	,	PUNCT
iajs-2677	288	4	0	0	NUM
iajs-2677	288	5	)	)	PUNCT
iajs-2677	288	6	(	(	PUNCT
iajs-2677	288	7	46	46	NUM
iajs-2677	288	8	,	,	PUNCT
iajs-2677	288	9	9	9	NUM
iajs-2677	288	10	)	)	PUNCT
iajs-2677	288	11	9	9	NUM
iajs-2677	288	12	ibn	ibn	PROPN
iajs-2677	288	13	al	al	PROPN
iajs-2677	288	14	-	-	PUNCT
iajs-2677	288	15	haitham	haitham	PROPN
iajs-2677	288	16	jour	jour	X
iajs-2677	288	17	.	.	PROPN
iajs-2677	289	1	for	for	ADP
iajs-2677	289	2	pure	pure	ADJ
iajs-2677	289	3	&	&	CCONJ
iajs-2677	289	4	appl	appl	PROPN
iajs-2677	289	5	.	.	PUNCT
iajs-2677	290	1	sci	sci	PROPN
iajs-2677	290	2	.	.	PROPN
iajs-2677	291	1	34(3)2021	34(3)2021	NUM
iajs-2677	291	2	58	58	NUM
iajs-2677	291	3	the	the	DET
iajs-2677	291	4	proposed	propose	VERB
iajs-2677	291	5	algorithm	algorithm	NOUN
iajs-2677	291	6	was	be	AUX
iajs-2677	291	7	running	run	VERB
iajs-2677	291	8	and	and	CCONJ
iajs-2677	291	9	coding	code	VERB
iajs-2677	291	10	it	it	PRON
iajs-2677	291	11	in	in	ADP
iajs-2677	291	12	matlab	matlab	PROPN
iajs-2677	291	13	8.1	8.1	NUM
iajs-2677	291	14	(	(	PUNCT
iajs-2677	291	15	r2013a	r2013a	X
iajs-2677	291	16	)	)	PUNCT
iajs-2677	291	17	and	and	CCONJ
iajs-2677	291	18	implemented	implement	VERB
iajs-2677	291	19	on	on	ADP
iajs-2677	291	20	intel	intel	PROPN
iajs-2677	291	21	(	(	PUNCT
iajs-2677	291	22	r	r	NOUN
iajs-2677	291	23	)	)	PUNCT
iajs-2677	291	24	pentium	pentium	NOUN
iajs-2677	291	25	(	(	PUNCT
iajs-2677	291	26	r	r	NOUN
iajs-2677	291	27	)	)	PUNCT
iajs-2677	291	28	cpu	cpu	NOUN
iajs-2677	291	29	2117u@	2117u@	NUM
iajs-2677	291	30	1.80	1.80	NUM
iajs-2677	291	31	ghz	ghz	NOUN
iajs-2677	291	32	,	,	PUNCT
iajs-2677	291	33	with	with	ADP
iajs-2677	291	34	ram	ram	NOUN
iajs-2677	291	35	4.00	4.00	NUM
iajs-2677	291	36	gb	gb	ADP
iajs-2677	291	37	personal	personal	ADJ
iajs-2677	291	38	computer	computer	NOUN
iajs-2677	291	39	.	.	PUNCT
iajs-2677	292	1	8	8	X
iajs-2677	292	2	.	.	X
iajs-2677	292	3	conclusions	conclusion	NOUN
iajs-2677	292	4	and	and	CCONJ
iajs-2677	292	5	future	future	ADJ
iajs-2677	292	6	works	work	NOUN
iajs-2677	292	7	we	we	PRON
iajs-2677	292	8	presented	present	VERB
iajs-2677	292	9	a	a	DET
iajs-2677	292	10	novel	novel	ADJ
iajs-2677	292	11	heuristic	heuristic	ADJ
iajs-2677	292	12	algorithm	algorithm	NOUN
iajs-2677	292	13	to	to	PART
iajs-2677	292	14	minimize	minimize	VERB
iajs-2677	292	15	the	the	DET
iajs-2677	292	16	sum	sum	NOUN
iajs-2677	292	17	of	of	ADP
iajs-2677	292	18	maximum	maximum	ADJ
iajs-2677	292	19	earliness	earliness	NOUN
iajs-2677	292	20	and	and	CCONJ
iajs-2677	292	21	tardiness	tardiness	NOUN
iajs-2677	292	22	in	in	ADP
iajs-2677	292	23	single	single	ADJ
iajs-2677	292	24	-	-	PUNCT
iajs-2677	292	25	machine	machine	NOUN
iajs-2677	292	26	scheduling	scheduling	NOUN
iajs-2677	292	27	etmax	etmax	ADJ
iajs-2677	292	28	.	.	PUNCT
iajs-2677	293	1	the	the	DET
iajs-2677	293	2	algorithm	algorithm	NOUN
iajs-2677	293	3	depended	depend	VERB
iajs-2677	293	4	on	on	ADP
iajs-2677	293	5	a	a	DET
iajs-2677	293	6	new	new	ADJ
iajs-2677	293	7	idea	idea	NOUN
iajs-2677	293	8	that	that	PRON
iajs-2677	293	9	is	be	AUX
iajs-2677	293	10	presented	present	VERB
iajs-2677	293	11	for	for	ADP
iajs-2677	293	12	the	the	DET
iajs-2677	293	13	first	first	ADJ
iajs-2677	293	14	time	time	NOUN
iajs-2677	293	15	.	.	PUNCT
iajs-2677	294	1	the	the	DET
iajs-2677	294	2	algorithm	algorithm	NOUN
iajs-2677	294	3	was	be	AUX
iajs-2677	294	4	easy	easy	ADJ
iajs-2677	294	5	to	to	PART
iajs-2677	294	6	implement	implement	VERB
iajs-2677	294	7	and	and	CCONJ
iajs-2677	294	8	had	have	VERB
iajs-2677	294	9	a	a	DET
iajs-2677	294	10	simple	simple	ADJ
iajs-2677	294	11	structure	structure	NOUN
iajs-2677	294	12	comparing	compare	VERB
iajs-2677	294	13	with	with	ADP
iajs-2677	294	14	other	other	ADJ
iajs-2677	294	15	used	use	VERB
iajs-2677	294	16	algorithms	algorithm	NOUN
iajs-2677	294	17	such	such	ADJ
iajs-2677	294	18	as	as	ADP
iajs-2677	294	19	branch	branch	NOUN
iajs-2677	294	20	and	and	CCONJ
iajs-2677	294	21	bound	bound	ADJ
iajs-2677	294	22	algorithm	algorithm	NOUN
iajs-2677	294	23	.	.	PUNCT
iajs-2677	295	1	to	to	PART
iajs-2677	295	2	evaluate	evaluate	VERB
iajs-2677	295	3	the	the	DET
iajs-2677	295	4	efficiency	efficiency	NOUN
iajs-2677	295	5	of	of	ADP
iajs-2677	295	6	the	the	DET
iajs-2677	295	7	proposed	propose	VERB
iajs-2677	295	8	algorithm	algorithm	NOUN
iajs-2677	295	9	,	,	PUNCT
iajs-2677	295	10	the	the	DET
iajs-2677	295	11	algorithm	algorithm	NOUN
iajs-2677	295	12	was	be	AUX
iajs-2677	295	13	tested	test	VERB
iajs-2677	295	14	on	on	ADP
iajs-2677	295	15	(	(	PUNCT
iajs-2677	295	16	25	25	NUM
iajs-2677	295	17	)	)	PUNCT
iajs-2677	295	18	examples	example	NOUN
iajs-2677	295	19	for	for	ADP
iajs-2677	295	20	different	different	ADJ
iajs-2677	295	21	n.	n.	NOUN
iajs-2677	295	22	for	for	ADP
iajs-2677	295	23	n	n	NOUN
iajs-2677	295	24	=	=	SYM
iajs-2677	295	25	3	3	NUM
iajs-2677	295	26	,	,	PUNCT
iajs-2677	295	27	it	it	PRON
iajs-2677	295	28	solves	solve	VERB
iajs-2677	295	29	100	100	NUM
iajs-2677	295	30	%	%	NOUN
iajs-2677	295	31	of	of	ADP
iajs-2677	295	32	the	the	DET
iajs-2677	295	33	instances	instance	NOUN
iajs-2677	295	34	.	.	PUNCT
iajs-2677	296	1	for	for	ADP
iajs-2677	296	2	n	n	NOUN
iajs-2677	296	3	=	=	SYM
iajs-2677	296	4	4	4	NUM
iajs-2677	296	5	,	,	PUNCT
iajs-2677	296	6	it	it	PRON
iajs-2677	296	7	solves	solve	VERB
iajs-2677	296	8	100	100	NUM
iajs-2677	296	9	%	%	NOUN
iajs-2677	296	10	of	of	ADP
iajs-2677	296	11	the	the	DET
iajs-2677	296	12	instances	instance	NOUN
iajs-2677	296	13	.	.	PUNCT
iajs-2677	297	1	for	for	ADP
iajs-2677	297	2	n	n	NOUN
iajs-2677	297	3	=	=	SYM
iajs-2677	297	4	5	5	NUM
iajs-2677	297	5	,	,	PUNCT
iajs-2677	297	6	it	it	PRON
iajs-2677	297	7	solves	solve	VERB
iajs-2677	297	8	also	also	ADV
iajs-2677	297	9	100	100	NUM
iajs-2677	297	10	%	%	NOUN
iajs-2677	297	11	of	of	ADP
iajs-2677	297	12	the	the	DET
iajs-2677	297	13	instances	instance	NOUN
iajs-2677	297	14	.	.	PUNCT
iajs-2677	298	1	computational	computational	ADJ
iajs-2677	298	2	results	result	NOUN
iajs-2677	298	3	showed	show	VERB
iajs-2677	298	4	the	the	DET
iajs-2677	298	5	ability	ability	NOUN
iajs-2677	298	6	of	of	ADP
iajs-2677	298	7	the	the	DET
iajs-2677	298	8	algorithm	algorithm	NOUN
iajs-2677	298	9	.	.	PUNCT
iajs-2677	299	1	an	an	DET
iajs-2677	299	2	important	important	ADJ
iajs-2677	299	3	area	area	NOUN
iajs-2677	299	4	for	for	ADP
iajs-2677	299	5	future	future	ADJ
iajs-2677	299	6	research	research	NOUN
iajs-2677	299	7	is	be	AUX
iajs-2677	299	8	to	to	PART
iajs-2677	299	9	use	use	VERB
iajs-2677	299	10	the	the	DET
iajs-2677	299	11	presented	present	VERB
iajs-2677	299	12	idea	idea	NOUN
iajs-2677	299	13	for	for	ADP
iajs-2677	299	14	other	other	ADJ
iajs-2677	299	15	multi	multi	ADJ
iajs-2677	299	16	objective	objective	ADJ
iajs-2677	299	17	problems	problem	NOUN
iajs-2677	299	18	with	with	ADP
iajs-2677	299	19	a	a	DET
iajs-2677	299	20	variety	variety	NOUN
iajs-2677	299	21	of	of	ADP
iajs-2677	299	22	environments	environment	NOUN
iajs-2677	299	23	and	and	CCONJ
iajs-2677	299	24	conditions	condition	NOUN
iajs-2677	299	25	.	.	PUNCT
iajs-2677	300	1	references	reference	NOUN
iajs-2677	300	2	1	1	NUM
iajs-2677	300	3	.	.	PUNCT
iajs-2677	300	4	t'kindt	t'kindt	PROPN
iajs-2677	300	5	,	,	PUNCT
iajs-2677	300	6	v.	v.	PROPN
iajs-2677	300	7	;	;	PUNCT
iajs-2677	300	8	billaut	billaut	PROPN
iajs-2677	300	9	,	,	PUNCT
iajs-2677	300	10	j.-c	j.-c	PROPN
iajs-2677	300	11	.	.	PUNCT
iajs-2677	301	1	multicriteria	multicriteria	PROPN
iajs-2677	301	2	scheduling	scheduling	NOUN
iajs-2677	301	3	:	:	PUNCT
iajs-2677	301	4	theory	theory	NOUN
iajs-2677	301	5	,	,	PUNCT
iajs-2677	301	6	models	model	NOUN
iajs-2677	301	7	and	and	CCONJ
iajs-2677	301	8	algorithms	algorithm	NOUN
iajs-2677	301	9	,	,	PUNCT
iajs-2677	301	10	2nd	2nd	NOUN
iajs-2677	301	11	;	;	PUNCT
iajs-2677	301	12	springer	springer	NOUN
iajs-2677	301	13	:	:	PUNCT
iajs-2677	301	14	berlin	berlin	PROPN
iajs-2677	301	15	,	,	PUNCT
iajs-2677	301	16	2002	2002	NUM
iajs-2677	301	17	;	;	PUNCT
iajs-2677	301	18	9783540282303	9783540282303	NUM
iajs-2677	301	19	.	.	PUNCT
iajs-2677	302	1	2	2	X
iajs-2677	302	2	.	.	X
iajs-2677	302	3	joksch	joksch	PROPN
iajs-2677	302	4	,	,	PUNCT
iajs-2677	302	5	h.	h.	PROPN
iajs-2677	302	6	c.	c.	PROPN
iajs-2677	302	7	constraints	constraints	PROPN
iajs-2677	302	8	objectives	objective	NOUN
iajs-2677	302	9	,	,	PUNCT
iajs-2677	302	10	efficient	efficient	ADJ
iajs-2677	302	11	solutions	solution	NOUN
iajs-2677	302	12	and	and	CCONJ
iajs-2677	302	13	sub	sub	VERB
iajs-2677	302	14	optimization	optimization	NOUN
iajs-2677	302	15	in	in	ADP
iajs-2677	302	16	mathematical	mathematical	ADJ
iajs-2677	302	17	programming	programming	NOUN
iajs-2677	302	18	.	.	PUNCT
iajs-2677	303	1	journal	journal	PROPN
iajs-2677	303	2	of	of	ADP
iajs-2677	303	3	institutional	institutional	ADJ
iajs-2677	303	4	and	and	CCONJ
iajs-2677	303	5	theoretical	theoretical	ADJ
iajs-2677	303	6	economics	economic	NOUN
iajs-2677	303	7	.	.	PUNCT
iajs-2677	304	1	1996	1996	NUM
iajs-2677	304	2	,	,	PUNCT
iajs-2677	304	3	122	122	NUM
iajs-2677	304	4	,	,	PUNCT
iajs-2677	304	5	5	5	NUM
iajs-2677	304	6	-	-	SYM
iajs-2677	304	7	13	13	NUM
iajs-2677	304	8	.	.	PUNCT
iajs-2677	305	1	3	3	X
iajs-2677	305	2	.	.	X
iajs-2677	306	1	hoogeveen	hoogeveen	PROPN
iajs-2677	306	2	,	,	PUNCT
iajs-2677	306	3	j.a	j.a	PROPN
iajs-2677	306	4	.	.	PROPN
iajs-2677	306	5	single	single	ADJ
iajs-2677	306	6	-	-	PUNCT
iajs-2677	306	7	machine	machine	NOUN
iajs-2677	306	8	bicriteria	bicriteria	NOUN
iajs-2677	306	9	scheduling	scheduling	NOUN
iajs-2677	306	10	.	.	PUNCT
iajs-2677	307	1	ph.d	ph.d	PROPN
iajs-2677	307	2	.	.	PUNCT
iajs-2677	308	1	thesis	thesis	NOUN
iajs-2677	308	2	.	.	PUNCT
iajs-2677	309	1	cwi	cwi	NOUN
iajs-2677	309	2	,	,	PUNCT
iajs-2677	309	3	amsterdam	amsterdam	PROPN
iajs-2677	309	4	.	.	PROPN
iajs-2677	309	5	1992	1992	NUM
iajs-2677	309	6	.	.	PUNCT
iajs-2677	310	1	4	4	X
iajs-2677	310	2	.	.	X
iajs-2677	310	3	hoogeveen	hoogeveen	PROPN
iajs-2677	310	4	,	,	PUNCT
iajs-2677	310	5	j.	j.	PROPN
iajs-2677	310	6	a.	a.	NOUN
iajs-2677	310	7	minimizing	minimize	VERB
iajs-2677	310	8	maximum	maximum	ADJ
iajs-2677	310	9	promptness	promptness	ADJ
iajs-2677	310	10	and	and	CCONJ
iajs-2677	310	11	maximum	maximum	ADJ
iajs-2677	310	12	lateness	lateness	NOUN
iajs-2677	310	13	on	on	ADP
iajs-2677	310	14	a	a	DET
iajs-2677	310	15	single	single	ADJ
iajs-2677	310	16	machine	machine	NOUN
iajs-2677	310	17	.	.	PUNCT
iajs-2677	311	1	mathematics	mathematic	NOUN
iajs-2677	311	2	of	of	ADP
iajs-2677	311	3	operation	operation	NOUN
iajs-2677	311	4	research	research	NOUN
iajs-2677	311	5	.	.	PUNCT
iajs-2677	312	1	1996	1996	NUM
iajs-2677	312	2	,	,	PUNCT
iajs-2677	312	3	21	21	NUM
iajs-2677	312	4	,	,	PUNCT
iajs-2677	312	5	100	100	NUM
iajs-2677	312	6	-	-	SYM
iajs-2677	312	7	114	114	NUM
iajs-2677	312	8	,	,	PUNCT
iajs-2677	312	9	https://doi.org/10.1287/moor.2018.0943	https://doi.org/10.1287/moor.2018.0943	PROPN
iajs-2677	312	10	.	.	PROPN
iajs-2677	312	11	5	5	NUM
iajs-2677	312	12	.	.	X
iajs-2677	313	1	ayad	ayad	PROPN
iajs-2677	313	2	,	,	PUNCT
iajs-2677	313	3	m.	m.	PROPN
iajs-2677	313	4	ramadan	ramadan	PROPN
iajs-2677	313	5	.	.	PUNCT
iajs-2677	314	1	range	range	NOUN
iajs-2677	314	2	of	of	ADP
iajs-2677	314	3	lower	low	ADJ
iajs-2677	314	4	bounds	bound	NOUN
iajs-2677	314	5	.	.	PUNCT
iajs-2677	315	1	applied	apply	VERB
iajs-2677	315	2	mathematics	mathematic	NOUN
iajs-2677	315	3	and	and	CCONJ
iajs-2677	315	4	computation	computation	NOUN
iajs-2677	315	5	.	.	PUNCT
iajs-2677	316	1	2011	2011	NUM
iajs-2677	316	2	,	,	PUNCT
iajs-2677	316	3	218	218	NUM
iajs-2677	316	4	,	,	PUNCT
iajs-2677	316	5	1008	1008	NUM
iajs-2677	316	6	-	-	SYM
iajs-2677	316	7	1011	1011	NUM
iajs-2677	316	8	,	,	PUNCT
iajs-2677	316	9	https://doi.org/10.1016/j.amc.2020.125904	https://doi.org/10.1016/j.amc.2020.125904	PROPN
iajs-2677	316	10	6	6	NUM
iajs-2677	316	11	.	.	X
iajs-2677	317	1	amin	amin	PROPN
iajs-2677	317	2	-	-	PUNCT
iajs-2677	317	3	nayeri	nayeri	PROPN
iajs-2677	317	4	,	,	PUNCT
iajs-2677	317	5	m.r	m.r	PROPN
iajs-2677	317	6	.	.	PROPN
iajs-2677	317	7	;	;	PUNCT
iajs-2677	317	8	moslehi	moslehi	NOUN
iajs-2677	317	9	,	,	PUNCT
iajs-2677	317	10	g.	g.	PROPN
iajs-2677	317	11	optimal	optimal	ADJ
iajs-2677	317	12	algorithm	algorithm	NOUN
iajs-2677	317	13	for	for	ADP
iajs-2677	317	14	single	single	ADJ
iajs-2677	317	15	machine	machine	NOUN
iajs-2677	317	16	sequencing	sequence	VERB
iajs-2677	317	17	to	to	PART
iajs-2677	317	18	minimize	minimize	VERB
iajs-2677	317	19	early	early	ADJ
iajs-2677	317	20	/	/	SYM
iajs-2677	317	21	tardy	tardy	ADJ
iajs-2677	317	22	cost	cost	NOUN
iajs-2677	317	23	.	.	PUNCT
iajs-2677	318	1	esteghlal	esteghlal	PROPN
iajs-2677	318	2	journal	journal	PROPN
iajs-2677	318	3	of	of	ADP
iajs-2677	318	4	engineering	engineering	NOUN
iajs-2677	318	5	.	.	PUNCT
iajs-2677	319	1	2000	2000	NUM
iajs-2677	319	2	,	,	PUNCT
iajs-2677	319	3	19	19	NUM
iajs-2677	319	4	,	,	PUNCT
iajs-2677	319	5	35–48	35–48	NUM
iajs-2677	319	6	.	.	PUNCT
iajs-2677	320	1	7	7	NUM
iajs-2677	320	2	.	.	X
iajs-2677	320	3	jouni	jouni	PROPN
iajs-2677	320	4	,	,	PUNCT
iajs-2677	320	5	l.	l.	PROPN
iajs-2677	320	6	multi	multi	ADJ
iajs-2677	320	7	-	-	ADJ
iajs-2677	320	8	objective	objective	ADJ
iajs-2677	320	9	nonlinear	nonlinear	ADJ
iajs-2677	320	10	pareto	pareto	NOUN
iajs-2677	320	11	-	-	PUNCT
iajs-2677	320	12	optimization	optimization	NOUN
iajs-2677	320	13	.	.	PUNCT
iajs-2677	321	1	lappeenranta	lappeenranta	PROPN
iajs-2677	321	2	university	university	PROPN
iajs-2677	321	3	of	of	ADP
iajs-2677	321	4	technology	technology	NOUN
iajs-2677	321	5	,	,	PUNCT
iajs-2677	321	6	laboratory	laboratory	NOUN
iajs-2677	321	7	of	of	ADP
iajs-2677	321	8	information	information	NOUN
iajs-2677	321	9	processing	processing	NOUN
iajs-2677	321	10	.	.	PUNCT
iajs-2677	322	1	2000	2000	NUM
iajs-2677	322	2	.	.	PUNCT
iajs-2677	323	1	8	8	X
iajs-2677	323	2	.	.	X
iajs-2677	324	1	van	van	PROPN
iajs-2677	324	2	wassenhove	wassenhove	PROPN
iajs-2677	324	3	,	,	PUNCT
iajs-2677	324	4	l.	l.	PROPN
iajs-2677	324	5	n.	n.	PROPN
iajs-2677	324	6	;	;	PUNCT
iajs-2677	324	7	gelders	gelder	NOUN
iajs-2677	324	8	,	,	PUNCT
iajs-2677	324	9	f.	f.	PROPN
iajs-2677	324	10	solving	solve	VERB
iajs-2677	324	11	a	a	DET
iajs-2677	324	12	bicriterion	bicriterion	NOUN
iajs-2677	324	13	scheduling	scheduling	NOUN
iajs-2677	324	14	problem	problem	NOUN
iajs-2677	324	15	.	.	PUNCT
iajs-2677	325	1	european	european	ADJ
iajs-2677	325	2	journal	journal	PROPN
iajs-2677	325	3	of	of	ADP
iajs-2677	325	4	operational	operational	ADJ
iajs-2677	325	5	research	research	NOUN
iajs-2677	325	6	.	.	PUNCT
iajs-2677	326	1	1980	1980	NUM
iajs-2677	326	2	,	,	PUNCT
iajs-2677	326	3	4	4	NUM
iajs-2677	326	4	,	,	PUNCT
iajs-2677	326	5	42	42	NUM
iajs-2677	326	6	-	-	SYM
iajs-2677	326	7	48	48	NUM
iajs-2677	326	8	,	,	PUNCT
iajs-2677	326	9	https://doi.org/10.1016/j.ejor.2021.01.025	https://doi.org/10.1016/j.ejor.2021.01.025	NOUN
iajs-2677	326	10	.	.	NOUN
iajs-2677	327	1	9	9	X
iajs-2677	327	2	.	.	X
iajs-2677	327	3	abdul	abdul	NOUN
iajs-2677	327	4	-	-	PUNCT
iajs-2677	327	5	razaq	razaq	PROPN
iajs-2677	327	6	,	,	PUNCT
iajs-2677	327	7	t.	t.	PROPN
iajs-2677	327	8	s.	s.	PROPN
iajs-2677	327	9	;	;	PUNCT
iajs-2677	327	10	hussam	hussam	PROPN
iajs-2677	327	11	abid	abid	PROPN
iajs-2677	327	12	ali	ali	PROPN
iajs-2677	327	13	mohammed	mohammed	PROPN
iajs-2677	327	14	.	.	PROPN
iajs-2677	328	1	exact	exact	ADJ
iajs-2677	328	2	and	and	CCONJ
iajs-2677	328	3	approximation	approximation	NOUN
iajs-2677	328	4	approaches	approach	NOUN
iajs-2677	328	5	for	for	ADP
iajs-2677	328	6	solving	solve	VERB
iajs-2677	328	7	multiple	multiple	ADJ
iajs-2677	328	8	objective	objective	ADJ
iajs-2677	328	9	function	function	NOUN
iajs-2677	328	10	.	.	PUNCT
iajs-2677	329	1	al	al	PROPN
iajs-2677	329	2	-	-	PUNCT
iajs-2677	329	3	mustansiriyah	mustansiriyah	PROPN
iajs-2677	329	4	journal	journal	NOUN
iajs-2677	329	5	of	of	ADP
iajs-2677	329	6	science	science	NOUN
iajs-2677	329	7	.	.	PUNCT
iajs-2677	330	1	2016	2016	NUM
iajs-2677	330	2	,	,	PUNCT
iajs-2677	330	3	27	27	NUM
iajs-2677	330	4	,	,	PUNCT
iajs-2677	330	5	89	89	NUM
iajs-2677	330	6	-	-	SYM
iajs-2677	330	7	97	97	NUM
iajs-2677	330	8	,	,	PUNCT
iajs-2677	330	9	http://dx.doi.org/10.23851/mjs.v31i4.897	http://dx.doi.org/10.23851/mjs.v31i4.897	PROPN
iajs-2677	330	10	.	.	PUNCT
iajs-2677	331	1	10	10	NUM
iajs-2677	331	2	.	.	PUNCT
iajs-2677	332	1	moghaddam	moghaddam	NOUN
iajs-2677	332	2	,	,	PUNCT
iajs-2677	332	3	r.t	r.t	PROPN
iajs-2677	332	4	.	.	PROPN
iajs-2677	332	5	;	;	PUNCT
iajs-2677	332	6	moslehi	moslehi	NOUN
iajs-2677	332	7	,	,	PUNCT
iajs-2677	332	8	g.	g.	PROPN
iajs-2677	332	9	;	;	PUNCT
iajs-2677	332	10	vasei	vasei	ADJ
iajs-2677	332	11	,	,	PUNCT
iajs-2677	332	12	m.	m.	NOUN
iajs-2677	332	13	;	;	PUNCT
iajs-2677	332	14	azaron	azaron	PROPN
iajs-2677	332	15	,	,	PUNCT
iajs-2677	332	16	a.	a.	NOUN
iajs-2677	332	17	optimal	optimal	ADJ
iajs-2677	332	18	scheduling	scheduling	NOUN
iajs-2677	332	19	for	for	ADP
iajs-2677	332	20	a	a	DET
iajs-2677	332	21	single	single	ADJ
iajs-2677	332	22	machine	machine	NOUN
iajs-2677	332	23	to	to	PART
iajs-2677	332	24	minimize	minimize	VERB
iajs-2677	332	25	the	the	DET
iajs-2677	332	26	sum	sum	NOUN
iajs-2677	332	27	of	of	ADP
iajs-2677	332	28	maximum	maximum	ADJ
iajs-2677	332	29	earliness	earliness	NOUN
iajs-2677	332	30	and	and	CCONJ
iajs-2677	332	31	tardiness	tardiness	NOUN
iajs-2677	332	32	considering	consider	VERB
iajs-2677	332	33	idle	idle	ADJ
iajs-2677	332	34	insert	insert	PROPN
iajs-2677	332	35	.	.	PUNCT
iajs-2677	333	1	applied	apply	VERB
iajs-2677	333	2	mathematics	mathematic	NOUN
iajs-2677	333	3	and	and	CCONJ
iajs-2677	333	4	computation	computation	NOUN
iajs-2677	333	5	.	.	PUNCT
iajs-2677	334	1	2005	2005	NUM
iajs-2677	334	2	,	,	PUNCT
iajs-2677	334	3	167	167	NUM
iajs-2677	334	4	,	,	PUNCT
iajs-2677	334	5	1430	1430	NUM
iajs-2677	334	6	-	-	SYM
iajs-2677	334	7	1450	1450	NUM
iajs-2677	334	8	,	,	PUNCT
iajs-2677	334	9	https://doi.org/10.1016/j.amc.2020.125904	https://doi.org/10.1016/j.amc.2020.125904	PROPN
iajs-2677	334	10	.	.	PUNCT
iajs-2677	335	1	https://doi.org/10.1287/moor.2018.0943	https://doi.org/10.1287/moor.2018.0943	PROPN
iajs-2677	335	2	https://www.sciencedirect.com/science/journal/00963003	https://www.sciencedirect.com/science/journal/00963003	X
iajs-2677	335	3	https://www.sciencedirect.com/science/journal/00963003/218/3	https://www.sciencedirect.com/science/journal/00963003/218/3	PROPN
iajs-2677	335	4	https://doi.org/10.1016/j.amc.2020.125904	https://doi.org/10.1016/j.amc.2020.125904	PROPN
iajs-2677	335	5	https://doi.org/10.1016/j.ejor.2021.01.025	https://doi.org/10.1016/j.ejor.2021.01.025	X
iajs-2677	335	6	https://doi.org/10.1016/j.amc.2020.125904	https://doi.org/10.1016/j.amc.2020.125904	PUNCT
iajs-2677	335	7	ibn	ibn	PROPN
iajs-2677	335	8	al	al	PROPN
iajs-2677	335	9	-	-	PUNCT
iajs-2677	335	10	haitham	haitham	PROPN
iajs-2677	335	11	jour	jour	X
iajs-2677	335	12	.	.	PROPN
iajs-2677	336	1	for	for	ADP
iajs-2677	336	2	pure	pure	ADJ
iajs-2677	336	3	&	&	CCONJ
iajs-2677	336	4	appl	appl	PROPN
iajs-2677	336	5	.	.	PUNCT
iajs-2677	337	1	sci	sci	PROPN
iajs-2677	337	2	.	.	PROPN
iajs-2677	338	1	34(3)2021	34(3)2021	NUM
iajs-2677	338	2	59	59	NUM
iajs-2677	338	3	11	11	NUM
iajs-2677	338	4	.	.	PUNCT
iajs-2677	339	1	abdul	abdul	PROPN
iajs-2677	339	2	-	-	PUNCT
iajs-2677	339	3	razaq	razaq	PROPN
iajs-2677	339	4	,	,	PUNCT
iajs-2677	339	5	t.	t.	PROPN
iajs-2677	339	6	s.	s.	PROPN
iajs-2677	339	7	;	;	PUNCT
iajs-2677	339	8	akram	akram	PROPN
iajs-2677	339	9	,	,	PUNCT
iajs-2677	339	10	a.	a.	NOUN
iajs-2677	339	11	o.	o.	PROPN
iajs-2677	339	12	local	local	ADJ
iajs-2677	339	13	search	search	NOUN
iajs-2677	339	14	algorithms	algorithm	NOUN
iajs-2677	339	15	for	for	ADP
iajs-2677	339	16	multi	multi	ADJ
iajs-2677	339	17	-	-	ADJ
iajs-2677	339	18	criteria	criteria	ADJ
iajs-2677	339	19	single	single	ADJ
iajs-2677	339	20	machine	machine	NOUN
iajs-2677	339	21	scheduling	scheduling	NOUN
iajs-2677	339	22	problem	problem	NOUN
iajs-2677	339	23	.	.	PUNCT
iajs-2677	340	1	ibn	ibn	PROPN
iajs-2677	340	2	al	al	PROPN
iajs-2677	340	3	-	-	PUNCT
iajs-2677	340	4	haitham	haitham	PROPN
iajs-2677	340	5	journal	journal	PROPN
iajs-2677	340	6	for	for	ADP
iajs-2677	340	7	pure	pure	ADJ
iajs-2677	340	8	and	and	CCONJ
iajs-2677	340	9	applied	apply	VERB
iajs-2677	340	10	science	science	NOUN
iajs-2677	340	11	(	(	PUNCT
iajs-2677	340	12	special	special	ADJ
iajs-2677	340	13	issue	issue	NOUN
iajs-2677	340	14	)	)	PUNCT
iajs-2677	340	15	.	.	PUNCT
iajs-2677	341	1	2017	2017	NUM
iajs-2677	341	2	,	,	PUNCT
iajs-2677	341	3	436	436	NUM
iajs-2677	341	4	-	-	SYM
iajs-2677	341	5	451	451	NUM
iajs-2677	341	6	,	,	PUNCT
iajs-2677	341	7	http://dx.doi.org/10.30526/2017.ihsciconf.1817	http://dx.doi.org/10.30526/2017.ihsciconf.1817	NUM
iajs-2677	341	8	.	.	NOUN
iajs-2677	341	9	12	12	NUM
iajs-2677	341	10	.	.	PUNCT
iajs-2677	342	1	abdullah	abdullah	PROPN
iajs-2677	342	2	,	,	PUNCT
iajs-2677	342	3	h.	h.	PROPN
iajs-2677	342	4	f.	f.	PROPN
iajs-2677	342	5	multicriteria	multicriteria	PROPN
iajs-2677	342	6	scheduling	scheduling	NOUN
iajs-2677	342	7	problems	problem	NOUN
iajs-2677	342	8	to	to	PART
iajs-2677	342	9	minimize	minimize	VERB
iajs-2677	342	10	total	total	ADJ
iajs-2677	342	11	tardiness	tardiness	NOUN
iajs-2677	342	12	subject	subject	NOUN
iajs-2677	342	13	to	to	ADP
iajs-2677	342	14	maximum	maximum	ADJ
iajs-2677	342	15	earliness	earliness	NOUN
iajs-2677	342	16	or	or	CCONJ
iajs-2677	342	17	tardiness	tardiness	NOUN
iajs-2677	342	18	.	.	PUNCT
iajs-2677	343	1	ibn	ibn	PROPN
iajs-2677	343	2	al	al	PROPN
iajs-2677	343	3	-	-	PUNCT
iajs-2677	343	4	haitham	haitham	PROPN
iajs-2677	343	5	journal	journal	PROPN
iajs-2677	343	6	for	for	ADP
iajs-2677	343	7	pure	pure	ADJ
iajs-2677	343	8	and	and	CCONJ
iajs-2677	343	9	applied	applied	ADJ
iajs-2677	343	10	science	science	NOUN
iajs-2677	343	11	.	.	PUNCT
iajs-2677	344	1	2010	2010	NUM
iajs-2677	344	2	,	,	PUNCT
iajs-2677	344	3	23	23	NUM
iajs-2677	344	4	,	,	PUNCT
iajs-2677	344	5	311	311	NUM
iajs-2677	344	6	-	-	SYM
iajs-2677	344	7	320	320	NUM
iajs-2677	344	8	,	,	PUNCT
iajs-2677	344	9	http://dx.doi.org/10.30526/2017.ihsciconf.1817	http://dx.doi.org/10.30526/2017.ihsciconf.1817	NUM
iajs-2677	344	10	.	.	NOUN
iajs-2677	345	1	13	13	NUM
iajs-2677	345	2	.	.	PUNCT
iajs-2677	345	3	tavakkoli	tavakkoli	NOUN
iajs-2677	345	4	-	-	PUNCT
iajs-2677	345	5	moghaddam	moghaddam	NOUN
iajs-2677	345	6	,	,	PUNCT
iajs-2677	345	7	r.	r.	PROPN
iajs-2677	345	8	;	;	PUNCT
iajs-2677	345	9	moslehi	moslehi	NOUN
iajs-2677	345	10	,	,	PUNCT
iajs-2677	345	11	g.	g.	PROPN
iajs-2677	345	12	;	;	PUNCT
iajs-2677	345	13	vasei	vasei	ADJ
iajs-2677	345	14	,	,	PUNCT
iajs-2677	345	15	m.	m.	NOUN
iajs-2677	345	16	;	;	PUNCT
iajs-2677	345	17	azaron	azaron	PROPN
iajs-2677	345	18	,	,	PUNCT
iajs-2677	345	19	a.	a.	NOUN
iajs-2677	345	20	a	a	DET
iajs-2677	345	21	branch	branch	NOUN
iajs-2677	345	22	-	-	PUNCT
iajs-2677	345	23	and	and	CCONJ
iajs-2677	345	24	-	-	PUNCT
iajs-2677	345	25	bound	bind	VERB
iajs-2677	345	26	algorithm	algorithm	NOUN
iajs-2677	345	27	for	for	ADP
iajs-2677	345	28	a	a	DET
iajs-2677	345	29	single	single	ADJ
iajs-2677	345	30	machine	machine	NOUN
iajs-2677	345	31	sequencing	sequence	VERB
iajs-2677	345	32	to	to	PART
iajs-2677	345	33	minimize	minimize	VERB
iajs-2677	345	34	the	the	DET
iajs-2677	345	35	sum	sum	NOUN
iajs-2677	345	36	of	of	ADP
iajs-2677	345	37	maximum	maximum	ADJ
iajs-2677	345	38	earliness	earliness	NOUN
iajs-2677	345	39	and	and	CCONJ
iajs-2677	345	40	tardiness	tardiness	NOUN
iajs-2677	345	41	with	with	ADP
iajs-2677	345	42	idle	idle	ADJ
iajs-2677	345	43	insert	insert	NOUN
iajs-2677	345	44	.	.	PUNCT
iajs-2677	346	1	applied	apply	VERB
iajs-2677	346	2	mathematics	mathematic	NOUN
iajs-2677	346	3	and	and	CCONJ
iajs-2677	346	4	computation	computation	NOUN
iajs-2677	346	5	.	.	PUNCT
iajs-2677	347	1	2006	2006	NUM
iajs-2677	347	2	,	,	PUNCT
iajs-2677	347	3	174	174	NUM
iajs-2677	347	4	,	,	PUNCT
iajs-2677	347	5	388–408	388–408	NUM
iajs-2677	347	6	,	,	PUNCT
iajs-2677	347	7	https://doi.org/10.1016/j.amc.2020.125904	https://doi.org/10.1016/j.amc.2020.125904	PROPN
iajs-2677	347	8	.	.	PUNCT
iajs-2677	348	1	14	14	NUM
iajs-2677	348	2	.	.	PUNCT
iajs-2677	349	1	mahnam	mahnam	PROPN
iajs-2677	349	2	,	,	PUNCT
iajs-2677	349	3	m.	m.	NOUN
iajs-2677	349	4	;	;	PUNCT
iajs-2677	349	5	moslehi	moslehi	NOUN
iajs-2677	349	6	,	,	PUNCT
iajs-2677	349	7	g.	g.	PROPN
iajs-2677	349	8	a	a	DET
iajs-2677	349	9	branch	branch	NOUN
iajs-2677	349	10	and	and	CCONJ
iajs-2677	349	11	bound	bind	VERB
iajs-2677	349	12	algorithm	algorithm	NOUN
iajs-2677	349	13	for	for	ADP
iajs-2677	349	14	minimizing	minimize	VERB
iajs-2677	349	15	the	the	DET
iajs-2677	349	16	sum	sum	NOUN
iajs-2677	349	17	of	of	ADP
iajs-2677	349	18	maximum	maximum	ADJ
iajs-2677	349	19	earliness	earliness	NOUN
iajs-2677	349	20	and	and	CCONJ
iajs-2677	349	21	tardiness	tardiness	NOUN
iajs-2677	349	22	with	with	ADP
iajs-2677	349	23	unequal	unequal	ADJ
iajs-2677	349	24	release	release	NOUN
iajs-2677	349	25	times	time	NOUN
iajs-2677	349	26	.	.	PUNCT
iajs-2677	350	1	engineering	engineer	VERB
iajs-2677	350	2	optimization	optimization	NOUN
iajs-2677	350	3	.	.	PUNCT
iajs-2677	351	1	2009	2009	NUM
iajs-2677	351	2	,	,	PUNCT
iajs-2677	351	3	41	41	NUM
iajs-2677	351	4	,	,	PUNCT
iajs-2677	351	5	521–536	521–536	NUM
iajs-2677	351	6	.	.	PUNCT
iajs-2677	352	1	15	15	NUM
iajs-2677	352	2	.	.	PUNCT
iajs-2677	352	3	moslehi	moslehi	NOUN
iajs-2677	352	4	,	,	PUNCT
iajs-2677	352	5	g.	g.	PROPN
iajs-2677	352	6	;	;	PUNCT
iajs-2677	352	7	mahnam	mahnam	PROPN
iajs-2677	352	8	,	,	PUNCT
iajs-2677	352	9	m.	m.	NOUN
iajs-2677	352	10	;	;	PUNCT
iajs-2677	352	11	amin	amin	NOUN
iajs-2677	352	12	-	-	NOUN
iajs-2677	352	13	nayeri	nayeri	PROPN
iajs-2677	352	14	,	,	PUNCT
iajs-2677	352	15	m.	m.	NOUN
iajs-2677	352	16	;	;	PUNCT
iajs-2677	352	17	azaron	azaron	PROPN
iajs-2677	352	18	,	,	PUNCT
iajs-2677	352	19	a.	a.	NOUN
iajs-2677	352	20	a	a	DET
iajs-2677	352	21	branch	branch	NOUN
iajs-2677	352	22	-	-	PUNCT
iajs-2677	352	23	and	and	CCONJ
iajs-2677	352	24	-	-	PUNCT
iajs-2677	352	25	bound	bind	VERB
iajs-2677	352	26	algorithm	algorithm	NOUN
iajs-2677	352	27	to	to	PART
iajs-2677	352	28	minimize	minimize	VERB
iajs-2677	352	29	the	the	DET
iajs-2677	352	30	sum	sum	NOUN
iajs-2677	352	31	of	of	ADP
iajs-2677	352	32	maximum	maximum	ADJ
iajs-2677	352	33	earliness	earliness	NOUN
iajs-2677	352	34	and	and	CCONJ
iajs-2677	352	35	tardiness	tardiness	NOUN
iajs-2677	352	36	in	in	ADP
iajs-2677	352	37	the	the	DET
iajs-2677	352	38	single	single	ADJ
iajs-2677	352	39	machine	machine	NOUN
iajs-2677	352	40	.	.	PUNCT
iajs-2677	353	1	int	int	NOUN
iajs-2677	353	2	.	.	PUNCT
iajs-2677	354	1	journal	journal	PROPN
iajs-2677	354	2	operational	operational	ADJ
iajs-2677	354	3	research	research	NOUN
iajs-2677	354	4	.	.	PUNCT
iajs-2677	355	1	2010	2010	NUM
iajs-2677	355	2	,	,	PUNCT
iajs-2677	355	3	8	8	NUM
iajs-2677	355	4	,	,	PUNCT
iajs-2677	355	5	458	458	NUM
iajs-2677	355	6	-	-	SYM
iajs-2677	355	7	482	482	NUM
iajs-2677	355	8	.	.	PROPN
iajs-2677	356	1	16	16	NUM
iajs-2677	356	2	.	.	PUNCT
iajs-2677	357	1	hoogeveen	hoogeveen	PROPN
iajs-2677	357	2	,	,	PUNCT
iajs-2677	357	3	j.a	j.a	PROPN
iajs-2677	357	4	.	.	PROPN
iajs-2677	357	5	;	;	PUNCT
iajs-2677	357	6	van	van	PROPN
iajs-2677	357	7	de	de	PROPN
iajs-2677	357	8	velde	velde	PROPN
iajs-2677	357	9	,	,	PUNCT
iajs-2677	357	10	s.l	s.l	PROPN
iajs-2677	357	11	.	.	NOUN
iajs-2677	357	12	minimizing	minimize	VERB
iajs-2677	357	13	total	total	ADJ
iajs-2677	357	14	completion	completion	NOUN
iajs-2677	357	15	time	time	NOUN
iajs-2677	357	16	and	and	CCONJ
iajs-2677	357	17	maximum	maximum	ADJ
iajs-2677	357	18	cost	cost	NOUN
iajs-2677	357	19	simultaneously	simultaneously	ADV
iajs-2677	357	20	is	be	AUX
iajs-2677	357	21	solvable	solvable	ADJ
iajs-2677	357	22	in	in	ADP
iajs-2677	357	23	polynomial	polynomial	ADJ
iajs-2677	357	24	time	time	NOUN
iajs-2677	357	25	.	.	PUNCT
iajs-2677	358	1	operations	operation	NOUN
iajs-2677	358	2	research	research	NOUN
iajs-2677	358	3	letters	letter	NOUN
iajs-2677	358	4	.	.	PUNCT
iajs-2677	359	1	1995	1995	NUM
iajs-2677	359	2	,	,	PUNCT
iajs-2677	359	3	17	17	NUM
iajs-2677	359	4	,	,	PUNCT
iajs-2677	359	5	205	205	NUM
iajs-2677	359	6	–	–	PUNCT
iajs-2677	359	7	208	208	NUM
iajs-2677	359	8	.	.	PUNCT
iajs-2677	360	1	https://www.iasj.net/iasj/journal/44/issues	https://www.iasj.net/iasj/journal/44/issue	NOUN
iajs-2677	360	2	https://dx.doi.org/10.30526/2017.ihsciconf.1817	https://dx.doi.org/10.30526/2017.ihsciconf.1817	X
iajs-2677	360	3	https://www.iasj.net/iasj/search?query=au:%22h.%20f%20abdullah.%22	https://www.iasj.net/iasj/search?query=au:%22h.%20f%20abdullah.%22	VERB
iajs-2677	360	4	https://www.iasj.net/iasj/journal/44/issues	https://www.iasj.net/iasj/journal/44/issue	NOUN
iajs-2677	360	5	https://www.iasj.net/iasj/issue/227	https://www.iasj.net/iasj/issue/227	PROPN
iajs-2677	360	6	https://dx.doi.org/10.30526/2017.ihsciconf.1817	https://dx.doi.org/10.30526/2017.ihsciconf.1817	X
iajs-2677	360	7	https://doi.org/10.1016/j.amc.2020.125904	https://doi.org/10.1016/j.amc.2020.125904	PUNCT