id	sid	tid	token	lemma	pos
iajs-553	1	1	mathematics	mathematic	NOUN
iajs-553	1	2	356	356	NUM
iajs-553	1	3	مجلة	مجلة	NOUN
iajs-553	1	4	إبن	إبن	VERB
iajs-553	1	5	الهيثم	الهيثم	ADJ
iajs-553	1	6	للعلوم	للعلوم	NOUN
iajs-553	1	7	الصرفة	الصرفة	NOUN
iajs-553	1	8	و	و	PRON
iajs-553	1	9	التطبيقية	التطبيقية	ADJ
iajs-553	1	10	2012	2012	NUM
iajs-553	1	11	السنة	السنة	NOUN
iajs-553	1	12	25	25	NUM
iajs-553	1	13	المجلد	المجلد	NOUN
iajs-553	1	14	3	3	NUM
iajs-553	1	15	العدد	العدد	PROPN
iajs-553	1	16	ibn	ibn	PROPN
iajs-553	1	17	al	al	PROPN
iajs-553	1	18	-	-	PUNCT
iajs-553	1	19	haitham	haitham	PROPN
iajs-553	1	20	journal	journal	PROPN
iajs-553	1	21	for	for	ADP
iajs-553	1	22	pure	pure	ADJ
iajs-553	1	23	and	and	CCONJ
iajs-553	1	24	applied	apply	VERB
iajs-553	1	25	science	science	NOUN
iajs-553	1	26	no	no	NOUN
iajs-553	1	27	.	.	NOUN
iajs-553	1	28	3	3	NUM
iajs-553	1	29	vol	vol	NOUN
iajs-553	1	30	.	.	PUNCT
iajs-553	2	1	25	25	NUM
iajs-553	2	2	year	year	NOUN
iajs-553	2	3	2012	2012	NUM
iajs-553	2	4	minimizing	minimize	VERB
iajs-553	2	5	total	total	ADJ
iajs-553	2	6	completion	completion	NOUN
iajs-553	2	7	time	time	NOUN
iajs-553	2	8	and	and	CCONJ
iajs-553	2	9	maximum	maximum	ADJ
iajs-553	2	10	late	late	ADJ
iajs-553	2	11	work	work	NOUN
iajs-553	2	12	simultaneously	simultaneously	ADV
iajs-553	2	13	t.	t.	PROPN
iajs-553	2	14	s.	s.	PROPN
iajs-553	2	15	abdul	abdul	PROPN
iajs-553	2	16	-	-	PUNCT
iajs-553	2	17	razaq	razaq	PROPN
iajs-553	2	18	and	and	CCONJ
iajs-553	2	19	f.	f.	PROPN
iajs-553	2	20	sh	sh	PROPN
iajs-553	2	21	.	.	PROPN
iajs-553	2	22	fandi	fandi	PROPN
iajs-553	2	23	department	department	PROPN
iajs-553	2	24	of	of	ADP
iajs-553	2	25	mathematics	mathematics	PROPN
iajs-553	2	26	,	,	PUNCT
iajs-553	2	27	college	college	NOUN
iajs-553	2	28	of	of	ADP
iajs-553	2	29	science	science	NOUN
iajs-553	2	30	,	,	PUNCT
iajs-553	2	31	al_mustansiriya	al_mustansiriya	PROPN
iajs-553	2	32	university	university	PROPN
iajs-553	2	33	department	department	PROPN
iajs-553	2	34	of	of	ADP
iajs-553	2	35	mathematics	mathematics	PROPN
iajs-553	2	36	,	,	PUNCT
iajs-553	2	37	college	college	NOUN
iajs-553	2	38	of	of	ADP
iajs-553	2	39	education	education	NOUN
iajs-553	2	40	,	,	PUNCT
iajs-553	2	41	for	for	ADP
iajs-553	2	42	pure	pure	ADJ
iajs-553	2	43	sciences	science	NOUN
iajs-553	2	44	,	,	PUNCT
iajs-553	2	45	al	al	PROPN
iajs-553	2	46	-	-	PUNCT
iajs-553	2	47	anbar	anbar	PROPN
iajs-553	2	48	university	university	NOUN
iajs-553	2	49	received	receive	VERB
iajs-553	2	50	in	in	ADP
iajs-553	2	51	:	:	PUNCT
iajs-553	2	52	1	1	NUM
iajs-553	2	53	april	april	PROPN
iajs-553	2	54	2012	2012	NUM
iajs-553	2	55	accepted	accept	VERB
iajs-553	2	56	in	in	ADP
iajs-553	2	57	:	:	PUNCT
iajs-553	2	58	22	22	NUM
iajs-553	2	59	april	april	PROPN
iajs-553	2	60	2012	2012	NUM
iajs-553	2	61	abstract	abstract	NOUN
iajs-553	2	62	in	in	ADP
iajs-553	2	63	this	this	DET
iajs-553	2	64	paper	paper	NOUN
iajs-553	2	65	,	,	PUNCT
iajs-553	2	66	the	the	DET
iajs-553	2	67	problem	problem	NOUN
iajs-553	2	68	of	of	ADP
iajs-553	2	69	scheduling	scheduling	NOUN
iajs-553	2	70	jobs	job	NOUN
iajs-553	2	71	on	on	ADP
iajs-553	2	72	one	one	NUM
iajs-553	2	73	machine	machine	NOUN
iajs-553	2	74	for	for	ADP
iajs-553	2	75	a	a	DET
iajs-553	2	76	variety	variety	NOUN
iajs-553	2	77	multicriteria	multicriteria	NOUN
iajs-553	2	78	are	be	AUX
iajs-553	2	79	considered	consider	VERB
iajs-553	2	80	to	to	PART
iajs-553	2	81	minimize	minimize	VERB
iajs-553	2	82	total	total	ADJ
iajs-553	2	83	completion	completion	NOUN
iajs-553	2	84	time	time	NOUN
iajs-553	2	85	and	and	CCONJ
iajs-553	2	86	maximum	maximum	ADJ
iajs-553	2	87	late	late	ADJ
iajs-553	2	88	work	work	NOUN
iajs-553	2	89	.	.	PUNCT
iajs-553	3	1	a	a	DET
iajs-553	3	2	set	set	NOUN
iajs-553	3	3	of	of	ADP
iajs-553	3	4	n	n	DET
iajs-553	3	5	independent	independent	ADJ
iajs-553	3	6	jobs	job	NOUN
iajs-553	3	7	has	have	VERB
iajs-553	3	8	to	to	PART
iajs-553	3	9	be	be	AUX
iajs-553	3	10	scheduled	schedule	VERB
iajs-553	3	11	on	on	ADP
iajs-553	3	12	a	a	DET
iajs-553	3	13	single	single	ADJ
iajs-553	3	14	machine	machine	NOUN
iajs-553	3	15	that	that	PRON
iajs-553	3	16	is	be	AUX
iajs-553	3	17	continuously	continuously	ADV
iajs-553	3	18	available	available	ADJ
iajs-553	3	19	from	from	ADP
iajs-553	3	20	time	time	NOUN
iajs-553	3	21	zero	zero	NUM
iajs-553	3	22	onwards	onwards	ADV
iajs-553	3	23	and	and	CCONJ
iajs-553	3	24	that	that	PRON
iajs-553	3	25	can	can	AUX
iajs-553	3	26	handle	handle	VERB
iajs-553	3	27	no	no	DET
iajs-553	3	28	more	more	ADJ
iajs-553	3	29	than	than	ADP
iajs-553	3	30	one	one	NUM
iajs-553	3	31	job	job	NOUN
iajs-553	3	32	at	at	ADP
iajs-553	3	33	a	a	DET
iajs-553	3	34	time	time	NOUN
iajs-553	3	35	.	.	PUNCT
iajs-553	4	1	job	job	NOUN
iajs-553	4	2	i,(i=1,	i,(i=1,	PROPN
iajs-553	4	3	…	…	PUNCT
iajs-553	4	4	,n	,n	NOUN
iajs-553	4	5	)	)	PUNCT
iajs-553	4	6	requires	require	VERB
iajs-553	4	7	processing	process	VERB
iajs-553	4	8	during	during	ADP
iajs-553	4	9	a	a	DET
iajs-553	4	10	given	give	VERB
iajs-553	4	11	positive	positive	ADJ
iajs-553	4	12	uninterrupted	uninterrupted	ADJ
iajs-553	4	13	time	time	NOUN
iajs-553	4	14	pi	pi	NOUN
iajs-553	4	15	,	,	PUNCT
iajs-553	4	16	and	and	CCONJ
iajs-553	4	17	its	its	PRON
iajs-553	4	18	due	due	ADJ
iajs-553	4	19	date	date	NOUN
iajs-553	4	20	di	di	X
iajs-553	4	21	.	.	PROPN
iajs-553	5	1	for	for	ADP
iajs-553	5	2	the	the	DET
iajs-553	5	3	bicriteria	bicriteria	PROPN
iajs-553	5	4	problems	problem	NOUN
iajs-553	5	5	,	,	PUNCT
iajs-553	5	6	some	some	DET
iajs-553	5	7	algorithms	algorithm	NOUN
iajs-553	5	8	are	be	AUX
iajs-553	5	9	proposed	propose	VERB
iajs-553	5	10	to	to	PART
iajs-553	5	11	find	find	VERB
iajs-553	5	12	efficient	efficient	ADJ
iajs-553	5	13	(	(	PUNCT
iajs-553	5	14	pareto	pareto	NOUN
iajs-553	5	15	)	)	PUNCT
iajs-553	5	16	solutions	solution	NOUN
iajs-553	5	17	for	for	ADP
iajs-553	5	18	simultaneous	simultaneous	ADJ
iajs-553	5	19	case	case	NOUN
iajs-553	5	20	.	.	PUNCT
iajs-553	6	1	also	also	ADV
iajs-553	6	2	for	for	ADP
iajs-553	6	3	the	the	DET
iajs-553	6	4	multicriteria	multicriteria	PROPN
iajs-553	6	5	problem	problem	NOUN
iajs-553	6	6	we	we	PRON
iajs-553	6	7	proposed	propose	VERB
iajs-553	6	8	general	general	ADJ
iajs-553	6	9	algorithms	algorithm	NOUN
iajs-553	6	10	which	which	PRON
iajs-553	6	11	gives	give	VERB
iajs-553	6	12	efficient	efficient	ADJ
iajs-553	6	13	solutions	solution	NOUN
iajs-553	6	14	within	within	ADP
iajs-553	6	15	the	the	DET
iajs-553	6	16	efficient	efficient	ADJ
iajs-553	6	17	range	range	NOUN
iajs-553	6	18	.	.	PUNCT
iajs-553	7	1	keyword	keyword	NOUN
iajs-553	7	2	:	:	PUNCT
iajs-553	7	3	schedule	schedule	NOUN
iajs-553	7	4	,	,	PUNCT
iajs-553	7	5	multicriteria	multicriteria	NOUN
iajs-553	7	6	,	,	PUNCT
iajs-553	7	7	single	single	ADJ
iajs-553	7	8	machine	machine	NOUN
iajs-553	7	9	,	,	PUNCT
iajs-553	7	10	bicriteria	bicriteria	PROPN
iajs-553	7	11	.	.	PUNCT
iajs-553	8	1	introduction	introduction	NOUN
iajs-553	8	2	the	the	DET
iajs-553	8	3	problem	problem	NOUN
iajs-553	8	4	of	of	ADP
iajs-553	8	5	scheduling	schedule	VERB
iajs-553	8	6	a	a	DET
iajs-553	8	7	set	set	NOUN
iajs-553	8	8	n={1,	n={1,	NUM
iajs-553	8	9	…	…	SYM
iajs-553	8	10	..	..	PUNCT
iajs-553	8	11	,n	,n	NOUN
iajs-553	8	12	}	}	PUNCT
iajs-553	8	13	of	of	ADP
iajs-553	8	14	n	n	PRON
iajs-553	8	15	jobs	job	NOUN
iajs-553	8	16	on	on	ADP
iajs-553	8	17	a	a	DET
iajs-553	8	18	single	single	ADJ
iajs-553	8	19	machine	machine	NOUN
iajs-553	8	20	to	to	PART
iajs-553	8	21	minimize	minimize	VERB
iajs-553	8	22	a	a	DET
iajs-553	8	23	variety	variety	NOUN
iajs-553	8	24	of	of	ADP
iajs-553	8	25	multicriteria	multicriteria	NOUN
iajs-553	8	26	may	may	AUX
iajs-553	8	27	be	be	AUX
iajs-553	8	28	stated	state	VERB
iajs-553	8	29	as	as	SCONJ
iajs-553	8	30	follows	follow	VERB
iajs-553	8	31	.	.	PUNCT
iajs-553	9	1	each	each	DET
iajs-553	9	2	job	job	NOUN
iajs-553	9	3	i	i	PRON
iajs-553	9	4	,	,	PUNCT
iajs-553	9	5	(	(	PUNCT
iajs-553	9	6	i=1,	i=1,	NOUN
iajs-553	9	7	…	…	PUNCT
iajs-553	9	8	.,n	.,n	NUM
iajs-553	9	9	)	)	PUNCT
iajs-553	9	10	is	be	AUX
iajs-553	9	11	to	to	PART
iajs-553	9	12	be	be	AUX
iajs-553	9	13	processed	process	VERB
iajs-553	9	14	on	on	ADP
iajs-553	9	15	a	a	DET
iajs-553	9	16	single	single	ADJ
iajs-553	9	17	machine	machine	NOUN
iajs-553	9	18	which	which	PRON
iajs-553	9	19	can	can	AUX
iajs-553	9	20	handle	handle	VERB
iajs-553	9	21	only	only	ADV
iajs-553	9	22	one	one	NUM
iajs-553	9	23	job	job	NOUN
iajs-553	9	24	at	at	ADP
iajs-553	9	25	a	a	DET
iajs-553	9	26	time	time	NOUN
iajs-553	9	27	.	.	PUNCT
iajs-553	10	1	associ	associ	PROPN
iajs-553	10	2	-	-	PUNCT
iajs-553	10	3	ated	ate	VERB
iajs-553	10	4	with	with	ADP
iajs-553	10	5	job	job	NOUN
iajs-553	10	6	i	i	PRON
iajs-553	10	7	its	its	PRON
iajs-553	10	8	processing	processing	NOUN
iajs-553	10	9	time	time	NOUN
iajs-553	10	10	pi	pi	NOUN
iajs-553	10	11	and	and	CCONJ
iajs-553	10	12	its	its	PRON
iajs-553	10	13	due	due	ADJ
iajs-553	10	14	date	date	NOUN
iajs-553	10	15	di	di	X
iajs-553	10	16	.	.	PUNCT
iajs-553	11	1	all	all	DET
iajs-553	11	2	jobs	job	NOUN
iajs-553	11	3	are	be	AUX
iajs-553	11	4	available	available	ADJ
iajs-553	11	5	for	for	ADP
iajs-553	11	6	processing	processing	NOUN
iajs-553	11	7	at	at	ADP
iajs-553	11	8	time	time	NOUN
iajs-553	11	9	zero	zero	NUM
iajs-553	11	10	.	.	PUNCT
iajs-553	12	1	a	a	DET
iajs-553	12	2	schedule	schedule	NOUN
iajs-553	12	3	σ=(1,	σ=(1,	VERB
iajs-553	12	4	…	…	SYM
iajs-553	12	5	,n	,n	NOUN
iajs-553	12	6	)	)	PUNCT
iajs-553	12	7	specifies	specifie	NOUN
iajs-553	12	8	for	for	ADP
iajs-553	12	9	each	each	DET
iajs-553	12	10	job	job	NOUN
iajs-553	12	11	when	when	SCONJ
iajs-553	12	12	it	it	PRON
iajs-553	12	13	is	be	AUX
iajs-553	12	14	executed	execute	VERB
iajs-553	12	15	while	while	SCONJ
iajs-553	12	16	observing	observe	VERB
iajs-553	12	17	the	the	DET
iajs-553	12	18	machine	machine	NOUN
iajs-553	12	19	availability	availability	NOUN
iajs-553	12	20	constraints	constraint	NOUN
iajs-553	12	21	and	and	CCONJ
iajs-553	12	22	the	the	DET
iajs-553	12	23	schedule	schedule	NOUN
iajs-553	12	24	produce	produce	VERB
iajs-553	12	25	a	a	DET
iajs-553	12	26	completion	completion	NOUN
iajs-553	12	27	time	time	NOUN
iajs-553	12	28	ci	ci	NOUN
iajs-553	12	29	=	=	NOUN
iajs-553	12	30	σpi	σpi	NOUN
iajs-553	12	31	for	for	ADP
iajs-553	12	32	each	each	DET
iajs-553	12	33	job	job	NOUN
iajs-553	13	1	i	i	PRON
iajs-553	13	2	,	,	PUNCT
iajs-553	13	3	in	in	ADP
iajs-553	13	4	this	this	DET
iajs-553	13	5	paper	paper	NOUN
iajs-553	13	6	,	,	PUNCT
iajs-553	13	7	for	for	ADP
iajs-553	13	8	the	the	DET
iajs-553	13	9	first	first	ADJ
iajs-553	13	10	time	time	NOUN
iajs-553	13	11	.	.	PUNCT
iajs-553	14	1	we	we	PRON
iajs-553	14	2	use	use	VERB
iajs-553	14	3	the	the	DET
iajs-553	14	4	late	late	ADJ
iajs-553	14	5	work	work	NOUN
iajs-553	14	6	object	object	NOUN
iajs-553	14	7	in	in	ADP
iajs-553	14	8	multicriteria	multicriteria	PROPN
iajs-553	14	9	scheduling	scheduling	NOUN
iajs-553	14	10	problem	problem	NOUN
iajs-553	14	11	.	.	PUNCT
iajs-553	15	1	given	give	VERB
iajs-553	15	2	a	a	DET
iajs-553	15	3	schedule	schedule	NOUN
iajs-553	15	4	σ	σ	NOUN
iajs-553	15	5	,	,	PUNCT
iajs-553	15	6	the	the	DET
iajs-553	15	7	late	late	ADJ
iajs-553	15	8	work	work	NOUN
iajs-553	15	9	vi(σ	vi(σ	NOUN
iajs-553	15	10	)	)	PUNCT
iajs-553	15	11	for	for	ADP
iajs-553	15	12	job	job	NOUN
iajs-553	15	13	i,(i=1,	i,(i=1,	X
iajs-553	15	14	…	…	X
iajs-553	15	15	,n	,n	NOUN
iajs-553	15	16	)	)	PUNCT
iajs-553	15	17	which	which	PRON
iajs-553	15	18	is	be	AUX
iajs-553	15	19	amount	amount	NOUN
iajs-553	15	20	of	of	ADP
iajs-553	15	21	processing	processing	NOUN
iajs-553	15	22	performed	perform	VERB
iajs-553	15	23	on	on	ADP
iajs-553	15	24	job	job	NOUN
iajs-553	15	25	i	i	PRON
iajs-553	15	26	after	after	ADP
iajs-553	15	27	its	its	PRON
iajs-553	15	28	due	due	ADJ
iajs-553	15	29	date	date	NOUN
iajs-553	15	30	di	di	NOUN
iajs-553	15	31	,	,	PUNCT
iajs-553	15	32	is	be	AUX
iajs-553	15	33	easy	easy	ADJ
iajs-553	15	34	compute	compute	NOUN
iajs-553	15	35	.	.	PUNCT
iajs-553	16	1	we	we	PRON
iajs-553	16	2	abbreviate	abbreviate	VERB
iajs-553	16	3	vi(σ	vi(σ	NOUN
iajs-553	16	4	)	)	PUNCT
iajs-553	16	5	to	to	PART
iajs-553	16	6	vi	vi	VERB
iajs-553	16	7	for	for	ADP
iajs-553	16	8	each	each	DET
iajs-553	16	9	job	job	NOUN
iajs-553	16	10	i	i	PRON
iajs-553	16	11	,	,	PUNCT
iajs-553	16	12	hence	hence	ADV
iajs-553	16	13	we	we	PRON
iajs-553	16	14	have	have	VERB
iajs-553	16	15	:	:	PUNCT
iajs-553	16	16	(	(	PUNCT
iajs-553	16	17	1	1	X
iajs-553	16	18	)	)	PUNCT
iajs-553	16	19	if	if	SCONJ
iajs-553	16	20	vi=0	vi=0	ADJ
iajs-553	16	21	,	,	PUNCT
iajs-553	16	22	then	then	ADV
iajs-553	16	23	job	job	NOUN
iajs-553	16	24	i	i	PRON
iajs-553	16	25	is	be	AUX
iajs-553	16	26	early	early	ADJ
iajs-553	16	27	with	with	ADP
iajs-553	16	28	ci	ci	NOUN
iajs-553	16	29	≤	≤	PROPN
iajs-553	16	30	di	di	NOUN
iajs-553	16	31	.	.	PUNCT
iajs-553	17	1	(	(	PUNCT
iajs-553	17	2	2	2	X
iajs-553	17	3	)	)	PUNCT
iajs-553	17	4	if	if	SCONJ
iajs-553	17	5	0	0	NUM
iajs-553	17	6	<	<	X
iajs-553	17	7	vi	vi	X
iajs-553	17	8	<	<	X
iajs-553	17	9	pi	pi	NOUN
iajs-553	17	10	,	,	PUNCT
iajs-553	17	11	then	then	ADV
iajs-553	17	12	job	job	NOUN
iajs-553	17	13	i	i	PRON
iajs-553	17	14	is	be	AUX
iajs-553	17	15	partially	partially	ADV
iajs-553	17	16	early	early	ADJ
iajs-553	17	17	.	.	PUNCT
iajs-553	18	1	(	(	PUNCT
iajs-553	18	2	3	3	X
iajs-553	18	3	)	)	PUNCT
iajs-553	18	4	if	if	SCONJ
iajs-553	18	5	vi	vi	NOUN
iajs-553	18	6	=	=	SYM
iajs-553	18	7	pi	pi	NOUN
iajs-553	18	8	,	,	PUNCT
iajs-553	18	9	then	then	ADV
iajs-553	18	10	job	job	NOUN
iajs-553	18	11	i	i	PRON
iajs-553	18	12	is	be	AUX
iajs-553	18	13	late	late	ADJ
iajs-553	18	14	with	with	ADP
iajs-553	18	15	ci	ci	PROPN
iajs-553	18	16	≥	≥	PROPN
iajs-553	18	17	di	di	NOUN
iajs-553	18	18	+	+	CCONJ
iajs-553	18	19	pi	pi	NOUN
iajs-553	18	20	.	.	PUNCT
iajs-553	19	1	this	this	PRON
iajs-553	19	2	means	mean	VERB
iajs-553	19	3	that	that	SCONJ
iajs-553	19	4	the	the	DET
iajs-553	19	5	late	late	ADJ
iajs-553	19	6	work	work	NOUN
iajs-553	19	7	for	for	ADP
iajs-553	19	8	job	job	NOUN
iajs-553	19	9	i	i	PRON
iajs-553	19	10	is	be	AUX
iajs-553	19	11	given	give	VERB
iajs-553	19	12	by	by	ADP
iajs-553	19	13	vi=	vi=	NOUN
iajs-553	19	14	notation	notation	NOUN
iajs-553	19	15	and	and	CCONJ
iajs-553	19	16	basic	basic	ADJ
iajs-553	19	17	concepts	concept	NOUN
iajs-553	19	18	:	:	PUNCT
iajs-553	19	19	the	the	DET
iajs-553	19	20	following	follow	VERB
iajs-553	19	21	notation	notation	NOUN
iajs-553	19	22	will	will	AUX
iajs-553	19	23	be	be	AUX
iajs-553	19	24	used	use	VERB
iajs-553	19	25	in	in	ADP
iajs-553	19	26	this	this	DET
iajs-553	19	27	paper	paper	NOUN
iajs-553	19	28	:	:	PUNCT
iajs-553	19	29	n	n	NOUN
iajs-553	19	30	=	=	NOUN
iajs-553	19	31	number	number	NOUN
iajs-553	19	32	of	of	ADP
iajs-553	19	33	jobs	job	NOUN
iajs-553	19	34	.	.	PUNCT
iajs-553	20	1	pi	pi	NOUN
iajs-553	21	1	=	=	NOUN
iajs-553	21	2	processing	processing	NOUN
iajs-553	21	3	time	time	NOUN
iajs-553	21	4	of	of	ADP
iajs-553	21	5	job	job	NOUN
iajs-553	21	6	i.	i.	NOUN
iajs-553	21	7	di	di	PROPN
iajs-553	21	8	=	=	PUNCT
iajs-553	21	9	due	due	ADJ
iajs-553	21	10	date	date	NOUN
iajs-553	21	11	of	of	ADP
iajs-553	21	12	job	job	NOUN
iajs-553	21	13	i.	i.	NOUN
iajs-553	21	14	ci	ci	PROPN
iajs-553	21	15	=	=	PUNCT
iajs-553	21	16	completion	completion	NOUN
iajs-553	21	17	time	time	NOUN
iajs-553	21	18	of	of	ADP
iajs-553	21	19	job	job	NOUN
iajs-553	21	20	i.	i.	NOUN
iajs-553	21	21	σci=	σci=	VERB
iajs-553	21	22	the	the	DET
iajs-553	21	23	total	total	ADJ
iajs-553	21	24	completion	completion	NOUN
iajs-553	21	25	times	time	NOUN
iajs-553	21	26	.	.	PUNCT
iajs-553	22	1	mathematics	mathematic	NOUN
iajs-553	22	2	357	357	NUM
iajs-553	22	3	مجلة	مجلة	NOUN
iajs-553	22	4	إبن	إبن	VERB
iajs-553	22	5	الهيثم	الهيثم	ADJ
iajs-553	22	6	للعلوم	للعلوم	NOUN
iajs-553	22	7	الصرفة	الصرفة	NOUN
iajs-553	22	8	و	و	PRON
iajs-553	22	9	التطبيقية	التطبيقية	ADJ
iajs-553	22	10	2012	2012	NUM
iajs-553	22	11	السنة	السنة	NOUN
iajs-553	22	12	25	25	NUM
iajs-553	22	13	المجلد	المجلد	NOUN
iajs-553	22	14	3	3	NUM
iajs-553	22	15	العدد	العدد	PROPN
iajs-553	22	16	ibn	ibn	PROPN
iajs-553	22	17	al	al	PROPN
iajs-553	22	18	-	-	PUNCT
iajs-553	22	19	haitham	haitham	PROPN
iajs-553	22	20	journal	journal	PROPN
iajs-553	22	21	for	for	ADP
iajs-553	22	22	pure	pure	ADJ
iajs-553	22	23	and	and	CCONJ
iajs-553	22	24	applied	apply	VERB
iajs-553	22	25	science	science	NOUN
iajs-553	22	26	no	no	NOUN
iajs-553	22	27	.	.	NOUN
iajs-553	22	28	3	3	NUM
iajs-553	22	29	vol	vol	NOUN
iajs-553	22	30	.	.	PUNCT
iajs-553	23	1	25	25	NUM
iajs-553	23	2	year	year	NOUN
iajs-553	23	3	2012	2012	NUM
iajs-553	23	4	vi=	vi=	NOUN
iajs-553	23	5	the	the	DET
iajs-553	23	6	late	late	ADJ
iajs-553	23	7	work	work	NOUN
iajs-553	23	8	penalty	penalty	NOUN
iajs-553	23	9	for	for	ADP
iajs-553	23	10	job	job	NOUN
iajs-553	23	11	i.	i.	NOUN
iajs-553	23	12	vmax=	vmax=	NUM
iajs-553	23	13	max	max	PROPN
iajs-553	23	14	{	{	PUNCT
iajs-553	23	15	vi	vi	PROPN
iajs-553	23	16	}	}	PUNCT
iajs-553	23	17	,	,	PUNCT
iajs-553	23	18	the	the	DET
iajs-553	23	19	maximum	maximum	ADJ
iajs-553	23	20	late	late	ADJ
iajs-553	23	21	work	work	NOUN
iajs-553	23	22	.	.	PUNCT
iajs-553	24	1	li	li	PROPN
iajs-553	25	1	=	=	PUNCT
iajs-553	25	2	lateness	lateness	NOUN
iajs-553	25	3	of	of	ADP
iajs-553	25	4	job	job	NOUN
iajs-553	25	5	i	i	PRON
iajs-553	25	6	,	,	PUNCT
iajs-553	25	7	li	li	PROPN
iajs-553	25	8	=	=	PROPN
iajs-553	25	9	ci	ci	PROPN
iajs-553	25	10	di	di	PROPN
iajs-553	25	11	.	.	PROPN
iajs-553	25	12	ti	ti	PROPN
iajs-553	26	1	=	=	NOUN
iajs-553	26	2	tardiness	tardiness	NOUN
iajs-553	26	3	of	of	ADP
iajs-553	26	4	job	job	NOUN
iajs-553	26	5	i	i	PRON
iajs-553	26	6	,	,	PUNCT
iajs-553	26	7	ti	ti	PROPN
iajs-553	26	8	=	=	PROPN
iajs-553	26	9	max	max	PROPN
iajs-553	26	10	{	{	PUNCT
iajs-553	26	11	ci	ci	PROPN
iajs-553	26	12	di	di	X
iajs-553	26	13	,	,	PUNCT
iajs-553	26	14	0	0	NUM
iajs-553	26	15	}	}	PUNCT
iajs-553	26	16	.	.	PUNCT
iajs-553	27	1	lmax	lmax	NOUN
iajs-553	27	2	=	=	SYM
iajs-553	27	3	max{li	max{li	NOUN
iajs-553	27	4	}	}	PUNCT
iajs-553	27	5	,	,	PUNCT
iajs-553	27	6	maximum	maximum	ADJ
iajs-553	27	7	lateness	lateness	NOUN
iajs-553	27	8	of	of	ADP
iajs-553	27	9	all	all	DET
iajs-553	27	10	job	job	NOUN
iajs-553	27	11	in	in	ADP
iajs-553	27	12	a	a	DET
iajs-553	27	13	schedule	schedule	NOUN
iajs-553	27	14	.	.	PUNCT
iajs-553	28	1	tmax	tmax	ADV
iajs-553	28	2	=	=	PUNCT
iajs-553	28	3	max{ti	max{ti	X
iajs-553	28	4	}	}	PUNCT
iajs-553	28	5	,	,	PUNCT
iajs-553	28	6	maximum	maximum	ADJ
iajs-553	28	7	tardiness	tardiness	NOUN
iajs-553	28	8	of	of	ADP
iajs-553	28	9	all	all	DET
iajs-553	28	10	job	job	NOUN
iajs-553	28	11	in	in	ADP
iajs-553	28	12	a	a	DET
iajs-553	28	13	schedule	schedule	NOUN
iajs-553	28	14	.	.	PUNCT
iajs-553	29	1	the	the	DET
iajs-553	29	2	cost	cost	NOUN
iajs-553	29	3	fi	fi	NOUN
iajs-553	29	4	for	for	ADP
iajs-553	29	5	each	each	DET
iajs-553	29	6	job	job	NOUN
iajs-553	29	7	i	i	PRON
iajs-553	29	8	,	,	PUNCT
iajs-553	29	9	(	(	PUNCT
iajs-553	29	10	i=1,	i=1,	NOUN
iajs-553	29	11	…	…	PUNCT
iajs-553	29	12	,n	,n	NOUN
iajs-553	29	13	)	)	PUNCT
iajs-553	29	14	usually	usually	ADV
iajs-553	29	15	takes	take	VERB
iajs-553	29	16	on	on	ADP
iajs-553	29	17	the	the	DET
iajs-553	29	18	variable	variable	ADJ
iajs-553	29	19	ci	ci	PROPN
iajs-553	29	20	.	.	PUNCT
iajs-553	30	1	common	common	ADJ
iajs-553	30	2	optimality	optimality	NOUN
iajs-553	30	3	criteria	criterion	NOUN
iajs-553	30	4	are	be	AUX
iajs-553	30	5	usually	usually	ADV
iajs-553	30	6	in	in	ADP
iajs-553	30	7	the	the	DET
iajs-553	30	8	form	form	NOUN
iajs-553	30	9	σfi	σfi	PROPN
iajs-553	30	10	and	and	CCONJ
iajs-553	30	11	fmax=	fmax=	NUM
iajs-553	30	12	max{fi	max{fi	NOUN
iajs-553	30	13	}	}	PUNCT
iajs-553	30	14	.	.	PUNCT
iajs-553	31	1	theorem(1)(jackson	theorem(1)(jackson	NUM
iajs-553	31	2	1955)[1	1955)[1	NUM
iajs-553	31	3	]	]	PUNCT
iajs-553	31	4	.	.	PUNCT
iajs-553	32	1	the	the	DET
iajs-553	32	2	1//	1//	PROPN
iajs-553	32	3	tmax	tmax	PROPN
iajs-553	32	4	problem	problem	NOUN
iajs-553	32	5	is	be	AUX
iajs-553	32	6	minimized	minimize	VERB
iajs-553	32	7	by	by	ADP
iajs-553	32	8	sequencing	sequence	VERB
iajs-553	32	9	the	the	DET
iajs-553	32	10	jobs	job	NOUN
iajs-553	32	11	according	accord	VERB
iajs-553	32	12	to	to	ADP
iajs-553	32	13	the	the	DET
iajs-553	32	14	earliest	early	ADV
iajs-553	32	15	-	-	PUNCT
iajs-553	32	16	duedate	duedate	NOUN
iajs-553	32	17	(	(	PUNCT
iajs-553	32	18	edd	edd	PROPN
iajs-553	32	19	)	)	PUNCT
iajs-553	32	20	rule	rule	NOUN
iajs-553	32	21	,	,	PUNCT
iajs-553	32	22	that	that	ADV
iajs-553	32	23	is	is	ADV
iajs-553	32	24	,	,	PUNCT
iajs-553	32	25	in	in	ADP
iajs-553	32	26	order	order	NOUN
iajs-553	32	27	of	of	ADP
iajs-553	32	28	non	non	ADJ
iajs-553	32	29	-	-	ADJ
iajs-553	32	30	decreasing	decrease	VERB
iajs-553	32	31	di	di	NOUN
iajs-553	32	32	.	.	PUNCT
iajs-553	33	1	■	■	PUNCT
iajs-553	33	2	theorem	theorem	ADJ
iajs-553	33	3	(	(	PUNCT
iajs-553	33	4	2)(smith	2)(smith	PROPN
iajs-553	33	5	1956)[2	1956)[2	NUM
iajs-553	33	6	]	]	PUNCT
iajs-553	33	7	.	.	PUNCT
iajs-553	34	1	the	the	DET
iajs-553	34	2	1//	1//	NUM
iajs-553	34	3	problem	problem	NOUN
iajs-553	34	4	is	be	AUX
iajs-553	34	5	minimized	minimize	VERB
iajs-553	34	6	by	by	ADP
iajs-553	34	7	sequencing	sequence	VERB
iajs-553	34	8	the	the	DET
iajs-553	34	9	jobs	job	NOUN
iajs-553	34	10	according	accord	VERB
iajs-553	34	11	to	to	ADP
iajs-553	34	12	the	the	DET
iajs-553	34	13	shortest	short	ADJ
iajs-553	34	14	–	–	PUNCT
iajs-553	34	15	processing	processing	NOUN
iajs-553	34	16	-	-	PUNCT
iajs-553	34	17	time	time	NOUN
iajs-553	34	18	(	(	PUNCT
iajs-553	34	19	spt	spt	NOUN
iajs-553	34	20	)	)	PUNCT
iajs-553	34	21	rule	rule	NOUN
iajs-553	34	22	,	,	PUNCT
iajs-553	34	23	that	that	ADV
iajs-553	34	24	is	is	ADV
iajs-553	34	25	,	,	PUNCT
iajs-553	34	26	in	in	ADP
iajs-553	34	27	order	order	NOUN
iajs-553	34	28	of	of	ADP
iajs-553	34	29	non	non	ADJ
iajs-553	34	30	-	-	ADJ
iajs-553	34	31	decreasing	decrease	VERB
iajs-553	34	32	pi	pi	NOUN
iajs-553	34	33	.	.	PUNCT
iajs-553	35	1	■	■	PUNCT
iajs-553	35	2	theorem(3)(lawler	theorem(3)(lawler	VERB
iajs-553	35	3	1973)[3].the	1973)[3].the	DET
iajs-553	35	4	1//fmax	1//fmax	PROPN
iajs-553	35	5	problem	problem	NOUN
iajs-553	35	6	,	,	PUNCT
iajs-553	35	7	fmax	fmax	PROPN
iajs-553	35	8	is	be	AUX
iajs-553	35	9	minimized	minimize	VERB
iajs-553	35	10	as	as	SCONJ
iajs-553	35	11	follows	follow	VERB
iajs-553	35	12	:	:	PUNCT
iajs-553	35	13	while	while	SCONJ
iajs-553	35	14	there	there	PRON
iajs-553	35	15	are	be	VERB
iajs-553	35	16	unassigned	unassigned	ADJ
iajs-553	35	17	jobs	job	NOUN
iajs-553	35	18	,	,	PUNCT
iajs-553	35	19	assign	assign	VERB
iajs-553	35	20	the	the	DET
iajs-553	35	21	job	job	NOUN
iajs-553	35	22	that	that	PRON
iajs-553	35	23	has	have	VERB
iajs-553	35	24	minimum	minimum	ADJ
iajs-553	35	25	cost	cost	NOUN
iajs-553	35	26	when	when	SCONJ
iajs-553	35	27	scheduled	schedule	VERB
iajs-553	35	28	in	in	ADP
iajs-553	35	29	the	the	DET
iajs-553	35	30	last	last	ADJ
iajs-553	35	31	unassigned	unassigned	ADJ
iajs-553	35	32	position	position	NOUN
iajs-553	35	33	in	in	ADP
iajs-553	35	34	that	that	DET
iajs-553	35	35	position	position	NOUN
iajs-553	35	36	.	.	PUNCT
iajs-553	36	1	■	■	PUNCT
iajs-553	36	2	definition(1)[4	definition(1)[4	X
iajs-553	36	3	]	]	X
iajs-553	36	4	:	:	PUNCT
iajs-553	36	5	a	a	DET
iajs-553	36	6	feasible	feasible	ADJ
iajs-553	36	7	schedule	schedule	NOUN
iajs-553	36	8	for	for	ADP
iajs-553	36	9	a	a	DET
iajs-553	36	10	problem	problem	NOUN
iajs-553	36	11	1//lex(f	1//lex(f	NUM
iajs-553	36	12	,	,	PUNCT
iajs-553	36	13	g	g	NOUN
iajs-553	36	14	)	)	PUNCT
iajs-553	36	15	is	be	AUX
iajs-553	36	16	a	a	DET
iajs-553	36	17	schedule	schedule	NOUN
iajs-553	36	18	in	in	ADP
iajs-553	36	19	which	which	PRON
iajs-553	36	20	the	the	DET
iajs-553	36	21	primary	primary	ADJ
iajs-553	36	22	criterion	criterion	NOUN
iajs-553	36	23	f	f	PROPN
iajs-553	36	24	is	be	AUX
iajs-553	36	25	satisfied	satisfied	ADJ
iajs-553	36	26	.	.	PUNCT
iajs-553	37	1	definition(2)[4	definition(2)[4	VERB
iajs-553	37	2	]	]	X
iajs-553	37	3	:	:	PUNCT
iajs-553	37	4	an	an	DET
iajs-553	37	5	optimal	optimal	ADJ
iajs-553	37	6	schedule	schedule	NOUN
iajs-553	37	7	for	for	ADP
iajs-553	37	8	1//lex(f	1//lex(f	NUM
iajs-553	37	9	,	,	PUNCT
iajs-553	37	10	g	g	NOUN
iajs-553	37	11	)	)	PUNCT
iajs-553	37	12	is	be	AUX
iajs-553	37	13	a	a	DET
iajs-553	37	14	feasible	feasible	ADJ
iajs-553	37	15	schedule	schedule	NOUN
iajs-553	37	16	that	that	PRON
iajs-553	37	17	minimizes	minimize	VERB
iajs-553	37	18	the	the	DET
iajs-553	37	19	secondary	secondary	ADJ
iajs-553	37	20	criterion	criterion	NOUN
iajs-553	37	21	g.	g.	PROPN
iajs-553	37	22	definition(3):a	definition(3):a	PROPN
iajs-553	37	23	feasible	feasible	ADJ
iajs-553	37	24	schedule	schedule	NOUN
iajs-553	37	25	σ	σ	PROPN
iajs-553	37	26	*	*	PROPN
iajs-553	37	27	is	be	AUX
iajs-553	37	28	pareto	pareto	VERB
iajs-553	37	29	optimal	optimal	ADJ
iajs-553	37	30	,	,	PUNCT
iajs-553	37	31	or	or	CCONJ
iajs-553	37	32	non	non	ADJ
iajs-553	37	33	-	-	NOUN
iajs-553	37	34	dominated(efficient	dominated(efficient	PROPN
iajs-553	37	35	)	)	PUNCT
iajs-553	37	36	,	,	PUNCT
iajs-553	37	37	with	with	ADP
iajs-553	37	38	respect	respect	NOUN
iajs-553	37	39	to	to	ADP
iajs-553	37	40	the	the	DET
iajs-553	37	41	performance	performance	NOUN
iajs-553	37	42	criteria	criterion	NOUN
iajs-553	37	43	f	f	PROPN
iajs-553	37	44	and	and	CCONJ
iajs-553	37	45	g	g	PROPN
iajs-553	37	46	if	if	SCONJ
iajs-553	37	47	there	there	PRON
iajs-553	37	48	is	be	VERB
iajs-553	37	49	no	no	DET
iajs-553	37	50	feasible	feasible	ADJ
iajs-553	37	51	schedule	schedule	NOUN
iajs-553	37	52	π	π	NOUN
iajs-553	37	53	such	such	ADJ
iajs-553	37	54	that	that	SCONJ
iajs-553	37	55	both	both	DET
iajs-553	37	56	f(π	f(π	PROPN
iajs-553	37	57	)	)	PUNCT
iajs-553	37	58	≤	≤	NOUN
iajs-553	37	59	f(σ	f(σ	NOUN
iajs-553	37	60	*	*	NOUN
iajs-553	37	61	)	)	PUNCT
iajs-553	37	62	and	and	CCONJ
iajs-553	37	63	g(π)≤g(σ	g(π)≤g(σ	NOUN
iajs-553	37	64	*	*	PROPN
iajs-553	37	65	)	)	PUNCT
iajs-553	37	66	,	,	PUNCT
iajs-553	37	67	where	where	SCONJ
iajs-553	37	68	at	at	ADV
iajs-553	37	69	least	least	ADV
iajs-553	37	70	one	one	NUM
iajs-553	37	71	of	of	ADP
iajs-553	37	72	the	the	DET
iajs-553	37	73	inequalities	inequality	NOUN
iajs-553	37	74	is	be	AUX
iajs-553	37	75	strict	strict	ADJ
iajs-553	37	76	.	.	PUNCT
iajs-553	38	1	definition(4)[5	definition(4)[5	NOUN
iajs-553	38	2	]	]	PUNCT
iajs-553	38	3	:	:	PUNCT
iajs-553	38	4	the	the	DET
iajs-553	38	5	function	function	NOUN
iajs-553	38	6	f(f	f(f	PROPN
iajs-553	38	7	,	,	PUNCT
iajs-553	38	8	g	g	NOUN
iajs-553	38	9	)	)	PUNCT
iajs-553	38	10	is	be	AUX
iajs-553	38	11	said	say	VERB
iajs-553	38	12	to	to	PART
iajs-553	38	13	be	be	AUX
iajs-553	38	14	non	non	ADJ
iajs-553	38	15	-	-	ADJ
iajs-553	38	16	decreasing	decrease	VERB
iajs-553	38	17	in	in	ADP
iajs-553	38	18	both	both	DET
iajs-553	38	19	argument	argument	NOUN
iajs-553	38	20	,	,	PUNCT
iajs-553	38	21	if	if	SCONJ
iajs-553	38	22	for	for	ADP
iajs-553	38	23	any	any	DET
iajs-553	38	24	pair	pair	NOUN
iajs-553	38	25	of	of	ADP
iajs-553	38	26	outcome	outcome	NOUN
iajs-553	38	27	value	value	NOUN
iajs-553	38	28	(	(	PUNCT
iajs-553	38	29	x	x	X
iajs-553	38	30	,	,	PUNCT
iajs-553	38	31	y	y	NOUN
iajs-553	38	32	)	)	PUNCT
iajs-553	38	33	of	of	ADP
iajs-553	38	34	the	the	DET
iajs-553	38	35	functions	function	NOUN
iajs-553	38	36	f	f	PROPN
iajs-553	38	37	and	and	CCONJ
iajs-553	38	38	g	g	PROPN
iajs-553	38	39	,	,	PUNCT
iajs-553	38	40	we	we	PRON
iajs-553	38	41	have	have	VERB
iajs-553	38	42	f(x	f(x	PROPN
iajs-553	38	43	,	,	PUNCT
iajs-553	38	44	y	y	NOUN
iajs-553	38	45	)	)	PUNCT
iajs-553	38	46	≤	≤	NOUN
iajs-553	39	1	f	f	X
iajs-553	39	2	(	(	PUNCT
iajs-553	39	3	x+a	x+a	X
iajs-553	39	4	,	,	PUNCT
iajs-553	39	5	y+b	y+b	NUM
iajs-553	39	6	)	)	PUNCT
iajs-553	39	7	for	for	ADP
iajs-553	39	8	each	each	DET
iajs-553	39	9	pair	pair	NOUN
iajs-553	39	10	of	of	ADP
iajs-553	39	11	non	non	ADJ
iajs-553	39	12	-	-	ADJ
iajs-553	39	13	negative	negative	ADJ
iajs-553	39	14	value	value	NOUN
iajs-553	39	15	a	a	PRON
iajs-553	39	16	and	and	CCONJ
iajs-553	39	17	b.	b.	PROPN
iajs-553	39	18	theorem	theorem	PROPN
iajs-553	39	19	(	(	PUNCT
iajs-553	39	20	4)[6	4)[6	NUM
iajs-553	39	21	]	]	X
iajs-553	39	22	:	:	PUNCT
iajs-553	39	23	if	if	SCONJ
iajs-553	39	24	the	the	DET
iajs-553	39	25	composite	composite	ADJ
iajs-553	39	26	objective	objective	ADJ
iajs-553	39	27	function	function	NOUN
iajs-553	39	28	f(f	f(f	PROPN
iajs-553	39	29	,	,	PUNCT
iajs-553	39	30	g	g	NOUN
iajs-553	39	31	)	)	PUNCT
iajs-553	39	32	is	be	AUX
iajs-553	39	33	non	non	ADJ
iajs-553	39	34	-	-	ADJ
iajs-553	39	35	decreasing	decrease	VERB
iajs-553	39	36	in	in	ADP
iajs-553	39	37	both	both	DET
iajs-553	39	38	argument	argument	NOUN
iajs-553	39	39	,	,	PUNCT
iajs-553	39	40	then	then	ADV
iajs-553	39	41	there	there	PRON
iajs-553	39	42	exists	exist	VERB
iajs-553	39	43	a	a	DET
iajs-553	39	44	pareto	pareto	ADJ
iajs-553	39	45	optimal	optimal	ADJ
iajs-553	39	46	schedule	schedule	NOUN
iajs-553	39	47	that	that	PRON
iajs-553	39	48	minimize	minimize	VERB
iajs-553	39	49	f.	f.	PROPN
iajs-553	39	50	definition(5)[7	definition(5)[7	PROPN
iajs-553	39	51	]	]	X
iajs-553	39	52	:	:	PUNCT
iajs-553	39	53	the	the	DET
iajs-553	39	54	term	term	NOUN
iajs-553	39	55	”	"	PUNCT
iajs-553	39	56	optimize	optimize	NOUN
iajs-553	39	57	”	"	PUNCT
iajs-553	39	58	in	in	ADP
iajs-553	39	59	a	a	DET
iajs-553	39	60	multi	multi	ADJ
iajs-553	39	61	-	-	ADJ
iajs-553	39	62	objective	objective	ADJ
iajs-553	39	63	decision	decision	NOUN
iajs-553	39	64	making	make	VERB
iajs-553	39	65	problem	problem	NOUN
iajs-553	39	66	refers	refer	VERB
iajs-553	39	67	to	to	ADP
iajs-553	39	68	a	a	DET
iajs-553	39	69	solution	solution	NOUN
iajs-553	39	70	around	around	ADP
iajs-553	39	71	which	which	PRON
iajs-553	39	72	there	there	PRON
iajs-553	39	73	is	be	VERB
iajs-553	39	74	no	no	DET
iajs-553	39	75	way	way	NOUN
iajs-553	39	76	of	of	ADP
iajs-553	39	77	improving	improve	VERB
iajs-553	39	78	any	any	DET
iajs-553	39	79	objective	objective	NOUN
iajs-553	39	80	without	without	ADP
iajs-553	39	81	worsening	worsen	VERB
iajs-553	39	82	at	at	ADV
iajs-553	39	83	least	least	ADV
iajs-553	39	84	one	one	NUM
iajs-553	39	85	other	other	ADJ
iajs-553	39	86	objective	objective	NOUN
iajs-553	39	87	.	.	PUNCT
iajs-553	40	1	definition	definition	NOUN
iajs-553	40	2	(	(	PUNCT
iajs-553	40	3	6)[8	6)[8	ADP
iajs-553	40	4	]	]	X
iajs-553	40	5	:	:	PUNCT
iajs-553	40	6	a	a	DET
iajs-553	40	7	point	point	NOUN
iajs-553	40	8	x	x	X
iajs-553	40	9	=	=	SYM
iajs-553	40	10	(	(	PUNCT
iajs-553	40	11	x1	x1	PROPN
iajs-553	40	12	,	,	PUNCT
iajs-553	40	13	.	.	PUNCT
iajs-553	40	14	.	.	PUNCT
iajs-553	40	15	.	.	PUNCT
iajs-553	41	1	,	,	PUNCT
iajs-553	41	2	xk	xk	X
iajs-553	41	3	)	)	PUNCT
iajs-553	41	4	is	be	AUX
iajs-553	41	5	pareto	pareto	VERB
iajs-553	41	6	optimal	optimal	ADJ
iajs-553	41	7	within	within	ADP
iajs-553	41	8	a	a	DET
iajs-553	41	9	given	give	VERB
iajs-553	41	10	set	set	NOUN
iajs-553	41	11	s	s	PROPN
iajs-553	41	12	,	,	PUNCT
iajs-553	41	13	if	if	SCONJ
iajs-553	41	14	s	s	PRON
iajs-553	41	15	does	do	AUX
iajs-553	41	16	not	not	PART
iajs-553	41	17	contain	contain	VERB
iajs-553	41	18	any	any	DET
iajs-553	41	19	other	other	ADJ
iajs-553	41	20	point	point	NOUN
iajs-553	41	21	y=(y1	y=(y1	NOUN
iajs-553	41	22	,	,	PUNCT
iajs-553	41	23	.	.	PUNCT
iajs-553	41	24	.	.	PUNCT
iajs-553	42	1	.	.	PUNCT
iajs-553	43	1	,	,	PUNCT
iajs-553	43	2	yk	yk	PROPN
iajs-553	43	3	)	)	PUNCT
iajs-553	43	4	with	with	ADP
iajs-553	43	5	yi	yi	NOUN
iajs-553	43	6	≤	≤	NOUN
iajs-553	43	7	xi	xi	X
iajs-553	43	8	for	for	ADP
iajs-553	43	9	i	i	PRON
iajs-553	43	10	=	=	NOUN
iajs-553	43	11	1	1	NUM
iajs-553	43	12	,	,	PUNCT
iajs-553	43	13	.	.	PUNCT
iajs-553	43	14	.	.	PUNCT
iajs-553	44	1	.	.	PUNCT
iajs-553	45	1	,	,	PUNCT
iajs-553	45	2	k.	k.	PROPN
iajs-553	45	3	correspondingly	correspondingly	ADV
iajs-553	45	4	,	,	PUNCT
iajs-553	45	5	a	a	DET
iajs-553	45	6	schedule	schedule	NOUN
iajs-553	45	7	σ	σ	NOUN
iajs-553	45	8	corresponds	correspond	VERB
iajs-553	45	9	to	to	ADP
iajs-553	45	10	a	a	DET
iajs-553	45	11	pareto	pareto	ADJ
iajs-553	45	12	optimal	optimal	ADJ
iajs-553	45	13	point	point	NOUN
iajs-553	45	14	if	if	SCONJ
iajs-553	45	15	there	there	PRON
iajs-553	45	16	is	be	VERB
iajs-553	45	17	no	no	DET
iajs-553	45	18	feasible	feasible	ADJ
iajs-553	45	19	schedule	schedule	NOUN
iajs-553	45	20	with	with	ADP
iajs-553	45	21	≤	≤	NOUN
iajs-553	45	22	for	for	ADP
iajs-553	45	23	k=1	k=1	X
iajs-553	45	24	,	,	PUNCT
iajs-553	45	25	.	.	PUNCT
iajs-553	45	26	.	.	PUNCT
iajs-553	45	27	.	.	PUNCT
iajs-553	46	1	,	,	PUNCT
iajs-553	46	2	k	k	NOUN
iajs-553	46	3	,	,	PUNCT
iajs-553	46	4	where	where	SCONJ
iajs-553	46	5	at	at	ADV
iajs-553	46	6	least	least	ADV
iajs-553	46	7	one	one	NUM
iajs-553	46	8	of	of	ADP
iajs-553	46	9	the	the	DET
iajs-553	46	10	inequalities	inequality	NOUN
iajs-553	46	11	is	be	AUX
iajs-553	46	12	strict	strict	ADJ
iajs-553	46	13	;	;	PUNCT
iajs-553	46	14	in	in	ADP
iajs-553	46	15	this	this	DET
iajs-553	46	16	case	case	NOUN
iajs-553	46	17	,	,	PUNCT
iajs-553	46	18	we	we	PRON
iajs-553	46	19	say	say	VERB
iajs-553	46	20	that	that	SCONJ
iajs-553	46	21	σ	σ	PROPN
iajs-553	46	22	is	be	AUX
iajs-553	46	23	not	not	PART
iajs-553	46	24	dominated	dominate	VERB
iajs-553	46	25	.	.	PUNCT
iajs-553	47	1	definition(7)[8]:hierarchical	definition(7)[8]:hierarchical	PROPN
iajs-553	47	2	minimization	minimization	NOUN
iajs-553	47	3	:	:	PUNCT
iajs-553	47	4	the	the	DET
iajs-553	47	5	performance	performance	NOUN
iajs-553	47	6	criteria	criterion	NOUN
iajs-553	47	7	f1	f1	NOUN
iajs-553	47	8	,	,	PUNCT
iajs-553	47	9	.	.	PUNCT
iajs-553	47	10	.	.	PUNCT
iajs-553	47	11	.	.	PUNCT
iajs-553	48	1	,	,	PUNCT
iajs-553	48	2	fk	fk	INTJ
iajs-553	48	3	are	be	AUX
iajs-553	48	4	indexed	index	VERB
iajs-553	48	5	in	in	ADP
iajs-553	48	6	order	order	NOUN
iajs-553	48	7	of	of	ADP
iajs-553	48	8	decreasing	decrease	VERB
iajs-553	48	9	importance	importance	NOUN
iajs-553	48	10	.	.	PUNCT
iajs-553	49	1	first	first	ADV
iajs-553	49	2	,	,	PUNCT
iajs-553	49	3	f1	f1	NOUN
iajs-553	49	4	is	be	AUX
iajs-553	49	5	minimized	minimize	VERB
iajs-553	49	6	.	.	PUNCT
iajs-553	50	1	next	next	ADV
iajs-553	50	2	,	,	PUNCT
iajs-553	50	3	f2	f2	PROPN
iajs-553	50	4	is	be	AUX
iajs-553	50	5	minimized	minimize	VERB
iajs-553	50	6	subject	subject	ADJ
iajs-553	50	7	to	to	ADP
iajs-553	50	8	the	the	DET
iajs-553	50	9	constraint	constraint	NOUN
iajs-553	50	10	that	that	PRON
iajs-553	50	11	the	the	DET
iajs-553	50	12	schedule	schedule	NOUN
iajs-553	50	13	has	have	VERB
iajs-553	50	14	minimal	minimal	ADJ
iajs-553	50	15	f1	f1	NOUN
iajs-553	50	16	value	value	NOUN
iajs-553	50	17	.	.	PUNCT
iajs-553	51	1	if	if	SCONJ
iajs-553	51	2	necessary	necessary	ADJ
iajs-553	51	3	,	,	PUNCT
iajs-553	51	4	f3	f3	PROPN
iajs-553	51	5	is	be	AUX
iajs-553	51	6	minimized	minimize	VERB
iajs-553	51	7	subject	subject	ADJ
iajs-553	51	8	to	to	ADP
iajs-553	51	9	the	the	DET
iajs-553	51	10	constraint	constraint	NOUN
iajs-553	51	11	that	that	PRON
iajs-553	51	12	the	the	DET
iajs-553	51	13	values	value	NOUN
iajs-553	51	14	for	for	ADP
iajs-553	51	15	f1	f1	NOUN
iajs-553	51	16	and	and	CCONJ
iajs-553	51	17	f2	f2	PROPN
iajs-553	51	18	are	be	AUX
iajs-553	51	19	equal	equal	ADJ
iajs-553	51	20	to	to	ADP
iajs-553	51	21	the	the	DET
iajs-553	51	22	values	value	NOUN
iajs-553	51	23	determined	determine	VERB
iajs-553	51	24	in	in	ADP
iajs-553	51	25	the	the	DET
iajs-553	51	26	previous	previous	ADJ
iajs-553	51	27	step	step	NOUN
iajs-553	51	28	.	.	PUNCT
iajs-553	52	1	theorem(5)[9	theorem(5)[9	ADV
iajs-553	52	2	]	]	PUNCT
iajs-553	52	3	:	:	PUNCT
iajs-553	52	4	consider	consider	VERB
iajs-553	52	5	the	the	DET
iajs-553	52	6	composite	composite	ADJ
iajs-553	52	7	objective	objective	ADJ
iajs-553	52	8	function	function	NOUN
iajs-553	52	9	f	f	PROPN
iajs-553	52	10	with	with	ADP
iajs-553	52	11	f(π	f(π	PROPN
iajs-553	52	12	)	)	PUNCT
iajs-553	52	13	=	=	SYM
iajs-553	52	14	f(f1(π),	f(f1(π),	NOUN
iajs-553	52	15	…	…	PUNCT
iajs-553	52	16	,fk(π	,fk(π	NOUN
iajs-553	52	17	)	)	PUNCT
iajs-553	52	18	)	)	PUNCT
iajs-553	52	19	,	,	PUNCT
iajs-553	52	20	where	where	SCONJ
iajs-553	52	21	f	f	PROPN
iajs-553	52	22	is	be	AUX
iajs-553	52	23	nondecreasing	nondecrease	VERB
iajs-553	52	24	in	in	ADP
iajs-553	52	25	all	all	DET
iajs-553	52	26	performance	performance	NOUN
iajs-553	52	27	criteria	criterion	NOUN
iajs-553	52	28	fk	fk	INTJ
iajs-553	52	29	.	.	PUNCT
iajs-553	53	1	there	there	PRON
iajs-553	53	2	is	be	VERB
iajs-553	53	3	a	a	DET
iajs-553	53	4	pareto	pareto	ADJ
iajs-553	53	5	optimal	optimal	ADJ
iajs-553	53	6	schedule	schedule	NOUN
iajs-553	53	7	with	with	ADP
iajs-553	53	8	respect	respect	NOUN
iajs-553	53	9	to	to	ADP
iajs-553	53	10	f1,	f1,	VERB
iajs-553	53	11	…	…	PUNCT
iajs-553	53	12	,fk	,fk	PUNCT
iajs-553	53	13	that	that	PRON
iajs-553	53	14	minimizes	minimize	VERB
iajs-553	53	15	the	the	DET
iajs-553	53	16	function	function	NOUN
iajs-553	53	17	f.	f.	PROPN
iajs-553	53	18	fmax	fmax	PROPN
iajs-553	53	19	is	be	AUX
iajs-553	53	20	regular	regular	ADJ
iajs-553	53	21	measure	measure	NOUN
iajs-553	53	22	:	:	PUNCT
iajs-553	53	23	now	now	ADV
iajs-553	53	24	,	,	PUNCT
iajs-553	53	25	we	we	PRON
iajs-553	53	26	will	will	AUX
iajs-553	53	27	consider	consider	VERB
iajs-553	53	28	the	the	DET
iajs-553	53	29	bicriteria	bicriteria	NOUN
iajs-553	53	30	that	that	PRON
iajs-553	53	31	concerns	concern	VERB
iajs-553	53	32	the	the	DET
iajs-553	53	33	hierarchical	hierarchical	ADJ
iajs-553	53	34	and	and	CCONJ
iajs-553	53	35	simultaneous	simultaneous	ADJ
iajs-553	53	36	minimization	minimization	NOUN
iajs-553	53	37	of	of	ADP
iajs-553	53	38	bicriteria	bicriteria	PROPN
iajs-553	53	39	regular	regular	ADJ
iajs-553	53	40	cost	cost	NOUN
iajs-553	53	41	function	function	NOUN
iajs-553	53	42	for	for	ADP
iajs-553	53	43	jobs	job	NOUN
iajs-553	53	44	i	i	PRON
iajs-553	53	45	,	,	PUNCT
iajs-553	53	46	which	which	PRON
iajs-553	53	47	means	mean	VERB
iajs-553	53	48	that	that	SCONJ
iajs-553	53	49	fi(ci	fi(ci	NOUN
iajs-553	53	50	)	)	PUNCT
iajs-553	53	51	does	do	AUX
iajs-553	53	52	not	not	PART
iajs-553	53	53	decrease	decrease	VERB
iajs-553	53	54	when	when	SCONJ
iajs-553	53	55	ci	ci	PROPN
iajs-553	53	56	increased	increase	VERB
iajs-553	53	57	.	.	PUNCT
iajs-553	54	1	hoogeveen	hoogeveen	PROPN
iajs-553	54	2	and	and	CCONJ
iajs-553	54	3	van	van	PROPN
iajs-553	54	4	de	de	PROPN
iajs-553	54	5	valde	valde	PROPN
iajs-553	54	6	[	[	X
iajs-553	54	7	10	10	NUM
iajs-553	54	8	]	]	PUNCT
iajs-553	54	9	proved	prove	VERB
iajs-553	54	10	that	that	SCONJ
iajs-553	54	11	1//f(σci	1//f(σci	NOUN
iajs-553	54	12	,	,	PUNCT
iajs-553	54	13	fmax	fmax	PROPN
iajs-553	54	14	)	)	PUNCT
iajs-553	54	15	mathematics	mathematic	NOUN
iajs-553	54	16	358	358	NUM
iajs-553	54	17	مجلة	مجلة	VERB
iajs-553	54	18	إبن	إبن	NOUN
iajs-553	54	19	الهيثم	الهيثم	ADJ
iajs-553	54	20	للعلوم	للعلوم	NOUN
iajs-553	54	21	الصرفة	الصرفة	NOUN
iajs-553	54	22	و	و	PRON
iajs-553	54	23	التطبيقية	التطبيقية	ADJ
iajs-553	54	24	2012	2012	NUM
iajs-553	54	25	السنة	السنة	NOUN
iajs-553	55	1	25	25	NUM
iajs-553	55	2	المجلد	المجلد	NOUN
iajs-553	55	3	3	3	NUM
iajs-553	55	4	العدد	العدد	PROPN
iajs-553	55	5	ibn	ibn	PROPN
iajs-553	55	6	al	al	PROPN
iajs-553	55	7	-	-	PUNCT
iajs-553	55	8	haitham	haitham	PROPN
iajs-553	55	9	journal	journal	PROPN
iajs-553	55	10	for	for	ADP
iajs-553	55	11	pure	pure	ADJ
iajs-553	55	12	and	and	CCONJ
iajs-553	55	13	applied	apply	VERB
iajs-553	55	14	science	science	NOUN
iajs-553	55	15	no	no	NOUN
iajs-553	55	16	.	.	NOUN
iajs-553	55	17	3	3	NUM
iajs-553	55	18	vol	vol	NOUN
iajs-553	55	19	.	.	PUNCT
iajs-553	55	20	25	25	NUM
iajs-553	55	21	year	year	NOUN
iajs-553	55	22	2012	2012	NUM
iajs-553	55	23	problem	problem	NOUN
iajs-553	55	24	is	be	AUX
iajs-553	55	25	solved	solve	VERB
iajs-553	55	26	in	in	ADP
iajs-553	55	27	polynomial	polynomial	ADJ
iajs-553	55	28	time	time	NOUN
iajs-553	55	29	,	,	PUNCT
iajs-553	55	30	van	van	NOUN
iajs-553	55	31	wassenhove	wassenhove	NOUN
iajs-553	55	32	and	and	CCONJ
iajs-553	55	33	gelders	gelder	NOUN
iajs-553	55	34	[	[	X
iajs-553	55	35	11	11	NUM
iajs-553	55	36	]	]	PUNCT
iajs-553	55	37	solved	solve	VERB
iajs-553	55	38	1//f(σci	1//f(σci	NOUN
iajs-553	55	39	,	,	PUNCT
iajs-553	55	40	tmax	tmax	NUM
iajs-553	55	41	)	)	PUNCT
iajs-553	55	42	problem	problem	NOUN
iajs-553	55	43	,	,	PUNCT
iajs-553	55	44	emmons	emmon	VERB
iajs-553	56	1	[	[	X
iajs-553	56	2	12	12	NUM
iajs-553	56	3	]	]	PUNCT
iajs-553	56	4	presented	present	VERB
iajs-553	56	5	the	the	DET
iajs-553	56	6	hierarchical	hierarchical	ADJ
iajs-553	56	7	problem	problem	NOUN
iajs-553	56	8	1//lex(fmax	1//lex(fmax	NUM
iajs-553	56	9	,	,	PUNCT
iajs-553	56	10	σci	σci	PROPN
iajs-553	56	11	)	)	PUNCT
iajs-553	56	12	,	,	PUNCT
iajs-553	56	13	where	where	SCONJ
iajs-553	56	14	f*=min{fmax	f*=min{fmax	ADV
iajs-553	56	15	}	}	PUNCT
iajs-553	56	16	denotes	denote	VERB
iajs-553	56	17	the	the	DET
iajs-553	56	18	optimal	optimal	ADJ
iajs-553	56	19	solution	solution	NOUN
iajs-553	56	20	value	value	NOUN
iajs-553	56	21	of	of	ADP
iajs-553	56	22	the	the	DET
iajs-553	56	23	1//	1//	PROPN
iajs-553	56	24	fmax	fmax	PROPN
iajs-553	56	25	problem	problem	NOUN
iajs-553	56	26	,	,	PUNCT
iajs-553	56	27	which	which	PRON
iajs-553	56	28	is	be	AUX
iajs-553	56	29	solved	solve	VERB
iajs-553	56	30	in	in	ADP
iajs-553	56	31	o(n2	o(n2	ADJ
iajs-553	56	32	)	)	PUNCT
iajs-553	56	33	time	time	NOUN
iajs-553	56	34	by	by	ADP
iajs-553	56	35	lawler	lawler	PROPN
iajs-553	56	36	algorithm[3	algorithm[3	PROPN
iajs-553	56	37	]	]	PUNCT
iajs-553	56	38	.	.	PUNCT
iajs-553	57	1	let	let	VERB
iajs-553	57	2	fmax=	fmax=	PROPN
iajs-553	57	3	vmax	vmax	PROPN
iajs-553	57	4	in	in	ADP
iajs-553	57	5	our	our	PRON
iajs-553	57	6	study	study	NOUN
iajs-553	57	7	,	,	PUNCT
iajs-553	57	8	since	since	SCONJ
iajs-553	57	9	criterion	criterion	NOUN
iajs-553	57	10	vmax	vmax	PROPN
iajs-553	57	11	is	be	AUX
iajs-553	57	12	a	a	DET
iajs-553	57	13	particular	particular	ADJ
iajs-553	57	14	case	case	NOUN
iajs-553	57	15	of	of	ADP
iajs-553	57	16	the	the	DET
iajs-553	57	17	function	function	NOUN
iajs-553	57	18	fmax	fmax	PROPN
iajs-553	57	19	.	.	PUNCT
iajs-553	58	1	now	now	ADV
iajs-553	58	2	,	,	PUNCT
iajs-553	58	3	consider	consider	VERB
iajs-553	58	4	the	the	DET
iajs-553	58	5	following	follow	VERB
iajs-553	58	6	two	two	NUM
iajs-553	58	7	problems	problem	NOUN
iajs-553	58	8	:	:	PUNCT
iajs-553	58	9	1//lex(σci	1//lex(σci	NUM
iajs-553	58	10	,	,	PUNCT
iajs-553	58	11	vmax	vmax	ADJ
iajs-553	58	12	)	)	PUNCT
iajs-553	58	13	problem	problem	NOUN
iajs-553	58	14	,	,	PUNCT
iajs-553	58	15	and	and	CCONJ
iajs-553	58	16	1//lex(vmax	1//lex(vmax	NUM
iajs-553	58	17	,	,	PUNCT
iajs-553	58	18	σci	σci	ADJ
iajs-553	58	19	)	)	PUNCT
iajs-553	58	20	problem	problem	NOUN
iajs-553	58	21	.	.	PUNCT
iajs-553	59	1	the	the	DET
iajs-553	59	2	1//lex(σci	1//lex(σci	NUM
iajs-553	59	3	,	,	PUNCT
iajs-553	59	4	vmax	vmax	PROPN
iajs-553	59	5	)	)	PUNCT
iajs-553	59	6	problem	problem	NOUN
iajs-553	59	7	(	(	PUNCT
iajs-553	59	8	p1	p1	NOUN
iajs-553	59	9	):	):	PUNCT
iajs-553	59	10	this	this	DET
iajs-553	59	11	problem	problem	NOUN
iajs-553	59	12	can	can	AUX
iajs-553	59	13	be	be	AUX
iajs-553	59	14	written	write	VERB
iajs-553	59	15	as	as	ADP
iajs-553	59	16	:	:	PUNCT
iajs-553	59	17	min	min	PROPN
iajs-553	59	18	vmax	vmax	PROPN
iajs-553	59	19	s.t	s.t	PROPN
iajs-553	59	20	cσ(i	cσ(i	PROPN
iajs-553	59	21	)	)	PUNCT
iajs-553	59	22	≥	≥	NOUN
iajs-553	59	23	pσ(i	pσ(i	NOUN
iajs-553	59	24	)	)	PUNCT
iajs-553	59	25	i=1,	i=1,	PROPN
iajs-553	59	26	…	…	PUNCT
iajs-553	59	27	,n	,n	NUM
iajs-553	59	28	.	.	PUNCT
iajs-553	59	29	cσ(i	cσ(i	X
iajs-553	59	30	)	)	PUNCT
iajs-553	59	31	=	=	SYM
iajs-553	60	1	cσ(i-1	cσ(i-1	NOUN
iajs-553	60	2	)	)	PUNCT
iajs-553	61	1	+	+	NUM
iajs-553	61	2	pσ(i	pσ(i	X
iajs-553	61	3	)	)	PUNCT
iajs-553	61	4	i=2,	i=2,	NOUN
iajs-553	61	5	…	…	PUNCT
iajs-553	61	6	,n	,n	X
iajs-553	61	7	.	.	PUNCT
iajs-553	62	1	(	(	PUNCT
iajs-553	62	2	)	)	PUNCT
iajs-553	62	3	(	(	PUNCT
iajs-553	62	4	)	)	PUNCT
iajs-553	62	5	(	(	PUNCT
iajs-553	62	6	)	)	PUNCT
iajs-553	62	7	(	(	PUNCT
iajs-553	62	8	)	)	PUNCT
iajs-553	62	9	(	(	PUNCT
iajs-553	62	10	)	)	PUNCT
iajs-553	62	11	(	(	PUNCT
iajs-553	62	12	)	)	PUNCT
iajs-553	62	13	(	(	PUNCT
iajs-553	62	14	)	)	PUNCT
iajs-553	62	15	(	(	PUNCT
iajs-553	62	16	)	)	PUNCT
iajs-553	62	17	(	(	PUNCT
iajs-553	62	18	)	)	PUNCT
iajs-553	62	19	(	(	PUNCT
iajs-553	62	20	)	)	PUNCT
iajs-553	62	21	(	(	PUNCT
iajs-553	62	22	)	)	PUNCT
iajs-553	62	23	(	(	PUNCT
iajs-553	62	24	)	)	PUNCT
iajs-553	62	25			PROPN
iajs-553	62	26			PROPN
iajs-553	62	27			PROPN
iajs-553	62	28			PROPN
iajs-553	62	29			PROPN
iajs-553	62	30			VERB
iajs-553	62	31			X
iajs-553	62	32			NOUN
iajs-553	62	33	=	=	NOUN
iajs-553	62	34	≤+	≤+	NOUN
iajs-553	62	35	=	=	PUNCT
iajs-553	63	1	+	+	PROPN
iajs-553	63	2	<	<	X
iajs-553	63	3	<	<	X
iajs-553	63	4	=	=	ADJ
iajs-553	63	5	≤	≤	NOUN
iajs-553	63	6	=	=	PUNCT
iajs-553	63	7	n	n	PRON
iajs-553	63	8	1,	1,	NUM
iajs-553	63	9	...	...	PUNCT
iajs-553	63	10	,i	,i	PUNCT
iajs-553	63	11	,	,	PUNCT
iajs-553	63	12	iσc	iσc	PROPN
iajs-553	63	13	iσpiσd	iσpiσd	NOUN
iajs-553	63	14	if	if	SCONJ
iajs-553	63	15	iσp	iσp	PROPN
iajs-553	63	16	n1,	n1,	PROPN
iajs-553	63	17	...	...	NOUN
iajs-553	63	18	,i	,i	PUNCT
iajs-553	63	19	,	,	PUNCT
iajs-553	63	20	iσpid	iσpid	ADJ
iajs-553	63	21	iσc	iσc	NOUN
iajs-553	63	22	iσd	iσd	INTJ
iajs-553	63	23	if	if	SCONJ
iajs-553	63	24	iσdiσc	iσdiσc	PROPN
iajs-553	63	25	n1,	n1,	PROPN
iajs-553	63	26	...	...	PUNCT
iajs-553	63	27	,i	,i	PUNCT
iajs-553	63	28	,	,	PUNCT
iajs-553	63	29	iσd	iσd	PROPN
iajs-553	63	30	iσc	iσc	VERB
iajs-553	64	1	if	if	SCONJ
iajs-553	64	2	0	0	NUM
iajs-553	64	3	iσv	iσv	X
iajs-553	64	4	pσ(i	pσ(i	PROPN
iajs-553	64	5	)	)	PUNCT
iajs-553	64	6	≥	≥	NOUN
iajs-553	64	7	vσ(i	vσ(i	NOUN
iajs-553	64	8	)	)	PUNCT
iajs-553	64	9	i=1,	i=1,	NOUN
iajs-553	64	10	…	…	PUNCT
iajs-553	64	11	,n	,n	X
iajs-553	64	12	.	.	PUNCT
iajs-553	64	13	vσ(i	vσ(i	NUM
iajs-553	64	14	)	)	PUNCT
iajs-553	64	15	≥	≥	NOUN
iajs-553	64	16	0	0	NUM
iajs-553	64	17	i=1,	i=1,	NOUN
iajs-553	64	18	…	…	PUNCT
iajs-553	64	19	,n	,n	NOUN
iajs-553	64	20	.	.	PUNCT
iajs-553	64	21	σci	σci	PROPN
iajs-553	64	22	=	=	SYM
iajs-553	64	23	∆	∆	PROPN
iajs-553	64	24	,	,	PUNCT
iajs-553	64	25	where	where	SCONJ
iajs-553	64	26	∆=	∆=	VERB
iajs-553	64	27	σci(spt	σci(spt	NOUN
iajs-553	64	28	)	)	PUNCT
iajs-553	64	29	.	.	PUNCT
iajs-553	65	1	it	it	PRON
iajs-553	65	2	is	be	AUX
iajs-553	65	3	clear	clear	ADJ
iajs-553	65	4	that	that	SCONJ
iajs-553	65	5	the	the	DET
iajs-553	65	6	spt	spt	PROPN
iajs-553	65	7	rule	rule	NOUN
iajs-553	65	8	is	be	AUX
iajs-553	65	9	feasible	feasible	ADJ
iajs-553	65	10	for	for	ADP
iajs-553	65	11	problem(p1	problem(p1	NOUN
iajs-553	65	12	)	)	PUNCT
iajs-553	65	13	.	.	PUNCT
iajs-553	66	1	also	also	ADV
iajs-553	66	2	the	the	DET
iajs-553	66	3	spt	spt	PROPN
iajs-553	66	4	rule	rule	NOUN
iajs-553	66	5	is	be	AUX
iajs-553	66	6	optimal	optimal	ADJ
iajs-553	66	7	for	for	ADP
iajs-553	66	8	problem(p1	problem(p1	NOUN
iajs-553	66	9	)	)	PUNCT
iajs-553	66	10	if	if	SCONJ
iajs-553	66	11	there	there	PRON
iajs-553	66	12	exist	exist	VERB
iajs-553	66	13	a	a	DET
iajs-553	66	14	tie	tie	NOUN
iajs-553	66	15	(	(	PUNCT
iajs-553	66	16	jobs	job	NOUN
iajs-553	66	17	with	with	ADP
iajs-553	66	18	equal	equal	ADJ
iajs-553	66	19	processing	processing	NOUN
iajs-553	66	20	times	time	NOUN
iajs-553	66	21	)	)	PUNCT
iajs-553	66	22	then	then	ADV
iajs-553	66	23	order	order	VERB
iajs-553	66	24	these	these	DET
iajs-553	66	25	jobs	job	NOUN
iajs-553	66	26	so	so	SCONJ
iajs-553	66	27	that	that	SCONJ
iajs-553	66	28	vmax	vmax	PROPN
iajs-553	66	29	is	be	AUX
iajs-553	66	30	minimum	minimum	ADJ
iajs-553	66	31	.	.	PUNCT
iajs-553	67	1	the	the	DET
iajs-553	67	2	1//lex(vmax	1//lex(vmax	NUM
iajs-553	67	3	,	,	PUNCT
iajs-553	67	4	σci	σci	NOUN
iajs-553	67	5	)	)	PUNCT
iajs-553	67	6	problem(p2	problem(p2	PROPN
iajs-553	67	7	):	):	PUNCT
iajs-553	67	8	this	this	DET
iajs-553	67	9	problem	problem	NOUN
iajs-553	67	10	can	can	AUX
iajs-553	67	11	be	be	AUX
iajs-553	67	12	written	write	VERB
iajs-553	67	13	as	as	ADP
iajs-553	67	14	:	:	PUNCT
iajs-553	67	15	min	min	PROPN
iajs-553	67	16	σci	σci	PROPN
iajs-553	67	17	s.t	s.t	PROPN
iajs-553	67	18	cσ(i	cσ(i	PROPN
iajs-553	67	19	)	)	PUNCT
iajs-553	67	20	≥	≥	NOUN
iajs-553	67	21	pσ(i	pσ(i	NOUN
iajs-553	67	22	)	)	PUNCT
iajs-553	67	23	i=1,	i=1,	PROPN
iajs-553	67	24	…	…	PUNCT
iajs-553	67	25	,n	,n	NUM
iajs-553	67	26	.	.	PUNCT
iajs-553	67	27	cσ(i	cσ(i	X
iajs-553	67	28	)	)	PUNCT
iajs-553	67	29	=	=	SYM
iajs-553	67	30	cσ(i-1	cσ(i-1	NOUN
iajs-553	67	31	)	)	PUNCT
iajs-553	67	32	+	+	NUM
iajs-553	67	33	pσ(i	pσ(i	X
iajs-553	67	34	)	)	PUNCT
iajs-553	67	35	i=2,	i=2,	NOUN
iajs-553	67	36	…	…	PUNCT
iajs-553	67	37	,n	,n	X
iajs-553	67	38	.	.	PUNCT
iajs-553	68	1	(	(	PUNCT
iajs-553	68	2	)	)	PUNCT
iajs-553	68	3	(	(	PUNCT
iajs-553	68	4	)	)	PUNCT
iajs-553	68	5	(	(	PUNCT
iajs-553	68	6	)	)	PUNCT
iajs-553	68	7	(	(	PUNCT
iajs-553	68	8	)	)	PUNCT
iajs-553	68	9	(	(	PUNCT
iajs-553	68	10	)	)	PUNCT
iajs-553	68	11	(	(	PUNCT
iajs-553	68	12	)	)	PUNCT
iajs-553	68	13	(	(	PUNCT
iajs-553	68	14	)	)	PUNCT
iajs-553	68	15	(	(	PUNCT
iajs-553	68	16	)	)	PUNCT
iajs-553	68	17	(	(	PUNCT
iajs-553	68	18	)	)	PUNCT
iajs-553	68	19	(	(	PUNCT
iajs-553	68	20	)	)	PUNCT
iajs-553	68	21	(	(	PUNCT
iajs-553	68	22	)	)	PUNCT
iajs-553	68	23	(	(	PUNCT
iajs-553	68	24	)	)	PUNCT
iajs-553	68	25			PROPN
iajs-553	68	26			PROPN
iajs-553	68	27			PROPN
iajs-553	68	28			PROPN
iajs-553	68	29			PROPN
iajs-553	68	30			VERB
iajs-553	68	31			X
iajs-553	68	32			NOUN
iajs-553	68	33	=	=	NOUN
iajs-553	68	34	≤+	≤+	NOUN
iajs-553	68	35	=	=	PUNCT
iajs-553	69	1	+	+	PROPN
iajs-553	69	2	<	<	X
iajs-553	69	3	<	<	X
iajs-553	69	4	=	=	ADJ
iajs-553	69	5	≤	≤	NOUN
iajs-553	69	6	=	=	PUNCT
iajs-553	69	7	n	n	PRON
iajs-553	69	8	1,	1,	NUM
iajs-553	69	9	...	...	PUNCT
iajs-553	69	10	,i	,i	PUNCT
iajs-553	69	11	,	,	PUNCT
iajs-553	69	12	iσc	iσc	PROPN
iajs-553	69	13	iσpiσd	iσpiσd	NOUN
iajs-553	69	14	if	if	SCONJ
iajs-553	69	15	iσp	iσp	PROPN
iajs-553	69	16	n1,	n1,	PROPN
iajs-553	69	17	...	...	NOUN
iajs-553	69	18	,i	,i	PUNCT
iajs-553	69	19	,	,	PUNCT
iajs-553	69	20	iσpid	iσpid	ADJ
iajs-553	69	21	iσc	iσc	NOUN
iajs-553	69	22	iσd	iσd	INTJ
iajs-553	69	23	if	if	SCONJ
iajs-553	69	24	iσdiσc	iσdiσc	PROPN
iajs-553	69	25	n1,	n1,	PROPN
iajs-553	69	26	...	...	PUNCT
iajs-553	69	27	,i	,i	PUNCT
iajs-553	69	28	,	,	PUNCT
iajs-553	69	29	iσd	iσd	PROPN
iajs-553	69	30	iσc	iσc	VERB
iajs-553	70	1	if	if	SCONJ
iajs-553	70	2	0	0	NUM
iajs-553	70	3	iσv	iσv	X
iajs-553	70	4	pσ(i	pσ(i	PROPN
iajs-553	70	5	)	)	PUNCT
iajs-553	70	6	≥	≥	NOUN
iajs-553	70	7	vσ(i	vσ(i	NOUN
iajs-553	70	8	)	)	PUNCT
iajs-553	70	9	i=1,	i=1,	NOUN
iajs-553	70	10	…	…	PUNCT
iajs-553	70	11	,n	,n	X
iajs-553	70	12	.	.	PUNCT
iajs-553	70	13	vσ(i	vσ(i	NUM
iajs-553	70	14	)	)	PUNCT
iajs-553	70	15	≥	≥	NOUN
iajs-553	70	16	0	0	NUM
iajs-553	70	17	i=1,	i=1,	NOUN
iajs-553	70	18	…	…	PUNCT
iajs-553	70	19	,n	,n	X
iajs-553	70	20	.	.	PUNCT
iajs-553	70	21	vmax=	vmax=	NUM
iajs-553	70	22	∆	∆	PROPN
iajs-553	70	23	,	,	PUNCT
iajs-553	70	24	where	where	SCONJ
iajs-553	70	25	∆=	∆=	VERB
iajs-553	70	26	vmax(lawler	vmax(lawler	NOUN
iajs-553	70	27	)	)	PUNCT
iajs-553	70	28	.	.	PUNCT
iajs-553	71	1	algorithm(1	algorithm(1	PROPN
iajs-553	71	2	)	)	PUNCT
iajs-553	71	3	for	for	ADP
iajs-553	71	4	finding	find	VERB
iajs-553	71	5	an	an	DET
iajs-553	71	6	optimal	optimal	ADJ
iajs-553	71	7	value	value	NOUN
iajs-553	71	8	for	for	ADP
iajs-553	71	9	problem(p2	problem(p2	NOUN
iajs-553	71	10	):	):	PUNCT
iajs-553	71	11	mathematics	mathematic	NOUN
iajs-553	71	12	359	359	NUM
iajs-553	71	13	مجلة	مجلة	VERB
iajs-553	71	14	إبن	إبن	NOUN
iajs-553	71	15	الهيثم	الهيثم	ADJ
iajs-553	71	16	للعلوم	للعلوم	NOUN
iajs-553	71	17	الصرفة	الصرفة	NOUN
iajs-553	71	18	و	و	PRON
iajs-553	71	19	التطبيقية	التطبيقية	ADJ
iajs-553	71	20	2012	2012	NUM
iajs-553	71	21	السنة	السنة	NOUN
iajs-553	71	22	25	25	NUM
iajs-553	71	23	المجلد	المجلد	NOUN
iajs-553	71	24	3	3	NUM
iajs-553	71	25	العدد	العدد	PROPN
iajs-553	71	26	ibn	ibn	PROPN
iajs-553	71	27	al	al	PROPN
iajs-553	71	28	-	-	PUNCT
iajs-553	71	29	haitham	haitham	PROPN
iajs-553	71	30	journal	journal	PROPN
iajs-553	71	31	for	for	ADP
iajs-553	71	32	pure	pure	ADJ
iajs-553	71	33	and	and	CCONJ
iajs-553	71	34	applied	apply	VERB
iajs-553	71	35	science	science	NOUN
iajs-553	71	36	no	no	NOUN
iajs-553	71	37	.	.	NOUN
iajs-553	71	38	3	3	NUM
iajs-553	71	39	vol	vol	NOUN
iajs-553	71	40	.	.	PUNCT
iajs-553	72	1	25	25	NUM
iajs-553	72	2	year	year	NOUN
iajs-553	72	3	2012	2012	NUM
iajs-553	72	4	step(0	step(0	NOUN
iajs-553	72	5	):	):	PUNCT
iajs-553	72	6	compute	compute	NOUN
iajs-553	72	7	vmax	vmax	PROPN
iajs-553	72	8	by	by	ADP
iajs-553	72	9	using	use	VERB
iajs-553	72	10	(	(	PUNCT
iajs-553	72	11	lawler	lawler	PROPN
iajs-553	72	12	algorithm	algorithm	PROPN
iajs-553	72	13	)	)	PUNCT
iajs-553	73	1	and	and	CCONJ
iajs-553	73	2	set	set	VERB
iajs-553	73	3	σ=	σ=	PROPN
iajs-553	73	4	(	(	PUNCT
iajs-553	73	5	φ	φ	PROPN
iajs-553	73	6	)	)	PUNCT
iajs-553	73	7	.	.	PUNCT
iajs-553	74	1	step(1	step(1	NOUN
iajs-553	74	2	):	):	PUNCT
iajs-553	74	3	put	put	VERB
iajs-553	74	4	∆=	∆=	NOUN
iajs-553	74	5	vmax(lawler	vmax(lawler	NOUN
iajs-553	74	6	)	)	PUNCT
iajs-553	74	7	,	,	PUNCT
iajs-553	74	8	n={1,	n={1,	NUM
iajs-553	74	9	…	…	PUNCT
iajs-553	74	10	,n	,n	NOUN
iajs-553	74	11	}	}	PUNCT
iajs-553	74	12	,	,	PUNCT
iajs-553	74	13	k	k	NOUN
iajs-553	74	14	=	=	SYM
iajs-553	74	15	n	n	X
iajs-553	74	16	,	,	PUNCT
iajs-553	74	17	t	t	PROPN
iajs-553	74	18	=	=	SYM
iajs-553	74	19	cmax=	cmax=	NUM
iajs-553	74	20	σpi	σpi	NOUN
iajs-553	74	21	.	.	PUNCT
iajs-553	75	1	step(2	step(2	ADJ
iajs-553	75	2	):	):	PUNCT
iajs-553	75	3	calculate	calculate	NOUN
iajs-553	75	4	vi	vi	PROPN
iajs-553	75	5	,	,	PUNCT
iajs-553	75	6	i	i	PRON
iajs-553	75	7	n	n	ADV
iajs-553	75	8	as	as	SCONJ
iajs-553	75	9	follows	follow	VERB
iajs-553	75	10	:	:	PUNCT
iajs-553	75	11			PROPN
iajs-553	75	12			PROPN
iajs-553	75	13			PROPN
iajs-553	75	14			NOUN
iajs-553	75	15			PRON
iajs-553	75	16			NOUN
iajs-553	75	17	=	=	NOUN
iajs-553	75	18	≤+	≤+	NOUN
iajs-553	75	19	=	=	PUNCT
iajs-553	75	20	+	+	PROPN
iajs-553	75	21	<	<	X
iajs-553	75	22	<	<	X
iajs-553	75	23	=	=	ADJ
iajs-553	75	24	≤	≤	NOUN
iajs-553	75	25	=	=	PUNCT
iajs-553	75	26	n	n	PRON
iajs-553	75	27	1,	1,	NUM
iajs-553	75	28	...	...	PUNCT
iajs-553	75	29	,i	,i	PUNCT
iajs-553	75	30	,	,	PUNCT
iajs-553	75	31	ic	ic	PROPN
iajs-553	75	32	ipid	ipid	ADJ
iajs-553	75	33	if	if	SCONJ
iajs-553	75	34	ip	ip	PRON
iajs-553	75	35	n1,	n1,	NOUN
iajs-553	75	36	...	...	PUNCT
iajs-553	75	37	,i	,i	PUNCT
iajs-553	75	38	,	,	PUNCT
iajs-553	75	39	ipid	ipid	PROPN
iajs-553	75	40	ic	ic	PROPN
iajs-553	76	1	i	i	PROPN
iajs-553	76	2	d	d	PROPN
iajs-553	76	3	if	if	SCONJ
iajs-553	76	4	idic	idic	ADJ
iajs-553	76	5	n1,	n1,	NOUN
iajs-553	76	6	...	...	PUNCT
iajs-553	76	7	,i	,i	PUNCT
iajs-553	76	8	,	,	PUNCT
iajs-553	76	9	i	i	PROPN
iajs-553	76	10	d	d	PROPN
iajs-553	76	11	ic	ic	PROPN
iajs-553	76	12	if	if	SCONJ
iajs-553	76	13	0	0	NUM
iajs-553	76	14	iv	iv	NUM
iajs-553	76	15	step(3	step(3	PROPN
iajs-553	76	16	):	):	PUNCT
iajs-553	76	17	find	find	VERB
iajs-553	76	18	a	a	DET
iajs-553	76	19	job	job	NOUN
iajs-553	76	20	j	j	PROPN
iajs-553	76	21	*	*	PROPN
iajs-553	76	22	n	n	CCONJ
iajs-553	76	23	,	,	PUNCT
iajs-553	76	24	such	such	ADJ
iajs-553	76	25	that	that	SCONJ
iajs-553	76	26	1.vj*≤	1.vj*≤	NUM
iajs-553	76	27	∆.	∆.	PROPN
iajs-553	76	28	2	2	NUM
iajs-553	76	29	.	.	PUNCT
iajs-553	76	30	pj*≥	pj*≥	PROPN
iajs-553	77	1	pi	pi	PROPN
iajs-553	77	2	,	,	PUNCT
iajs-553	77	3	j	j	PROPN
iajs-553	77	4	*	*	PROPN
iajs-553	77	5	,	,	PUNCT
iajs-553	77	6	i	i	PRON
iajs-553	77	7	n	n	PROPN
iajs-553	77	8	and	and	CCONJ
iajs-553	77	9	vi	vi	NOUN
iajs-553	77	10	≤	≤	NOUN
iajs-553	78	1	∆.	∆.	X
iajs-553	78	2	then	then	ADV
iajs-553	78	3	assign	assign	VERB
iajs-553	78	4	job	job	NOUN
iajs-553	78	5	j	j	PROPN
iajs-553	78	6	*	*	VERB
iajs-553	78	7	in	in	ADP
iajs-553	78	8	position	position	NOUN
iajs-553	78	9	k	k	PROPN
iajs-553	78	10	of	of	ADP
iajs-553	78	11	σ	σ	PROPN
iajs-553	78	12	=(	=(	PROPN
iajs-553	78	13	σ(k	σ(k	PROPN
iajs-553	78	14	)	)	PUNCT
iajs-553	78	15	,	,	PUNCT
iajs-553	78	16	σ	σ	PROPN
iajs-553	78	17	)	)	PUNCT
iajs-553	78	18	.	.	PUNCT
iajs-553	79	1	step(4	step(4	NOUN
iajs-553	79	2	):	):	PUNCT
iajs-553	79	3	set	set	VERB
iajs-553	79	4	t	t	PROPN
iajs-553	79	5	=	=	PROPN
iajs-553	79	6	t	t	PROPN
iajs-553	79	7	-	-	PUNCT
iajs-553	79	8	pj	pj	PROPN
iajs-553	79	9	*	*	PROPN
iajs-553	79	10	,	,	PUNCT
iajs-553	79	11	n	n	CCONJ
iajs-553	79	12	=	=	PROPN
iajs-553	79	13	n-{j	n-{j	PROPN
iajs-553	79	14	*	*	PUNCT
iajs-553	79	15	}	}	PUNCT
iajs-553	79	16	,	,	PUNCT
iajs-553	79	17	k	k	PROPN
iajs-553	79	18	=	=	NOUN
iajs-553	79	19	k-1	k-1	NOUN
iajs-553	79	20	,	,	PUNCT
iajs-553	79	21	if	if	SCONJ
iajs-553	79	22	k	k	PROPN
iajs-553	79	23	>	>	X
iajs-553	79	24	1	1	NUM
iajs-553	79	25	go	go	VERB
iajs-553	79	26	to	to	ADP
iajs-553	79	27	step(2	step(2	ADJ
iajs-553	79	28	)	)	PUNCT
iajs-553	79	29	,	,	PUNCT
iajs-553	79	30	otherwise	otherwise	ADV
iajs-553	79	31	go	go	VERB
iajs-553	79	32	to	to	ADP
iajs-553	79	33	step(5	step(5	NUM
iajs-553	79	34	)	)	PUNCT
iajs-553	79	35	.	.	PUNCT
iajs-553	80	1	step(5	step(5	ADV
iajs-553	80	2	):	):	PUNCT
iajs-553	80	3	calculate	calculate	NOUN
iajs-553	80	4	σcσ(i	σcσ(i	PROPN
iajs-553	80	5	)	)	PUNCT
iajs-553	80	6	for	for	ADP
iajs-553	80	7	the	the	DET
iajs-553	80	8	sequence	sequence	NOUN
iajs-553	80	9	jobs	job	NOUN
iajs-553	80	10	σ	σ	PROPN
iajs-553	80	11	=(	=(	PROPN
iajs-553	80	12	σ(1),	σ(1),	PROPN
iajs-553	80	13	…	…	PUNCT
iajs-553	80	14	,σ(n	,σ(n	PUNCT
iajs-553	80	15	)	)	PUNCT
iajs-553	80	16	)	)	PUNCT
iajs-553	80	17	.	.	PUNCT
iajs-553	81	1	step(6	step(6	PROPN
iajs-553	81	2	):	):	PUNCT
iajs-553	81	3	stop	stop	NOUN
iajs-553	81	4	.	.	PUNCT
iajs-553	82	1	proposition(1	proposition(1	NOUN
iajs-553	82	2	):	):	PUNCT
iajs-553	82	3	algorithm(1	algorithm(1	NOUN
iajs-553	82	4	)	)	PUNCT
iajs-553	82	5	gives	give	VERB
iajs-553	82	6	an	an	DET
iajs-553	82	7	optimal	optimal	ADJ
iajs-553	82	8	solution	solution	NOUN
iajs-553	82	9	of	of	ADP
iajs-553	82	10	1//lex(vmax	1//lex(vmax	NUM
iajs-553	82	11	,	,	PUNCT
iajs-553	82	12	σci	σci	NOUN
iajs-553	82	13	)	)	PUNCT
iajs-553	82	14	problem	problem	NOUN
iajs-553	82	15	.	.	PUNCT
iajs-553	83	1	proof	proof	NOUN
iajs-553	83	2	:	:	PUNCT
iajs-553	83	3	since	since	SCONJ
iajs-553	83	4	the	the	DET
iajs-553	83	5	problem	problem	NOUN
iajs-553	83	6	1//lex(vmax	1//lex(vmax	NUM
iajs-553	83	7	,	,	PUNCT
iajs-553	83	8	σci	σci	PROPN
iajs-553	83	9	)	)	PUNCT
iajs-553	83	10	can	can	AUX
iajs-553	83	11	be	be	AUX
iajs-553	83	12	written	write	VERB
iajs-553	83	13	as	as	ADP
iajs-553	83	14	:	:	PUNCT
iajs-553	83	15	min	min	PROPN
iajs-553	83	16	σci	σci	PROPN
iajs-553	83	17	s.t	s.t	PROPN
iajs-553	83	18	vi	vi	PROPN
iajs-553	83	19	≤	≤	PROPN
iajs-553	83	20	vmax	vmax	X
iajs-553	83	21	(	(	PUNCT
iajs-553	83	22	lawler	lawler	PROPN
iajs-553	83	23	)	)	PUNCT
iajs-553	83	24	i=1,	i=1,	PROPN
iajs-553	83	25	…	…	PUNCT
iajs-553	83	26	,n	,n	PUNCT
iajs-553	83	27	first	first	ADV
iajs-553	83	28	notice	notice	VERB
iajs-553	83	29	that	that	SCONJ
iajs-553	83	30	at	at	ADP
iajs-553	83	31	each	each	DET
iajs-553	83	32	decision	decision	NOUN
iajs-553	83	33	point	point	NOUN
iajs-553	83	34	the	the	DET
iajs-553	83	35	set	set	NOUN
iajs-553	83	36	of	of	ADP
iajs-553	83	37	schedulable	schedulable	ADJ
iajs-553	83	38	jobs	job	NOUN
iajs-553	83	39	is	be	AUX
iajs-553	83	40	inspected	inspect	VERB
iajs-553	83	41	(	(	PUNCT
iajs-553	83	42	i.e.	i.e.	X
iajs-553	83	43	these	these	DET
iajs-553	83	44	jobs	job	NOUN
iajs-553	83	45	that	that	PRON
iajs-553	83	46	can	can	AUX
iajs-553	83	47	be	be	AUX
iajs-553	83	48	scheduled	schedule	VERB
iajs-553	83	49	without	without	ADP
iajs-553	83	50	violating	violate	VERB
iajs-553	83	51	the	the	DET
iajs-553	83	52	maximum	maximum	ADJ
iajs-553	83	53	late	late	ADJ
iajs-553	83	54	work	work	NOUN
iajs-553	83	55	(	(	PUNCT
iajs-553	83	56	vmax(lawler))(which	vmax(lawler))(which	PRON
iajs-553	83	57	is	be	AUX
iajs-553	83	58	obtained	obtain	VERB
iajs-553	83	59	by	by	ADP
iajs-553	83	60	lawler	lawler	PROPN
iajs-553	83	61	algorithm	algorithm	PROPN
iajs-553	83	62	)	)	PUNCT
iajs-553	83	63	)	)	PUNCT
iajs-553	83	64	,	,	PUNCT
iajs-553	83	65	any	any	DET
iajs-553	83	66	job	job	NOUN
iajs-553	83	67	j	j	NOUN
iajs-553	83	68	*	*	NOUN
iajs-553	83	69	that	that	PRON
iajs-553	83	70	is	be	AUX
iajs-553	83	71	chosen	choose	VERB
iajs-553	83	72	in	in	ADP
iajs-553	83	73	step	step	NOUN
iajs-553	83	74	(	(	PUNCT
iajs-553	83	75	3	3	NUM
iajs-553	83	76	)	)	PUNCT
iajs-553	83	77	of	of	ADP
iajs-553	83	78	algorithm(1	algorithm(1	NOUN
iajs-553	83	79	)	)	PUNCT
iajs-553	83	80	to	to	PART
iajs-553	83	81	be	be	AUX
iajs-553	83	82	scheduled	schedule	VERB
iajs-553	83	83	last	last	ADV
iajs-553	83	84	.	.	PUNCT
iajs-553	84	1	second	second	ADJ
iajs-553	84	2	,	,	PUNCT
iajs-553	84	3	if	if	SCONJ
iajs-553	84	4	there	there	PRON
iajs-553	84	5	exists	exist	VERB
iajs-553	84	6	a	a	DET
iajs-553	84	7	tie	tie	NOUN
iajs-553	84	8	(	(	PUNCT
iajs-553	84	9	more	more	ADJ
iajs-553	84	10	than	than	ADP
iajs-553	84	11	one	one	NUM
iajs-553	84	12	schedulable	schedulable	ADJ
iajs-553	84	13	job	job	NOUN
iajs-553	84	14	i	i	PROPN
iajs-553	84	15	)	)	PUNCT
iajs-553	84	16	then	then	ADV
iajs-553	84	17	we	we	PRON
iajs-553	84	18	choose	choose	VERB
iajs-553	84	19	the	the	DET
iajs-553	84	20	job	job	NOUN
iajs-553	84	21	j	j	NOUN
iajs-553	84	22	*	*	PROPN
iajs-553	84	23	with	with	ADP
iajs-553	84	24	largest	large	ADJ
iajs-553	84	25	pj	pj	PROPN
iajs-553	84	26	*	*	PUNCT
iajs-553	84	27	to	to	PART
iajs-553	84	28	be	be	AUX
iajs-553	84	29	schedule	schedule	NOUN
iajs-553	84	30	last	last	ADJ
iajs-553	84	31	which	which	PRON
iajs-553	84	32	minimizes	minimize	VERB
iajs-553	84	33	σci	σci	NOUN
iajs-553	84	34	also	also	ADV
iajs-553	84	35	.	.	PUNCT
iajs-553	85	1	hence	hence	ADV
iajs-553	85	2	,	,	PUNCT
iajs-553	85	3	any	any	DET
iajs-553	85	4	schedule	schedule	NOUN
iajs-553	85	5	constructed	construct	VERB
iajs-553	85	6	by	by	ADP
iajs-553	85	7	algorithm(1	algorithm(1	NOUN
iajs-553	85	8	)	)	PUNCT
iajs-553	85	9	is	be	AUX
iajs-553	85	10	optimal	optimal	ADJ
iajs-553	85	11	.	.	PUNCT
iajs-553	86	1	■	■	PUNCT
iajs-553	86	2	algorithm(1	algorithm(1	NOUN
iajs-553	86	3	)	)	PUNCT
iajs-553	86	4	is	be	AUX
iajs-553	86	5	a	a	DET
iajs-553	86	6	general	general	ADJ
iajs-553	86	7	algorithm	algorithm	NOUN
iajs-553	86	8	can	can	AUX
iajs-553	86	9	be	be	AUX
iajs-553	86	10	used	use	VERB
iajs-553	86	11	for	for	ADP
iajs-553	86	12	solving	solve	VERB
iajs-553	86	13	problems	problem	NOUN
iajs-553	86	14	of	of	ADP
iajs-553	86	15	the	the	DET
iajs-553	86	16	following	follow	VERB
iajs-553	86	17	forms	form	NOUN
iajs-553	86	18	:	:	PUNCT
iajs-553	86	19	(	(	PUNCT
iajs-553	86	20	1	1	X
iajs-553	86	21	)	)	PUNCT
iajs-553	86	22	1//lex(fmax	1//lex(fmax	NUM
iajs-553	86	23	,	,	PUNCT
iajs-553	86	24	σci	σci	PROPN
iajs-553	86	25	)	)	PUNCT
iajs-553	86	26	,	,	PUNCT
iajs-553	86	27	where	where	SCONJ
iajs-553	86	28	fmax	fmax	PROPN
iajs-553	86	29	{	{	PUNCT
iajs-553	86	30	lmax	lmax	PROPN
iajs-553	86	31	,	,	PUNCT
iajs-553	86	32	tmax	tmax	PRON
iajs-553	86	33	,	,	PUNCT
iajs-553	86	34	vmax	vmax	PROPN
iajs-553	86	35	,	,	PUNCT
iajs-553	86	36	}	}	PUNCT
iajs-553	86	37	.	.	PUNCT
iajs-553	87	1	(	(	PUNCT
iajs-553	87	2	2	2	NUM
iajs-553	87	3	)	)	PUNCT
iajs-553	87	4	1//lex(fmax	1//lex(fmax	NUM
iajs-553	87	5	,	,	PUNCT
iajs-553	87	6	)	)	PUNCT
iajs-553	87	7	,	,	PUNCT
iajs-553	87	8	where	where	SCONJ
iajs-553	87	9	fmax	fmax	PROPN
iajs-553	87	10	{	{	PUNCT
iajs-553	87	11	lmax	lmax	PROPN
iajs-553	87	12	,	,	PUNCT
iajs-553	87	13	tmax	tmax	PRON
iajs-553	87	14	,	,	PUNCT
iajs-553	87	15	vmax	vmax	PROPN
iajs-553	87	16	,	,	PUNCT
iajs-553	87	17	}	}	PUNCT
iajs-553	87	18	.	.	PUNCT
iajs-553	88	1	the	the	DET
iajs-553	88	2	1//lex	1//lex	PROPN
iajs-553	88	3	(	(	PUNCT
iajs-553	88	4	,	,	PUNCT
iajs-553	88	5	tmax	tmax	NUM
iajs-553	88	6	)	)	PUNCT
iajs-553	88	7	problem(p3	problem(p3	NOUN
iajs-553	88	8	):	):	PUNCT
iajs-553	88	9	this	this	DET
iajs-553	88	10	problem	problem	NOUN
iajs-553	88	11	can	can	AUX
iajs-553	88	12	be	be	AUX
iajs-553	88	13	written	write	VERB
iajs-553	88	14	as	as	ADP
iajs-553	88	15	:	:	PUNCT
iajs-553	88	16	min	min	NOUN
iajs-553	88	17	tmax	tmax	ADP
iajs-553	88	18	s.t	s.t	PROPN
iajs-553	88	19	=	=	NOUN
iajs-553	88	20	∆	∆	PROPN
iajs-553	88	21	,	,	PUNCT
iajs-553	88	22	where	where	SCONJ
iajs-553	88	23	∆=	∆=	NOUN
iajs-553	88	24	(	(	PUNCT
iajs-553	88	25	lawler	lawler	PROPN
iajs-553	88	26	)	)	PUNCT
iajs-553	88	27	.	.	PUNCT
iajs-553	89	1	algorithm(2	algorithm(2	PROPN
iajs-553	89	2	)	)	PUNCT
iajs-553	90	1	for	for	ADP
iajs-553	90	2	finding	find	VERB
iajs-553	90	3	an	an	DET
iajs-553	90	4	optimal	optimal	ADJ
iajs-553	90	5	value	value	NOUN
iajs-553	90	6	for	for	ADP
iajs-553	90	7	problem(p3	problem(p3	NOUN
iajs-553	90	8	):	):	PUNCT
iajs-553	90	9	mathematics	mathematic	NOUN
iajs-553	90	10	360	360	NUM
iajs-553	90	11	مجلة	مجلة	VERB
iajs-553	90	12	إبن	إبن	VERB
iajs-553	90	13	الهيثم	الهيثم	ADJ
iajs-553	90	14	للعلوم	للعلوم	NOUN
iajs-553	90	15	الصرفة	الصرفة	NOUN
iajs-553	90	16	و	و	PRON
iajs-553	90	17	التطبيقية	التطبيقية	ADJ
iajs-553	90	18	2012	2012	NUM
iajs-553	90	19	السنة	السنة	NOUN
iajs-553	90	20	25	25	NUM
iajs-553	90	21	المجلد	المجلد	NOUN
iajs-553	90	22	3	3	NUM
iajs-553	90	23	العدد	العدد	PROPN
iajs-553	90	24	ibn	ibn	PROPN
iajs-553	90	25	al	al	PROPN
iajs-553	90	26	-	-	PUNCT
iajs-553	90	27	haitham	haitham	PROPN
iajs-553	90	28	journal	journal	PROPN
iajs-553	90	29	for	for	ADP
iajs-553	90	30	pure	pure	ADJ
iajs-553	90	31	and	and	CCONJ
iajs-553	90	32	applied	apply	VERB
iajs-553	90	33	science	science	NOUN
iajs-553	90	34	no	no	NOUN
iajs-553	90	35	.	.	NOUN
iajs-553	90	36	3	3	NUM
iajs-553	90	37	vol	vol	NOUN
iajs-553	90	38	.	.	PUNCT
iajs-553	91	1	25	25	NUM
iajs-553	91	2	year	year	NOUN
iajs-553	91	3	2012	2012	NUM
iajs-553	91	4	step(0	step(0	NOUN
iajs-553	91	5	):	):	PUNCT
iajs-553	91	6	compute	compute	NOUN
iajs-553	91	7	=	=	SYM
iajs-553	91	8	min{max{wivi	min{max{wivi	NOUN
iajs-553	91	9	}	}	PUNCT
iajs-553	91	10	}	}	PUNCT
iajs-553	91	11	,	,	PUNCT
iajs-553	91	12	by	by	ADP
iajs-553	91	13	using	use	VERB
iajs-553	91	14	(	(	PUNCT
iajs-553	91	15	lawler	lawler	PROPN
iajs-553	91	16	algorithm	algorithm	PROPN
iajs-553	91	17	)	)	PUNCT
iajs-553	91	18	.	.	PUNCT
iajs-553	92	1	step(1	step(1	NOUN
iajs-553	92	2	):	):	PUNCT
iajs-553	92	3	put	put	VERB
iajs-553	92	4	∆=	∆=	NOUN
iajs-553	92	5	(	(	PUNCT
iajs-553	92	6	lawler	lawler	PROPN
iajs-553	92	7	)	)	PUNCT
iajs-553	92	8	,	,	PUNCT
iajs-553	92	9	n={1,	n={1,	NUM
iajs-553	92	10	…	…	PUNCT
iajs-553	92	11	,n	,n	NOUN
iajs-553	92	12	}	}	PUNCT
iajs-553	92	13	,	,	PUNCT
iajs-553	92	14	k	k	NOUN
iajs-553	92	15	=	=	SYM
iajs-553	92	16	n	n	X
iajs-553	92	17	,	,	PUNCT
iajs-553	92	18	t	t	NOUN
iajs-553	92	19	=	=	NOUN
iajs-553	92	20	cmax	cmax	NOUN
iajs-553	92	21	=	=	SYM
iajs-553	92	22	σpi	σpi	NOUN
iajs-553	92	23	and	and	CCONJ
iajs-553	92	24	set	set	VERB
iajs-553	92	25	σ=	σ=	PROPN
iajs-553	92	26	(	(	PUNCT
iajs-553	92	27	φ	φ	PROPN
iajs-553	92	28	)	)	PUNCT
iajs-553	92	29	.	.	PUNCT
iajs-553	93	1	step(2	step(2	ADJ
iajs-553	93	2	):	):	PUNCT
iajs-553	93	3	calculate	calculate	NOUN
iajs-553	93	4	wivi	wivi	NOUN
iajs-553	93	5	,	,	PUNCT
iajs-553	93	6	i	i	PRON
iajs-553	93	7	n	n	ADV
iajs-553	93	8	as	as	SCONJ
iajs-553	93	9	follows	follow	VERB
iajs-553	93	10	:	:	PUNCT
iajs-553	93	11			PROPN
iajs-553	93	12			PROPN
iajs-553	93	13			PROPN
iajs-553	93	14			NOUN
iajs-553	93	15			PRON
iajs-553	93	16			NOUN
iajs-553	93	17	=	=	NOUN
iajs-553	93	18	≤+	≤+	NOUN
iajs-553	93	19	=	=	PUNCT
iajs-553	93	20	+	+	PROPN
iajs-553	93	21	<	<	X
iajs-553	93	22	<	<	X
iajs-553	93	23	=	=	ADJ
iajs-553	93	24	≤	≤	NOUN
iajs-553	93	25	=	=	PUNCT
iajs-553	93	26	n	n	PRON
iajs-553	93	27	1,	1,	NUM
iajs-553	93	28	...	...	PUNCT
iajs-553	93	29	,i	,i	PUNCT
iajs-553	93	30	,	,	PUNCT
iajs-553	93	31	ic	ic	PROPN
iajs-553	93	32	ipid	ipid	ADJ
iajs-553	93	33	if	if	SCONJ
iajs-553	93	34	ipiw	ipiw	NOUN
iajs-553	93	35	n1,	n1,	ADJ
iajs-553	93	36	...	...	NOUN
iajs-553	93	37	,i	,i	PUNCT
iajs-553	93	38	,	,	PUNCT
iajs-553	93	39	ipid	ipid	PROPN
iajs-553	93	40	ic	ic	PROPN
iajs-553	94	1	i	i	PROPN
iajs-553	94	2	d	d	PROPN
iajs-553	94	3	if	if	SCONJ
iajs-553	94	4	)	)	PUNCT
iajs-553	94	5	idi(ciw	idi(ciw	PROPN
iajs-553	94	6	n1,	n1,	PROPN
iajs-553	94	7	...	...	PROPN
iajs-553	94	8	,i	,i	PUNCT
iajs-553	94	9	,	,	PUNCT
iajs-553	94	10	i	i	PROPN
iajs-553	94	11	d	d	PROPN
iajs-553	94	12	ic	ic	PROPN
iajs-553	94	13	if	if	SCONJ
iajs-553	94	14	0	0	NUM
iajs-553	94	15	iviw	iviw	NOUN
iajs-553	94	16	step(3):find	step(3):find	ADP
iajs-553	94	17	a	a	DET
iajs-553	94	18	job	job	NOUN
iajs-553	94	19	j*∈n	j*∈n	NOUN
iajs-553	94	20	,	,	PUNCT
iajs-553	94	21	such	such	ADJ
iajs-553	94	22	that	that	SCONJ
iajs-553	94	23	1	1	NUM
iajs-553	94	24	.	.	PUNCT
iajs-553	94	25	wj*vj*≤	wj*vj*≤	VERB
iajs-553	95	1	∆.	∆.	PROPN
iajs-553	95	2	2	2	NUM
iajs-553	95	3	.	.	PUNCT
iajs-553	95	4	dj*≥	dj*≥	PROPN
iajs-553	95	5	di	di	PROPN
iajs-553	95	6	,	,	PUNCT
iajs-553	95	7	j*,i	j*,i	VERB
iajs-553	95	8	n	n	ADV
iajs-553	95	9	and	and	CCONJ
iajs-553	95	10	wivi	wivi	NOUN
iajs-553	95	11	≤	≤	NOUN
iajs-553	96	1	∆.	∆.	X
iajs-553	96	2	then	then	ADV
iajs-553	96	3	assign	assign	VERB
iajs-553	96	4	job	job	NOUN
iajs-553	96	5	j	j	PROPN
iajs-553	96	6	*	*	VERB
iajs-553	96	7	in	in	ADP
iajs-553	96	8	position	position	NOUN
iajs-553	96	9	k	k	PROPN
iajs-553	96	10	of	of	ADP
iajs-553	96	11	σ	σ	PROPN
iajs-553	96	12	=(	=(	PROPN
iajs-553	96	13	σ(k	σ(k	PROPN
iajs-553	96	14	)	)	PUNCT
iajs-553	96	15	,	,	PUNCT
iajs-553	96	16	σ	σ	PROPN
iajs-553	96	17	)	)	PUNCT
iajs-553	96	18	.	.	PUNCT
iajs-553	97	1	step(4	step(4	NOUN
iajs-553	97	2	):	):	PUNCT
iajs-553	97	3	set	set	VERB
iajs-553	97	4	t	t	PROPN
iajs-553	97	5	=	=	PROPN
iajs-553	97	6	t	t	PROPN
iajs-553	97	7	-	-	PUNCT
iajs-553	97	8	pj	pj	PROPN
iajs-553	97	9	*	*	PROPN
iajs-553	97	10	,	,	PUNCT
iajs-553	97	11	n	n	PROPN
iajs-553	97	12	=	=	PROPN
iajs-553	97	13	n-{j	n-{j	PROPN
iajs-553	97	14	*	*	PUNCT
iajs-553	97	15	}	}	PUNCT
iajs-553	97	16	,	,	PUNCT
iajs-553	97	17	k	k	PROPN
iajs-553	97	18	=	=	NOUN
iajs-553	97	19	k-1	k-1	NOUN
iajs-553	97	20	,	,	PUNCT
iajs-553	97	21	if	if	SCONJ
iajs-553	97	22	k	k	PROPN
iajs-553	97	23	>	>	X
iajs-553	97	24	1	1	NUM
iajs-553	97	25	go	go	VERB
iajs-553	97	26	to	to	ADP
iajs-553	97	27	step(2	step(2	ADJ
iajs-553	97	28	)	)	PUNCT
iajs-553	97	29	,	,	PUNCT
iajs-553	97	30	otherwise	otherwise	ADV
iajs-553	97	31	go	go	VERB
iajs-553	97	32	to	to	ADP
iajs-553	97	33	step(5	step(5	NUM
iajs-553	97	34	)	)	PUNCT
iajs-553	97	35	.	.	PUNCT
iajs-553	98	1	step(5	step(5	ADV
iajs-553	98	2	):	):	PUNCT
iajs-553	98	3	calculate	calculate	NOUN
iajs-553	98	4	tmax(σ	tmax(σ	PROPN
iajs-553	98	5	)	)	PUNCT
iajs-553	98	6	for	for	ADP
iajs-553	98	7	the	the	DET
iajs-553	98	8	sequence	sequence	NOUN
iajs-553	98	9	jobs	job	NOUN
iajs-553	98	10	σ	σ	PROPN
iajs-553	98	11	=(	=(	PROPN
iajs-553	98	12	σ(1),	σ(1),	PROPN
iajs-553	98	13	…	…	PUNCT
iajs-553	98	14	,σ(n	,σ(n	PUNCT
iajs-553	98	15	)	)	PUNCT
iajs-553	98	16	)	)	PUNCT
iajs-553	98	17	.	.	PUNCT
iajs-553	99	1	step(6	step(6	PROPN
iajs-553	99	2	):	):	PUNCT
iajs-553	99	3	stop	stop	NOUN
iajs-553	99	4	.	.	PUNCT
iajs-553	100	1	example(1	example(1	NOUN
iajs-553	100	2	):	):	PUNCT
iajs-553	100	3	consider	consider	VERB
iajs-553	100	4	the	the	DET
iajs-553	100	5	problem	problem	NOUN
iajs-553	100	6	1//lex	1//lex	PROPN
iajs-553	100	7	(	(	PUNCT
iajs-553	100	8	,	,	PUNCT
iajs-553	100	9	tmax	tmax	NUM
iajs-553	100	10	)	)	PUNCT
iajs-553	100	11	with	with	ADP
iajs-553	100	12	the	the	DET
iajs-553	100	13	following	follow	VERB
iajs-553	100	14	data	datum	NOUN
iajs-553	100	15	:	:	PUNCT
iajs-553	100	16	i	i	NOUN
iajs-553	100	17	1	1	NUM
iajs-553	100	18	2	2	NUM
iajs-553	100	19	3	3	NUM
iajs-553	100	20	4	4	NUM
iajs-553	100	21	pi	pi	NOUN
iajs-553	100	22	3	3	NUM
iajs-553	100	23	1	1	NUM
iajs-553	100	24	2	2	NUM
iajs-553	100	25	4	4	NUM
iajs-553	100	26	di	di	NOUN
iajs-553	100	27	4	4	NUM
iajs-553	100	28	6	6	NUM
iajs-553	100	29	1	1	NUM
iajs-553	100	30	2	2	NUM
iajs-553	100	31	wi	wi	PROPN
iajs-553	100	32	2	2	NUM
iajs-553	100	33	3	3	NUM
iajs-553	100	34	2	2	NUM
iajs-553	100	35	5	5	NUM
iajs-553	100	36	by	by	ADP
iajs-553	100	37	applying	apply	VERB
iajs-553	100	38	lawler	lawler	NOUN
iajs-553	100	39	,	,	PUNCT
iajs-553	100	40	s	s	PART
iajs-553	100	41	algorithm	algorithm	NOUN
iajs-553	100	42	(	(	PUNCT
iajs-553	100	43	step(0	step(0	NOUN
iajs-553	100	44	)	)	PUNCT
iajs-553	100	45	)	)	PUNCT
iajs-553	101	1	we	we	PRON
iajs-553	101	2	get	get	VERB
iajs-553	101	3	a	a	DET
iajs-553	101	4	schedule	schedule	NOUN
iajs-553	101	5	σ=(4,1,3,2	σ=(4,1,3,2	NOUN
iajs-553	101	6	)	)	PUNCT
iajs-553	101	7	with	with	ADP
iajs-553	101	8	=	=	NOUN
iajs-553	101	9	10	10	NUM
iajs-553	101	10	and	and	CCONJ
iajs-553	101	11	tmax=8	tmax=8	PROPN
iajs-553	101	12	.	.	PUNCT
iajs-553	101	13	put	put	PROPN
iajs-553	101	14	∆=10	∆=10	NOUN
iajs-553	101	15	.	.	PUNCT
iajs-553	102	1	i	i	PRON
iajs-553	102	2	1	1	NUM
iajs-553	102	3	2	2	NUM
iajs-553	102	4	3	3	NUM
iajs-553	102	5	4	4	NUM
iajs-553	102	6	job	job	NOUN
iajs-553	102	7	j	j	PROPN
iajs-553	102	8	*	*	PROPN
iajs-553	102	9	t	t	PROPN
iajs-553	102	10	=	=	NOUN
iajs-553	102	11	cmax	cmax	NOUN
iajs-553	102	12	wivi	wivi	NOUN
iajs-553	102	13	10	10	NUM
iajs-553	102	14	6	6	NUM
iajs-553	102	15	4	4	NUM
iajs-553	102	16	20	20	NUM
iajs-553	102	17	2	2	NUM
iajs-553	102	18	9	9	NUM
iajs-553	102	19	*	*	SYM
iajs-553	102	20	4	4	NUM
iajs-553	102	21	20	20	NUM
iajs-553	102	22	1	1	NUM
iajs-553	102	23	6	6	NUM
iajs-553	102	24	*	*	PUNCT
iajs-553	102	25	*	*	PUNCT
iajs-553	102	26	20	20	NUM
iajs-553	102	27	3	3	NUM
iajs-553	102	28	4	4	NUM
iajs-553	102	29	*	*	PUNCT
iajs-553	102	30	*	*	PUNCT
iajs-553	103	1	*	*	PUNCT
iajs-553	103	2	4	4	NUM
iajs-553	103	3	hence	hence	ADV
iajs-553	103	4	,	,	PUNCT
iajs-553	103	5	we	we	PRON
iajs-553	103	6	get	get	VERB
iajs-553	103	7	optimal	optimal	ADJ
iajs-553	103	8	schedule	schedule	NOUN
iajs-553	103	9	σ	σ	NOUN
iajs-553	103	10	=	=	SYM
iajs-553	103	11	(	(	PUNCT
iajs-553	103	12	4,3,1,2	4,3,1,2	NUM
iajs-553	103	13	)	)	PUNCT
iajs-553	103	14	with	with	ADP
iajs-553	103	15	=	=	NOUN
iajs-553	103	16	10	10	NUM
iajs-553	103	17	and	and	CCONJ
iajs-553	103	18	tmax=5	tmax=5	PROPN
iajs-553	103	19	.	.	PROPN
iajs-553	104	1	7	7	X
iajs-553	104	2	.	.	X
iajs-553	104	3	minimizing	minimize	VERB
iajs-553	104	4	total	total	ADJ
iajs-553	104	5	completion	completion	NOUN
iajs-553	104	6	time	time	NOUN
iajs-553	104	7	and	and	CCONJ
iajs-553	104	8	maximum	maximum	ADJ
iajs-553	104	9	late	late	ADJ
iajs-553	104	10	work	work	NOUN
iajs-553	104	11	.	.	PUNCT
iajs-553	105	1	in	in	ADP
iajs-553	105	2	this	this	DET
iajs-553	105	3	section	section	NOUN
iajs-553	105	4	we	we	PRON
iajs-553	105	5	will	will	AUX
iajs-553	105	6	try	try	VERB
iajs-553	105	7	to	to	PART
iajs-553	105	8	find	find	VERB
iajs-553	105	9	all	all	PRON
iajs-553	105	10	efficient	efficient	ADJ
iajs-553	105	11	(	(	PUNCT
iajs-553	105	12	pareto	pareto	ADJ
iajs-553	105	13	optimal	optimal	ADJ
iajs-553	105	14	)	)	PUNCT
iajs-553	105	15	solutions	solution	NOUN
iajs-553	105	16	for	for	ADP
iajs-553	105	17	1//f(σci	1//f(σci	NUM
iajs-553	105	18	,	,	PUNCT
iajs-553	105	19	vmax	vmax	PROPN
iajs-553	105	20	)	)	PUNCT
iajs-553	105	21	problem	problem	NOUN
iajs-553	105	22	which	which	PRON
iajs-553	105	23	is	be	AUX
iajs-553	105	24	denoted	denote	VERB
iajs-553	105	25	by	by	ADP
iajs-553	105	26	problem(p4	problem(p4	NOUN
iajs-553	105	27	)	)	PUNCT
iajs-553	105	28	.	.	PUNCT
iajs-553	106	1	7.1	7.1	NUM
iajs-553	106	2	the	the	DET
iajs-553	106	3	1//f(vmax	1//f(vmax	NUM
iajs-553	106	4	,	,	PUNCT
iajs-553	106	5	σci	σci	NOUN
iajs-553	106	6	)	)	PUNCT
iajs-553	106	7	problem(p4	problem(p4	NOUN
iajs-553	106	8	):	):	PUNCT
iajs-553	106	9	the	the	DET
iajs-553	106	10	1//f(σci	1//f(σci	NUM
iajs-553	106	11	,	,	PUNCT
iajs-553	106	12	vmax	vmax	PROPN
iajs-553	106	13	)	)	PUNCT
iajs-553	106	14	problem	problem	NOUN
iajs-553	106	15	can	can	AUX
iajs-553	106	16	be	be	AUX
iajs-553	106	17	written	write	VERB
iajs-553	106	18	as	as	ADP
iajs-553	106	19	:	:	PUNCT
iajs-553	106	20	min	min	PROPN
iajs-553	106	21	σci	σci	PROPN
iajs-553	106	22	s.t	s.t	PROPN
iajs-553	106	23	.	.	PROPN
iajs-553	106	24	vmax	vmax	PROPN
iajs-553	106	25	≤	≤	NUM
iajs-553	106	26	∆	∆	PROPN
iajs-553	106	27	,	,	PUNCT
iajs-553	106	28	where	where	SCONJ
iajs-553	106	29	∆	∆	PROPN
iajs-553	106	30	[	[	X
iajs-553	106	31	vmax(lawler	vmax(lawler	X
iajs-553	106	32	)	)	PUNCT
iajs-553	106	33	,	,	PUNCT
iajs-553	106	34	vmax(spt	vmax(spt	NOUN
iajs-553	106	35	)	)	PUNCT
iajs-553	106	36	]	]	PUNCT
iajs-553	106	37	.	.	PUNCT
iajs-553	107	1	it	it	PRON
iajs-553	107	2	is	be	AUX
iajs-553	107	3	clear	clear	ADJ
iajs-553	107	4	that	that	SCONJ
iajs-553	107	5	the	the	DET
iajs-553	107	6	1//f(σci	1//f(σci	NUM
iajs-553	107	7	,	,	PUNCT
iajs-553	107	8	vmax	vmax	PROPN
iajs-553	107	9	)	)	PUNCT
iajs-553	107	10	problem	problem	NOUN
iajs-553	107	11	originates	originate	NOUN
iajs-553	107	12	from	from	ADP
iajs-553	107	13	1//	1//	NUM
iajs-553	107	14	σci	σci	PROPN
iajs-553	107	15	problem	problem	NOUN
iajs-553	107	16	and	and	CCONJ
iajs-553	107	17	1//vmax	1//vmax	NUM
iajs-553	107	18	problem	problem	NOUN
iajs-553	107	19	,	,	PUNCT
iajs-553	107	20	both	both	DET
iajs-553	107	21	problems	problem	NOUN
iajs-553	107	22	are	be	AUX
iajs-553	107	23	solvable	solvable	ADJ
iajs-553	107	24	in	in	ADP
iajs-553	107	25	o(n	o(n	NUM
iajs-553	107	26	log	log	NOUN
iajs-553	107	27	n	n	CCONJ
iajs-553	107	28	)	)	PUNCT
iajs-553	107	29	time	time	NOUN
iajs-553	107	30	.	.	PUNCT
iajs-553	108	1	in	in	ADP
iajs-553	108	2	order	order	NOUN
iajs-553	108	3	to	to	PART
iajs-553	108	4	find	find	VERB
iajs-553	108	5	the	the	DET
iajs-553	108	6	set	set	NOUN
iajs-553	108	7	of	of	ADP
iajs-553	108	8	pareto	pareto	ADJ
iajs-553	108	9	optimal	optimal	ADJ
iajs-553	108	10	points	point	NOUN
iajs-553	108	11	,	,	PUNCT
iajs-553	108	12	we	we	PRON
iajs-553	108	13	solve	solve	VERB
iajs-553	108	14	the	the	DET
iajs-553	108	15	problem	problem	NOUN
iajs-553	108	16	of	of	ADP
iajs-553	108	17	minimizing	minimize	VERB
iajs-553	108	18	σci	σci	NOUN
iajs-553	108	19	subject	subject	ADJ
iajs-553	108	20	to	to	ADP
iajs-553	108	21	vmax≤	vmax≤	ADJ
iajs-553	108	22	∆	∆	PROPN
iajs-553	108	23	,	,	PUNCT
iajs-553	108	24	where	where	SCONJ
iajs-553	108	25	∆	∆	PROPN
iajs-553	108	26	corresponds	correspond	VERB
iajs-553	108	27	to	to	ADP
iajs-553	108	28	the	the	DET
iajs-553	108	29	vmax	vmax	PROPN
iajs-553	108	30	value	value	NOUN
iajs-553	108	31	of	of	ADP
iajs-553	108	32	a	a	DET
iajs-553	108	33	pareto	pareto	ADJ
iajs-553	108	34	optimal	optimal	ADJ
iajs-553	108	35	point	point	NOUN
iajs-553	108	36	.	.	PUNCT
iajs-553	109	1	mathematics	mathematic	NOUN
iajs-553	109	2	361	361	NUM
iajs-553	109	3	مجلة	مجلة	NOUN
iajs-553	109	4	إبن	إبن	VERB
iajs-553	109	5	الهيثم	الهيثم	ADJ
iajs-553	109	6	للعلوم	للعلوم	NOUN
iajs-553	109	7	الصرفة	الصرفة	NOUN
iajs-553	110	1	و	و	PRON
iajs-553	110	2	التطبيقية	التطبيقية	ADJ
iajs-553	110	3	2012	2012	NUM
iajs-553	110	4	السنة	السنة	NOUN
iajs-553	110	5	25	25	NUM
iajs-553	110	6	المجلد	المجلد	NOUN
iajs-553	110	7	3	3	NUM
iajs-553	110	8	العدد	العدد	PROPN
iajs-553	110	9	ibn	ibn	PROPN
iajs-553	110	10	al	al	PROPN
iajs-553	110	11	-	-	PUNCT
iajs-553	110	12	haitham	haitham	PROPN
iajs-553	110	13	journal	journal	PROPN
iajs-553	110	14	for	for	ADP
iajs-553	110	15	pure	pure	ADJ
iajs-553	110	16	and	and	CCONJ
iajs-553	110	17	applied	apply	VERB
iajs-553	110	18	science	science	NOUN
iajs-553	110	19	no	no	NOUN
iajs-553	110	20	.	.	NOUN
iajs-553	110	21	3	3	NUM
iajs-553	110	22	vol	vol	NOUN
iajs-553	110	23	.	.	PUNCT
iajs-553	111	1	25	25	NUM
iajs-553	111	2	year	year	NOUN
iajs-553	111	3	2012	2012	NUM
iajs-553	111	4	algorithm(3	algorithm(3	NOUN
iajs-553	111	5	)	)	PUNCT
iajs-553	111	6	for	for	ADP
iajs-553	111	7	finding	find	VERB
iajs-553	111	8	a	a	DET
iajs-553	111	9	set	set	NOUN
iajs-553	111	10	of	of	ADP
iajs-553	111	11	all	all	DET
iajs-553	111	12	efficient	efficient	ADJ
iajs-553	111	13	solutions	solution	NOUN
iajs-553	111	14	for	for	ADP
iajs-553	111	15	problem(p4	problem(p4	NOUN
iajs-553	111	16	):	):	PUNCT
iajs-553	111	17	step(0	step(0	ADJ
iajs-553	111	18	):	):	PUNCT
iajs-553	111	19	put	put	VERB
iajs-553	111	20	∆=	∆=	PROPN
iajs-553	111	21	σpi	σpi	NOUN
iajs-553	111	22	,	,	PUNCT
iajs-553	111	23	n={1,	n={1,	NUM
iajs-553	111	24	...	...	PUNCT
iajs-553	111	25	,n	,n	PUNCT
iajs-553	111	26	}	}	PUNCT
iajs-553	111	27	,	,	PUNCT
iajs-553	111	28	k	k	NOUN
iajs-553	111	29	=	=	SYM
iajs-553	111	30	n	n	X
iajs-553	111	31	,	,	PUNCT
iajs-553	111	32	t	t	NOUN
iajs-553	111	33	=	=	NOUN
iajs-553	111	34	cmax	cmax	NOUN
iajs-553	111	35	=	=	SYM
iajs-553	111	36	σpi	σpi	NOUN
iajs-553	111	37	and	and	CCONJ
iajs-553	111	38	set	set	VERB
iajs-553	111	39	σ	σ	PROPN
iajs-553	111	40	=	=	SYM
iajs-553	111	41	(	(	PUNCT
iajs-553	111	42	φ	φ	NOUN
iajs-553	111	43	)	)	PUNCT
iajs-553	111	44	.	.	PUNCT
iajs-553	112	1	step(1	step(1	NOUN
iajs-553	112	2	):	):	PUNCT
iajs-553	112	3	calculate	calculate	NOUN
iajs-553	112	4	vi	vi	PROPN
iajs-553	112	5	,	,	PUNCT
iajs-553	112	6	i	i	PRON
iajs-553	112	7	n	n	ADV
iajs-553	112	8	as	as	SCONJ
iajs-553	112	9	follows	follow	VERB
iajs-553	112	10	:	:	PUNCT
iajs-553	112	11			PROPN
iajs-553	112	12			PROPN
iajs-553	112	13			PROPN
iajs-553	112	14			NOUN
iajs-553	112	15			PRON
iajs-553	112	16			NOUN
iajs-553	112	17	=	=	NOUN
iajs-553	112	18	≤+	≤+	NOUN
iajs-553	112	19	=	=	PUNCT
iajs-553	113	1	+	+	PROPN
iajs-553	113	2	<	<	X
iajs-553	113	3	<	<	X
iajs-553	113	4	=	=	ADJ
iajs-553	113	5	≤	≤	NOUN
iajs-553	113	6	=	=	PUNCT
iajs-553	113	7	n	n	PRON
iajs-553	113	8	1,	1,	NUM
iajs-553	113	9	...	...	PUNCT
iajs-553	113	10	,i	,i	PUNCT
iajs-553	113	11	,	,	PUNCT
iajs-553	113	12	ic	ic	PROPN
iajs-553	113	13	ipid	ipid	ADJ
iajs-553	113	14	if	if	SCONJ
iajs-553	113	15	ip	ip	PRON
iajs-553	113	16	n1,	n1,	NOUN
iajs-553	113	17	...	...	PUNCT
iajs-553	113	18	,i	,i	PUNCT
iajs-553	113	19	,	,	PUNCT
iajs-553	113	20	ipid	ipid	PROPN
iajs-553	113	21	ic	ic	PROPN
iajs-553	114	1	i	i	PROPN
iajs-553	114	2	d	d	PROPN
iajs-553	114	3	if	if	SCONJ
iajs-553	114	4	idic	idic	ADJ
iajs-553	114	5	n1,	n1,	NOUN
iajs-553	114	6	...	...	PUNCT
iajs-553	114	7	,i	,i	PUNCT
iajs-553	114	8	,	,	PUNCT
iajs-553	114	9	i	i	PROPN
iajs-553	114	10	d	d	PROPN
iajs-553	114	11	ic	ic	PROPN
iajs-553	114	12	if	if	SCONJ
iajs-553	114	13	0	0	NUM
iajs-553	114	14	iv	iv	NUM
iajs-553	114	15	step(2	step(2	ADJ
iajs-553	114	16	):	):	PUNCT
iajs-553	114	17	find	find	VERB
iajs-553	114	18	a	a	DET
iajs-553	114	19	job	job	NOUN
iajs-553	114	20	j	j	PROPN
iajs-553	114	21	*	*	PROPN
iajs-553	114	22	n	n	CCONJ
iajs-553	114	23	,	,	PUNCT
iajs-553	114	24	such	such	ADJ
iajs-553	114	25	that	that	SCONJ
iajs-553	114	26	1.vj*≤	1.vj*≤	NUM
iajs-553	114	27	∆.	∆.	PROPN
iajs-553	114	28	2	2	NUM
iajs-553	114	29	.	.	PUNCT
iajs-553	115	1	pj	pj	PROPN
iajs-553	115	2	*	*	PUNCT
iajs-553	115	3	>	>	X
iajs-553	115	4	pi	pi	PROPN
iajs-553	115	5	,	,	PUNCT
iajs-553	115	6	j	j	PROPN
iajs-553	115	7	*	*	PROPN
iajs-553	115	8	,	,	PUNCT
iajs-553	115	9	i	i	PRON
iajs-553	115	10	n	n	PROPN
iajs-553	115	11	and	and	CCONJ
iajs-553	115	12	vi	vi	NOUN
iajs-553	115	13	≤	≤	NUM
iajs-553	115	14	∆	∆	NOUN
iajs-553	115	15	,	,	PUNCT
iajs-553	115	16	if	if	SCONJ
iajs-553	115	17	pj*=	pj*=	PROPN
iajs-553	115	18	pi	pi	NOUN
iajs-553	115	19	choose	choose	VERB
iajs-553	115	20	the	the	DET
iajs-553	115	21	job	job	NOUN
iajs-553	115	22	with	with	ADP
iajs-553	115	23	smallest	small	ADJ
iajs-553	115	24	vj	vj	NOUN
iajs-553	115	25	*	*	PROPN
iajs-553	115	26	.	.	PUNCT
iajs-553	116	1	then	then	ADV
iajs-553	116	2	assign	assign	VERB
iajs-553	116	3	job	job	NOUN
iajs-553	116	4	j	j	PROPN
iajs-553	116	5	*	*	VERB
iajs-553	116	6	in	in	ADP
iajs-553	116	7	position	position	NOUN
iajs-553	116	8	k	k	PROPN
iajs-553	116	9	of	of	ADP
iajs-553	116	10	σ	σ	PROPN
iajs-553	116	11	=(	=(	PROPN
iajs-553	116	12	σ(k	σ(k	PROPN
iajs-553	116	13	)	)	PUNCT
iajs-553	116	14	,	,	PUNCT
iajs-553	116	15	σ	σ	PROPN
iajs-553	116	16	)	)	PUNCT
iajs-553	116	17	.	.	PUNCT
iajs-553	117	1	if	if	SCONJ
iajs-553	117	2	no	no	DET
iajs-553	117	3	job	job	NOUN
iajs-553	117	4	with	with	ADP
iajs-553	117	5	vj*≤	vj*≤	NOUN
iajs-553	117	6	∆	∆	X
iajs-553	117	7	go	go	VERB
iajs-553	117	8	to	to	ADP
iajs-553	117	9	step(5	step(5	NUM
iajs-553	117	10	)	)	PUNCT
iajs-553	117	11	.	.	PUNCT
iajs-553	118	1	step(3	step(3	PROPN
iajs-553	118	2	):	):	PUNCT
iajs-553	118	3	set	set	VERB
iajs-553	118	4	t	t	PROPN
iajs-553	118	5	=	=	PROPN
iajs-553	118	6	t	t	PROPN
iajs-553	118	7	-	-	PUNCT
iajs-553	118	8	pj	pj	PROPN
iajs-553	118	9	*	*	PROPN
iajs-553	118	10	,	,	PUNCT
iajs-553	118	11	n	n	PROPN
iajs-553	118	12	=	=	PROPN
iajs-553	118	13	n-{j	n-{j	PROPN
iajs-553	118	14	*	*	PUNCT
iajs-553	118	15	}	}	PUNCT
iajs-553	118	16	,	,	PUNCT
iajs-553	118	17	k	k	PROPN
iajs-553	118	18	=	=	NOUN
iajs-553	118	19	k-1	k-1	NOUN
iajs-553	118	20	,	,	PUNCT
iajs-553	118	21	if	if	SCONJ
iajs-553	118	22	k	k	PROPN
iajs-553	118	23	>	>	X
iajs-553	118	24	1	1	NUM
iajs-553	118	25	go	go	VERB
iajs-553	118	26	to	to	ADP
iajs-553	118	27	step(1	step(1	NOUN
iajs-553	118	28	)	)	PUNCT
iajs-553	118	29	,	,	PUNCT
iajs-553	118	30	otherwise	otherwise	ADV
iajs-553	118	31	go	go	VERB
iajs-553	118	32	to	to	ADP
iajs-553	118	33	step(4	step(4	NOUN
iajs-553	118	34	)	)	PUNCT
iajs-553	118	35	.	.	PUNCT
iajs-553	119	1	step(4	step(4	NOUN
iajs-553	119	2	):	):	PUNCT
iajs-553	119	3	compute	compute	NOUN
iajs-553	119	4	vmax(σ	vmax(σ	NOUN
iajs-553	119	5	)	)	PUNCT
iajs-553	119	6	for	for	ADP
iajs-553	119	7	the	the	DET
iajs-553	119	8	sequence	sequence	NOUN
iajs-553	119	9	jobs	job	NOUN
iajs-553	119	10	σ	σ	PROPN
iajs-553	119	11	=(	=(	PROPN
iajs-553	119	12	σ(1	σ(1	PROPN
iajs-553	119	13	)	)	PUNCT
iajs-553	119	14	,	,	PUNCT
iajs-553	119	15	…	…	PUNCT
iajs-553	119	16	,	,	PUNCT
iajs-553	119	17	σ(n	σ(n	PROPN
iajs-553	119	18	)	)	PUNCT
iajs-553	119	19	)	)	PUNCT
iajs-553	119	20	and	and	CCONJ
iajs-553	119	21	∆=	∆=	VERB
iajs-553	119	22	vmax	vmax	PROPN
iajs-553	119	23	-1	-1	PROPN
iajs-553	119	24	,	,	PUNCT
iajs-553	119	25	set	set	VERB
iajs-553	119	26	t	t	NOUN
iajs-553	119	27	=	=	NOUN
iajs-553	119	28	cmax	cmax	NOUN
iajs-553	119	29	,	,	PUNCT
iajs-553	119	30	n={1,	n={1,	NUM
iajs-553	119	31	...	...	PUNCT
iajs-553	119	32	,n	,n	PUNCT
iajs-553	119	33	}	}	PUNCT
iajs-553	119	34	,	,	PUNCT
iajs-553	119	35	k	k	NOUN
iajs-553	119	36	=	=	SYM
iajs-553	119	37	n	n	X
iajs-553	119	38	,	,	PUNCT
iajs-553	119	39	σ=	σ=	X
iajs-553	119	40	(	(	PUNCT
iajs-553	119	41	φ	φ	PROPN
iajs-553	119	42	)	)	PUNCT
iajs-553	119	43	,	,	PUNCT
iajs-553	119	44	go	go	VERB
iajs-553	119	45	to	to	ADP
iajs-553	119	46	step(1	step(1	NOUN
iajs-553	119	47	)	)	PUNCT
iajs-553	119	48	.	.	PUNCT
iajs-553	120	1	step(5	step(5	ADV
iajs-553	120	2	):	):	PUNCT
iajs-553	120	3	stop	stop	NOUN
iajs-553	120	4	.	.	PUNCT
iajs-553	121	1	computational	computational	ADJ
iajs-553	121	2	results	result	NOUN
iajs-553	121	3	for	for	ADP
iajs-553	121	4	algorithm(3	algorithm(3	NOUN
iajs-553	121	5	)	)	PUNCT
iajs-553	121	6	for	for	ADP
iajs-553	121	7	problem(p4	problem(p4	NOUN
iajs-553	121	8	):	):	PUNCT
iajs-553	121	9	8.1test	8.1t	ADJ
iajs-553	121	10	problems	problem	NOUN
iajs-553	121	11	:	:	PUNCT
iajs-553	121	12	algorithm(3	algorithm(3	NOUN
iajs-553	121	13	)	)	PUNCT
iajs-553	121	14	was	be	AUX
iajs-553	121	15	tested	test	VERB
iajs-553	121	16	by	by	ADP
iajs-553	121	17	coding	code	VERB
iajs-553	121	18	it	it	PRON
iajs-553	121	19	in	in	ADP
iajs-553	121	20	matlab	matlab	PROPN
iajs-553	121	21	7.9.0(r2009b	7.9.0(r2009b	NUM
iajs-553	121	22	)	)	PUNCT
iajs-553	121	23	and	and	CCONJ
iajs-553	121	24	implemented	implement	VERB
iajs-553	121	25	on	on	ADP
iajs-553	121	26	intel	intel	PROPN
iajs-553	121	27	core	core	PROPN
iajs-553	121	28	(	(	PUNCT
iajs-553	121	29	tm	tm	NOUN
iajs-553	121	30	)	)	PUNCT
iajs-553	121	31	i3	i3	NOUN
iajs-553	121	32	cpu	cpu	NOUN
iajs-553	121	33	m380	m380	X
iajs-553	121	34	@	@	ADP
iajs-553	121	35	2.53	2.53	NUM
iajs-553	121	36	ghz	ghz	NOUN
iajs-553	121	37	,	,	PUNCT
iajs-553	121	38	with	with	ADP
iajs-553	121	39	ram	ram	NOUN
iajs-553	121	40	4.00	4.00	NUM
iajs-553	121	41	gb	gb	ADP
iajs-553	121	42	personal	personal	ADJ
iajs-553	121	43	computer	computer	NOUN
iajs-553	121	44	.	.	PUNCT
iajs-553	122	1	test	test	NOUN
iajs-553	122	2	problems	problem	NOUN
iajs-553	122	3	were	be	AUX
iajs-553	122	4	generated	generate	VERB
iajs-553	122	5	as	as	SCONJ
iajs-553	122	6	follows	follow	VERB
iajs-553	122	7	:	:	PUNCT
iajs-553	122	8	for	for	ADP
iajs-553	122	9	each	each	DET
iajs-553	122	10	job	job	NOUN
iajs-553	122	11	j	j	PROPN
iajs-553	122	12	,	,	PUNCT
iajs-553	122	13	an	an	DET
iajs-553	122	14	integer	integer	NOUN
iajs-553	122	15	processing	processing	NOUN
iajs-553	122	16	time	time	NOUN
iajs-553	122	17	pj	pj	PROPN
iajs-553	122	18	was	be	AUX
iajs-553	122	19	generated	generate	VERB
iajs-553	122	20	from	from	ADP
iajs-553	122	21	the	the	DET
iajs-553	122	22	uniform	uniform	ADJ
iajs-553	122	23	distribution	distribution	NOUN
iajs-553	122	24	[	[	X
iajs-553	122	25	1,10	1,10	NUM
iajs-553	122	26	]	]	PUNCT
iajs-553	122	27	.	.	PUNCT
iajs-553	123	1	also	also	ADV
iajs-553	123	2	,	,	PUNCT
iajs-553	123	3	for	for	ADP
iajs-553	123	4	each	each	DET
iajs-553	123	5	job	job	NOUN
iajs-553	123	6	j	j	PROPN
iajs-553	123	7	,	,	PUNCT
iajs-553	123	8	an	an	DET
iajs-553	123	9	integer	integer	NOUN
iajs-553	123	10	due	due	ADJ
iajs-553	123	11	date	date	NOUN
iajs-553	123	12	is	be	AUX
iajs-553	123	13	generated	generate	VERB
iajs-553	123	14	from	from	ADP
iajs-553	123	15	the	the	DET
iajs-553	123	16	distribution[pi	distribution[pi	PROPN
iajs-553	123	17	,	,	PUNCT
iajs-553	123	18	σpi	σpi	NOUN
iajs-553	123	19	]	]	PUNCT
iajs-553	123	20	.	.	PUNCT
iajs-553	124	1	results	result	NOUN
iajs-553	124	2	for	for	ADP
iajs-553	124	3	10,15	10,15	NUM
iajs-553	124	4	,	,	PUNCT
iajs-553	124	5	30	30	NUM
iajs-553	124	6	and	and	CCONJ
iajs-553	124	7	50	50	NUM
iajs-553	124	8	job	job	NOUN
iajs-553	124	9	problems	problem	NOUN
iajs-553	124	10	are	be	AUX
iajs-553	124	11	given	give	VERB
iajs-553	124	12	in	in	ADP
iajs-553	124	13	table	table	NOUN
iajs-553	124	14	(	(	PUNCT
iajs-553	124	15	1	1	NUM
iajs-553	124	16	)	)	PUNCT
iajs-553	124	17	because	because	SCONJ
iajs-553	124	18	of	of	ADP
iajs-553	124	19	page	page	NOUN
iajs-553	124	20	limitations	limitation	NOUN
iajs-553	124	21	,	,	PUNCT
iajs-553	124	22	only	only	ADV
iajs-553	124	23	five	five	NUM
iajs-553	124	24	examples	example	NOUN
iajs-553	124	25	are	be	AUX
iajs-553	124	26	given	give	VERB
iajs-553	124	27	for	for	ADP
iajs-553	124	28	each	each	DET
iajs-553	124	29	problem	problem	NOUN
iajs-553	124	30	size	size	NOUN
iajs-553	124	31	.	.	PUNCT
iajs-553	125	1	table(1	table(1	PROPN
iajs-553	125	2	)	)	PUNCT
iajs-553	125	3	should	should	AUX
iajs-553	125	4	be	be	AUX
iajs-553	125	5	read	read	VERB
iajs-553	125	6	as	as	SCONJ
iajs-553	125	7	follows	follow	VERB
iajs-553	125	8	:	:	PUNCT
iajs-553	125	9	nep	nep	PROPN
iajs-553	125	10	=	=	NOUN
iajs-553	125	11	the	the	DET
iajs-553	125	12	actual	actual	ADJ
iajs-553	125	13	number	number	NOUN
iajs-553	125	14	of	of	ADP
iajs-553	125	15	efficient	efficient	ADJ
iajs-553	125	16	points	point	NOUN
iajs-553	125	17	for	for	ADP
iajs-553	125	18	the	the	DET
iajs-553	125	19	problem	problem	NOUN
iajs-553	125	20	at	at	ADP
iajs-553	125	21	hand	hand	NOUN
iajs-553	125	22	.	.	PUNCT
iajs-553	126	1	remember	remember	VERB
iajs-553	126	2	that	that	SCONJ
iajs-553	126	3	the	the	DET
iajs-553	126	4	procedure	procedure	NOUN
iajs-553	126	5	finds	find	VERB
iajs-553	126	6	all	all	DET
iajs-553	126	7	these	these	DET
iajs-553	126	8	points	point	NOUN
iajs-553	126	9	.	.	PUNCT
iajs-553	127	1	mnep	mnep	NOUN
iajs-553	127	2	=	=	SYM
iajs-553	127	3	maximum	maximum	ADJ
iajs-553	127	4	possible	possible	ADJ
iajs-553	127	5	number	number	NOUN
iajs-553	127	6	of	of	ADP
iajs-553	127	7	efficient	efficient	ADJ
iajs-553	127	8	points	point	NOUN
iajs-553	127	9	for	for	ADP
iajs-553	127	10	the	the	DET
iajs-553	127	11	problem	problem	NOUN
iajs-553	127	12	at	at	ADP
iajs-553	127	13	hand	hand	NOUN
iajs-553	127	14	.	.	PUNCT
iajs-553	128	1	since	since	SCONJ
iajs-553	128	2	an	an	DET
iajs-553	128	3	efficient	efficient	ADJ
iajs-553	128	4	point	point	NOUN
iajs-553	128	5	could	could	AUX
iajs-553	128	6	exist	exist	VERB
iajs-553	128	7	for	for	ADP
iajs-553	128	8	each	each	DET
iajs-553	128	9	value	value	NOUN
iajs-553	128	10	of	of	ADP
iajs-553	128	11	the	the	DET
iajs-553	128	12	maximum	maximum	ADJ
iajs-553	128	13	late	late	ADJ
iajs-553	128	14	work	work	NOUN
iajs-553	128	15	between	between	ADP
iajs-553	128	16	v(spt	v(spt	NOUN
iajs-553	128	17	*	*	PUNCT
iajs-553	128	18	)	)	PUNCT
iajs-553	128	19	and	and	CCONJ
iajs-553	128	20	v(lawler	v(lawler	NOUN
iajs-553	128	21	)	)	PUNCT
iajs-553	128	22	,	,	PUNCT
iajs-553	128	23	this	this	DET
iajs-553	128	24	maximum	maximum	ADJ
iajs-553	128	25	possible	possible	ADJ
iajs-553	128	26	number	number	NOUN
iajs-553	128	27	equals	equal	VERB
iajs-553	128	28	vmax(spt	vmax(spt	NOUN
iajs-553	128	29	*	*	PUNCT
iajs-553	128	30	)	)	PUNCT
iajs-553	128	31	–	–	PUNCT
iajs-553	128	32	vmax(lawler	vmax(lawler	NOUN
iajs-553	128	33	)	)	PUNCT
iajs-553	129	1	+	+	CCONJ
iajs-553	129	2	1	1	X
iajs-553	129	3	.	.	X
iajs-553	129	4	from	from	ADP
iajs-553	129	5	our	our	PRON
iajs-553	129	6	computational	computational	ADJ
iajs-553	129	7	results	result	NOUN
iajs-553	129	8	we	we	PRON
iajs-553	129	9	conclude	conclude	VERB
iajs-553	129	10	that	that	PRON
iajs-553	129	11	:	:	PUNCT
iajs-553	129	12	(	(	PUNCT
iajs-553	129	13	a	a	X
iajs-553	129	14	)	)	PUNCT
iajs-553	129	15	the	the	DET
iajs-553	129	16	number	number	NOUN
iajs-553	129	17	of	of	ADP
iajs-553	129	18	efficient	efficient	ADJ
iajs-553	129	19	points	point	NOUN
iajs-553	129	20	is	be	AUX
iajs-553	129	21	usually	usually	ADV
iajs-553	129	22	small	small	ADJ
iajs-553	129	23	.	.	PUNCT
iajs-553	130	1	therefore	therefore	ADV
iajs-553	130	2	,	,	PUNCT
iajs-553	130	3	the	the	DET
iajs-553	130	4	decision	decision	NOUN
iajs-553	130	5	maker	maker	NOUN
iajs-553	130	6	should	should	AUX
iajs-553	130	7	be	be	AUX
iajs-553	130	8	able	able	ADJ
iajs-553	130	9	to	to	PART
iajs-553	130	10	make	make	VERB
iajs-553	130	11	his	his	PRON
iajs-553	130	12	choice	choice	NOUN
iajs-553	130	13	.	.	PUNCT
iajs-553	131	1	(	(	PUNCT
iajs-553	131	2	b	b	X
iajs-553	131	3	)	)	PUNCT
iajs-553	131	4	we	we	PRON
iajs-553	131	5	can	can	AUX
iajs-553	131	6	find	find	VERB
iajs-553	131	7	all	all	DET
iajs-553	131	8	efficient	efficient	ADJ
iajs-553	131	9	points	point	NOUN
iajs-553	131	10	.	.	PUNCT
iajs-553	132	1	this	this	PRON
iajs-553	132	2	allows	allow	VERB
iajs-553	132	3	for	for	ADP
iajs-553	132	4	a	a	DET
iajs-553	132	5	justified	justified	ADJ
iajs-553	132	6	choice	choice	NOUN
iajs-553	132	7	of	of	ADP
iajs-553	132	8	a	a	DET
iajs-553	132	9	sequence	sequence	NOUN
iajs-553	132	10	that	that	PRON
iajs-553	132	11	takes	take	VERB
iajs-553	132	12	both	both	DET
iajs-553	132	13	objective	objective	ADJ
iajs-553	132	14	functions	function	NOUN
iajs-553	132	15	into	into	ADP
iajs-553	132	16	account	account	NOUN
iajs-553	132	17	and	and	CCONJ
iajs-553	132	18	that	that	PRON
iajs-553	132	19	is	be	AUX
iajs-553	132	20	not	not	PART
iajs-553	132	21	dominated	dominate	VERB
iajs-553	132	22	by	by	ADP
iajs-553	132	23	any	any	DET
iajs-553	132	24	other	other	ADJ
iajs-553	132	25	sequence	sequence	NOUN
iajs-553	132	26	.	.	PUNCT
iajs-553	133	1	very	very	ADV
iajs-553	133	2	attractive	attractive	ADJ
iajs-553	133	3	efficient	efficient	ADJ
iajs-553	133	4	points	point	NOUN
iajs-553	133	5	are	be	AUX
iajs-553	133	6	found	find	VERB
iajs-553	133	7	for	for	ADP
iajs-553	133	8	all	all	DET
iajs-553	133	9	the	the	DET
iajs-553	133	10	test	test	NOUN
iajs-553	133	11	problems	problem	NOUN
iajs-553	133	12	.	.	PUNCT
iajs-553	134	1	in	in	ADP
iajs-553	134	2	most	most	ADJ
iajs-553	134	3	cases	case	NOUN
iajs-553	134	4	we	we	PRON
iajs-553	134	5	discovered	discover	VERB
iajs-553	134	6	efficient	efficient	ADJ
iajs-553	134	7	point	point	NOUN
iajs-553	134	8	that	that	PRON
iajs-553	134	9	were	be	AUX
iajs-553	134	10	surprisingly	surprisingly	ADV
iajs-553	134	11	close	close	ADJ
iajs-553	134	12	to	to	ADP
iajs-553	134	13	the	the	DET
iajs-553	134	14	optimum	optimum	ADJ
iajs-553	134	15	value	value	NOUN
iajs-553	134	16	for	for	ADP
iajs-553	134	17	both	both	DET
iajs-553	134	18	objectives	objective	NOUN
iajs-553	134	19	.	.	PUNCT
iajs-553	135	1	remark	remark	NOUN
iajs-553	135	2	1	1	NUM
iajs-553	135	3	:	:	PUNCT
iajs-553	135	4	if	if	SCONJ
iajs-553	135	5	we	we	PRON
iajs-553	135	6	replace	replace	VERB
iajs-553	135	7	the	the	DET
iajs-553	135	8	criterion	criterion	NOUN
iajs-553	135	9	vmax	vmax	PROPN
iajs-553	135	10	in	in	ADP
iajs-553	135	11	problem(p4	problem(p4	PROPN
iajs-553	135	12	)	)	PUNCT
iajs-553	135	13	by	by	ADP
iajs-553	135	14	the	the	DET
iajs-553	135	15	criterion	criterion	NOUN
iajs-553	135	16	fmax	fmax	PROPN
iajs-553	135	17	{	{	PUNCT
iajs-553	135	18	lmax	lmax	PROPN
iajs-553	135	19	,	,	PUNCT
iajs-553	135	20	tmax	tmax	ADV
iajs-553	135	21	,	,	PUNCT
iajs-553	135	22	,	,	PUNCT
iajs-553	135	23	}	}	PUNCT
iajs-553	135	24	then	then	ADV
iajs-553	135	25	the	the	DET
iajs-553	135	26	efficient	efficient	ADJ
iajs-553	135	27	algorithm(3	algorithm(3	NOUN
iajs-553	135	28	)	)	PUNCT
iajs-553	135	29	above	above	ADV
iajs-553	135	30	can	can	AUX
iajs-553	135	31	be	be	AUX
iajs-553	135	32	used	use	VERB
iajs-553	135	33	for	for	ADP
iajs-553	135	34	their	their	PRON
iajs-553	135	35	solutions	solution	NOUN
iajs-553	135	36	.	.	PUNCT
iajs-553	136	1	also	also	ADV
iajs-553	136	2	for	for	ADP
iajs-553	136	3	the	the	DET
iajs-553	136	4	1//f(σci	1//f(σci	NUM
iajs-553	136	5	,	,	PUNCT
iajs-553	136	6	tmax	tmax	NUM
iajs-553	136	7	)	)	PUNCT
iajs-553	136	8	problem	problem	NOUN
iajs-553	136	9	,	,	PUNCT
iajs-553	136	10	which	which	PRON
iajs-553	136	11	is	be	AUX
iajs-553	136	12	solved	solve	VERB
iajs-553	136	13	by	by	ADP
iajs-553	136	14	vanwassenhove	vanwassenhove	NOUN
iajs-553	136	15	and	and	CCONJ
iajs-553	136	16	gelder	gelder	NOUN
iajs-553	137	1	[	[	X
iajs-553	137	2	11	11	NUM
iajs-553	137	3	]	]	PUNCT
iajs-553	137	4	.	.	PUNCT
iajs-553	138	1	this	this	PRON
iajs-553	138	2	means	mean	VERB
iajs-553	138	3	that	that	SCONJ
iajs-553	138	4	algorithm(3	algorithm(3	NOUN
iajs-553	138	5	)	)	PUNCT
iajs-553	138	6	is	be	AUX
iajs-553	138	7	a	a	DET
iajs-553	138	8	general	general	ADJ
iajs-553	138	9	one	one	NOUN
iajs-553	138	10	and	and	CCONJ
iajs-553	138	11	simple	simple	NOUN
iajs-553	138	12	that	that	PRON
iajs-553	138	13	can	can	AUX
iajs-553	138	14	solve	solve	VERB
iajs-553	138	15	problems	problem	NOUN
iajs-553	138	16	of	of	ADP
iajs-553	138	17	form	form	NOUN
iajs-553	138	18	1//f(σci	1//f(σci	NUM
iajs-553	138	19	,	,	PUNCT
iajs-553	138	20	fmax	fmax	PROPN
iajs-553	138	21	)	)	PUNCT
iajs-553	138	22	.	.	PUNCT
iajs-553	139	1	analysis	analysis	NOUN
iajs-553	139	2	of	of	ADP
iajs-553	139	3	the	the	DET
iajs-553	139	4	three	three	NUM
iajs-553	139	5	criteria	criterion	NOUN
iajs-553	139	6	.	.	PUNCT
iajs-553	140	1	mathematics	mathematic	NOUN
iajs-553	140	2	362	362	NUM
iajs-553	140	3	مجلة	مجلة	PROPN
iajs-553	140	4	إبن	إبن	VERB
iajs-553	140	5	الهيثم	الهيثم	ADJ
iajs-553	140	6	للعلوم	للعلوم	NOUN
iajs-553	140	7	الصرفة	الصرفة	NOUN
iajs-553	141	1	و	و	PRON
iajs-553	141	2	التطبيقية	التطبيقية	ADJ
iajs-553	141	3	2012	2012	NUM
iajs-553	141	4	السنة	السنة	NOUN
iajs-553	141	5	25	25	NUM
iajs-553	141	6	المجلد	المجلد	NOUN
iajs-553	141	7	3	3	NUM
iajs-553	141	8	العدد	العدد	PROPN
iajs-553	141	9	ibn	ibn	PROPN
iajs-553	141	10	al	al	PROPN
iajs-553	141	11	-	-	PUNCT
iajs-553	141	12	haitham	haitham	PROPN
iajs-553	141	13	journal	journal	PROPN
iajs-553	141	14	for	for	ADP
iajs-553	141	15	pure	pure	ADJ
iajs-553	141	16	and	and	CCONJ
iajs-553	141	17	applied	apply	VERB
iajs-553	141	18	science	science	NOUN
iajs-553	141	19	no	no	NOUN
iajs-553	141	20	.	.	NOUN
iajs-553	141	21	3	3	NUM
iajs-553	141	22	vol	vol	NOUN
iajs-553	141	23	.	.	PUNCT
iajs-553	142	1	25	25	NUM
iajs-553	142	2	year	year	NOUN
iajs-553	142	3	2012	2012	NUM
iajs-553	142	4	first	first	ADV
iajs-553	142	5	,	,	PUNCT
iajs-553	142	6	we	we	PRON
iajs-553	142	7	present	present	VERB
iajs-553	142	8	the	the	DET
iajs-553	142	9	main	main	ADJ
iajs-553	142	10	multicriteria	multicriteria	NOUN
iajs-553	142	11	scheduling	scheduling	NOUN
iajs-553	142	12	results	result	NOUN
iajs-553	142	13	that	that	PRON
iajs-553	142	14	have	have	AUX
iajs-553	142	15	appeared	appear	VERB
iajs-553	142	16	in	in	ADP
iajs-553	142	17	the	the	DET
iajs-553	142	18	literature	literature	NOUN
iajs-553	142	19	.	.	PUNCT
iajs-553	143	1	hoogeveen[8	hoogeveen[8	SYM
iajs-553	143	2	]	]	PUNCT
iajs-553	143	3	solves	solve	VERB
iajs-553	143	4	the	the	DET
iajs-553	143	5	problem	problem	NOUN
iajs-553	143	6	1//f(fmax	1//f(fmax	NUM
iajs-553	143	7	,	,	PUNCT
iajs-553	143	8	gmax	gmax	PROPN
iajs-553	143	9	)	)	PUNCT
iajs-553	143	10	and	and	CCONJ
iajs-553	143	11	the	the	DET
iajs-553	143	12	problem	problem	NOUN
iajs-553	143	13	1//f(fmax	1//f(fmax	NUM
iajs-553	143	14	,	,	PUNCT
iajs-553	143	15	gmax	gmax	PROPN
iajs-553	143	16	,	,	PUNCT
iajs-553	143	17	hmax	hmax	PROPN
iajs-553	143	18	)	)	PUNCT
iajs-553	143	19	.	.	PUNCT
iajs-553	144	1	he	he	PRON
iajs-553	144	2	presented	present	VERB
iajs-553	144	3	a	a	DET
iajs-553	144	4	polynomial	polynomial	ADJ
iajs-553	144	5	algorithm	algorithm	NOUN
iajs-553	144	6	for	for	ADP
iajs-553	144	7	both	both	DET
iajs-553	144	8	problems	problem	NOUN
iajs-553	144	9	and	and	CCONJ
iajs-553	144	10	he	he	PRON
iajs-553	144	11	showed	show	VERB
iajs-553	144	12	that	that	SCONJ
iajs-553	144	13	these	these	PRON
iajs-553	144	14	can	can	AUX
iajs-553	144	15	be	be	AUX
iajs-553	144	16	used	use	VERB
iajs-553	144	17	if	if	SCONJ
iajs-553	144	18	precedence	precedence	NOUN
iajs-553	144	19	constraints	constraint	NOUN
iajs-553	144	20	exist	exist	VERB
iajs-553	144	21	between	between	ADP
iajs-553	144	22	the	the	DET
iajs-553	144	23	jobs	job	NOUN
iajs-553	144	24	or	or	CCONJ
iajs-553	144	25	if	if	SCONJ
iajs-553	144	26	all	all	DET
iajs-553	144	27	penalty	penalty	NOUN
iajs-553	144	28	functions	function	NOUN
iajs-553	144	29	are	be	AUX
iajs-553	144	30	nondecreasing	nondecrease	VERB
iajs-553	144	31	in	in	ADP
iajs-553	144	32	the	the	DET
iajs-553	144	33	job	job	NOUN
iajs-553	144	34	completion	completion	NOUN
iajs-553	144	35	times	time	NOUN
iajs-553	144	36	.	.	PUNCT
iajs-553	145	1	hoogeveen[13	hoogeveen[13	PROPN
iajs-553	145	2	]	]	PUNCT
iajs-553	145	3	solves	solve	VERB
iajs-553	145	4	the	the	DET
iajs-553	145	5	general	general	ADJ
iajs-553	145	6	problem	problem	NOUN
iajs-553	145	7	1//f	1//f	NUM
iajs-553	145	8	(	(	PUNCT
iajs-553	145	9	,	,	PUNCT
iajs-553	145	10	…	…	PUNCT
iajs-553	145	11	,	,	PUNCT
iajs-553	145	12	)	)	PUNCT
iajs-553	145	13	,	,	PUNCT
iajs-553	145	14	k	k	PROPN
iajs-553	145	15	finite	finite	VERB
iajs-553	145	16	integer	integer	NOUN
iajs-553	145	17	number	number	NOUN
iajs-553	145	18	and	and	CCONJ
iajs-553	145	19	each	each	DET
iajs-553	145	20	one	one	NUM
iajs-553	145	21	of	of	ADP
iajs-553	145	22	these	these	DET
iajs-553	145	23	penalty	penalty	NOUN
iajs-553	145	24	functions	function	NOUN
iajs-553	145	25	is	be	AUX
iajs-553	145	26	assumed	assume	VERB
iajs-553	145	27	to	to	PART
iajs-553	145	28	be	be	AUX
iajs-553	145	29	non	non	ADJ
iajs-553	145	30	-	-	ADJ
iajs-553	145	31	decreasing	decrease	VERB
iajs-553	145	32	in	in	ADP
iajs-553	145	33	the	the	DET
iajs-553	145	34	job	job	NOUN
iajs-553	145	35	completion	completion	NOUN
iajs-553	145	36	time	time	NOUN
iajs-553	145	37	.	.	PUNCT
iajs-553	146	1	there	there	PRON
iajs-553	146	2	are	be	VERB
iajs-553	146	3	two	two	NUM
iajs-553	146	4	methods	method	NOUN
iajs-553	146	5	for	for	ADP
iajs-553	146	6	dealing	deal	VERB
iajs-553	146	7	with	with	ADP
iajs-553	146	8	conflicting	conflicting	ADJ
iajs-553	146	9	criteria	criterion	NOUN
iajs-553	146	10	,	,	PUNCT
iajs-553	146	11	the	the	DET
iajs-553	146	12	first	first	ADJ
iajs-553	146	13	one	one	NOUN
iajs-553	146	14	is	be	AUX
iajs-553	146	15	hierarchical	hierarchical	ADJ
iajs-553	146	16	minimization	minimization	NOUN
iajs-553	146	17	of	of	ADP
iajs-553	146	18	the	the	DET
iajs-553	146	19	performance	performance	NOUN
iajs-553	146	20	criteria	criterion	NOUN
iajs-553	146	21	,	,	PUNCT
iajs-553	146	22	,	,	PUNCT
iajs-553	146	23	…	…	PUNCT
iajs-553	146	24	,	,	PUNCT
iajs-553	146	25	which	which	PRON
iajs-553	146	26	are	be	AUX
iajs-553	146	27	indexed	index	VERB
iajs-553	146	28	in	in	ADP
iajs-553	146	29	order	order	NOUN
iajs-553	146	30	of	of	ADP
iajs-553	146	31	decreasing	decrease	VERB
iajs-553	146	32	importance	importance	NOUN
iajs-553	146	33	.	.	PUNCT
iajs-553	147	1	the	the	DET
iajs-553	147	2	second	second	ADJ
iajs-553	147	3	method	method	NOUN
iajs-553	147	4	is	be	AUX
iajs-553	147	5	simultaneous	simultaneous	ADJ
iajs-553	147	6	minimization	minimization	NOUN
iajs-553	147	7	.	.	PUNCT
iajs-553	148	1	the	the	DET
iajs-553	148	2	criteria	criterion	NOUN
iajs-553	148	3	are	be	AUX
iajs-553	148	4	aggregated	aggregate	VERB
iajs-553	148	5	into	into	ADP
iajs-553	148	6	a	a	DET
iajs-553	148	7	single	single	ADJ
iajs-553	148	8	composite	composite	ADJ
iajs-553	148	9	objective	objective	ADJ
iajs-553	148	10	function	function	NOUN
iajs-553	148	11	f	f	X
iajs-553	148	12	(	(	PUNCT
iajs-553	148	13	,	,	PUNCT
iajs-553	148	14	,	,	PUNCT
iajs-553	148	15	…	…	PUNCT
iajs-553	148	16	,	,	PUNCT
iajs-553	148	17	)	)	PUNCT
iajs-553	148	18	,	,	PUNCT
iajs-553	148	19	which	which	PRON
iajs-553	148	20	minimized	minimize	VERB
iajs-553	148	21	.	.	PUNCT
iajs-553	149	1	in	in	ADP
iajs-553	149	2	our	our	PRON
iajs-553	149	3	study	study	NOUN
iajs-553	149	4	we	we	PRON
iajs-553	149	5	are	be	AUX
iajs-553	149	6	looking	look	VERB
iajs-553	149	7	for	for	ADP
iajs-553	149	8	algorithms	algorithm	NOUN
iajs-553	149	9	,	,	PUNCT
iajs-553	149	10	that	that	PRON
iajs-553	149	11	can	can	AUX
iajs-553	149	12	be	be	AUX
iajs-553	149	13	used	use	VERB
iajs-553	149	14	for	for	ADP
iajs-553	149	15	solving	solve	VERB
iajs-553	149	16	multicriteria	multicriteria	PROPN
iajs-553	149	17	scheduling	scheduling	NOUN
iajs-553	149	18	problem	problem	NOUN
iajs-553	149	19	,	,	PUNCT
iajs-553	149	20	which	which	PRON
iajs-553	149	21	is	be	AUX
iajs-553	149	22	to	to	PART
iajs-553	149	23	find	find	VERB
iajs-553	149	24	the	the	DET
iajs-553	149	25	efficient	efficient	ADJ
iajs-553	149	26	solutions	solution	NOUN
iajs-553	149	27	or	or	CCONJ
iajs-553	149	28	at	at	ADP
iajs-553	149	29	least	least	ADJ
iajs-553	149	30	approximation	approximation	NOUN
iajs-553	149	31	to	to	ADP
iajs-553	149	32	it	it	PRON
iajs-553	149	33	.	.	PUNCT
iajs-553	150	1	hence	hence	ADV
iajs-553	150	2	we	we	PRON
iajs-553	150	3	search	search	VERB
iajs-553	150	4	for	for	ADP
iajs-553	150	5	feasible	feasible	ADJ
iajs-553	150	6	solutions	solution	NOUN
iajs-553	150	7	yielding	yield	VERB
iajs-553	150	8	the	the	DET
iajs-553	150	9	best	good	ADJ
iajs-553	150	10	compromise	compromise	NOUN
iajs-553	150	11	among	among	ADP
iajs-553	150	12	objectives	objective	NOUN
iajs-553	150	13	that	that	PRON
iajs-553	150	14	constitutes	constitute	VERB
iajs-553	150	15	a	a	DET
iajs-553	150	16	so	so	ADV
iajs-553	150	17	called	call	VERB
iajs-553	150	18	efficient	efficient	ADJ
iajs-553	150	19	solutions	solution	NOUN
iajs-553	150	20	set	set	VERB
iajs-553	150	21	.	.	PUNCT
iajs-553	151	1	the	the	DET
iajs-553	151	2	1//f	1//f	NUM
iajs-553	151	3	(	(	PUNCT
iajs-553	151	4	,	,	PUNCT
iajs-553	151	5	tmax	tmax	PROPN
iajs-553	151	6	,	,	PUNCT
iajs-553	151	7	vmax	vmax	PROPN
iajs-553	151	8	)	)	PUNCT
iajs-553	151	9	problem(p5	problem(p5	PROPN
iajs-553	151	10	):	):	PUNCT
iajs-553	151	11	in	in	ADP
iajs-553	151	12	this	this	DET
iajs-553	151	13	section	section	NOUN
iajs-553	151	14	,	,	PUNCT
iajs-553	151	15	we	we	PRON
iajs-553	151	16	will	will	AUX
iajs-553	151	17	try	try	VERB
iajs-553	151	18	to	to	PART
iajs-553	151	19	find	find	VERB
iajs-553	151	20	efficient	efficient	ADJ
iajs-553	151	21	(	(	PUNCT
iajs-553	151	22	pareto	pareto	ADJ
iajs-553	151	23	optimal	optimal	ADJ
iajs-553	151	24	)	)	PUNCT
iajs-553	151	25	solutions	solution	NOUN
iajs-553	151	26	for	for	ADP
iajs-553	151	27	1//f(σci	1//f(σci	NUM
iajs-553	151	28	,	,	PUNCT
iajs-553	151	29	tmax	tmax	PROPN
iajs-553	151	30	,	,	PUNCT
iajs-553	151	31	vmax	vmax	PROPN
iajs-553	151	32	)	)	PUNCT
iajs-553	151	33	.	.	PUNCT
iajs-553	152	1	this	this	DET
iajs-553	152	2	problem	problem	NOUN
iajs-553	152	3	can	can	AUX
iajs-553	152	4	be	be	AUX
iajs-553	152	5	defined	define	VERB
iajs-553	152	6	as	as	ADP
iajs-553	152	7	:	:	PUNCT
iajs-553	152	8	min	min	PROPN
iajs-553	152	9	s.t	s.t	PROPN
iajs-553	152	10	.	.	PROPN
iajs-553	152	11	ci	ci	PROPN
iajs-553	152	12	≥	≥	PROPN
iajs-553	152	13	pi	pi	PROPN
iajs-553	152	14	i=1,	i=1,	PROPN
iajs-553	152	15	…	…	PUNCT
iajs-553	152	16	,n	,n	NUM
iajs-553	152	17	.	.	PUNCT
iajs-553	153	1	ci	ci	PROPN
iajs-553	154	1	=	=	PRON
iajs-553	154	2	c(i-1)+	c(i-1)+	PROPN
iajs-553	154	3	pi	pi	PROPN
iajs-553	154	4	i=2,	i=2,	PROPN
iajs-553	154	5	…	…	PUNCT
iajs-553	154	6	,n	,n	X
iajs-553	154	7	.	.	PUNCT
iajs-553	155	1	…	…	PUNCT
iajs-553	155	2	..	..	PUNCT
iajs-553	156	1	p(5	p(5	NOUN
iajs-553	156	2	)	)	PUNCT
iajs-553	156	3	vi≤	vi≤	NOUN
iajs-553	156	4	pi	pi	PROPN
iajs-553	156	5	i=1,	i=1,	PROPN
iajs-553	156	6	…	…	PUNCT
iajs-553	156	7	,n	,n	X
iajs-553	156	8	.	.	PUNCT
iajs-553	157	1	vi≤	vi≤	NOUN
iajs-553	157	2	ti	ti	PROPN
iajs-553	157	3	i=1,	i=1,	NOUN
iajs-553	157	4	…	…	PUNCT
iajs-553	157	5	,n	,n	NUM
iajs-553	157	6	.	.	PUNCT
iajs-553	158	1	ti≥	ti≥	PROPN
iajs-553	158	2	ci	ci	PROPN
iajs-553	158	3	di	di	PROPN
iajs-553	158	4	i=1,	i=1,	PROPN
iajs-553	158	5	…	…	PUNCT
iajs-553	158	6	,n	,n	X
iajs-553	158	7	.	.	PUNCT
iajs-553	159	1	ti	ti	PROPN
iajs-553	159	2	≥	≥	NOUN
iajs-553	159	3	0	0	NUM
iajs-553	159	4	i=1,	i=1,	PROPN
iajs-553	159	5	…	…	PUNCT
iajs-553	159	6	,n	,n	NOUN
iajs-553	159	7	.	.	PUNCT
iajs-553	160	1	it	it	PRON
iajs-553	160	2	is	be	AUX
iajs-553	160	3	clear	clear	ADJ
iajs-553	160	4	that	that	SCONJ
iajs-553	160	5	this	this	DET
iajs-553	160	6	problem	problem	NOUN
iajs-553	160	7	is	be	AUX
iajs-553	160	8	difficult	difficult	ADJ
iajs-553	160	9	to	to	PART
iajs-553	160	10	solve	solve	VERB
iajs-553	160	11	,	,	PUNCT
iajs-553	160	12	we	we	PRON
iajs-553	160	13	will	will	AUX
iajs-553	160	14	present	present	VERB
iajs-553	160	15	later	later	ADV
iajs-553	160	16	local	local	ADJ
iajs-553	160	17	search	search	NOUN
iajs-553	160	18	algorithm	algorithm	NOUN
iajs-553	160	19	to	to	PART
iajs-553	160	20	find	find	VERB
iajs-553	160	21	near	near	ADP
iajs-553	160	22	optimal	optimal	ADJ
iajs-553	160	23	solution	solution	NOUN
iajs-553	160	24	.	.	PUNCT
iajs-553	161	1	this	this	DET
iajs-553	161	2	problem	problem	NOUN
iajs-553	161	3	has	have	VERB
iajs-553	161	4	the	the	DET
iajs-553	161	5	following	follow	VERB
iajs-553	161	6	special	special	ADJ
iajs-553	161	7	cases	case	NOUN
iajs-553	161	8	.	.	PUNCT
iajs-553	162	1	(	(	PUNCT
iajs-553	162	2	1	1	X
iajs-553	162	3	)	)	PUNCT
iajs-553	162	4	the	the	DET
iajs-553	162	5	1//lex	1//lex	PROPN
iajs-553	162	6	(	(	PUNCT
iajs-553	162	7	,	,	PUNCT
iajs-553	162	8	tmax	tmax	PROPN
iajs-553	162	9	,	,	PUNCT
iajs-553	162	10	vmax	vmax	ADJ
iajs-553	162	11	)	)	PUNCT
iajs-553	162	12	problem	problem	NOUN
iajs-553	162	13	.	.	PUNCT
iajs-553	163	1	(	(	PUNCT
iajs-553	163	2	2	2	X
iajs-553	163	3	)	)	PUNCT
iajs-553	163	4	the	the	DET
iajs-553	163	5	1//lex	1//lex	PROPN
iajs-553	163	6	(	(	PUNCT
iajs-553	163	7	,	,	PUNCT
iajs-553	163	8	vmax	vmax	PROPN
iajs-553	163	9	,	,	PUNCT
iajs-553	163	10	tmax	tmax	NUM
iajs-553	163	11	)	)	PUNCT
iajs-553	163	12	problem	problem	NOUN
iajs-553	163	13	.	.	PUNCT
iajs-553	164	1	(	(	PUNCT
iajs-553	164	2	3	3	X
iajs-553	164	3	)	)	PUNCT
iajs-553	164	4	the	the	DET
iajs-553	164	5	1//lex(tmax	1//lex(tmax	NUM
iajs-553	164	6	,	,	PUNCT
iajs-553	164	7	,	,	PUNCT
iajs-553	164	8	vmax	vmax	ADJ
iajs-553	164	9	)	)	PUNCT
iajs-553	164	10	problem	problem	NOUN
iajs-553	164	11	.	.	PUNCT
iajs-553	165	1	(	(	PUNCT
iajs-553	165	2	4	4	X
iajs-553	165	3	)	)	PUNCT
iajs-553	165	4	the	the	DET
iajs-553	165	5	1//lex(tmax	1//lex(tmax	NUM
iajs-553	165	6	,	,	PUNCT
iajs-553	165	7	vmax	vmax	PROPN
iajs-553	165	8	,	,	PUNCT
iajs-553	165	9	)	)	PUNCT
iajs-553	165	10	problem	problem	NOUN
iajs-553	165	11	.	.	PUNCT
iajs-553	166	1	(	(	PUNCT
iajs-553	166	2	5	5	X
iajs-553	166	3	)	)	PUNCT
iajs-553	166	4	the	the	DET
iajs-553	166	5	1//lex(vmax	1//lex(vmax	NUM
iajs-553	166	6	,	,	PUNCT
iajs-553	166	7	,	,	PUNCT
iajs-553	166	8	tmax	tmax	NUM
iajs-553	166	9	)	)	PUNCT
iajs-553	166	10	problem	problem	NOUN
iajs-553	166	11	.	.	PUNCT
iajs-553	167	1	(	(	PUNCT
iajs-553	167	2	6	6	NUM
iajs-553	167	3	)	)	PUNCT
iajs-553	167	4	the	the	DET
iajs-553	167	5	1//lex(vmax	1//lex(vmax	NUM
iajs-553	167	6	,	,	PUNCT
iajs-553	167	7	tmax	tmax	ADV
iajs-553	167	8	,	,	PUNCT
iajs-553	167	9	)	)	PUNCT
iajs-553	167	10	problem	problem	NOUN
iajs-553	167	11	.	.	PUNCT
iajs-553	168	1	algorithm(4	algorithm(4	ADV
iajs-553	168	2	)	)	PUNCT
iajs-553	169	1	for	for	ADP
iajs-553	169	2	finding	find	VERB
iajs-553	169	3	efficient	efficient	ADJ
iajs-553	169	4	solutions	solution	NOUN
iajs-553	169	5	for	for	ADP
iajs-553	169	6	problem	problem	NOUN
iajs-553	169	7	(	(	PUNCT
iajs-553	169	8	p5	p5	ADJ
iajs-553	169	9	):	):	PUNCT
iajs-553	169	10	mathematics	mathematic	NOUN
iajs-553	169	11	363	363	NUM
iajs-553	169	12	مجلة	مجلة	ADJ
iajs-553	169	13	إبن	إبن	VERB
iajs-553	169	14	الهيثم	الهيثم	ADJ
iajs-553	169	15	للعلوم	للعلوم	NOUN
iajs-553	169	16	الصرفة	الصرفة	NOUN
iajs-553	170	1	و	و	PRON
iajs-553	170	2	التطبيقية	التطبيقية	ADJ
iajs-553	170	3	2012	2012	NUM
iajs-553	170	4	السنة	السنة	NOUN
iajs-553	170	5	25	25	NUM
iajs-553	170	6	المجلد	المجلد	NOUN
iajs-553	170	7	3	3	NUM
iajs-553	170	8	العدد	العدد	PROPN
iajs-553	170	9	ibn	ibn	PROPN
iajs-553	170	10	al	al	PROPN
iajs-553	170	11	-	-	PUNCT
iajs-553	170	12	haitham	haitham	PROPN
iajs-553	170	13	journal	journal	PROPN
iajs-553	170	14	for	for	ADP
iajs-553	170	15	pure	pure	ADJ
iajs-553	170	16	and	and	CCONJ
iajs-553	170	17	applied	apply	VERB
iajs-553	170	18	science	science	NOUN
iajs-553	170	19	no	no	NOUN
iajs-553	170	20	.	.	NOUN
iajs-553	170	21	3	3	NUM
iajs-553	170	22	vol	vol	NOUN
iajs-553	170	23	.	.	PUNCT
iajs-553	171	1	25	25	NUM
iajs-553	171	2	year	year	NOUN
iajs-553	171	3	2012	2012	NUM
iajs-553	171	4	step(0	step(0	NOUN
iajs-553	171	5	):	):	PUNCT
iajs-553	171	6	put	put	VERB
iajs-553	171	7	∆=	∆=	NOUN
iajs-553	171	8	,	,	PUNCT
iajs-553	171	9	n={1,	n={1,	NUM
iajs-553	171	10	…	…	PUNCT
iajs-553	171	11	..	..	PUNCT
iajs-553	171	12	,n	,n	NOUN
iajs-553	171	13	}	}	PUNCT
iajs-553	171	14	,	,	PUNCT
iajs-553	171	15	k	k	NOUN
iajs-553	171	16	=	=	SYM
iajs-553	171	17	n	n	X
iajs-553	171	18	,	,	PUNCT
iajs-553	171	19	t	t	PROPN
iajs-553	171	20	=	=	SYM
iajs-553	171	21	cmax=	cmax=	NUM
iajs-553	171	22	,	,	PUNCT
iajs-553	171	23	and	and	CCONJ
iajs-553	171	24	σ=	σ=	NOUN
iajs-553	171	25	(	(	PUNCT
iajs-553	171	26	φ	φ	PROPN
iajs-553	171	27	)	)	PUNCT
iajs-553	171	28	.	.	PUNCT
iajs-553	172	1	step(1	step(1	NOUN
iajs-553	172	2	):	):	PUNCT
iajs-553	172	3	calculate	calculate	NOUN
iajs-553	172	4	ti	ti	NOUN
iajs-553	172	5	,	,	PUNCT
iajs-553	172	6	vi	vi	PROPN
iajs-553	172	7	,	,	PUNCT
iajs-553	172	8	i	i	PRON
iajs-553	172	9	n	n	ADV
iajs-553	172	10	as	as	SCONJ
iajs-553	172	11	follows	follow	VERB
iajs-553	172	12	:	:	PUNCT
iajs-553	172	13	ti	ti	X
iajs-553	172	14	=	=	SYM
iajs-553	172	15	max	max	PROPN
iajs-553	172	16	{	{	PUNCT
iajs-553	172	17	ci	ci	PROPN
iajs-553	172	18	di	di	PROPN
iajs-553	172	19	,	,	PUNCT
iajs-553	172	20	0}and	0}and	NOUN
iajs-553	172	21	vi	vi	NOUN
iajs-553	172	22	=	=	NOUN
iajs-553	172	23	min{ti	min{ti	X
iajs-553	172	24	,	,	PUNCT
iajs-553	172	25	pi	pi	NOUN
iajs-553	172	26	}	}	PUNCT
iajs-553	172	27	.	.	PUNCT
iajs-553	173	1	step(2	step(2	ADJ
iajs-553	173	2	):	):	PUNCT
iajs-553	173	3	find	find	VERB
iajs-553	173	4	a	a	DET
iajs-553	173	5	job	job	NOUN
iajs-553	173	6	j	j	NOUN
iajs-553	173	7	*	*	PROPN
iajs-553	173	8	n	n	PROPN
iajs-553	173	9	,	,	PUNCT
iajs-553	173	10	such	such	ADJ
iajs-553	173	11	that	that	SCONJ
iajs-553	173	12	tj*≤	tj*≤	NOUN
iajs-553	173	13	∆	∆	PROPN
iajs-553	173	14	and	and	CCONJ
iajs-553	173	15	pj	pj	PROPN
iajs-553	173	16	*	*	PROPN
iajs-553	173	17	>	>	X
iajs-553	173	18	pi	pi	PROPN
iajs-553	173	19	,	,	PUNCT
iajs-553	173	20	j	j	PROPN
iajs-553	173	21	*	*	PROPN
iajs-553	173	22	,	,	PUNCT
iajs-553	173	23	i	i	PRON
iajs-553	173	24	n	n	PROPN
iajs-553	173	25	and	and	CCONJ
iajs-553	173	26	ti	ti	X
iajs-553	173	27	≤	≤	ADJ
iajs-553	173	28	∆	∆	NOUN
iajs-553	173	29	,	,	PUNCT
iajs-553	173	30	if	if	SCONJ
iajs-553	173	31	pj*=pi	pj*=pi	PROPN
iajs-553	173	32	choose	choose	VERB
iajs-553	173	33	the	the	DET
iajs-553	173	34	job	job	NOUN
iajs-553	173	35	with	with	ADP
iajs-553	173	36	smallest	small	ADJ
iajs-553	173	37	tj	tj	NOUN
iajs-553	173	38	*	*	PUNCT
iajs-553	173	39	and	and	CCONJ
iajs-553	173	40	if	if	SCONJ
iajs-553	173	41	tj*=ti	tj*=ti	VERB
iajs-553	173	42	choose	choose	VERB
iajs-553	173	43	the	the	DET
iajs-553	173	44	job	job	NOUN
iajs-553	173	45	with	with	ADP
iajs-553	173	46	smallest	small	ADJ
iajs-553	173	47	vj	vj	NOUN
iajs-553	173	48	*	*	PROPN
iajs-553	173	49	.	.	PUNCT
iajs-553	174	1	then	then	ADV
iajs-553	174	2	assign	assign	VERB
iajs-553	174	3	job	job	NOUN
iajs-553	174	4	j	j	PROPN
iajs-553	174	5	*	*	VERB
iajs-553	174	6	in	in	ADP
iajs-553	174	7	position	position	NOUN
iajs-553	174	8	k	k	PROPN
iajs-553	174	9	of	of	ADP
iajs-553	174	10	σ	σ	PROPN
iajs-553	174	11	=(	=(	PROPN
iajs-553	174	12	σ(k	σ(k	PROPN
iajs-553	174	13	)	)	PUNCT
iajs-553	174	14	,	,	PUNCT
iajs-553	174	15	σ	σ	PROPN
iajs-553	174	16	)	)	PUNCT
iajs-553	174	17	,	,	PUNCT
iajs-553	174	18	if	if	SCONJ
iajs-553	174	19	no	no	DET
iajs-553	174	20	job	job	NOUN
iajs-553	174	21	with	with	ADP
iajs-553	174	22	tj*≤	tj*≤	NOUN
iajs-553	174	23	∆	∆	X
iajs-553	174	24	go	go	VERB
iajs-553	174	25	to	to	ADP
iajs-553	174	26	step(5	step(5	NUM
iajs-553	174	27	)	)	PUNCT
iajs-553	174	28	.	.	PUNCT
iajs-553	175	1	step(3	step(3	PROPN
iajs-553	175	2	):	):	PUNCT
iajs-553	175	3	set	set	VERB
iajs-553	175	4	t	t	PROPN
iajs-553	175	5	=	=	PROPN
iajs-553	175	6	t	t	PROPN
iajs-553	175	7	-	-	PUNCT
iajs-553	175	8	pj	pj	PROPN
iajs-553	175	9	*	*	PROPN
iajs-553	175	10	,	,	PUNCT
iajs-553	175	11	n	n	PROPN
iajs-553	175	12	=	=	PROPN
iajs-553	175	13	n-{j	n-{j	PROPN
iajs-553	175	14	*	*	PUNCT
iajs-553	175	15	}	}	PUNCT
iajs-553	175	16	,	,	PUNCT
iajs-553	175	17	k	k	PROPN
iajs-553	175	18	=	=	NOUN
iajs-553	175	19	k-1	k-1	NOUN
iajs-553	175	20	,	,	PUNCT
iajs-553	175	21	if	if	SCONJ
iajs-553	175	22	k	k	PROPN
iajs-553	175	23	>	>	X
iajs-553	175	24	1	1	NUM
iajs-553	175	25	go	go	VERB
iajs-553	175	26	to	to	ADP
iajs-553	175	27	step(1	step(1	NOUN
iajs-553	175	28	)	)	PUNCT
iajs-553	175	29	,	,	PUNCT
iajs-553	175	30	otherwise	otherwise	ADV
iajs-553	175	31	go	go	VERB
iajs-553	175	32	to	to	ADP
iajs-553	175	33	step(4	step(4	NOUN
iajs-553	175	34	)	)	PUNCT
iajs-553	175	35	.	.	PUNCT
iajs-553	176	1	step(4	step(4	NOUN
iajs-553	176	2	):	):	PUNCT
iajs-553	176	3	compute	compute	NOUN
iajs-553	176	4	σcσ(i),tmax(σ	σcσ(i),tmax(σ	NOUN
iajs-553	176	5	)	)	PUNCT
iajs-553	176	6	and	and	CCONJ
iajs-553	176	7	vmax(σ	vmax(σ	NOUN
iajs-553	176	8	)	)	PUNCT
iajs-553	176	9	for	for	ADP
iajs-553	176	10	the	the	DET
iajs-553	176	11	sequence	sequence	NOUN
iajs-553	176	12	jobs	job	NOUN
iajs-553	176	13	σ=(σ(1),	σ=(σ(1),	ADJ
iajs-553	176	14	…	…	SYM
iajs-553	176	15	,σ(n	,σ(n	PUNCT
iajs-553	176	16	)	)	PUNCT
iajs-553	176	17	)	)	PUNCT
iajs-553	176	18	,	,	PUNCT
iajs-553	176	19	and	and	CCONJ
iajs-553	176	20	set	set	VERB
iajs-553	176	21	∆=	∆=	NOUN
iajs-553	176	22	tmax(σ)-1	tmax(σ)-1	NOUN
iajs-553	176	23	,	,	PUNCT
iajs-553	176	24	set	set	VERB
iajs-553	176	25	t	t	NOUN
iajs-553	176	26	=	=	NOUN
iajs-553	176	27	cmax	cmax	NOUN
iajs-553	176	28	,	,	PUNCT
iajs-553	176	29	n={1,	n={1,	NUM
iajs-553	176	30	…	…	PUNCT
iajs-553	176	31	..	..	PUNCT
iajs-553	176	32	,n	,n	NOUN
iajs-553	176	33	}	}	PUNCT
iajs-553	176	34	,	,	PUNCT
iajs-553	176	35	k	k	NOUN
iajs-553	176	36	=	=	SYM
iajs-553	176	37	n	n	X
iajs-553	176	38	,	,	PUNCT
iajs-553	176	39	σ=	σ=	X
iajs-553	176	40	(	(	PUNCT
iajs-553	176	41	φ	φ	PROPN
iajs-553	176	42	)	)	PUNCT
iajs-553	176	43	,	,	PUNCT
iajs-553	176	44	go	go	VERB
iajs-553	176	45	to	to	ADP
iajs-553	176	46	step(1	step(1	NOUN
iajs-553	176	47	)	)	PUNCT
iajs-553	176	48	.	.	PUNCT
iajs-553	177	1	step(5	step(5	ADV
iajs-553	177	2	):	):	PUNCT
iajs-553	177	3	put	put	VERB
iajs-553	177	4	∆=vmax(σ)-1	∆=vmax(σ)-1	ADJ
iajs-553	177	5	,	,	PUNCT
iajs-553	177	6	n={1,	n={1,	NUM
iajs-553	177	7	...	...	PUNCT
iajs-553	177	8	,n	,n	PUNCT
iajs-553	177	9	}	}	PUNCT
iajs-553	177	10	,	,	PUNCT
iajs-553	177	11	k	k	NOUN
iajs-553	177	12	=	=	SYM
iajs-553	177	13	n	n	X
iajs-553	177	14	,	,	PUNCT
iajs-553	177	15	t	t	NOUN
iajs-553	177	16	=	=	NOUN
iajs-553	177	17	cmax	cmax	NOUN
iajs-553	177	18	,	,	PUNCT
iajs-553	177	19	and	and	CCONJ
iajs-553	177	20	σ=	σ=	NOUN
iajs-553	177	21	(	(	PUNCT
iajs-553	177	22	φ	φ	PROPN
iajs-553	177	23	)	)	PUNCT
iajs-553	177	24	.	.	PUNCT
iajs-553	178	1	step(6	step(6	PROPN
iajs-553	178	2	):	):	PUNCT
iajs-553	178	3	calculate	calculate	NOUN
iajs-553	178	4	vi	vi	PROPN
iajs-553	178	5	,	,	PUNCT
iajs-553	178	6	i	i	PRON
iajs-553	178	7	n	n	ADV
iajs-553	178	8	as	as	SCONJ
iajs-553	178	9	follows	follow	VERB
iajs-553	178	10	:	:	PUNCT
iajs-553	178	11			PROPN
iajs-553	178	12			PROPN
iajs-553	178	13			PROPN
iajs-553	178	14			NOUN
iajs-553	178	15			PRON
iajs-553	178	16			NOUN
iajs-553	178	17	=	=	NOUN
iajs-553	178	18	≤+	≤+	NOUN
iajs-553	178	19	=	=	PUNCT
iajs-553	179	1	+	+	PROPN
iajs-553	179	2	<	<	X
iajs-553	179	3	<	<	X
iajs-553	179	4	=	=	ADJ
iajs-553	179	5	≤	≤	NOUN
iajs-553	179	6	=	=	PUNCT
iajs-553	179	7	n	n	PRON
iajs-553	179	8	1,	1,	NUM
iajs-553	179	9	...	...	PUNCT
iajs-553	179	10	,i	,i	PUNCT
iajs-553	179	11	,	,	PUNCT
iajs-553	179	12	ic	ic	PROPN
iajs-553	179	13	ipid	ipid	ADJ
iajs-553	179	14	if	if	SCONJ
iajs-553	179	15	ip	ip	PRON
iajs-553	179	16	n1,	n1,	NOUN
iajs-553	179	17	...	...	PUNCT
iajs-553	179	18	,i	,i	PUNCT
iajs-553	179	19	,	,	PUNCT
iajs-553	179	20	ipid	ipid	PROPN
iajs-553	179	21	ic	ic	PROPN
iajs-553	180	1	i	i	PROPN
iajs-553	180	2	d	d	PROPN
iajs-553	180	3	if	if	SCONJ
iajs-553	180	4	idic	idic	ADJ
iajs-553	180	5	n1,	n1,	NOUN
iajs-553	180	6	...	...	PUNCT
iajs-553	180	7	,i	,i	PUNCT
iajs-553	180	8	,	,	PUNCT
iajs-553	180	9	i	i	PROPN
iajs-553	180	10	d	d	PROPN
iajs-553	180	11	ic	ic	PROPN
iajs-553	180	12	if	if	SCONJ
iajs-553	180	13	0	0	NUM
iajs-553	180	14	iv	iv	NUM
iajs-553	180	15	step(7	step(7	ADV
iajs-553	180	16	):	):	PUNCT
iajs-553	180	17	find	find	VERB
iajs-553	180	18	a	a	DET
iajs-553	180	19	job	job	NOUN
iajs-553	180	20	j	j	PROPN
iajs-553	180	21	*	*	PROPN
iajs-553	180	22	n	n	CCONJ
iajs-553	180	23	,	,	PUNCT
iajs-553	180	24	such	such	ADJ
iajs-553	180	25	that	that	SCONJ
iajs-553	180	26	vj*≤	vj*≤	NOUN
iajs-553	180	27	∆	∆	PROPN
iajs-553	180	28	and	and	CCONJ
iajs-553	180	29	pj	pj	PROPN
iajs-553	180	30	*	*	PUNCT
iajs-553	180	31	>	>	X
iajs-553	180	32	pi	pi	NOUN
iajs-553	180	33	,	,	PUNCT
iajs-553	180	34	j	j	PROPN
iajs-553	180	35	*	*	PROPN
iajs-553	180	36	,	,	PUNCT
iajs-553	180	37	i	i	PRON
iajs-553	180	38	n	n	PROPN
iajs-553	180	39	and	and	CCONJ
iajs-553	180	40	vi	vi	NOUN
iajs-553	180	41	≤	≤	NUM
iajs-553	180	42	∆	∆	NOUN
iajs-553	180	43	,	,	PUNCT
iajs-553	180	44	if	if	SCONJ
iajs-553	180	45	pj*=pi	pj*=pi	PROPN
iajs-553	180	46	choose	choose	VERB
iajs-553	180	47	the	the	DET
iajs-553	180	48	job	job	NOUN
iajs-553	180	49	with	with	ADP
iajs-553	180	50	smallest	small	ADJ
iajs-553	180	51	vj	vj	NOUN
iajs-553	180	52	*	*	PROPN
iajs-553	180	53	.	.	PUNCT
iajs-553	181	1	then	then	ADV
iajs-553	181	2	assign	assign	VERB
iajs-553	181	3	job	job	NOUN
iajs-553	181	4	j	j	PROPN
iajs-553	181	5	*	*	VERB
iajs-553	181	6	in	in	ADP
iajs-553	181	7	position	position	NOUN
iajs-553	181	8	k	k	PROPN
iajs-553	181	9	of	of	ADP
iajs-553	181	10	σ	σ	PROPN
iajs-553	181	11	=(	=(	PROPN
iajs-553	181	12	σ(k	σ(k	PROPN
iajs-553	181	13	)	)	PUNCT
iajs-553	181	14	,	,	PUNCT
iajs-553	181	15	σ	σ	PROPN
iajs-553	181	16	)	)	PUNCT
iajs-553	181	17	.	.	PUNCT
iajs-553	182	1	if	if	SCONJ
iajs-553	182	2	no	no	DET
iajs-553	182	3	job	job	NOUN
iajs-553	182	4	with	with	ADP
iajs-553	182	5	vj*≤	vj*≤	NOUN
iajs-553	182	6	∆	∆	X
iajs-553	182	7	go	go	VERB
iajs-553	182	8	to	to	ADP
iajs-553	182	9	step(10	step(10	PROPN
iajs-553	182	10	)	)	PUNCT
iajs-553	182	11	.	.	PUNCT
iajs-553	183	1	step(8	step(8	NOUN
iajs-553	183	2	):	):	PUNCT
iajs-553	183	3	set	set	VERB
iajs-553	183	4	t	t	PROPN
iajs-553	183	5	=	=	PROPN
iajs-553	183	6	t	t	PROPN
iajs-553	183	7	-	-	PUNCT
iajs-553	183	8	pj	pj	PROPN
iajs-553	183	9	*	*	PROPN
iajs-553	183	10	,	,	PUNCT
iajs-553	183	11	n	n	CCONJ
iajs-553	183	12	=	=	PROPN
iajs-553	183	13	n-{j	n-{j	PROPN
iajs-553	183	14	*	*	PUNCT
iajs-553	183	15	}	}	PUNCT
iajs-553	183	16	,	,	PUNCT
iajs-553	183	17	k	k	PROPN
iajs-553	183	18	=	=	NOUN
iajs-553	183	19	k-1	k-1	NOUN
iajs-553	183	20	,	,	PUNCT
iajs-553	183	21	if	if	SCONJ
iajs-553	183	22	k	k	PROPN
iajs-553	183	23	>	>	X
iajs-553	183	24	1	1	NUM
iajs-553	183	25	go	go	VERB
iajs-553	183	26	to	to	ADP
iajs-553	183	27	step(6	step(6	PROPN
iajs-553	183	28	)	)	PUNCT
iajs-553	183	29	,	,	PUNCT
iajs-553	183	30	otherwise	otherwise	ADV
iajs-553	183	31	go	go	VERB
iajs-553	183	32	to	to	ADP
iajs-553	183	33	step(9	step(9	PROPN
iajs-553	183	34	)	)	PUNCT
iajs-553	183	35	step(9	step(9	PROPN
iajs-553	183	36	):	):	PUNCT
iajs-553	183	37	calculate	calculate	NOUN
iajs-553	183	38	σcσ(i	σcσ(i	PROPN
iajs-553	183	39	)	)	PUNCT
iajs-553	183	40	,	,	PUNCT
iajs-553	184	1	tmax(σ	tmax(σ	ADP
iajs-553	184	2	)	)	PUNCT
iajs-553	184	3	and	and	CCONJ
iajs-553	184	4	vmax(σ	vmax(σ	NOUN
iajs-553	184	5	)	)	PUNCT
iajs-553	184	6	for	for	ADP
iajs-553	184	7	the	the	DET
iajs-553	184	8	sequence	sequence	NOUN
iajs-553	184	9	jobs	job	NOUN
iajs-553	184	10	σ=(σ(1),	σ=(σ(1),	ADJ
iajs-553	184	11	…	…	SYM
iajs-553	184	12	,σ(n	,σ(n	PUNCT
iajs-553	184	13	)	)	PUNCT
iajs-553	184	14	)	)	PUNCT
iajs-553	184	15	,	,	PUNCT
iajs-553	184	16	go	go	VERB
iajs-553	184	17	to	to	ADP
iajs-553	184	18	step(5	step(5	NUM
iajs-553	184	19	)	)	PUNCT
iajs-553	184	20	.	.	PUNCT
iajs-553	185	1	step(10	step(10	PROPN
iajs-553	185	2	):	):	PUNCT
iajs-553	185	3	stop	stop	NOUN
iajs-553	185	4	.	.	PUNCT
iajs-553	186	1	the	the	DET
iajs-553	186	2	1//f	1//f	NUM
iajs-553	186	3	(	(	PUNCT
iajs-553	186	4	σwici	σwici	NOUN
iajs-553	186	5	,	,	PUNCT
iajs-553	186	6	tmax	tmax	PROPN
iajs-553	186	7	,	,	PUNCT
iajs-553	186	8	vmax	vmax	PROPN
iajs-553	186	9	)	)	PUNCT
iajs-553	186	10	problem(p6	problem(p6	NOUN
iajs-553	186	11	):	):	PUNCT
iajs-553	186	12	in	in	ADP
iajs-553	186	13	this	this	DET
iajs-553	186	14	section	section	NOUN
iajs-553	186	15	,	,	PUNCT
iajs-553	186	16	we	we	PRON
iajs-553	186	17	will	will	AUX
iajs-553	186	18	try	try	VERB
iajs-553	186	19	to	to	PART
iajs-553	186	20	find	find	VERB
iajs-553	186	21	efficient	efficient	ADJ
iajs-553	186	22	(	(	PUNCT
iajs-553	186	23	pareto	pareto	ADJ
iajs-553	186	24	optimal	optimal	ADJ
iajs-553	186	25	)	)	PUNCT
iajs-553	186	26	solutions	solution	NOUN
iajs-553	186	27	for	for	ADP
iajs-553	186	28	1//f(σwici	1//f(σwici	NUM
iajs-553	186	29	,	,	PUNCT
iajs-553	186	30	tmax	tmax	PROPN
iajs-553	186	31	,	,	PUNCT
iajs-553	186	32	vmax	vmax	ADJ
iajs-553	186	33	)	)	PUNCT
iajs-553	186	34	problem	problem	NOUN
iajs-553	186	35	.	.	PUNCT
iajs-553	187	1	this	this	DET
iajs-553	187	2	problem	problem	NOUN
iajs-553	187	3	can	can	AUX
iajs-553	187	4	be	be	AUX
iajs-553	187	5	defined	define	VERB
iajs-553	187	6	as	as	ADP
iajs-553	187	7	:	:	PUNCT
iajs-553	187	8	min	min	PROPN
iajs-553	187	9	s.t	s.t	PROPN
iajs-553	187	10	.	.	PROPN
iajs-553	187	11	ci	ci	PROPN
iajs-553	187	12	≥	≥	PROPN
iajs-553	187	13	pi	pi	PROPN
iajs-553	187	14	i=1,	i=1,	PROPN
iajs-553	187	15	…	…	PUNCT
iajs-553	187	16	,n	,n	X
iajs-553	187	17	.	.	PUNCT
iajs-553	188	1	ci	ci	PROPN
iajs-553	189	1	=	=	PRON
iajs-553	189	2	c(i-1)+	c(i-1)+	PROPN
iajs-553	189	3	pi	pi	PROPN
iajs-553	189	4	i=2,	i=2,	PROPN
iajs-553	189	5	…	…	PUNCT
iajs-553	189	6	,n	,n	X
iajs-553	189	7	.	.	PUNCT
iajs-553	190	1	…	…	PUNCT
iajs-553	190	2	..	..	PUNCT
iajs-553	190	3	p(6	p(6	NOUN
iajs-553	190	4	)	)	PUNCT
iajs-553	190	5	vi	vi	PROPN
iajs-553	190	6	≤	≤	NUM
iajs-553	190	7	pi	pi	NOUN
iajs-553	190	8	i=1,	i=1,	PROPN
iajs-553	190	9	…	…	PUNCT
iajs-553	190	10	,n	,n	SYM
iajs-553	190	11	.	.	PUNCT
iajs-553	191	1	vi	vi	NOUN
iajs-553	191	2	≤	≤	NUM
iajs-553	191	3	ti	ti	NOUN
iajs-553	191	4	i=1,	i=1,	NOUN
iajs-553	191	5	…	…	PUNCT
iajs-553	191	6	,n	,n	X
iajs-553	191	7	.	.	PUNCT
iajs-553	192	1	ti	ti	PROPN
iajs-553	192	2	≥	≥	PROPN
iajs-553	192	3	ci	ci	PROPN
iajs-553	192	4	di	di	PROPN
iajs-553	192	5	i=1,	i=1,	PROPN
iajs-553	192	6	…	…	PUNCT
iajs-553	192	7	,n	,n	X
iajs-553	192	8	.	.	PUNCT
iajs-553	193	1	ti	ti	PROPN
iajs-553	193	2	≥	≥	NOUN
iajs-553	193	3	0	0	NUM
iajs-553	193	4	i=1,	i=1,	PROPN
iajs-553	193	5	…	…	PUNCT
iajs-553	193	6	,n	,n	NOUN
iajs-553	193	7	.	.	PUNCT
iajs-553	193	8	algorithm(5	algorithm(5	ADV
iajs-553	193	9	)	)	PUNCT
iajs-553	193	10	for	for	ADP
iajs-553	193	11	finding	find	VERB
iajs-553	193	12	efficient	efficient	ADJ
iajs-553	193	13	solutions	solution	NOUN
iajs-553	193	14	for	for	ADP
iajs-553	193	15	problem(p6	problem(p6	NOUN
iajs-553	193	16	):	):	PUNCT
iajs-553	193	17	mathematics	mathematic	NOUN
iajs-553	193	18	364	364	NUM
iajs-553	193	19	مجلة	مجلة	NOUN
iajs-553	193	20	إبن	إبن	VERB
iajs-553	193	21	الهيثم	الهيثم	ADJ
iajs-553	193	22	للعلوم	للعلوم	NOUN
iajs-553	193	23	الصرفة	الصرفة	NOUN
iajs-553	194	1	و	و	PRON
iajs-553	194	2	التطبيقية	التطبيقية	ADJ
iajs-553	194	3	2012	2012	NUM
iajs-553	194	4	السنة	السنة	NOUN
iajs-553	194	5	25	25	NUM
iajs-553	194	6	المجلد	المجلد	NOUN
iajs-553	194	7	3	3	NUM
iajs-553	194	8	العدد	العدد	PROPN
iajs-553	194	9	ibn	ibn	PROPN
iajs-553	194	10	al	al	PROPN
iajs-553	194	11	-	-	PUNCT
iajs-553	194	12	haitham	haitham	PROPN
iajs-553	194	13	journal	journal	PROPN
iajs-553	194	14	for	for	ADP
iajs-553	194	15	pure	pure	ADJ
iajs-553	194	16	and	and	CCONJ
iajs-553	194	17	applied	apply	VERB
iajs-553	194	18	science	science	NOUN
iajs-553	194	19	no	no	NOUN
iajs-553	194	20	.	.	NOUN
iajs-553	194	21	3	3	NUM
iajs-553	194	22	vol	vol	NOUN
iajs-553	194	23	.	.	PUNCT
iajs-553	195	1	25	25	NUM
iajs-553	195	2	year	year	NOUN
iajs-553	195	3	2012	2012	NUM
iajs-553	195	4	step(0	step(0	NOUN
iajs-553	195	5	):	):	PUNCT
iajs-553	195	6	put	put	VERB
iajs-553	195	7	∆=	∆=	NOUN
iajs-553	195	8	,	,	PUNCT
iajs-553	195	9	n={1,	n={1,	NUM
iajs-553	195	10	…	…	PUNCT
iajs-553	195	11	..	..	PUNCT
iajs-553	195	12	,n	,n	NOUN
iajs-553	195	13	}	}	PUNCT
iajs-553	195	14	,	,	PUNCT
iajs-553	195	15	k	k	NOUN
iajs-553	195	16	=	=	SYM
iajs-553	195	17	n	n	X
iajs-553	195	18	,	,	PUNCT
iajs-553	195	19	t	t	PROPN
iajs-553	195	20	=	=	SYM
iajs-553	195	21	cmax=	cmax=	NUM
iajs-553	195	22	,	,	PUNCT
iajs-553	195	23	and	and	CCONJ
iajs-553	195	24	σ=	σ=	NOUN
iajs-553	195	25	(	(	PUNCT
iajs-553	195	26	φ	φ	PROPN
iajs-553	195	27	)	)	PUNCT
iajs-553	195	28	.	.	PUNCT
iajs-553	196	1	step(1	step(1	NOUN
iajs-553	196	2	):	):	PUNCT
iajs-553	196	3	calculate	calculate	NOUN
iajs-553	196	4	ti	ti	NOUN
iajs-553	196	5	,	,	PUNCT
iajs-553	196	6	vi	vi	PROPN
iajs-553	196	7	,	,	PUNCT
iajs-553	196	8	i	i	PRON
iajs-553	196	9	n	n	ADV
iajs-553	196	10	as	as	SCONJ
iajs-553	196	11	follows	follow	VERB
iajs-553	196	12	:	:	PUNCT
iajs-553	196	13	ti	ti	X
iajs-553	196	14	=	=	SYM
iajs-553	196	15	max	max	PROPN
iajs-553	196	16	{	{	PUNCT
iajs-553	196	17	ci	ci	PROPN
iajs-553	196	18	di	di	X
iajs-553	196	19	,	,	PUNCT
iajs-553	196	20	0	0	NUM
iajs-553	196	21	}	}	PUNCT
iajs-553	196	22	and	and	CCONJ
iajs-553	196	23	vi	vi	NOUN
iajs-553	196	24	=	=	NOUN
iajs-553	196	25	min{ti	min{ti	X
iajs-553	196	26	,	,	PUNCT
iajs-553	196	27	pi	pi	NOUN
iajs-553	196	28	}	}	PUNCT
iajs-553	196	29	.	.	PUNCT
iajs-553	197	1	step(2	step(2	ADJ
iajs-553	197	2	):	):	PUNCT
iajs-553	197	3	find	find	VERB
iajs-553	197	4	a	a	DET
iajs-553	197	5	job	job	NOUN
iajs-553	197	6	j	j	PROPN
iajs-553	197	7	*	*	PROPN
iajs-553	197	8	n	n	CCONJ
iajs-553	197	9	,	,	PUNCT
iajs-553	197	10	such	such	ADJ
iajs-553	197	11	that	that	SCONJ
iajs-553	197	12	tj*≤	tj*≤	NOUN
iajs-553	197	13	∆	∆	PROPN
iajs-553	197	14	and	and	CCONJ
iajs-553	197	15	pj*/wj	pj*/wj	PROPN
iajs-553	197	16	*	*	PUNCT
iajs-553	197	17	>	>	X
iajs-553	197	18	pi	pi	PROPN
iajs-553	197	19	/	/	SYM
iajs-553	197	20	wi	wi	PROPN
iajs-553	197	21	,	,	PUNCT
iajs-553	197	22	j	j	PROPN
iajs-553	197	23	*	*	PROPN
iajs-553	197	24	,	,	PUNCT
iajs-553	197	25	i	i	PRON
iajs-553	197	26	n	n	PROPN
iajs-553	197	27	and	and	CCONJ
iajs-553	197	28	ti	ti	X
iajs-553	197	29	≤	≤	ADJ
iajs-553	197	30	∆	∆	NOUN
iajs-553	197	31	,	,	PUNCT
iajs-553	197	32	if	if	SCONJ
iajs-553	197	33	pj*/wj	pj*/wj	PROPN
iajs-553	197	34	*	*	SYM
iajs-553	197	35	=	=	SYM
iajs-553	197	36	pi	pi	PROPN
iajs-553	197	37	/	/	SYM
iajs-553	197	38	wi	wi	PROPN
iajs-553	197	39	choose	choose	VERB
iajs-553	197	40	the	the	DET
iajs-553	197	41	job	job	NOUN
iajs-553	197	42	with	with	ADP
iajs-553	197	43	smallest	small	ADJ
iajs-553	197	44	tj	tj	NOUN
iajs-553	197	45	*	*	PUNCT
iajs-553	197	46	and	and	CCONJ
iajs-553	197	47	if	if	SCONJ
iajs-553	197	48	tj*=ti	tj*=ti	VERB
iajs-553	197	49	choose	choose	VERB
iajs-553	197	50	the	the	DET
iajs-553	197	51	job	job	NOUN
iajs-553	197	52	with	with	ADP
iajs-553	197	53	smallest	small	ADJ
iajs-553	197	54	vj	vj	NOUN
iajs-553	197	55	*	*	PROPN
iajs-553	197	56	.	.	PUNCT
iajs-553	198	1	then	then	ADV
iajs-553	198	2	assign	assign	VERB
iajs-553	198	3	job	job	NOUN
iajs-553	198	4	j	j	PROPN
iajs-553	198	5	*	*	VERB
iajs-553	198	6	in	in	ADP
iajs-553	198	7	position	position	NOUN
iajs-553	198	8	k	k	PROPN
iajs-553	198	9	of	of	ADP
iajs-553	198	10	σ	σ	PROPN
iajs-553	198	11	=	=	SYM
iajs-553	198	12	(	(	PUNCT
iajs-553	198	13	σ(k	σ(k	PROPN
iajs-553	198	14	)	)	PUNCT
iajs-553	198	15	,	,	PUNCT
iajs-553	198	16	σ	σ	PROPN
iajs-553	198	17	)	)	PUNCT
iajs-553	198	18	.	.	PUNCT
iajs-553	199	1	if	if	SCONJ
iajs-553	199	2	no	no	DET
iajs-553	199	3	job	job	NOUN
iajs-553	199	4	with	with	ADP
iajs-553	199	5	tj*≤	tj*≤	NOUN
iajs-553	199	6	∆	∆	X
iajs-553	199	7	go	go	VERB
iajs-553	199	8	to	to	ADP
iajs-553	199	9	step(5	step(5	NUM
iajs-553	199	10	)	)	PUNCT
iajs-553	199	11	.	.	PUNCT
iajs-553	200	1	step(3	step(3	PROPN
iajs-553	200	2	):	):	PUNCT
iajs-553	200	3	set	set	VERB
iajs-553	200	4	t	t	PROPN
iajs-553	200	5	=	=	PROPN
iajs-553	200	6	t	t	PROPN
iajs-553	200	7	-	-	PUNCT
iajs-553	200	8	pj	pj	PROPN
iajs-553	200	9	*	*	PROPN
iajs-553	200	10	,	,	PUNCT
iajs-553	200	11	n	n	PROPN
iajs-553	200	12	=	=	PROPN
iajs-553	200	13	n-{j	n-{j	PROPN
iajs-553	200	14	*	*	PUNCT
iajs-553	200	15	}	}	PUNCT
iajs-553	200	16	,	,	PUNCT
iajs-553	200	17	k	k	PROPN
iajs-553	200	18	=	=	NOUN
iajs-553	200	19	k-1	k-1	NOUN
iajs-553	200	20	,	,	PUNCT
iajs-553	200	21	if	if	SCONJ
iajs-553	200	22	k	k	PROPN
iajs-553	200	23	>	>	X
iajs-553	200	24	1	1	NUM
iajs-553	200	25	go	go	VERB
iajs-553	200	26	to	to	ADP
iajs-553	200	27	step(1	step(1	NOUN
iajs-553	200	28	)	)	PUNCT
iajs-553	200	29	,	,	PUNCT
iajs-553	200	30	otherwise	otherwise	ADV
iajs-553	200	31	go	go	VERB
iajs-553	200	32	to	to	ADP
iajs-553	200	33	step(4	step(4	NOUN
iajs-553	200	34	)	)	PUNCT
iajs-553	200	35	.	.	PUNCT
iajs-553	201	1	step(4	step(4	NOUN
iajs-553	201	2	):	):	PUNCT
iajs-553	201	3	compute	compute	NOUN
iajs-553	201	4	σwσ(i)cσ(i	σwσ(i)cσ(i	NOUN
iajs-553	201	5	)	)	PUNCT
iajs-553	201	6	,	,	PUNCT
iajs-553	201	7	tmax(σ	tmax(σ	ADP
iajs-553	201	8	)	)	PUNCT
iajs-553	201	9	and	and	CCONJ
iajs-553	201	10	vmax(σ	vmax(σ	NOUN
iajs-553	201	11	)	)	PUNCT
iajs-553	201	12	for	for	ADP
iajs-553	201	13	the	the	DET
iajs-553	201	14	sequence	sequence	NOUN
iajs-553	201	15	jobs	job	NOUN
iajs-553	201	16	σ	σ	PROPN
iajs-553	201	17	=(	=(	PROPN
iajs-553	201	18	σ(1	σ(1	PROPN
iajs-553	201	19	)	)	PUNCT
iajs-553	201	20	,	,	PUNCT
iajs-553	201	21	…	…	PUNCT
iajs-553	201	22	,	,	PUNCT
iajs-553	201	23	σ(n	σ(n	PROPN
iajs-553	201	24	)	)	PUNCT
iajs-553	201	25	)	)	PUNCT
iajs-553	201	26	,	,	PUNCT
iajs-553	201	27	and	and	CCONJ
iajs-553	201	28	set	set	VERB
iajs-553	201	29	∆=	∆=	NOUN
iajs-553	201	30	tmax(σ	tmax(σ	NOUN
iajs-553	201	31	)	)	PUNCT
iajs-553	201	32	-1	-1	VERB
iajs-553	201	33	,	,	PUNCT
iajs-553	201	34	set	set	VERB
iajs-553	201	35	t	t	PROPN
iajs-553	201	36	=	=	SYM
iajs-553	201	37	cmax=	cmax=	NUM
iajs-553	201	38	,	,	PUNCT
iajs-553	201	39	n={1,	n={1,	NUM
iajs-553	201	40	…	…	PUNCT
iajs-553	201	41	..	..	PUNCT
iajs-553	201	42	,n	,n	NOUN
iajs-553	201	43	}	}	PUNCT
iajs-553	201	44	,	,	PUNCT
iajs-553	201	45	k	k	NOUN
iajs-553	201	46	=	=	SYM
iajs-553	201	47	n	n	X
iajs-553	201	48	,	,	PUNCT
iajs-553	201	49	σ=	σ=	X
iajs-553	201	50	(	(	PUNCT
iajs-553	201	51	φ	φ	NOUN
iajs-553	201	52	)	)	PUNCT
iajs-553	201	53	and	and	CCONJ
iajs-553	201	54	go	go	VERB
iajs-553	201	55	to	to	ADP
iajs-553	201	56	step(1	step(1	NOUN
iajs-553	201	57	)	)	PUNCT
iajs-553	201	58	.	.	PUNCT
iajs-553	202	1	step(5	step(5	ADV
iajs-553	202	2	):	):	PUNCT
iajs-553	202	3	put	put	VERB
iajs-553	202	4	∆=vmax(σ)-1	∆=vmax(σ)-1	ADJ
iajs-553	202	5	,	,	PUNCT
iajs-553	202	6	n={1,	n={1,	NUM
iajs-553	202	7	...	...	PUNCT
iajs-553	202	8	,n	,n	PUNCT
iajs-553	202	9	}	}	PUNCT
iajs-553	202	10	,	,	PUNCT
iajs-553	202	11	k	k	NOUN
iajs-553	202	12	=	=	SYM
iajs-553	202	13	n	n	X
iajs-553	202	14	,	,	PUNCT
iajs-553	202	15	t	t	NOUN
iajs-553	202	16	=	=	NOUN
iajs-553	202	17	cmax	cmax	NOUN
iajs-553	202	18	,	,	PUNCT
iajs-553	202	19	and	and	CCONJ
iajs-553	202	20	σ=	σ=	NOUN
iajs-553	202	21	(	(	PUNCT
iajs-553	202	22	φ	φ	PROPN
iajs-553	202	23	)	)	PUNCT
iajs-553	202	24	.	.	PUNCT
iajs-553	203	1	step(6	step(6	PROPN
iajs-553	203	2	):	):	PUNCT
iajs-553	203	3	calculate	calculate	NOUN
iajs-553	203	4	vi	vi	PROPN
iajs-553	203	5	,	,	PUNCT
iajs-553	203	6	i	i	PRON
iajs-553	203	7	n	n	ADV
iajs-553	203	8	as	as	SCONJ
iajs-553	203	9	follows	follow	VERB
iajs-553	203	10	:	:	PUNCT
iajs-553	203	11			ADJ
iajs-553	203	12			NOUN
iajs-553	203	13			PROPN
iajs-553	203	14			PROPN
iajs-553	203	15			PROPN
iajs-553	203	16			PROPN
iajs-553	203	17			NOUN
iajs-553	203	18			ADV
iajs-553	203	19			ADP
iajs-553	203	20			NOUN
iajs-553	203	21	=	=	NOUN
iajs-553	203	22	≤+	≤+	NOUN
iajs-553	203	23	=	=	PUNCT
iajs-553	204	1	+	+	PROPN
iajs-553	204	2	<	<	X
iajs-553	204	3	<	<	X
iajs-553	204	4	=	=	ADJ
iajs-553	204	5	≤	≤	NOUN
iajs-553	204	6	=	=	PUNCT
iajs-553	204	7	n	n	PRON
iajs-553	204	8	1,	1,	NUM
iajs-553	204	9	...	...	PUNCT
iajs-553	204	10	,i	,i	PUNCT
iajs-553	204	11	,	,	PUNCT
iajs-553	204	12	c	c	PROPN
iajs-553	204	13	pd	pd	PROPN
iajs-553	204	14	if	if	SCONJ
iajs-553	204	15	p	p	PROPN
iajs-553	204	16	n1,	n1,	NOUN
iajs-553	204	17	...	...	NOUN
iajs-553	204	18	,i	,i	PUNCT
iajs-553	204	19	,	,	PUNCT
iajs-553	204	20	pd	pd	PROPN
iajs-553	205	1	c	c	NOUN
iajs-553	205	2	d	d	NOUN
iajs-553	205	3	if	if	SCONJ
iajs-553	205	4	dc	dc	PROPN
iajs-553	205	5	n1,	n1,	PROPN
iajs-553	205	6	...	...	PROPN
iajs-553	205	7	,i	,i	PUNCT
iajs-553	205	8	,	,	PUNCT
iajs-553	206	1	d	d	X
iajs-553	206	2	c	c	NOUN
iajs-553	206	3	if	if	SCONJ
iajs-553	206	4	0	0	NUM
iajs-553	206	5	v	v	NOUN
iajs-553	206	6	iiii	iiii	PROPN
iajs-553	206	7	iiiiii	iiiiii	PROPN
iajs-553	206	8	ii	ii	PROPN
iajs-553	206	9	i	i	PRON
iajs-553	206	10	step(7	step(7	ADV
iajs-553	206	11	):	):	PUNCT
iajs-553	206	12	find	find	VERB
iajs-553	206	13	a	a	DET
iajs-553	206	14	job	job	NOUN
iajs-553	206	15	j	j	PROPN
iajs-553	206	16	*	*	PROPN
iajs-553	206	17	n	n	CCONJ
iajs-553	206	18	,	,	PUNCT
iajs-553	206	19	such	such	ADJ
iajs-553	206	20	that	that	SCONJ
iajs-553	206	21	vj*≤	vj*≤	NOUN
iajs-553	206	22	∆	∆	PROPN
iajs-553	206	23	and	and	CCONJ
iajs-553	206	24	pj*/wj	pj*/wj	PROPN
iajs-553	206	25	*	*	PUNCT
iajs-553	206	26	>	>	X
iajs-553	206	27	pi	pi	PROPN
iajs-553	206	28	/	/	SYM
iajs-553	206	29	wi	wi	PROPN
iajs-553	206	30	,	,	PUNCT
iajs-553	206	31	j*,i	j*,i	VERB
iajs-553	206	32	n	n	PROPN
iajs-553	206	33	and	and	CCONJ
iajs-553	206	34	vi	vi	NOUN
iajs-553	206	35	≤	≤	NUM
iajs-553	206	36	∆	∆	NOUN
iajs-553	206	37	,	,	PUNCT
iajs-553	206	38	if	if	SCONJ
iajs-553	206	39	pj*/wj	pj*/wj	PROPN
iajs-553	206	40	*	*	SYM
iajs-553	206	41	=	=	SYM
iajs-553	206	42	pi	pi	PROPN
iajs-553	206	43	/	/	SYM
iajs-553	206	44	wi	wi	PROPN
iajs-553	206	45	choose	choose	VERB
iajs-553	206	46	the	the	DET
iajs-553	206	47	job	job	NOUN
iajs-553	206	48	with	with	ADP
iajs-553	206	49	smallest	small	ADJ
iajs-553	206	50	vj	vj	NOUN
iajs-553	206	51	*	*	PROPN
iajs-553	206	52	.	.	PUNCT
iajs-553	207	1	then	then	ADV
iajs-553	207	2	assign	assign	VERB
iajs-553	207	3	job	job	NOUN
iajs-553	207	4	j	j	PROPN
iajs-553	207	5	*	*	VERB
iajs-553	207	6	in	in	ADP
iajs-553	207	7	position	position	NOUN
iajs-553	207	8	k	k	PROPN
iajs-553	207	9	of	of	ADP
iajs-553	207	10	σ	σ	PROPN
iajs-553	207	11	=(	=(	PROPN
iajs-553	207	12	σ(k	σ(k	PROPN
iajs-553	207	13	)	)	PUNCT
iajs-553	207	14	,	,	PUNCT
iajs-553	207	15	σ	σ	PROPN
iajs-553	207	16	)	)	PUNCT
iajs-553	207	17	.	.	PUNCT
iajs-553	208	1	if	if	SCONJ
iajs-553	208	2	no	no	DET
iajs-553	208	3	job	job	NOUN
iajs-553	208	4	with	with	ADP
iajs-553	208	5	vj*≤	vj*≤	NOUN
iajs-553	208	6	∆	∆	X
iajs-553	208	7	go	go	VERB
iajs-553	208	8	to	to	ADP
iajs-553	208	9	step(10	step(10	PROPN
iajs-553	208	10	)	)	PUNCT
iajs-553	208	11	.	.	PUNCT
iajs-553	209	1	step(8	step(8	NOUN
iajs-553	209	2	):	):	PUNCT
iajs-553	209	3	set	set	VERB
iajs-553	209	4	t	t	PROPN
iajs-553	209	5	=	=	PROPN
iajs-553	209	6	t	t	PROPN
iajs-553	209	7	-	-	PUNCT
iajs-553	209	8	pj	pj	PROPN
iajs-553	209	9	*	*	PROPN
iajs-553	209	10	,	,	PUNCT
iajs-553	209	11	n	n	CCONJ
iajs-553	209	12	=	=	PROPN
iajs-553	209	13	n-{j	n-{j	PROPN
iajs-553	209	14	*	*	PUNCT
iajs-553	209	15	}	}	PUNCT
iajs-553	209	16	,	,	PUNCT
iajs-553	209	17	k	k	PROPN
iajs-553	209	18	=	=	NOUN
iajs-553	209	19	k-1	k-1	NOUN
iajs-553	209	20	,	,	PUNCT
iajs-553	209	21	if	if	SCONJ
iajs-553	209	22	k	k	PROPN
iajs-553	209	23	>	>	X
iajs-553	209	24	1	1	NUM
iajs-553	209	25	go	go	VERB
iajs-553	209	26	to	to	ADP
iajs-553	209	27	step(6	step(6	PROPN
iajs-553	209	28	)	)	PUNCT
iajs-553	209	29	,	,	PUNCT
iajs-553	209	30	otherwise	otherwise	ADV
iajs-553	209	31	go	go	VERB
iajs-553	209	32	to	to	ADP
iajs-553	209	33	step(9	step(9	PROPN
iajs-553	209	34	)	)	PUNCT
iajs-553	209	35	.	.	PUNCT
iajs-553	210	1	step(9	step(9	PROPN
iajs-553	210	2	):	):	PUNCT
iajs-553	210	3	calculate	calculate	NOUN
iajs-553	210	4	σwσ(i)cσ(i	σwσ(i)cσ(i	NOUN
iajs-553	210	5	)	)	PUNCT
iajs-553	210	6	,	,	PUNCT
iajs-553	210	7	tmax(σ	tmax(σ	ADP
iajs-553	210	8	)	)	PUNCT
iajs-553	210	9	and	and	CCONJ
iajs-553	210	10	vmax(σ	vmax(σ	NOUN
iajs-553	210	11	)	)	PUNCT
iajs-553	210	12	for	for	ADP
iajs-553	210	13	the	the	DET
iajs-553	210	14	sequence	sequence	NOUN
iajs-553	210	15	jobs	job	NOUN
iajs-553	210	16	σ	σ	PROPN
iajs-553	210	17	=(	=(	PROPN
iajs-553	210	18	σ(1),	σ(1),	PROPN
iajs-553	210	19	…	…	PUNCT
iajs-553	210	20	,σ(n	,σ(n	PUNCT
iajs-553	210	21	)	)	PUNCT
iajs-553	210	22	)	)	PUNCT
iajs-553	210	23	,	,	PUNCT
iajs-553	210	24	go	go	VERB
iajs-553	210	25	to	to	ADP
iajs-553	210	26	step(5	step(5	NUM
iajs-553	210	27	)	)	PUNCT
iajs-553	210	28	.	.	PUNCT
iajs-553	211	1	step(10	step(10	PROPN
iajs-553	211	2	):	):	PUNCT
iajs-553	211	3	stop	stop	NOUN
iajs-553	211	4	.	.	PUNCT
iajs-553	212	1	example(2):consider	example(2):consider	VERB
iajs-553	212	2	the	the	DET
iajs-553	212	3	problem	problem	NOUN
iajs-553	213	1	1//f(σwici	1//f(σwici	NUM
iajs-553	213	2	,	,	PUNCT
iajs-553	213	3	tmax	tmax	PRON
iajs-553	213	4	,	,	PUNCT
iajs-553	213	5	vmax	vmax	PROPN
iajs-553	213	6	)	)	PUNCT
iajs-553	213	7	with	with	ADP
iajs-553	213	8	the	the	DET
iajs-553	213	9	following	follow	VERB
iajs-553	213	10	data	datum	NOUN
iajs-553	214	1	:	:	PUNCT
iajs-553	214	2	i	i	NOUN
iajs-553	214	3	1	1	NUM
iajs-553	214	4	2	2	NUM
iajs-553	214	5	3	3	NUM
iajs-553	214	6	4	4	NUM
iajs-553	214	7	5	5	NUM
iajs-553	214	8	pi	pi	NOUN
iajs-553	214	9	10	10	NUM
iajs-553	214	10	3	3	NUM
iajs-553	214	11	9	9	NUM
iajs-553	214	12	1	1	NUM
iajs-553	214	13	4	4	NUM
iajs-553	214	14	di	di	NOUN
iajs-553	214	15	20	20	NUM
iajs-553	214	16	14	14	NUM
iajs-553	214	17	25	25	NUM
iajs-553	214	18	29	29	NUM
iajs-553	214	19	16	16	NUM
iajs-553	214	20	wi	wi	PROPN
iajs-553	214	21	4	4	NUM
iajs-553	214	22	1	1	NUM
iajs-553	214	23	8	8	NUM
iajs-553	214	24	5	5	NUM
iajs-553	214	25	2	2	NUM
iajs-553	214	26	pi/	pi/	ADP
iajs-553	214	27	wi	wi	PROPN
iajs-553	214	28	5/2	5/2	NUM
iajs-553	214	29	3	3	NUM
iajs-553	214	30	9/8	9/8	NUM
iajs-553	214	31	1/5	1/5	NUM
iajs-553	214	32	2	2	NUM
iajs-553	214	33	hence	hence	ADV
iajs-553	214	34	,	,	PUNCT
iajs-553	214	35	efficient	efficient	ADJ
iajs-553	214	36	sequences	sequence	NOUN
iajs-553	214	37	for	for	ADP
iajs-553	214	38	the	the	DET
iajs-553	214	39	three	three	NUM
iajs-553	214	40	-	-	PUNCT
iajs-553	214	41	criterion	criterion	NOUN
iajs-553	214	42	problem(p6	problem(p6	NOUN
iajs-553	214	43	)	)	PUNCT
iajs-553	214	44	of	of	ADP
iajs-553	214	45	minimizing	minimize	VERB
iajs-553	214	46	σwici	σwici	NOUN
iajs-553	214	47	,	,	PUNCT
iajs-553	214	48	tmax	tmax	NOUN
iajs-553	214	49	and	and	CCONJ
iajs-553	214	50	vmax	vmax	PROPN
iajs-553	214	51	.	.	PUNCT
iajs-553	215	1	sequences	sequences	PROPN
iajs-553	215	2	σwici	σwici	PROPN
iajs-553	215	3	tmax	tmax	PROPN
iajs-553	215	4	vmax	vmax	PROPN
iajs-553	215	5	swpt=(4,3,5,1,2	swpt=(4,3,5,1,2	PROPN
iajs-553	215	6	)	)	PUNCT
iajs-553	215	7	236	236	NUM
iajs-553	215	8	13	13	NUM
iajs-553	215	9	4	4	NUM
iajs-553	215	10	(	(	PUNCT
iajs-553	215	11	4,3,5,2,1	4,3,5,2,1	NUM
iajs-553	215	12	)	)	PUNCT
iajs-553	215	13	238	238	NUM
iajs-553	215	14	7	7	NUM
iajs-553	215	15	7	7	NUM
iajs-553	215	16	(	(	PUNCT
iajs-553	215	17	4,5,1,2,3	4,5,1,2,3	NOUN
iajs-553	215	18	)	)	PUNCT
iajs-553	215	19	309	309	NUM
iajs-553	215	20	4	4	NUM
iajs-553	215	21	3	3	NUM
iajs-553	215	22	(	(	PUNCT
iajs-553	215	23	4,5,2,1,3	4,5,2,1,3	NUM
iajs-553	215	24	)	)	PUNCT
iajs-553	215	25	311	311	NUM
iajs-553	215	26	2	2	NUM
iajs-553	215	27	2	2	NUM
iajs-553	215	28	(	(	PUNCT
iajs-553	215	29	5,2,1,3,4	5,2,1,3,4	NUM
iajs-553	215	30	)	)	PUNCT
iajs-553	215	31	426	426	NUM
iajs-553	215	32	1	1	NUM
iajs-553	215	33	1	1	NUM
iajs-553	215	34	conclusions	conclusion	NOUN
iajs-553	215	35	in	in	ADP
iajs-553	215	36	this	this	DET
iajs-553	215	37	paper	paper	NOUN
iajs-553	215	38	,	,	PUNCT
iajs-553	215	39	the	the	DET
iajs-553	215	40	problems	problem	NOUN
iajs-553	215	41	of	of	ADP
iajs-553	215	42	scheduling	scheduling	NOUN
iajs-553	215	43	jobs	job	NOUN
iajs-553	215	44	on	on	ADP
iajs-553	215	45	one	one	NUM
iajs-553	215	46	machine	machine	NOUN
iajs-553	215	47	for	for	ADP
iajs-553	215	48	a	a	DET
iajs-553	215	49	variety	variety	NOUN
iajs-553	215	50	of	of	ADP
iajs-553	215	51	multicriteria	multicriteria	PROPN
iajs-553	215	52	are	be	AUX
iajs-553	215	53	considered	consider	VERB
iajs-553	215	54	.	.	PUNCT
iajs-553	216	1	we	we	PRON
iajs-553	216	2	proposed	propose	VERB
iajs-553	216	3	algorithms	algorithm	NOUN
iajs-553	216	4	,	,	PUNCT
iajs-553	216	5	which	which	PRON
iajs-553	216	6	give	give	VERB
iajs-553	216	7	all	all	DET
iajs-553	216	8	efficient	efficient	ADJ
iajs-553	216	9	solutions	solution	NOUN
iajs-553	216	10	within	within	ADP
iajs-553	216	11	the	the	DET
iajs-553	216	12	efficient	efficient	ADJ
iajs-553	216	13	range	range	NOUN
iajs-553	216	14	for	for	ADP
iajs-553	216	15	the	the	DET
iajs-553	216	16	problems	problem	NOUN
iajs-553	216	17	1//f(σfi	1//f(σfi	NUM
iajs-553	216	18	,	,	PUNCT
iajs-553	216	19	fmax	fmax	PROPN
iajs-553	216	20	)	)	PUNCT
iajs-553	216	21	,	,	PUNCT
iajs-553	216	22	1//f(σfi	1//f(σfi	NUM
iajs-553	216	23	,	,	PUNCT
iajs-553	216	24	fmax	fmax	PROPN
iajs-553	216	25	,	,	PUNCT
iajs-553	216	26	gmax	gmax	PROPN
iajs-553	216	27	)	)	PUNCT
iajs-553	216	28	,	,	PUNCT
iajs-553	216	29	where	where	SCONJ
iajs-553	216	30	σfi=	σfi=	PROPN
iajs-553	216	31	σci	σci	NOUN
iajs-553	216	32	and	and	CCONJ
iajs-553	216	33	fmax	fmax	PROPN
iajs-553	216	34	,	,	PUNCT
iajs-553	216	35	gmax	gmax	X
iajs-553	216	36	{	{	PUNCT
iajs-553	216	37	lmax	lmax	NOUN
iajs-553	216	38	,	,	PUNCT
iajs-553	216	39	tmax	tmax	PRON
iajs-553	216	40	,	,	PUNCT
iajs-553	216	41	vmax	vmax	X
iajs-553	216	42	}	}	PUNCT
iajs-553	216	43	.	.	PUNCT
iajs-553	217	1	mathematics	mathematic	NOUN
iajs-553	217	2	365	365	NUM
iajs-553	217	3	مجلة	مجلة	PROPN
iajs-553	217	4	إبن	إبن	VERB
iajs-553	217	5	الهيثم	الهيثم	ADJ
iajs-553	217	6	للعلوم	للعلوم	NOUN
iajs-553	217	7	الصرفة	الصرفة	NOUN
iajs-553	218	1	و	و	PRON
iajs-553	218	2	التطبيقية	التطبيقية	ADJ
iajs-553	218	3	2012	2012	NUM
iajs-553	218	4	السنة	السنة	NOUN
iajs-553	218	5	25	25	NUM
iajs-553	218	6	المجلد	المجلد	NOUN
iajs-553	218	7	3	3	NUM
iajs-553	218	8	العدد	العدد	PROPN
iajs-553	218	9	ibn	ibn	PROPN
iajs-553	218	10	al	al	PROPN
iajs-553	218	11	-	-	PUNCT
iajs-553	218	12	haitham	haitham	PROPN
iajs-553	218	13	journal	journal	PROPN
iajs-553	218	14	for	for	ADP
iajs-553	218	15	pure	pure	ADJ
iajs-553	218	16	and	and	CCONJ
iajs-553	218	17	applied	apply	VERB
iajs-553	218	18	science	science	NOUN
iajs-553	218	19	no	no	NOUN
iajs-553	218	20	.	.	NOUN
iajs-553	218	21	3	3	NUM
iajs-553	218	22	vol	vol	NOUN
iajs-553	218	23	.	.	PUNCT
iajs-553	219	1	25	25	NUM
iajs-553	219	2	year	year	NOUN
iajs-553	219	3	2012	2012	NUM
iajs-553	219	4	references	reference	NOUN
iajs-553	219	5	1	1	NUM
iajs-553	219	6	.	.	PUNCT
iajs-553	219	7	jackson	jackson	PROPN
iajs-553	219	8	j.r.(1955)."scheduling	j.r.(1955)."schedule	VERB
iajs-553	219	9	a	a	DET
iajs-553	219	10	production	production	NOUN
iajs-553	219	11	line	line	NOUN
iajs-553	219	12	to	to	PART
iajs-553	219	13	minimize	minimize	VERB
iajs-553	219	14	maximum	maximum	ADJ
iajs-553	219	15	tardiness	tardiness	NOUN
iajs-553	219	16	"	"	PUNCT
iajs-553	219	17	res	re	NOUN
iajs-553	219	18	.	.	PUNCT
iajs-553	220	1	report	report	VERB
iajs-553	220	2	43	43	NUM
iajs-553	220	3	management	management	NOUN
iajs-553	220	4	science	science	NOUN
iajs-553	220	5	,	,	PUNCT
iajs-553	220	6	res	re	NOUN
iajs-553	220	7	.	.	PROPN
iajs-553	220	8	project	project	PROPN
iajs-553	220	9	,	,	PUNCT
iajs-553	220	10	university	university	PROPN
iajs-553	220	11	of	of	ADP
iajs-553	220	12	california	california	PROPN
iajs-553	220	13	,	,	PUNCT
iajs-553	220	14	loss	loss	NOUN
iajs-553	220	15	angles	angle	NOUN
iajs-553	220	16	,	,	PUNCT
iajs-553	220	17	ca	ca	NOUN
iajs-553	220	18	,	,	PUNCT
iajs-553	220	19	2	2	X
iajs-553	220	20	.	.	X
iajs-553	221	1	smith	smith	PROPN
iajs-553	221	2	w.e.(1956)."various	w.e.(1956)."various	ADJ
iajs-553	221	3	optimizers	optimizer	NOUN
iajs-553	221	4	for	for	ADP
iajs-553	221	5	single	single	ADJ
iajs-553	221	6	stage	stage	NOUN
iajs-553	221	7	production	production	NOUN
iajs-553	221	8	"	"	PUNCT
iajs-553	221	9	,	,	PUNCT
iajs-553	221	10	naval	naval	ADJ
iajs-553	221	11	research	research	NOUN
iajs-553	221	12	logistics	logistic	NOUN
iajs-553	221	13	quarterly	quarterly	PROPN
iajs-553	221	14	3/1	3/1	NUM
iajs-553	221	15	,	,	PUNCT
iajs-553	221	16	59	59	NUM
iajs-553	221	17	-	-	SYM
iajs-553	221	18	66	66	NUM
iajs-553	221	19	.	.	PUNCT
iajs-553	222	1	3	3	X
iajs-553	222	2	.	.	X
iajs-553	222	3	lawler	lawler	PROPN
iajs-553	222	4	e.l.(1973)."optimal	e.l.(1973)."optimal	ADJ
iajs-553	222	5	sequencing	sequencing	NOUN
iajs-553	222	6	of	of	ADP
iajs-553	222	7	a	a	DET
iajs-553	222	8	single	single	ADJ
iajs-553	222	9	machine	machine	NOUN
iajs-553	222	10	subject	subject	NOUN
iajs-553	222	11	to	to	ADP
iajs-553	222	12	precedence	precedence	NOUN
iajs-553	222	13	constraints	constraint	NOUN
iajs-553	222	14	"	"	PUNCT
iajs-553	222	15	,	,	PUNCT
iajs-553	222	16	management	management	NOUN
iajs-553	222	17	science	science	NOUN
iajs-553	222	18	19/5	19/5	NUM
iajs-553	222	19	,	,	PUNCT
iajs-553	222	20	544	544	NUM
iajs-553	222	21	-	-	SYM
iajs-553	222	22	546	546	NUM
iajs-553	222	23	.	.	PUNCT
iajs-553	223	1	4	4	X
iajs-553	223	2	.	.	X
iajs-553	223	3	french	french	ADJ
iajs-553	223	4	s.	s.	PROPN
iajs-553	223	5	(	(	PUNCT
iajs-553	223	6	1982	1982	NUM
iajs-553	223	7	)	)	PUNCT
iajs-553	223	8	.	.	PUNCT
iajs-553	224	1	"	"	PUNCT
iajs-553	224	2	sequencing	sequence	VERB
iajs-553	224	3	and	and	CCONJ
iajs-553	224	4	scheduling	scheduling	NOUN
iajs-553	224	5	:	:	PUNCT
iajs-553	224	6	an	an	DET
iajs-553	224	7	introduction	introduction	NOUN
iajs-553	224	8	to	to	ADP
iajs-553	224	9	the	the	DET
iajs-553	224	10	mathematical	mathematical	NOUN
iajs-553	224	11	of	of	ADP
iajs-553	224	12	the	the	DET
iajs-553	224	13	job	job	NOUN
iajs-553	224	14	shop	shop	NOUN
iajs-553	224	15	"	"	PUNCT
iajs-553	224	16	,	,	PUNCT
iajs-553	224	17	john	john	PROPN
iajs-553	224	18	wiley	wiley	PROPN
iajs-553	224	19	and	and	CCONJ
iajs-553	224	20	sons	son	NOUN
iajs-553	224	21	,	,	PUNCT
iajs-553	224	22	new	new	PROPN
iajs-553	224	23	york	york	PROPN
iajs-553	224	24	.	.	PUNCT
iajs-553	225	1	5	5	X
iajs-553	225	2	.	.	X
iajs-553	225	3	hoogeveen	hoogeveen	PROPN
iajs-553	225	4	j.a	j.a	PROPN
iajs-553	225	5	.	.	PROPN
iajs-553	226	1	(	(	PUNCT
iajs-553	226	2	2005	2005	NUM
iajs-553	226	3	)	)	PUNCT
iajs-553	226	4	.	.	PUNCT
iajs-553	226	5	"	"	PUNCT
iajs-553	227	1	invited	invite	VERB
iajs-553	227	2	review	review	NOUN
iajs-553	227	3	multi	multi	ADJ
iajs-553	227	4	-	-	ADJ
iajs-553	227	5	criteria	criteria	ADJ
iajs-553	227	6	scheduling	scheduling	NOUN
iajs-553	227	7	"	"	PUNCT
iajs-553	227	8	,	,	PUNCT
iajs-553	227	9	european	european	PROPN
iajs-553	227	10	journal	journal	PROPN
iajs-553	227	11	of	of	ADP
iajs-553	227	12	operational	operational	ADJ
iajs-553	227	13	research	research	NOUN
iajs-553	227	14	167	167	NUM
iajs-553	227	15	,	,	PUNCT
iajs-553	227	16	592–623	592–623	NUM
iajs-553	227	17	.	.	PUNCT
iajs-553	228	1	6	6	NUM
iajs-553	228	2	.	.	X
iajs-553	228	3	fry	fry	PROPN
iajs-553	228	4	td	td	PROPN
iajs-553	228	5	,	,	PUNCT
iajs-553	228	6	armstrong	armstrong	PROPN
iajs-553	228	7	rd	rd	PROPN
iajs-553	228	8	.	.	PROPN
iajs-553	229	1	lewis	lewis	PROPN
iajs-553	229	2	,	,	PUNCT
iajs-553	229	3	h.	h.	PROPN
iajs-553	229	4	(	(	PUNCT
iajs-553	229	5	1989	1989	NUM
iajs-553	229	6	)	)	PUNCT
iajs-553	229	7	.	.	PUNCT
iajs-553	230	1	"	"	PUNCT
iajs-553	230	2	a	a	DET
iajs-553	230	3	framework	framework	NOUN
iajs-553	230	4	for	for	ADP
iajs-553	230	5	single	single	ADJ
iajs-553	230	6	machines	machine	NOUN
iajs-553	230	7	multiple	multiple	ADJ
iajs-553	230	8	objective	objective	ADJ
iajs-553	230	9	sequencing	sequence	VERB
iajs-553	230	10	research	research	NOUN
iajs-553	230	11	"	"	PUNCT
iajs-553	230	12	,	,	PUNCT
iajs-553	230	13	omega	omega	NOUN
iajs-553	230	14	;	;	PUNCT
iajs-553	230	15	17	17	NUM
iajs-553	230	16	(	(	PUNCT
iajs-553	230	17	6	6	NUM
iajs-553	230	18	):	):	PUNCT
iajs-553	230	19	595	595	NUM
iajs-553	230	20	-	-	SYM
iajs-553	230	21	607	607	NUM
iajs-553	230	22	.	.	PUNCT
iajs-553	231	1	7	7	X
iajs-553	231	2	.	.	X
iajs-553	231	3	landa	landa	PROPN
iajs-553	231	4	silva	silva	PROPN
iajs-553	231	5	e.	e.	PROPN
iajs-553	231	6	k.	k.	PROPN
iajs-553	231	7	and	and	CCONJ
iajs-553	231	8	burke	burke	PROPN
iajs-553	231	9	s.	s.	PROPN
iajs-553	231	10	petrovic	petrovic	PROPN
iajs-553	231	11	,	,	PUNCT
iajs-553	231	12	"	"	PUNCT
iajs-553	231	13	an	an	DET
iajs-553	231	14	introduction	introduction	NOUN
iajs-553	231	15	to	to	ADP
iajs-553	231	16	multiobjective	multiobjective	ADJ
iajs-553	231	17	metaheuristics	metaheuristic	NOUN
iajs-553	231	18	for	for	ADP
iajs-553	231	19	scheduling	scheduling	NOUN
iajs-553	231	20	and	and	CCONJ
iajs-553	231	21	time	time	NOUN
iajs-553	231	22	tabling	table	VERB
iajs-553	231	23	"	"	PUNCT
iajs-553	231	24	8	8	NUM
iajs-553	231	25	.	.	PUNCT
iajs-553	232	1	hoogeveen	hoogeveen	PROPN
iajs-553	232	2	,	,	PUNCT
iajs-553	232	3	j.a	j.a	PROPN
iajs-553	232	4	.	.	PROPN
iajs-553	232	5	(	(	PUNCT
iajs-553	232	6	1996	1996	NUM
iajs-553	232	7	)	)	PUNCT
iajs-553	232	8	.	.	PUNCT
iajs-553	232	9	”	"	PUNCT
iajs-553	233	1	single	single	ADJ
iajs-553	233	2	machine	machine	NOUN
iajs-553	233	3	scheduling	scheduling	NOUN
iajs-553	233	4	to	to	PART
iajs-553	233	5	minimize	minimize	VERB
iajs-553	233	6	a	a	DET
iajs-553	233	7	function	function	NOUN
iajs-553	233	8	of	of	ADP
iajs-553	233	9	two	two	NUM
iajs-553	233	10	or	or	CCONJ
iajs-553	233	11	three	three	NUM
iajs-553	233	12	maximum	maximum	ADJ
iajs-553	233	13	cost	cost	NOUN
iajs-553	233	14	criteria	criterion	NOUN
iajs-553	233	15	“	"	PUNCT
iajs-553	233	16	,	,	PUNCT
iajs-553	233	17	journal	journal	NOUN
iajs-553	233	18	of	of	ADP
iajs-553	233	19	algorithms	algorithm	NOUN
iajs-553	233	20	,	,	PUNCT
iajs-553	233	21	21,415	21,415	NUM
iajs-553	233	22	-	-	SYM
iajs-553	233	23	433	433	NUM
iajs-553	233	24	.	.	PUNCT
iajs-553	234	1	9	9	X
iajs-553	234	2	.	.	X
iajs-553	234	3	bagchi	bagchi	PROPN
iajs-553	234	4	t.p	t.p	PROPN
iajs-553	234	5	.	.	PROPN
iajs-553	234	6	,	,	PUNCT
iajs-553	234	7	(	(	PUNCT
iajs-553	234	8	1999	1999	NUM
iajs-553	234	9	)	)	PUNCT
iajs-553	234	10	.	.	PUNCT
iajs-553	235	1	"	"	PUNCT
iajs-553	235	2	multiobjective	multiobjective	ADJ
iajs-553	235	3	scheduling	scheduling	NOUN
iajs-553	235	4	by	by	ADP
iajs-553	235	5	genetic	genetic	ADJ
iajs-553	235	6	algorithms	algorithm	NOUN
iajs-553	235	7	"	"	PUNCT
iajs-553	235	8	,	,	PUNCT
iajs-553	235	9	kluwer	kluwer	PROPN
iajs-553	235	10	acadimic	acadimic	PROPN
iajs-553	235	11	publisher	publisher	NOUN
iajs-553	235	12	.	.	PUNCT
iajs-553	236	1	10	10	NUM
iajs-553	236	2	.	.	PUNCT
iajs-553	237	1	hoogeveen	hoogeveen	PROPN
iajs-553	237	2	,	,	PUNCT
iajs-553	237	3	j.a	j.a	PROPN
iajs-553	237	4	.	.	PROPN
iajs-553	237	5	and	and	CCONJ
iajs-553	237	6	van	van	PROPN
iajs-553	237	7	de	de	PROPN
iajs-553	237	8	velde	velde	PROPN
iajs-553	237	9	,	,	PUNCT
iajs-553	237	10	s.l	s.l	PROPN
iajs-553	237	11	.	.	PROPN
iajs-553	237	12	(	(	PUNCT
iajs-553	237	13	1995	1995	NUM
iajs-553	237	14	)	)	PUNCT
iajs-553	237	15	.	.	PUNCT
iajs-553	238	1	“	"	PUNCT
iajs-553	238	2	minimizing	minimize	VERB
iajs-553	238	3	total	total	ADJ
iajs-553	238	4	completion	completion	NOUN
iajs-553	238	5	time	time	NOUN
iajs-553	238	6	and	and	CCONJ
iajs-553	238	7	maximum	maximum	ADJ
iajs-553	238	8	cost	cost	NOUN
iajs-553	238	9	simultaneously	simultaneously	ADV
iajs-553	238	10	is	be	AUX
iajs-553	238	11	solvable	solvable	ADJ
iajs-553	238	12	in	in	ADP
iajs-553	238	13	polynomial	polynomial	ADJ
iajs-553	238	14	time	time	NOUN
iajs-553	238	15	”	"	PUNCT
iajs-553	238	16	,	,	PUNCT
iajs-553	238	17	operations	operation	NOUN
iajs-553	238	18	research	research	NOUN
iajs-553	238	19	letters	letter	NOUN
iajs-553	238	20	17	17	NUM
iajs-553	238	21	,	,	PUNCT
iajs-553	238	22	205–208	205–208	NUM
iajs-553	238	23	.	.	PUNCT
iajs-553	239	1	11	11	NUM
iajs-553	239	2	.	.	PUNCT
iajs-553	240	1	van	van	NOUN
iajs-553	240	2	wassenhove	wassenhove	PROPN
iajs-553	240	3	,	,	PUNCT
iajs-553	240	4	l.n	l.n	PROPN
iajs-553	240	5	.	.	PROPN
iajs-553	240	6	and	and	CCONJ
iajs-553	240	7	gelders	gelder	NOUN
iajs-553	240	8	.	.	PUNCT
iajs-553	241	1	f.	f.	PROPN
iajs-553	241	2	(	(	PUNCT
iajs-553	241	3	1980	1980	NUM
iajs-553	241	4	)	)	PUNCT
iajs-553	241	5	.	.	PUNCT
iajs-553	242	1	"	"	PUNCT
iajs-553	242	2	solving	solve	VERB
iajs-553	242	3	a	a	DET
iajs-553	242	4	bicriterion	bicriterion	NOUN
iajs-553	242	5	scheduling	scheduling	NOUN
iajs-553	242	6	problem	problem	NOUN
iajs-553	242	7	"	"	PUNCT
iajs-553	242	8	,	,	PUNCT
iajs-553	242	9	european	european	PROPN
iajs-553	242	10	journal	journal	PROPN
iajs-553	242	11	of	of	ADP
iajs-553	242	12	operational	operational	ADJ
iajs-553	242	13	research	research	NOUN
iajs-553	242	14	4/1	4/1	NUM
iajs-553	242	15	,	,	PUNCT
iajs-553	242	16	42	42	NUM
iajs-553	242	17	-	-	SYM
iajs-553	242	18	48	48	NUM
iajs-553	242	19	.	.	PUNCT
iajs-553	242	20	12	12	NUM
iajs-553	242	21	.	.	PUNCT
iajs-553	242	22	emmons	emmons	PROPN
iajs-553	242	23	,	,	PUNCT
iajs-553	242	24	h.	h.	PROPN
iajs-553	242	25	(	(	PUNCT
iajs-553	242	26	1975	1975	NUM
iajs-553	242	27	)	)	PUNCT
iajs-553	242	28	.	.	PUNCT
iajs-553	243	1	"	"	PUNCT
iajs-553	243	2	a	a	DET
iajs-553	243	3	note	note	NOUN
iajs-553	243	4	on	on	ADP
iajs-553	243	5	a	a	DET
iajs-553	243	6	scheduling	scheduling	NOUN
iajs-553	243	7	problem	problem	NOUN
iajs-553	243	8	with	with	ADP
iajs-553	243	9	dual	dual	ADJ
iajs-553	243	10	criteria	criterion	NOUN
iajs-553	243	11	"	"	PUNCT
iajs-553	243	12	,	,	PUNCT
iajs-553	243	13	naval	naval	ADJ
iajs-553	243	14	res	re	NOUN
iajs-553	243	15	.	.	PUNCT
iajs-553	244	1	logis	logis	PROPN
iajs-553	244	2	.	.	PUNCT
iajs-553	245	1	quarterly	quarterly	ADJ
iajs-553	245	2	,	,	PUNCT
iajs-553	245	3	22	22	NUM
iajs-553	245	4	,	,	PUNCT
iajs-553	245	5	615	615	NUM
iajs-553	245	6	-	-	SYM
iajs-553	245	7	516	516	NUM
iajs-553	245	8	.	.	PUNCT
iajs-553	246	1	13	13	NUM
iajs-553	246	2	.	.	PUNCT
iajs-553	247	1	hoogeveen	hoogeveen	PROPN
iajs-553	247	2	,	,	PUNCT
iajs-553	247	3	j.a	j.a	PROPN
iajs-553	247	4	.	.	PROPN
iajs-553	247	5	(	(	PUNCT
iajs-553	247	6	1991	1991	NUM
iajs-553	247	7	)	)	PUNCT
iajs-553	247	8	.	.	PUNCT
iajs-553	247	9	”	"	PUNCT
iajs-553	248	1	single	single	ADJ
iajs-553	248	2	machine	machine	NOUN
iajs-553	248	3	scheduling	scheduling	NOUN
iajs-553	248	4	to	to	PART
iajs-553	248	5	minimize	minimize	VERB
iajs-553	248	6	a	a	DET
iajs-553	248	7	function	function	NOUN
iajs-553	248	8	of	of	ADP
iajs-553	248	9	k	k	PROPN
iajs-553	248	10	maximum	maximum	PROPN
iajs-553	248	11	cost	cost	NOUN
iajs-553	248	12	criteria	criterion	NOUN
iajs-553	248	13	“	"	PUNCT
iajs-553	248	14	,	,	PUNCT
iajs-553	248	15	cwi	cwi	NOUN
iajs-553	248	16	,	,	PUNCT
iajs-553	248	17	bs	bs	NOUN
iajs-553	248	18	-	-	PUNCT
iajs-553	248	19	r9113	r9113	NOUN
iajs-553	248	20	.	.	PUNCT
iajs-553	249	1	table(1	table(1	PROPN
iajs-553	249	2	):	):	PUNCT
iajs-553	249	3	computational	computational	ADJ
iajs-553	249	4	results	result	NOUN
iajs-553	249	5	problem	problem	NOUN
iajs-553	249	6	size	size	NOUN
iajs-553	249	7	problem	problem	NOUN
iajs-553	249	8	number	number	NOUN
iajs-553	249	9	nep	nep	PROPN
iajs-553	249	10	mnep	mnep	PROPN
iajs-553	249	11	efficient	efficient	ADJ
iajs-553	249	12	points	point	NOUN
iajs-553	249	13	10	10	NUM
iajs-553	249	14	1	1	NUM
iajs-553	249	15	2	2	NUM
iajs-553	249	16	2	2	NUM
iajs-553	249	17	(	(	PUNCT
iajs-553	249	18	273	273	NUM
iajs-553	249	19	,	,	PUNCT
iajs-553	249	20	8)	8)	NUM
iajs-553	249	21	,	,	PUNCT
iajs-553	249	22	(	(	PUNCT
iajs-553	249	23	262	262	NUM
iajs-553	249	24	,	,	PUNCT
iajs-553	249	25	9	9	NUM
iajs-553	249	26	)	)	SYM
iajs-553	249	27	2	2	NUM
iajs-553	249	28	2	2	NUM
iajs-553	249	29	2	2	NUM
iajs-553	249	30	(	(	PUNCT
iajs-553	249	31	208	208	NUM
iajs-553	249	32	,	,	PUNCT
iajs-553	249	33	8)	8)	NUM
iajs-553	249	34	,	,	PUNCT
iajs-553	249	35	(	(	PUNCT
iajs-553	249	36	189	189	NUM
iajs-553	249	37	,	,	PUNCT
iajs-553	249	38	10	10	NUM
iajs-553	249	39	)	)	PUNCT
iajs-553	249	40	3	3	NUM
iajs-553	249	41	4	4	NUM
iajs-553	249	42	4	4	NUM
iajs-553	249	43	(	(	PUNCT
iajs-553	249	44	290	290	NUM
iajs-553	249	45	,	,	PUNCT
iajs-553	249	46	7	7	NUM
iajs-553	249	47	)	)	PUNCT
iajs-553	249	48	,	,	PUNCT
iajs-553	249	49	(	(	PUNCT
iajs-553	249	50	227	227	NUM
iajs-553	249	51	,	,	PUNCT
iajs-553	249	52	8)	8)	NUM
iajs-553	249	53	,	,	PUNCT
iajs-553	249	54	(	(	PUNCT
iajs-553	249	55	211	211	NUM
iajs-553	249	56	,	,	PUNCT
iajs-553	249	57	9	9	NUM
iajs-553	249	58	)	)	PUNCT
iajs-553	249	59	,	,	PUNCT
iajs-553	249	60	(	(	PUNCT
iajs-553	249	61	202	202	NUM
iajs-553	249	62	,	,	PUNCT
iajs-553	249	63	10	10	NUM
iajs-553	249	64	)	)	PUNCT
iajs-553	249	65	4	4	NUM
iajs-553	249	66	1	1	NUM
iajs-553	249	67	1	1	NUM
iajs-553	249	68	(	(	PUNCT
iajs-553	249	69	194	194	NUM
iajs-553	249	70	,	,	PUNCT
iajs-553	249	71	10	10	NUM
iajs-553	249	72	)	)	PUNCT
iajs-553	249	73	5	5	NUM
iajs-553	249	74	3	3	NUM
iajs-553	249	75	4	4	NUM
iajs-553	249	76	(	(	PUNCT
iajs-553	249	77	353	353	NUM
iajs-553	249	78	,	,	PUNCT
iajs-553	249	79	7	7	NUM
iajs-553	249	80	)	)	PUNCT
iajs-553	249	81	,	,	PUNCT
iajs-553	249	82	(	(	PUNCT
iajs-553	249	83	317	317	NUM
iajs-553	249	84	,	,	PUNCT
iajs-553	249	85	8)	8)	NUM
iajs-553	249	86	,	,	PUNCT
iajs-553	249	87	(	(	PUNCT
iajs-553	249	88	293	293	NUM
iajs-553	249	89	,	,	PUNCT
iajs-553	249	90	10	10	NUM
iajs-553	249	91	)	)	PUNCT
iajs-553	249	92	15	15	NUM
iajs-553	249	93	1	1	NUM
iajs-553	249	94	3	3	NUM
iajs-553	249	95	3	3	NUM
iajs-553	249	96	(	(	PUNCT
iajs-553	249	97	388	388	NUM
iajs-553	249	98	,	,	PUNCT
iajs-553	249	99	8)	8)	NUM
iajs-553	249	100	,	,	PUNCT
iajs-553	249	101	(	(	PUNCT
iajs-553	249	102	354	354	NUM
iajs-553	249	103	,	,	PUNCT
iajs-553	249	104	9	9	NUM
iajs-553	249	105	)	)	PUNCT
iajs-553	249	106	,	,	PUNCT
iajs-553	249	107	(	(	PUNCT
iajs-553	249	108	337	337	NUM
iajs-553	249	109	,	,	PUNCT
iajs-553	249	110	10	10	NUM
iajs-553	249	111	)	)	SYM
iajs-553	249	112	2	2	NUM
iajs-553	249	113	2	2	NUM
iajs-553	249	114	2	2	NUM
iajs-553	249	115	(	(	PUNCT
iajs-553	249	116	657	657	NUM
iajs-553	249	117	,	,	PUNCT
iajs-553	249	118	9	9	NUM
iajs-553	249	119	)	)	PUNCT
iajs-553	249	120	,	,	PUNCT
iajs-553	249	121	(	(	PUNCT
iajs-553	249	122	571	571	NUM
iajs-553	249	123	,	,	PUNCT
iajs-553	249	124	10	10	NUM
iajs-553	249	125	)	)	PUNCT
iajs-553	249	126	3	3	NUM
iajs-553	249	127	3	3	NUM
iajs-553	249	128	4	4	NUM
iajs-553	249	129	(	(	PUNCT
iajs-553	249	130	752	752	NUM
iajs-553	249	131	,	,	PUNCT
iajs-553	249	132	7	7	NUM
iajs-553	249	133	)	)	PUNCT
iajs-553	249	134	,	,	PUNCT
iajs-553	249	135	(	(	PUNCT
iajs-553	249	136	613	613	NUM
iajs-553	249	137	,	,	PUNCT
iajs-553	249	138	9	9	NUM
iajs-553	249	139	)	)	PUNCT
iajs-553	249	140	,	,	PUNCT
iajs-553	249	141	(	(	PUNCT
iajs-553	249	142	511	511	NUM
iajs-553	249	143	,	,	PUNCT
iajs-553	249	144	10	10	NUM
iajs-553	249	145	)	)	PUNCT
iajs-553	249	146	4	4	NUM
iajs-553	249	147	2	2	NUM
iajs-553	249	148	2	2	NUM
iajs-553	249	149	(	(	PUNCT
iajs-553	249	150	599	599	NUM
iajs-553	249	151	,	,	PUNCT
iajs-553	249	152	9	9	NUM
iajs-553	249	153	)	)	PUNCT
iajs-553	249	154	,	,	PUNCT
iajs-553	249	155	(	(	PUNCT
iajs-553	249	156	501	501	NUM
iajs-553	249	157	,	,	PUNCT
iajs-553	249	158	10	10	NUM
iajs-553	249	159	)	)	PUNCT
iajs-553	249	160	5	5	NUM
iajs-553	249	161	2	2	NUM
iajs-553	249	162	2	2	NUM
iajs-553	249	163	(	(	PUNCT
iajs-553	249	164	618	618	NUM
iajs-553	249	165	,	,	PUNCT
iajs-553	249	166	8)	8)	NUM
iajs-553	249	167	,	,	PUNCT
iajs-553	249	168	(	(	PUNCT
iajs-553	249	169	474	474	NUM
iajs-553	249	170	,	,	PUNCT
iajs-553	249	171	9	9	NUM
iajs-553	249	172	)	)	PUNCT
iajs-553	249	173	30	30	NUM
iajs-553	249	174	1	1	NUM
iajs-553	249	175	4	4	NUM
iajs-553	249	176	4	4	NUM
iajs-553	249	177	(	(	PUNCT
iajs-553	249	178	2737	2737	NUM
iajs-553	249	179	,	,	PUNCT
iajs-553	249	180	7	7	NUM
iajs-553	249	181	)	)	PUNCT
iajs-553	249	182	,	,	PUNCT
iajs-553	249	183	(	(	PUNCT
iajs-553	249	184	2418	2418	NUM
iajs-553	249	185	,	,	PUNCT
iajs-553	249	186	8)	8)	NUM
iajs-553	249	187	,	,	PUNCT
iajs-553	249	188	(	(	PUNCT
iajs-553	249	189	2283	2283	NUM
iajs-553	249	190	,	,	PUNCT
iajs-553	249	191	9	9	NUM
iajs-553	249	192	)	)	PUNCT
iajs-553	249	193	,	,	PUNCT
iajs-553	249	194	(	(	PUNCT
iajs-553	249	195	2206	2206	NUM
iajs-553	249	196	,	,	PUNCT
iajs-553	249	197	10	10	NUM
iajs-553	249	198	)	)	SYM
iajs-553	249	199	2	2	NUM
iajs-553	249	200	2	2	NUM
iajs-553	249	201	2	2	NUM
iajs-553	249	202	(	(	PUNCT
iajs-553	249	203	1833	1833	NUM
iajs-553	249	204	,	,	PUNCT
iajs-553	249	205	9	9	NUM
iajs-553	249	206	)	)	PUNCT
iajs-553	249	207	,	,	PUNCT
iajs-553	249	208	(	(	PUNCT
iajs-553	249	209	1755	1755	NUM
iajs-553	249	210	,	,	PUNCT
iajs-553	249	211	10	10	NUM
iajs-553	249	212	)	)	PUNCT
iajs-553	249	213	3	3	NUM
iajs-553	249	214	4	4	NUM
iajs-553	249	215	4	4	NUM
iajs-553	249	216	(	(	PUNCT
iajs-553	249	217	2275	2275	NUM
iajs-553	249	218	,	,	PUNCT
iajs-553	249	219	7	7	NUM
iajs-553	249	220	)	)	PUNCT
iajs-553	249	221	,	,	PUNCT
iajs-553	249	222	(	(	PUNCT
iajs-553	249	223	2165	2165	NUM
iajs-553	249	224	,	,	PUNCT
iajs-553	249	225	8)	8)	NUM
iajs-553	249	226	,	,	PUNCT
iajs-553	249	227	(	(	PUNCT
iajs-553	249	228	1861	1861	NUM
iajs-553	249	229	,	,	PUNCT
iajs-553	249	230	9	9	NUM
iajs-553	249	231	)	)	PUNCT
iajs-553	249	232	,	,	PUNCT
iajs-553	249	233	(	(	PUNCT
iajs-553	249	234	1749	1749	NUM
iajs-553	249	235	,	,	PUNCT
iajs-553	249	236	10	10	NUM
iajs-553	249	237	)	)	PUNCT
iajs-553	249	238	4	4	NUM
iajs-553	249	239	6	6	NUM
iajs-553	249	240	6	6	NUM
iajs-553	249	241	(	(	PUNCT
iajs-553	249	242	2599	2599	NUM
iajs-553	249	243	,	,	PUNCT
iajs-553	249	244	5	5	NUM
iajs-553	249	245	)	)	PUNCT
iajs-553	249	246	,	,	PUNCT
iajs-553	249	247	(	(	PUNCT
iajs-553	249	248	2499	2499	NUM
iajs-553	249	249	,	,	PUNCT
iajs-553	249	250	6	6	NUM
iajs-553	249	251	)	)	PUNCT
iajs-553	249	252	,	,	PUNCT
iajs-553	249	253	(	(	PUNCT
iajs-553	249	254	2384	2384	NUM
iajs-553	249	255	,	,	PUNCT
iajs-553	249	256	7	7	NUM
iajs-553	249	257	)	)	PUNCT
iajs-553	249	258	,	,	PUNCT
iajs-553	249	259	(	(	PUNCT
iajs-553	249	260	2283	2283	NUM
iajs-553	249	261	,	,	PUNCT
iajs-553	249	262	8)	8)	NUM
iajs-553	249	263	,	,	PUNCT
iajs-553	249	264	(	(	PUNCT
iajs-553	249	265	2226	2226	NUM
iajs-553	249	266	,	,	PUNCT
iajs-553	249	267	9	9	NUM
iajs-553	249	268	)	)	PUNCT
iajs-553	249	269	,	,	PUNCT
iajs-553	249	270	(	(	PUNCT
iajs-553	249	271	2214	2214	NUM
iajs-553	249	272	,	,	PUNCT
iajs-553	249	273	10	10	NUM
iajs-553	249	274	)	)	PUNCT
iajs-553	249	275	5	5	NUM
iajs-553	249	276	1	1	NUM
iajs-553	249	277	1	1	NUM
iajs-553	249	278	(	(	PUNCT
iajs-553	249	279	1982,10	1982,10	NUM
iajs-553	249	280	)	)	PUNCT
iajs-553	249	281	50	50	NUM
iajs-553	249	282	1	1	NUM
iajs-553	249	283	5	5	NUM
iajs-553	249	284	5	5	NUM
iajs-553	249	285	(	(	PUNCT
iajs-553	249	286	6192	6192	NUM
iajs-553	249	287	,	,	PUNCT
iajs-553	249	288	6	6	NUM
iajs-553	249	289	)	)	PUNCT
iajs-553	249	290	,	,	PUNCT
iajs-553	249	291	(	(	PUNCT
iajs-553	249	292	5869	5869	NUM
iajs-553	249	293	,	,	PUNCT
iajs-553	249	294	7	7	NUM
iajs-553	249	295	)	)	PUNCT
iajs-553	249	296	,	,	PUNCT
iajs-553	249	297	(	(	PUNCT
iajs-553	249	298	5477	5477	NUM
iajs-553	249	299	,	,	PUNCT
iajs-553	249	300	8)	8)	NUM
iajs-553	249	301	,	,	PUNCT
iajs-553	249	302	(	(	PUNCT
iajs-553	249	303	5110	5110	NUM
iajs-553	249	304	,	,	PUNCT
iajs-553	249	305	9	9	NUM
iajs-553	249	306	)	)	PUNCT
iajs-553	249	307	,	,	PUNCT
iajs-553	249	308	(	(	PUNCT
iajs-553	249	309	4863	4863	NUM
iajs-553	249	310	,	,	PUNCT
iajs-553	249	311	10	10	NUM
iajs-553	249	312	)	)	SYM
iajs-553	249	313	2	2	NUM
iajs-553	249	314	2	2	NUM
iajs-553	249	315	2	2	NUM
iajs-553	249	316	(	(	PUNCT
iajs-553	249	317	6223	6223	NUM
iajs-553	249	318	,	,	PUNCT
iajs-553	249	319	9	9	NUM
iajs-553	249	320	)	)	PUNCT
iajs-553	249	321	,	,	PUNCT
iajs-553	249	322	(	(	PUNCT
iajs-553	249	323	5518	5518	NUM
iajs-553	249	324	)	)	PUNCT
iajs-553	249	325	3	3	NUM
iajs-553	249	326	4	4	NUM
iajs-553	249	327	4	4	NUM
iajs-553	249	328	(	(	PUNCT
iajs-553	249	329	5945	5945	NUM
iajs-553	249	330	,	,	PUNCT
iajs-553	249	331	7	7	NUM
iajs-553	249	332	)	)	PUNCT
iajs-553	249	333	,	,	PUNCT
iajs-553	249	334	(	(	PUNCT
iajs-553	249	335	5794	5794	NUM
iajs-553	249	336	,	,	PUNCT
iajs-553	249	337	8)	8)	NUM
iajs-553	249	338	,	,	PUNCT
iajs-553	249	339	(	(	PUNCT
iajs-553	249	340	5437	5437	NUM
iajs-553	249	341	,	,	PUNCT
iajs-553	249	342	9	9	NUM
iajs-553	249	343	)	)	PUNCT
iajs-553	249	344	,	,	PUNCT
iajs-553	249	345	(	(	PUNCT
iajs-553	249	346	5228	5228	NUM
iajs-553	249	347	,	,	PUNCT
iajs-553	249	348	10	10	NUM
iajs-553	249	349	)	)	PUNCT
iajs-553	249	350	4	4	NUM
iajs-553	249	351	6	6	NUM
iajs-553	249	352	6	6	NUM
iajs-553	249	353	(	(	PUNCT
iajs-553	249	354	5715	5715	NUM
iajs-553	249	355	,	,	PUNCT
iajs-553	249	356	4	4	NUM
iajs-553	249	357	)	)	PUNCT
iajs-553	249	358	,	,	PUNCT
iajs-553	249	359	(	(	PUNCT
iajs-553	249	360	5276	5276	NUM
iajs-553	249	361	,	,	PUNCT
iajs-553	249	362	5	5	NUM
iajs-553	249	363	)	)	PUNCT
iajs-553	249	364	,	,	PUNCT
iajs-553	249	365	(	(	PUNCT
iajs-553	249	366	5105	5105	NUM
iajs-553	249	367	,	,	PUNCT
iajs-553	249	368	6	6	NUM
iajs-553	249	369	)	)	PUNCT
iajs-553	249	370	,	,	PUNCT
iajs-553	249	371	(	(	PUNCT
iajs-553	249	372	4810	4810	NUM
iajs-553	249	373	,	,	PUNCT
iajs-553	249	374	7	7	NUM
iajs-553	249	375	)	)	PUNCT
iajs-553	249	376	,	,	PUNCT
iajs-553	249	377	(	(	PUNCT
iajs-553	249	378	4652	4652	NUM
iajs-553	249	379	,	,	PUNCT
iajs-553	249	380	8)	8)	NUM
iajs-553	249	381	,	,	PUNCT
iajs-553	249	382	(	(	PUNCT
iajs-553	249	383	4641	4641	NUM
iajs-553	249	384	,	,	PUNCT
iajs-553	249	385	9	9	NUM
iajs-553	249	386	)	)	PUNCT
iajs-553	249	387	5	5	NUM
iajs-553	249	388	2	2	NUM
iajs-553	249	389	2	2	NUM
iajs-553	249	390	(	(	PUNCT
iajs-553	249	391	5432	5432	NUM
iajs-553	249	392	,	,	PUNCT
iajs-553	249	393	10	10	NUM
iajs-553	249	394	)	)	PUNCT
iajs-553	249	395	,	,	PUNCT
iajs-553	249	396	(	(	PUNCT
iajs-553	249	397	6607	6607	NUM
iajs-553	249	398	,	,	PUNCT
iajs-553	249	399	9	9	NUM
iajs-553	249	400	)	)	PUNCT
iajs-553	249	401	mathematics	mathematic	NOUN
iajs-553	249	402	366	366	NUM
iajs-553	249	403	مجلة	مجلة	ADJ
iajs-553	249	404	إبن	إبن	NOUN
iajs-553	249	405	الهيثم	الهيثم	ADJ
iajs-553	249	406	للعلوم	للعلوم	NOUN
iajs-553	249	407	الصرفة	الصرفة	NOUN
iajs-553	249	408	و	و	PRON
iajs-553	249	409	التطبيقية	التطبيقية	ADJ
iajs-553	249	410	2012	2012	NUM
iajs-553	249	411	السنة	السنة	NOUN
iajs-553	249	412	25	25	NUM
iajs-553	249	413	المجلد	المجلد	NOUN
iajs-553	249	414	3	3	NUM
iajs-553	249	415	العدد	العدد	PROPN
iajs-553	249	416	ibn	ibn	PROPN
iajs-553	249	417	al	al	PROPN
iajs-553	249	418	-	-	PUNCT
iajs-553	249	419	haitham	haitham	PROPN
iajs-553	249	420	journal	journal	PROPN
iajs-553	249	421	for	for	ADP
iajs-553	249	422	pure	pure	ADJ
iajs-553	249	423	and	and	CCONJ
iajs-553	249	424	applied	apply	VERB
iajs-553	249	425	science	science	NOUN
iajs-553	249	426	no	no	NOUN
iajs-553	249	427	.	.	NOUN
iajs-553	249	428	3	3	NUM
iajs-553	249	429	vol	vol	NOUN
iajs-553	249	430	.	.	PUNCT
iajs-553	250	1	25	25	NUM
iajs-553	250	2	year	year	NOUN
iajs-553	250	3	2012	2012	NUM
iajs-553	250	4	مجموع	مجموع	NOUN
iajs-553	250	5	أوقات	أوقات	NOUN
iajs-553	250	6	اإلتمام	اإلتمام	PROPN
iajs-553	250	7	مع	مع	ADP
iajs-553	250	8	أعظم	أعظم	PROPN
iajs-553	250	9	عمل	عمل	PROPN
iajs-553	250	10	تأخير	تأخير	PROPN
iajs-553	250	11	فراس	فراس	PROPN
iajs-553	250	12	شاكر	شاكر	PROPN
iajs-553	250	13	فندي	فندي	PROPN
iajs-553	250	14	و	و	PRON
iajs-553	250	15	صالح	صالح	NOUN
iajs-553	250	16	عبد	عبد	NOUN
iajs-553	250	17	الرزاقطارق	الرزاقطارق	NOUN
iajs-553	250	18	قسم	قسم	PROPN
iajs-553	250	19	الرياضيات	الرياضيات	PROPN
iajs-553	250	20	،	،	PROPN
iajs-553	250	21	كلية	كلية	PROPN
iajs-553	250	22	العلوم	العلوم	PROPN
iajs-553	250	23	،	،	PROPN
iajs-553	250	24	الجامعة	الجامعة	PROPN
iajs-553	250	25	المستنصرية	المستنصرية	PROPN
iajs-553	250	26	.	.	PUNCT
iajs-553	251	1	للعلوم	للعلوم	PROPN
iajs-553	251	2	الصرفة	الصرفة	PROPN
iajs-553	251	3	،	،	PROPN
iajs-553	251	4	جامعة	جامعة	PROPN
iajs-553	251	5	األنبار	األنبار	VERB
iajs-553	251	6	قسم	قسم	PROPN
iajs-553	251	7	الرياضيات	الرياضيات	PROPN
iajs-553	251	8	،	،	PROPN
iajs-553	251	9	كلية	كلية	PROPN
iajs-553	251	10	التربية	التربية	NOUN
iajs-553	251	11	2012نيسان	2012نيسان	PROPN
iajs-553	251	12	22قبل	22قبل	NOUN
iajs-553	251	13	البحث	البحث	NOUN
iajs-553	251	14	:	:	PUNCT
iajs-553	251	15	2012نيسان	2012نيسان	NUM
iajs-553	251	16	1استلم	1استلم	NUM
iajs-553	251	17	البحث	البحث	NOUN
iajs-553	251	18	في	في	ADP
iajs-553	251	19	:	:	PUNCT
iajs-553	251	20	الخالصة	الخالصة	PROPN
iajs-553	251	21	هذا	هذا	PROPN
iajs-553	251	22	البحث	البحث	PROPN
iajs-553	251	23	المسألة	المسألة	PROPN
iajs-553	251	24	لجدولة	لجدولة	PROPN
iajs-553	251	25	الوظائف	الوظائف	PROPN
iajs-553	251	26	على	على	PROPN
iajs-553	251	27	الماكنة	الماكنة	PROPN
iajs-553	251	28	الواحدة	الواحدة	ADJ
iajs-553	251	29	للمعايير	للمعايير	NOUN
iajs-553	251	30	المتنوعة	المتنوعة	NOUN
iajs-553	251	31	درست	درست	PROPN
iajs-553	251	32	المسألة	المسألة	ADJ
iajs-553	251	33	لتصغير	لتصغير	ADJ
iajs-553	251	34	مجموع	مجموع	NOUN
iajs-553	251	35	في	في	SCONJ
iajs-553	251	36	من	من	PROPN
iajs-553	251	37	الوظائف	الوظائف	PROPN
iajs-553	251	38	المستقلة	المستقلة	PROPN
iajs-553	251	39	التي	التي	PROPN
iajs-553	251	40	يمكن	يمكن	PROPN
iajs-553	251	41	جدولتها	جدولتها	PROPN
iajs-553	251	42	على	على	VERB
iajs-553	251	43	ماكنة	ماكنة	PROPN
iajs-553	251	44	واحدة	واحدة	PROPN
iajs-553	251	45	والتي	والتي	PROPN
iajs-553	251	46	nمع	nمع	PROPN
iajs-553	251	47	أعظم	أعظم	PROPN
iajs-553	251	48	عمل	عمل	PROPN
iajs-553	251	49	تأخير	تأخير	NOUN
iajs-553	251	50	.	.	PUNCT
iajs-553	252	1	المجموعة	المجموعة	ADJ
iajs-553	252	2	أوقات	أوقات	NOUN
iajs-553	252	3	اإلتمام	اإلتمام	NOUN
iajs-553	252	4	وصاعدا	وصاعدا	NOUN
iajs-553	252	5	ولذلك	ولذلك	NOUN
iajs-553	252	6	ال	ال	ADP
iajs-553	252	7	يمكن	يمكن	PROPN
iajs-553	252	8	ان	ان	AUX
iajs-553	252	9	تعالج	تعالج	PROPN
iajs-553	252	10	اكثر	اكثر	PROPN
iajs-553	253	1	من	من	PROPN
iajs-553	253	2	وظيفة	وظيفة	PROPN
iajs-553	254	1	واحد	واحد	INTJ
iajs-553	254	2	في	في	PRON
iajs-553	254	3	وقت	وقت	PROPN
iajs-553	254	4	واحد	واحد	PROPN
iajs-553	254	5	.	.	PUNCT
iajs-553	255	1	الوظيفة	الوظيفة	PROPN
iajs-553	255	2	0تتطلب	0تتطلب	PROPN
iajs-553	255	3	معالجة	معالجة	NOUN
iajs-553	255	4	باستمرار	باستمرار	PROPN
iajs-553	255	5	من	من	PRON
iajs-553	255	6	الوقت	الوقت	PROPN
iajs-553	255	7	صفر	صفر	PROPN
iajs-553	255	8	i	i	PRON
iajs-553	255	9	تتطلب	تتطلب	VERB
iajs-553	255	10	وقت	وقت	PROPN
iajs-553	255	11	معالجة	معالجة	PROPN
iajs-553	255	12	موجب	موجب	PROPN
iajs-553	255	13	معطى	معطى	PROPN
iajs-553	255	14	مستمر	مستمر	PROPN
iajs-553	255	15	pi	pi	PROPN
iajs-553	255	16	الموعد	الموعد	PROPN
iajs-553	255	17	المثالي	المثالي	PROPN
iajs-553	255	18	إلكمال	إلكمال	PROPN
iajs-553	255	19	الوظيفة	الوظيفة	PROPN
iajs-553	255	20	،	،	PROPN
iajs-553	255	21	di	di	X
iajs-553	255	22	.	.	PUNCT
iajs-553	256	1	معايرها	معايرها	X
iajs-553	256	2	فوءة	فوءة	PROPN
iajs-553	256	3	في	في	PRON
iajs-553	256	4	حالة	حالة	NOUN
iajs-553	256	5	المسائل	المسائل	VERB
iajs-553	256	6	التيلمسائل	التيلمسائل	VERB
iajs-553	257	1	جدولة	جدولة	NOUN
iajs-553	257	2	المعايير	المعايير	NOUN
iajs-553	257	3	الثنائية	الثنائية	PROPN
iajs-553	257	4	،	،	PROPN
iajs-553	257	5	بعض	بعض	PROPN
iajs-553	257	6	الخوارزميات	الخوارزميات	PROPN
iajs-553	257	7	اقترحت	اقترحت	PROPN
iajs-553	257	8	إليجاد	إليجاد	PROPN
iajs-553	257	9	الحلول	الحلول	ADJ
iajs-553	257	10	الك	الك	PROPN
iajs-553	257	11	،	،	PROPN
iajs-553	257	12	فقد	فقد	PROPN
iajs-553	258	1	اقترحنا	اقترحنا	PROPN
iajs-553	258	2	خوارزميات	خوارزميات	PROPN
iajs-553	258	3	عامة	عامة	ADJ
iajs-553	258	4	إلعطاء	إلعطاء	NOUN
iajs-553	258	5	الحلول	الحلول	INTJ
iajs-553	258	6	الكفوءة	الكفوءة	PROPN
iajs-553	258	7	ضمن	ضمن	PROPN
iajs-553	258	8	المدى	المدى	PROPN
iajs-553	258	9	ايضالمسائل	ايضالمسائل	PROPN
iajs-553	258	10	المعايير	المعايير	NOUN
iajs-553	258	11	المتعددة	المتعددة	VERB
iajs-553	258	12	و	و	PRON
iajs-553	258	13	.	.	PUNCT
iajs-553	259	1	متساوية	متساوية	PROPN
iajs-553	259	2	األهمية	األهمية	PROPN
iajs-553	259	3	الكفوء	الكفوء	PROPN
iajs-553	259	4	.	.	PUNCT
iajs-553	260	1	الجدولة	الجدولة	PROPN
iajs-553	260	2	،	،	PROPN
iajs-553	260	3	المعايير	المعايير	NOUN
iajs-553	260	4	المتعددة	المتعددة	VERB
iajs-553	260	5	،	،	PROPN
iajs-553	260	6	الماكنة	الماكنة	PROPN
iajs-553	260	7	الواحدة	الواحدة	PROPN
iajs-553	260	8	،	،	PROPN
iajs-553	260	9	المعايير	المعايير	NOUN
iajs-553	260	10	الثنائية	الثنائية	PROPN
iajs-553	260	11	.	.	PUNCT
iajs-553	261	1	-الكلمات	-الكلمات	ADJ
iajs-553	261	2	المفتاحية	المفتاحية	NOUN
iajs-553	261	3	:	:	PUNCT