id	sid	tid	token	lemma	pos
cana-539	1	1	communications	communication	NOUN
cana-539	1	2	on	on	ADP
cana-539	1	3	applied	apply	VERB
cana-539	1	4	nonlinear	nonlinear	ADJ
cana-539	1	5	analysis	analysis	NOUN
cana-539	1	6	issn	issn	NOUN
cana-539	1	7	:	:	PUNCT
cana-539	1	8	1074	1074	NUM
cana-539	1	9	-	-	PUNCT
cana-539	1	10	133x	133x	NUM
cana-539	1	11	vol	vol	NOUN
cana-539	1	12	31	31	NUM
cana-539	1	13	no	no	NOUN
cana-539	1	14	.	.	NOUN
cana-539	1	15	2	2	NUM
cana-539	1	16	(	(	PUNCT
cana-539	1	17	2024	2024	NUM
cana-539	1	18	)	)	PUNCT
cana-539	1	19	240	240	NUM
cana-539	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	1	21	a	a	DET
cana-539	1	22	two	two	NUM
cana-539	1	23	-	-	PUNCT
cana-539	1	24	warehouse	warehouse	NOUN
cana-539	1	25	inventory	inventory	NOUN
cana-539	1	26	system	system	NOUN
cana-539	1	27	with	with	ADP
cana-539	1	28	time	time	NOUN
cana-539	1	29	-	-	PUNCT
cana-539	1	30	dependent	dependent	ADJ
cana-539	1	31	demand	demand	NOUN
cana-539	1	32	and	and	CCONJ
cana-539	1	33	preservation	preservation	NOUN
cana-539	1	34	technology	technology	PROPN
cana-539	1	35	puneet	puneet	PROPN
cana-539	1	36	kumar1	kumar1	PROPN
cana-539	1	37	,	,	PUNCT
cana-539	1	38	dr	dr	PROPN
cana-539	1	39	.	.	PROPN
cana-539	1	40	abhinav	abhinav	PROPN
cana-539	1	41	saxena2	saxena2	PROPN
cana-539	1	42	,	,	PUNCT
cana-539	1	43	dr	dr	PROPN
cana-539	1	44	.	.	PROPN
cana-539	1	45	kamesh	kamesh	PROPN
cana-539	1	46	kumar3	kumar3	PROPN
cana-539	2	1	1,2,3department	1,2,3department	NUM
cana-539	2	2	of	of	ADP
cana-539	2	3	mathematics	mathematic	NOUN
cana-539	2	4	,	,	PUNCT
cana-539	2	5	faculty	faculty	NOUN
cana-539	2	6	of	of	ADP
cana-539	2	7	engineering	engineering	NOUN
cana-539	2	8	,	,	PUNCT
cana-539	2	9	teerthanker	teerthanker	NOUN
cana-539	2	10	mahaveer	mahaveer	PROPN
cana-539	2	11	university	university	PROPN
cana-539	2	12	,	,	PUNCT
cana-539	2	13	moradabad	moradabad	PROPN
cana-539	2	14	,	,	PUNCT
cana-539	2	15	up	up	ADP
cana-539	2	16	,	,	PUNCT
cana-539	2	17	india	india	PROPN
cana-539	2	18	.	.	PUNCT
cana-539	3	1	e-mail1nirankari2608@gmail.com	e-mail1nirankari2608@gmail.com	PROPN
cana-539	3	2	,	,	PUNCT
cana-539	3	3	2drabhinav.engineering@tmu.ac.in	2drabhinav.engineering@tmu.ac.in	NUM
cana-539	3	4	,	,	PUNCT
cana-539	3	5	3drkamesh.engineering@tmu.ac.in	3drkamesh.engineering@tmu.ac.in	NUM
cana-539	3	6	article	article	NOUN
cana-539	3	7	history	history	NOUN
cana-539	3	8	:	:	PUNCT
cana-539	3	9	received	receive	VERB
cana-539	3	10	:	:	PUNCT
cana-539	3	11	30	30	NUM
cana-539	3	12	-	-	SYM
cana-539	3	13	01	01	NUM
cana-539	3	14	-	-	PUNCT
cana-539	3	15	2024	2024	NUM
cana-539	3	16	revised	revise	VERB
cana-539	3	17	:	:	PUNCT
cana-539	3	18	20	20	NUM
cana-539	3	19	-	-	PUNCT
cana-539	3	20	04	04	NUM
cana-539	3	21	-	-	PUNCT
cana-539	3	22	2024	2024	NUM
cana-539	3	23	accepted	accept	VERB
cana-539	3	24	:	:	PUNCT
cana-539	3	25	01	01	NUM
cana-539	3	26	-	-	PUNCT
cana-539	3	27	05	05	NUM
cana-539	3	28	-	-	PUNCT
cana-539	3	29	2024	2024	NUM
cana-539	3	30	abstract	abstract	NOUN
cana-539	3	31	:	:	PUNCT
cana-539	3	32	because	because	SCONJ
cana-539	3	33	of	of	ADP
cana-539	3	34	rapid	rapid	ADJ
cana-539	3	35	environmental	environmental	ADJ
cana-539	3	36	changes	change	NOUN
cana-539	3	37	in	in	ADP
cana-539	3	38	current	current	ADJ
cana-539	3	39	worldwide	worldwide	ADJ
cana-539	3	40	society	society	NOUN
cana-539	3	41	,	,	PUNCT
cana-539	3	42	preserving	preserve	VERB
cana-539	3	43	technique	technique	NOUN
cana-539	3	44	is	be	AUX
cana-539	3	45	becoming	become	VERB
cana-539	3	46	increasingly	increasingly	ADV
cana-539	3	47	crucial	crucial	ADJ
cana-539	3	48	.	.	PUNCT
cana-539	4	1	with	with	ADP
cana-539	4	2	the	the	DET
cana-539	4	3	aim	aim	NOUN
cana-539	4	4	to	to	PART
cana-539	4	5	examine	examine	VERB
cana-539	4	6	this	this	DET
cana-539	4	7	idea	idea	NOUN
cana-539	4	8	,	,	PUNCT
cana-539	4	9	we	we	PRON
cana-539	4	10	created	create	VERB
cana-539	4	11	a	a	DET
cana-539	4	12	model	model	NOUN
cana-539	4	13	for	for	ADP
cana-539	4	14	two	two	NUM
cana-539	4	15	-	-	PUNCT
cana-539	4	16	warehouse	warehouse	NOUN
cana-539	4	17	inventory	inventory	NOUN
cana-539	4	18	system	system	NOUN
cana-539	4	19	that	that	PRON
cana-539	4	20	incorporates	incorporate	VERB
cana-539	4	21	preservation	preservation	NOUN
cana-539	4	22	technique	technique	NOUN
cana-539	4	23	investments	investment	NOUN
cana-539	4	24	.	.	PUNCT
cana-539	5	1	the	the	DET
cana-539	5	2	model	model	NOUN
cana-539	5	3	considers	consider	VERB
cana-539	5	4	time	time	NOUN
cana-539	5	5	as	as	ADP
cana-539	5	6	a	a	DET
cana-539	5	7	linear	linear	ADJ
cana-539	5	8	function	function	NOUN
cana-539	5	9	representing	represent	VERB
cana-539	5	10	the	the	DET
cana-539	5	11	rate	rate	NOUN
cana-539	5	12	of	of	ADP
cana-539	5	13	demand	demand	NOUN
cana-539	5	14	.	.	PUNCT
cana-539	6	1	time	time	NOUN
cana-539	6	2	-	-	PUNCT
cana-539	6	3	dependent	dependent	ADJ
cana-539	6	4	demand	demand	NOUN
cana-539	6	5	is	be	AUX
cana-539	6	6	a	a	DET
cana-539	6	7	common	common	ADJ
cana-539	6	8	feature	feature	NOUN
cana-539	6	9	in	in	ADP
cana-539	6	10	many	many	ADJ
cana-539	6	11	industries	industry	NOUN
cana-539	6	12	,	,	PUNCT
cana-539	6	13	where	where	SCONJ
cana-539	6	14	demand	demand	NOUN
cana-539	6	15	fluctuates	fluctuate	VERB
cana-539	6	16	over	over	ADP
cana-539	6	17	time	time	NOUN
cana-539	6	18	due	due	ADP
cana-539	6	19	to	to	ADP
cana-539	6	20	various	various	ADJ
cana-539	6	21	factors	factor	NOUN
cana-539	6	22	such	such	ADJ
cana-539	6	23	as	as	ADP
cana-539	6	24	seasonality	seasonality	NOUN
cana-539	6	25	and	and	CCONJ
cana-539	6	26	market	market	NOUN
cana-539	6	27	trends	trend	NOUN
cana-539	6	28	.	.	PUNCT
cana-539	7	1	the	the	DET
cana-539	7	2	stock	stock	NOUN
cana-539	7	3	is	be	AUX
cana-539	7	4	kept	keep	VERB
cana-539	7	5	in	in	ADP
cana-539	7	6	the	the	DET
cana-539	7	7	restricted	restricted	ADJ
cana-539	7	8	storage	storage	NOUN
cana-539	7	9	area	area	NOUN
cana-539	7	10	(	(	PUNCT
cana-539	7	11	ow	ow	INTJ
cana-539	7	12	)	)	PUNCT
cana-539	7	13	and	and	CCONJ
cana-539	7	14	other	other	ADJ
cana-539	7	15	warehouse	warehouse	NOUN
cana-539	7	16	(	(	PUNCT
cana-539	7	17	rented	rent	VERB
cana-539	7	18	)	)	PUNCT
cana-539	7	19	is	be	AUX
cana-539	7	20	utilized	utilize	VERB
cana-539	7	21	for	for	ADP
cana-539	7	22	keep	keep	VERB
cana-539	7	23	any	any	DET
cana-539	7	24	excess	excess	ADJ
cana-539	7	25	stock	stock	NOUN
cana-539	7	26	that	that	PRON
cana-539	7	27	exceeds	exceed	VERB
cana-539	7	28	the	the	DET
cana-539	7	29	ow	ow	PROPN
cana-539	7	30	's	's	PART
cana-539	7	31	storage	storage	NOUN
cana-539	7	32	limit	limit	NOUN
cana-539	7	33	.	.	PUNCT
cana-539	8	1	the	the	DET
cana-539	8	2	stock	stock	NOUN
cana-539	8	3	in	in	ADP
cana-539	8	4	rw	rw	PROPN
cana-539	8	5	is	be	AUX
cana-539	8	6	consumed	consume	VERB
cana-539	8	7	first	first	ADV
cana-539	8	8	,	,	PUNCT
cana-539	8	9	followed	follow	VERB
cana-539	8	10	by	by	ADP
cana-539	8	11	the	the	DET
cana-539	8	12	stock	stock	NOUN
cana-539	8	13	in	in	ADP
cana-539	8	14	ow	ow	PROPN
cana-539	8	15	,	,	PUNCT
cana-539	8	16	as	as	SCONJ
cana-539	8	17	the	the	DET
cana-539	8	18	cost	cost	NOUN
cana-539	8	19	of	of	ADP
cana-539	8	20	holding	holding	NOUN
cana-539	8	21	of	of	ADP
cana-539	8	22	the	the	DET
cana-539	8	23	rented	rent	VERB
cana-539	8	24	warehouse	warehouse	NOUN
cana-539	8	25	(	(	PUNCT
cana-539	8	26	rw	rw	NOUN
cana-539	8	27	)	)	PUNCT
cana-539	8	28	is	be	AUX
cana-539	8	29	more	more	ADJ
cana-539	8	30	than	than	ADP
cana-539	8	31	that	that	PRON
cana-539	8	32	of	of	ADP
cana-539	8	33	the	the	DET
cana-539	8	34	owned	own	VERB
cana-539	8	35	warehouse	warehouse	NOUN
cana-539	8	36	(	(	PUNCT
cana-539	8	37	ow	ow	INTJ
cana-539	8	38	)	)	PUNCT
cana-539	8	39	.	.	PUNCT
cana-539	9	1	this	this	DET
cana-539	9	2	paper	paper	NOUN
cana-539	9	3	does	do	AUX
cana-539	9	4	not	not	PART
cana-539	9	5	allow	allow	VERB
cana-539	9	6	for	for	ADP
cana-539	9	7	shortages	shortage	NOUN
cana-539	9	8	.	.	PUNCT
cana-539	10	1	we	we	PRON
cana-539	10	2	use	use	VERB
cana-539	10	3	numerical	numerical	ADJ
cana-539	10	4	simulations	simulation	NOUN
cana-539	10	5	to	to	PART
cana-539	10	6	illustrate	illustrate	VERB
cana-539	10	7	the	the	DET
cana-539	10	8	effectiveness	effectiveness	NOUN
cana-539	10	9	of	of	ADP
cana-539	10	10	our	our	PRON
cana-539	10	11	proposed	propose	VERB
cana-539	10	12	model	model	NOUN
cana-539	10	13	under	under	ADP
cana-539	10	14	various	various	ADJ
cana-539	10	15	parameters	parameter	NOUN
cana-539	10	16	.	.	PUNCT
cana-539	11	1	keywords	keyword	NOUN
cana-539	11	2	:	:	PUNCT
cana-539	11	3	inventory	inventory	NOUN
cana-539	11	4	system	system	NOUN
cana-539	11	5	,	,	PUNCT
cana-539	11	6	preservation	preservation	NOUN
cana-539	11	7	technique	technique	NOUN
cana-539	11	8	,	,	PUNCT
cana-539	11	9	rented	rent	VERB
cana-539	11	10	warehouse	warehouse	NOUN
cana-539	11	11	,	,	PUNCT
cana-539	11	12	timedependent	timedependent	NOUN
cana-539	11	13	demand	demand	NOUN
cana-539	11	14	.	.	PUNCT
cana-539	12	1	1	1	X
cana-539	12	2	.	.	X
cana-539	12	3	introduction	introduction	NOUN
cana-539	12	4	to	to	PART
cana-539	12	5	keep	keep	VERB
cana-539	12	6	long	long	ADJ
cana-539	12	7	-	-	PUNCT
cana-539	12	8	term	term	NOUN
cana-539	12	9	relationships	relationship	NOUN
cana-539	12	10	with	with	ADP
cana-539	12	11	clients	client	NOUN
cana-539	12	12	,	,	PUNCT
cana-539	12	13	every	every	DET
cana-539	12	14	firm	firm	NOUN
cana-539	12	15	keeps	keep	VERB
cana-539	12	16	things	thing	NOUN
cana-539	12	17	in	in	ADP
cana-539	12	18	storage	storage	NOUN
cana-539	12	19	.	.	PUNCT
cana-539	13	1	stock	stock	NOUN
cana-539	13	2	exceeding	exceed	VERB
cana-539	13	3	the	the	DET
cana-539	13	4	owned	own	VERB
cana-539	13	5	warehouse	warehouse	NOUN
cana-539	13	6	's	's	PART
cana-539	13	7	storage	storage	NOUN
cana-539	13	8	space	space	NOUN
cana-539	13	9	,	,	PUNCT
cana-539	13	10	which	which	PRON
cana-539	13	11	is	be	AUX
cana-539	13	12	only	only	ADV
cana-539	13	13	capable	capable	ADJ
cana-539	13	14	of	of	ADP
cana-539	13	15	holding	hold	VERB
cana-539	13	16	a	a	DET
cana-539	13	17	particular	particular	ADJ
cana-539	13	18	amount	amount	NOUN
cana-539	13	19	of	of	ADP
cana-539	13	20	inventory	inventory	NOUN
cana-539	13	21	,	,	PUNCT
cana-539	13	22	is	be	AUX
cana-539	13	23	a	a	DET
cana-539	13	24	common	common	ADJ
cana-539	13	25	problem	problem	NOUN
cana-539	13	26	.	.	PUNCT
cana-539	14	1	in	in	ADP
cana-539	14	2	this	this	DET
cana-539	14	3	case	case	NOUN
cana-539	14	4	,	,	PUNCT
cana-539	14	5	the	the	DET
cana-539	14	6	company	company	NOUN
cana-539	14	7	pays	pay	VERB
cana-539	14	8	a	a	DET
cana-539	14	9	high	high	ADJ
cana-539	14	10	storage	storage	NOUN
cana-539	14	11	cost	cost	NOUN
cana-539	14	12	to	to	PART
cana-539	14	13	rent	rent	VERB
cana-539	14	14	a	a	DET
cana-539	14	15	warehouse	warehouse	NOUN
cana-539	14	16	due	due	ADP
cana-539	14	17	to	to	ADP
cana-539	14	18	good	good	ADJ
cana-539	14	19	preservation	preservation	NOUN
cana-539	14	20	techniques	technique	NOUN
cana-539	14	21	in	in	ADP
cana-539	14	22	the	the	DET
cana-539	14	23	rented	rent	VERB
cana-539	14	24	warehouse	warehouse	NOUN
cana-539	14	25	.	.	PUNCT
cana-539	15	1	the	the	DET
cana-539	15	2	twowarehouse	twowarehouse	NOUN
cana-539	15	3	inventory	inventory	NOUN
cana-539	15	4	model	model	NOUN
cana-539	15	5	is	be	AUX
cana-539	15	6	a	a	DET
cana-539	15	7	well	well	ADV
cana-539	15	8	-	-	PUNCT
cana-539	15	9	established	establish	VERB
cana-539	15	10	approach	approach	NOUN
cana-539	15	11	for	for	ADP
cana-539	15	12	managing	manage	VERB
cana-539	15	13	inventory	inventory	NOUN
cana-539	15	14	in	in	ADP
cana-539	15	15	such	such	ADJ
cana-539	15	16	environments	environment	NOUN
cana-539	15	17	,	,	PUNCT
cana-539	15	18	where	where	SCONJ
cana-539	15	19	one	one	NUM
cana-539	15	20	warehouse	warehouse	NOUN
cana-539	15	21	serves	serve	VERB
cana-539	15	22	as	as	ADP
cana-539	15	23	a	a	DET
cana-539	15	24	regular	regular	ADJ
cana-539	15	25	storage	storage	NOUN
cana-539	15	26	facility	facility	NOUN
cana-539	15	27	while	while	SCONJ
cana-539	15	28	the	the	DET
cana-539	15	29	other	other	ADJ
cana-539	15	30	acts	act	VERB
cana-539	15	31	as	as	ADP
cana-539	15	32	a	a	DET
cana-539	15	33	backup	backup	NOUN
cana-539	15	34	or	or	CCONJ
cana-539	15	35	emergency	emergency	NOUN
cana-539	15	36	storage	storage	NOUN
cana-539	15	37	.	.	PUNCT
cana-539	16	1	in	in	ADP
cana-539	16	2	real	real	ADJ
cana-539	16	3	-	-	PUNCT
cana-539	16	4	world	world	NOUN
cana-539	16	5	scenarios	scenario	NOUN
cana-539	16	6	,	,	PUNCT
cana-539	16	7	demand	demand	NOUN
cana-539	16	8	for	for	ADP
cana-539	16	9	several	several	ADJ
cana-539	16	10	products	product	NOUN
cana-539	16	11	is	be	AUX
cana-539	16	12	not	not	PART
cana-539	16	13	constant	constant	ADJ
cana-539	16	14	but	but	CCONJ
cana-539	16	15	changes	change	NOUN
cana-539	16	16	over	over	ADP
cana-539	16	17	time	time	NOUN
cana-539	16	18	due	due	ADP
cana-539	16	19	to	to	ADP
cana-539	16	20	aspects	aspect	NOUN
cana-539	16	21	like	like	ADP
cana-539	16	22	seasonality	seasonality	NOUN
cana-539	16	23	,	,	PUNCT
cana-539	16	24	promotions	promotion	NOUN
cana-539	16	25	and	and	CCONJ
cana-539	16	26	consumer	consumer	NOUN
cana-539	16	27	preferences	preference	NOUN
cana-539	16	28	.	.	PUNCT
cana-539	17	1	before	before	ADP
cana-539	17	2	storing	store	VERB
cana-539	17	3	the	the	DET
cana-539	17	4	units	unit	NOUN
cana-539	17	5	in	in	ADP
cana-539	17	6	the	the	DET
cana-539	17	7	rented	rent	VERB
cana-539	17	8	warehouse	warehouse	NOUN
cana-539	17	9	,	,	PUNCT
cana-539	17	10	it	it	PRON
cana-539	17	11	is	be	AUX
cana-539	17	12	reasonable	reasonable	ADJ
cana-539	17	13	to	to	PART
cana-539	17	14	keep	keep	VERB
cana-539	17	15	the	the	DET
cana-539	17	16	units	unit	NOUN
cana-539	17	17	in	in	ADP
cana-539	17	18	the	the	DET
cana-539	17	19	owned	own	VERB
cana-539	17	20	warehouse	warehouse	NOUN
cana-539	17	21	first	first	ADV
cana-539	17	22	as	as	SCONJ
cana-539	17	23	the	the	DET
cana-539	17	24	cost	cost	NOUN
cana-539	17	25	of	of	ADP
cana-539	17	26	holding	holding	NOUN
cana-539	17	27	of	of	ADP
cana-539	17	28	rented	rent	VERB
cana-539	17	29	warehouse	warehouse	NOUN
cana-539	17	30	is	be	AUX
cana-539	17	31	comparatively	comparatively	ADV
cana-539	17	32	greater	great	ADJ
cana-539	17	33	than	than	ADP
cana-539	17	34	the	the	DET
cana-539	17	35	cost	cost	NOUN
cana-539	17	36	of	of	ADP
cana-539	17	37	holding	holding	NOUN
cana-539	17	38	of	of	ADP
cana-539	17	39	owned	own	VERB
cana-539	17	40	warehouse	warehouse	NOUN
cana-539	17	41	,	,	PUNCT
cana-539	17	42	which	which	PRON
cana-539	17	43	results	result	VERB
cana-539	17	44	in	in	ADP
cana-539	17	45	reduction	reduction	NOUN
cana-539	17	46	of	of	ADP
cana-539	17	47	inventory	inventory	NOUN
cana-539	17	48	cost	cost	NOUN
cana-539	17	49	.	.	PUNCT
cana-539	18	1	for	for	ADP
cana-539	18	2	deteriorating	deteriorate	VERB
cana-539	18	3	items	item	NOUN
cana-539	18	4	,	,	PUNCT
cana-539	18	5	hartley	hartley	PROPN
cana-539	19	1	[	[	X
cana-539	19	2	1	1	NUM
cana-539	19	3	]	]	PUNCT
cana-539	19	4	&	&	CCONJ
cana-539	19	5	sarma	sarma	PROPN
cana-539	19	6	[	[	X
cana-539	19	7	2	2	NUM
cana-539	19	8	]	]	PUNCT
cana-539	19	9	initiated	initiate	VERB
cana-539	19	10	to	to	PART
cana-539	19	11	introduce	introduce	VERB
cana-539	19	12	the	the	DET
cana-539	19	13	idea	idea	NOUN
cana-539	19	14	of	of	ADP
cana-539	19	15	model	model	NOUN
cana-539	19	16	for	for	ADP
cana-539	19	17	two	two	NUM
cana-539	19	18	-	-	PUNCT
cana-539	19	19	warehouse	warehouse	NOUN
cana-539	19	20	.	.	PUNCT
cana-539	20	1	singh	singh	PROPN
cana-539	20	2	&	&	CCONJ
cana-539	20	3	rathore	rathore	PROPN
cana-539	21	1	[	[	X
cana-539	21	2	3	3	NUM
cana-539	21	3	]	]	PUNCT
cana-539	21	4	,	,	PUNCT
cana-539	21	5	kumar	kumar	PROPN
cana-539	21	6	et	et	PROPN
cana-539	21	7	al	al	PROPN
cana-539	21	8	.	.	PUNCT
cana-539	22	1	[	[	X
cana-539	22	2	4	4	NUM
cana-539	22	3	]	]	PUNCT
cana-539	22	4	,	,	PUNCT
cana-539	22	5	singh	singh	PROPN
cana-539	22	6	&	&	CCONJ
cana-539	22	7	rathore	rathore	PROPN
cana-539	23	1	[	[	X
cana-539	23	2	5	5	NUM
cana-539	23	3	]	]	PUNCT
cana-539	23	4	,	,	PUNCT
cana-539	23	5	sharma	sharma	PROPN
cana-539	23	6	&	&	CCONJ
cana-539	23	7	chaudhary	chaudhary	PROPN
cana-539	24	1	[	[	X
cana-539	24	2	6	6	NUM
cana-539	24	3	]	]	PUNCT
cana-539	24	4	,	,	PUNCT
cana-539	24	5	agrawal	agrawal	PROPN
cana-539	24	6	&	&	CCONJ
cana-539	24	7	banerjee	banerjee	PROPN
cana-539	25	1	[	[	X
cana-539	25	2	7	7	NUM
cana-539	25	3	]	]	PUNCT
cana-539	25	4	and	and	CCONJ
cana-539	25	5	singh	singh	PROPN
cana-539	25	6	et	et	PROPN
cana-539	25	7	al	al	PROPN
cana-539	25	8	.	.	PUNCT
cana-539	26	1	[	[	X
cana-539	26	2	8	8	NUM
cana-539	26	3	]	]	PUNCT
cana-539	26	4	considered	consider	VERB
cana-539	26	5	the	the	DET
cana-539	26	6	two	two	NUM
cana-539	26	7	-	-	PUNCT
cana-539	26	8	warehouse	warehouse	NOUN
cana-539	26	9	issue	issue	NOUN
cana-539	26	10	having	have	VERB
cana-539	26	11	shortages	shortage	NOUN
cana-539	26	12	&	&	CCONJ
cana-539	26	13	backlogging	backlogging	NOUN
cana-539	26	14	.	.	PUNCT
cana-539	27	1	zhou	zhou	PROPN
cana-539	27	2	&	&	CCONJ
cana-539	27	3	yang	yang	PROPN
cana-539	28	1	[	[	X
cana-539	28	2	9	9	NUM
cana-539	28	3	]	]	PUNCT
cana-539	28	4	examined	examine	VERB
cana-539	28	5	the	the	DET
cana-539	28	6	two	two	NUM
cana-539	28	7	-	-	PUNCT
cana-539	28	8	warehouse	warehouse	NOUN
cana-539	28	9	issue	issue	NOUN
cana-539	28	10	communications	communication	NOUN
cana-539	28	11	on	on	ADP
cana-539	28	12	applied	apply	VERB
cana-539	28	13	nonlinear	nonlinear	ADJ
cana-539	28	14	analysis	analysis	NOUN
cana-539	28	15	issn	issn	NOUN
cana-539	28	16	:	:	PUNCT
cana-539	28	17	1074	1074	NUM
cana-539	28	18	-	-	PUNCT
cana-539	28	19	133x	133x	NUM
cana-539	28	20	vol	vol	NOUN
cana-539	28	21	31	31	NUM
cana-539	28	22	no	no	NOUN
cana-539	28	23	.	.	NOUN
cana-539	28	24	2	2	NUM
cana-539	28	25	(	(	PUNCT
cana-539	28	26	2024	2024	NUM
cana-539	28	27	)	)	PUNCT
cana-539	28	28	241	241	NUM
cana-539	28	29	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	28	30	for	for	ADP
cana-539	28	31	demand	demand	NOUN
cana-539	28	32	as	as	ADP
cana-539	28	33	stock	stock	NOUN
cana-539	28	34	dependent	dependent	ADJ
cana-539	28	35	.	.	PUNCT
cana-539	29	1	gupta	gupta	NOUN
cana-539	29	2	et	et	PROPN
cana-539	29	3	al	al	PROPN
cana-539	29	4	.	.	PUNCT
cana-539	30	1	[	[	X
cana-539	30	2	10	10	NUM
cana-539	30	3	,	,	PUNCT
cana-539	30	4	11	11	NUM
cana-539	30	5	]	]	PUNCT
cana-539	30	6	conducted	conduct	VERB
cana-539	30	7	an	an	DET
cana-539	30	8	investigation	investigation	NOUN
cana-539	30	9	on	on	ADP
cana-539	30	10	applications	application	NOUN
cana-539	30	11	of	of	ADP
cana-539	30	12	warehouse	warehouse	NOUN
cana-539	30	13	and	and	CCONJ
cana-539	30	14	supply	supply	VERB
cana-539	30	15	chain	chain	NOUN
cana-539	30	16	management	management	NOUN
cana-539	30	17	.	.	PUNCT
cana-539	31	1	saxena	saxena	PROPN
cana-539	32	1	[	[	X
cana-539	32	2	12	12	NUM
cana-539	32	3	,	,	PUNCT
cana-539	32	4	13	13	NUM
cana-539	32	5	]	]	PUNCT
cana-539	32	6	also	also	ADV
cana-539	32	7	evaluated	evaluate	VERB
cana-539	32	8	the	the	DET
cana-539	32	9	eoq	eoq	NOUN
cana-539	32	10	models	model	NOUN
cana-539	32	11	for	for	ADP
cana-539	32	12	degrading	degrade	VERB
cana-539	32	13	items	item	NOUN
cana-539	32	14	.	.	PUNCT
cana-539	33	1	rastogi	rastogi	ADV
cana-539	33	2	et	et	PROPN
cana-539	33	3	al	al	PROPN
cana-539	33	4	.	.	PUNCT
cana-539	34	1	[	[	X
cana-539	34	2	14	14	NUM
cana-539	34	3	]	]	PUNCT
cana-539	34	4	presented	present	VERB
cana-539	34	5	a	a	DET
cana-539	34	6	model	model	NOUN
cana-539	34	7	for	for	ADP
cana-539	34	8	dual	dual	ADJ
cana-539	34	9	-	-	PUNCT
cana-539	34	10	warehouse	warehouse	NOUN
cana-539	34	11	incorporating	incorporate	VERB
cana-539	34	12	price	price	NOUN
cana-539	34	13	-	-	PUNCT
cana-539	34	14	sensitive	sensitive	ADJ
cana-539	34	15	demand	demand	NOUN
cana-539	34	16	with	with	ADP
cana-539	34	17	decaying	decay	VERB
cana-539	34	18	characteristics	characteristic	NOUN
cana-539	34	19	.	.	PUNCT
cana-539	35	1	mandal	mandal	PROPN
cana-539	35	2	&	&	CCONJ
cana-539	35	3	phaujdar	phaujdar	PROPN
cana-539	36	1	[	[	X
cana-539	36	2	15	15	NUM
cana-539	36	3	]	]	PUNCT
cana-539	36	4	also	also	ADV
cana-539	36	5	worked	work	VERB
cana-539	36	6	on	on	ADP
cana-539	36	7	dual	dual	ADJ
cana-539	36	8	warehouse	warehouse	NOUN
cana-539	36	9	having	have	VERB
cana-539	36	10	stock	stock	NOUN
cana-539	36	11	-	-	PUNCT
cana-539	36	12	dependent	dependent	ADJ
cana-539	36	13	demand	demand	NOUN
cana-539	36	14	.	.	PUNCT
cana-539	37	1	technology	technology	NOUN
cana-539	37	2	for	for	ADP
cana-539	37	3	product	product	NOUN
cana-539	37	4	preservation	preservation	NOUN
cana-539	37	5	is	be	AUX
cana-539	37	6	becoming	become	VERB
cana-539	37	7	increasingly	increasingly	ADV
cana-539	37	8	crucial	crucial	ADJ
cana-539	37	9	and	and	CCONJ
cana-539	37	10	necessary	necessary	ADJ
cana-539	37	11	because	because	SCONJ
cana-539	37	12	of	of	ADP
cana-539	37	13	environment	environment	NOUN
cana-539	37	14	's	's	PART
cana-539	37	15	continuous	continuous	ADJ
cana-539	37	16	changes	change	NOUN
cana-539	37	17	.	.	PUNCT
cana-539	38	1	the	the	DET
cana-539	38	2	rate	rate	NOUN
cana-539	38	3	of	of	ADP
cana-539	38	4	deterioration	deterioration	NOUN
cana-539	38	5	can	can	AUX
cana-539	38	6	be	be	AUX
cana-539	38	7	reduced	reduce	VERB
cana-539	38	8	to	to	ADP
cana-539	38	9	a	a	DET
cana-539	38	10	definite	definite	ADJ
cana-539	38	11	extent	extent	NOUN
cana-539	38	12	by	by	ADP
cana-539	38	13	using	use	VERB
cana-539	38	14	safety	safety	NOUN
cana-539	38	15	techniques	technique	NOUN
cana-539	38	16	and	and	CCONJ
cana-539	38	17	some	some	DET
cana-539	38	18	procedural	procedural	ADJ
cana-539	38	19	changes	change	NOUN
cana-539	38	20	.	.	PUNCT
cana-539	39	1	in	in	ADP
cana-539	39	2	this	this	DET
cana-539	39	3	study	study	NOUN
cana-539	39	4	,	,	PUNCT
cana-539	39	5	we	we	PRON
cana-539	39	6	have	have	AUX
cana-539	39	7	formed	form	VERB
cana-539	39	8	an	an	DET
cana-539	39	9	inventory	inventory	NOUN
cana-539	39	10	control	control	NOUN
cana-539	39	11	model	model	NOUN
cana-539	39	12	for	for	ADP
cana-539	39	13	two	two	NUM
cana-539	39	14	-	-	PUNCT
cana-539	39	15	warehouse	warehouse	NOUN
cana-539	39	16	having	have	VERB
cana-539	39	17	deteriorating	deteriorate	VERB
cana-539	39	18	items	item	NOUN
cana-539	39	19	by	by	ADP
cana-539	39	20	considering	consider	VERB
cana-539	39	21	the	the	DET
cana-539	39	22	facilities	facility	NOUN
cana-539	39	23	of	of	ADP
cana-539	39	24	preservation	preservation	NOUN
cana-539	39	25	.	.	PUNCT
cana-539	40	1	firstly	firstly	ADV
cana-539	40	2	,	,	PUNCT
cana-539	40	3	the	the	DET
cana-539	40	4	items	item	NOUN
cana-539	40	5	are	be	AUX
cana-539	40	6	consumed	consume	VERB
cana-539	40	7	from	from	ADP
cana-539	40	8	rented	rent	VERB
cana-539	40	9	warehouse	warehouse	NOUN
cana-539	40	10	and	and	CCONJ
cana-539	40	11	then	then	ADV
cana-539	40	12	consumed	consume	VERB
cana-539	40	13	from	from	ADP
cana-539	40	14	owned	own	VERB
cana-539	40	15	warehouse	warehouse	NOUN
cana-539	40	16	owing	owe	VERB
cana-539	40	17	to	to	ADP
cana-539	40	18	the	the	DET
cana-539	40	19	higher	high	ADJ
cana-539	40	20	holding	hold	VERB
cana-539	40	21	cost	cost	NOUN
cana-539	40	22	of	of	ADP
cana-539	40	23	rw	rw	NOUN
cana-539	40	24	than	than	ADP
cana-539	40	25	owned	own	VERB
cana-539	40	26	warehouse	warehouse	NOUN
cana-539	40	27	.	.	PUNCT
cana-539	41	1	the	the	DET
cana-539	41	2	demand	demand	NOUN
cana-539	41	3	’s	’s	PART
cana-539	41	4	rate	rate	NOUN
cana-539	41	5	is	be	AUX
cana-539	41	6	taken	take	VERB
cana-539	41	7	as	as	ADP
cana-539	41	8	time	time	NOUN
cana-539	41	9	dependent	dependent	ADJ
cana-539	41	10	.	.	PUNCT
cana-539	42	1	however	however	ADV
cana-539	42	2	,	,	PUNCT
cana-539	42	3	shortages	shortage	NOUN
cana-539	42	4	are	be	AUX
cana-539	42	5	n’t	not	PART
cana-539	42	6	allowed	allow	VERB
cana-539	42	7	.	.	PUNCT
cana-539	43	1	we	we	PRON
cana-539	43	2	have	have	AUX
cana-539	43	3	also	also	ADV
cana-539	43	4	considered	consider	VERB
cana-539	43	5	a	a	DET
cana-539	43	6	linear	linear	ADJ
cana-539	43	7	function	function	NOUN
cana-539	43	8	of	of	ADP
cana-539	43	9	demand	demand	NOUN
cana-539	43	10	.	.	PUNCT
cana-539	44	1	the	the	DET
cana-539	44	2	primary	primary	ADJ
cana-539	44	3	focus	focus	NOUN
cana-539	44	4	of	of	ADP
cana-539	44	5	formulation	formulation	NOUN
cana-539	44	6	of	of	ADP
cana-539	44	7	this	this	DET
cana-539	44	8	model	model	NOUN
cana-539	44	9	aims	aim	VERB
cana-539	44	10	to	to	PART
cana-539	44	11	reduce	reduce	VERB
cana-539	44	12	the	the	DET
cana-539	44	13	total	total	ADJ
cana-539	44	14	inventory	inventory	NOUN
cana-539	44	15	cost	cost	NOUN
cana-539	44	16	.	.	PUNCT
cana-539	45	1	in	in	ADP
cana-539	45	2	the	the	DET
cana-539	45	3	final	final	ADJ
cana-539	45	4	,	,	PUNCT
cana-539	45	5	numerical	numerical	ADJ
cana-539	45	6	case	case	NOUN
cana-539	45	7	is	be	AUX
cana-539	45	8	given	give	VERB
cana-539	45	9	to	to	PART
cana-539	45	10	verify	verify	VERB
cana-539	45	11	the	the	DET
cana-539	45	12	model	model	NOUN
cana-539	45	13	.	.	PUNCT
cana-539	46	1	2	2	X
cana-539	46	2	.	.	NUM
cana-539	46	3	notations	notation	NOUN
cana-539	46	4	z	z	X
cana-539	46	5	(	(	PUNCT
cana-539	46	6	i(t	i(t	PROPN
cana-539	46	7	)	)	PUNCT
cana-539	46	8	):	):	PUNCT
cana-539	46	9	instantaneous	instantaneous	ADJ
cana-539	46	10	time	time	NOUN
cana-539	46	11	dependent	dependent	ADJ
cana-539	46	12	rate	rate	NOUN
cana-539	46	13	of	of	ADP
cana-539	46	14	demand	demand	NOUN
cana-539	46	15	;	;	PUNCT
cana-539	46	16	q	q	X
cana-539	46	17	:	:	PUNCT
cana-539	46	18	quantity	quantity	NOUN
cana-539	46	19	of	of	ADP
cana-539	46	20	order	order	NOUN
cana-539	46	21	;	;	PUNCT
cana-539	46	22	𝛳	𝛳	ADJ
cana-539	46	23	:	:	PUNCT
cana-539	46	24	constant	constant	ADJ
cana-539	46	25	rate	rate	NOUN
cana-539	46	26	of	of	ADP
cana-539	46	27	deterioration	deterioration	NOUN
cana-539	46	28	;	;	PUNCT
cana-539	46	29	m(𝜉	m(𝜉	PROPN
cana-539	46	30	):	):	PUNCT
cana-539	46	31	(=	(=	X
cana-539	46	32	(	(	PUNCT
cana-539	46	33	1	1	NUM
cana-539	46	34	-	-	PUNCT
cana-539	46	35	e	e	NOUN
cana-539	46	36	-	-	NOUN
cana-539	46	37	a𝜉	a𝜉	NOUN
cana-539	46	38	)	)	PUNCT
cana-539	46	39	)	)	PUNCT
cana-539	46	40	reduction	reduction	NOUN
cana-539	46	41	in	in	ADP
cana-539	46	42	deterioration	deterioration	NOUN
cana-539	46	43	rate	rate	NOUN
cana-539	46	44	𝜉>0	𝜉>0	PROPN
cana-539	46	45	;	;	PUNCT
cana-539	46	46	𝜎𝛳	𝜎𝛳	ADJ
cana-539	46	47	:	:	PUNCT
cana-539	46	48	aggregate	aggregate	ADJ
cana-539	46	49	rate	rate	NOUN
cana-539	46	50	of	of	ADP
cana-539	46	51	deterioration	deterioration	NOUN
cana-539	46	52	𝜎	𝜎	PROPN
cana-539	47	1	=	=	PUNCT
cana-539	47	2	(	(	PUNCT
cana-539	47	3	𝛳m	𝛳m	PROPN
cana-539	47	4	(	(	PUNCT
cana-539	47	5	𝜉	𝜉	NOUN
cana-539	47	6	)	)	PUNCT
cana-539	47	7	)	)	PUNCT
cana-539	47	8	;	;	PUNCT
cana-539	47	9	o	o	X
cana-539	47	10	:	:	PUNCT
cana-539	47	11	cost	cost	NOUN
cana-539	47	12	of	of	ADP
cana-539	47	13	ordering	ordering	NOUN
cana-539	47	14	;	;	PUNCT
cana-539	47	15	h1	h1	NOUN
cana-539	47	16	:	:	PUNCT
cana-539	47	17	cost	cost	NOUN
cana-539	47	18	of	of	ADP
cana-539	47	19	holding	hold	VERB
cana-539	47	20	of	of	ADP
cana-539	47	21	rented	rent	VERB
cana-539	47	22	warehouse	warehouse	NOUN
cana-539	47	23	(	(	PUNCT
cana-539	47	24	rw	rw	NOUN
cana-539	47	25	)	)	PUNCT
cana-539	47	26	;	;	PUNCT
cana-539	47	27	h2	h2	NOUN
cana-539	47	28	:	:	PUNCT
cana-539	47	29	cost	cost	NOUN
cana-539	47	30	of	of	ADP
cana-539	47	31	holding	holding	NOUN
cana-539	47	32	of	of	ADP
cana-539	47	33	owned	own	VERB
cana-539	47	34	warehouse	warehouse	NOUN
cana-539	47	35	(	(	PUNCT
cana-539	47	36	ow	ow	PROPN
cana-539	47	37	)	)	PUNCT
cana-539	47	38	;	;	PUNCT
cana-539	47	39	x	x	X
cana-539	47	40	:	:	PUNCT
cana-539	47	41	cost	cost	NOUN
cana-539	47	42	of	of	ADP
cana-539	47	43	unit	unit	NOUN
cana-539	47	44	purchasing	purchasing	NOUN
cana-539	47	45	;	;	PUNCT
cana-539	47	46	so	so	ADV
cana-539	47	47	:	:	PUNCT
cana-539	47	48	amount	amount	NOUN
cana-539	47	49	of	of	ADP
cana-539	47	50	inventory	inventory	NOUN
cana-539	47	51	in	in	ADP
cana-539	47	52	own	own	ADJ
cana-539	47	53	warehouse	warehouse	NOUN
cana-539	47	54	;	;	PUNCT
cana-539	47	55	s1	s1	NOUN
cana-539	47	56	:	:	PUNCT
cana-539	47	57	amount	amount	NOUN
cana-539	47	58	of	of	ADP
cana-539	47	59	inventory	inventory	NOUN
cana-539	47	60	in	in	ADP
cana-539	47	61	rented	rent	VERB
cana-539	47	62	warehouse	warehouse	NOUN
cana-539	47	63	;	;	PUNCT
cana-539	47	64	tr	tr	VERB
cana-539	47	65	:	:	PUNCT
cana-539	47	66	the	the	DET
cana-539	47	67	period	period	NOUN
cana-539	47	68	of	of	ADP
cana-539	47	69	time	time	NOUN
cana-539	47	70	in	in	ADP
cana-539	47	71	which	which	PRON
cana-539	47	72	rw	rw	NOUN
cana-539	47	73	inventory	inventory	NOUN
cana-539	47	74	level	level	NOUN
cana-539	47	75	drops	drop	VERB
cana-539	47	76	to	to	ADP
cana-539	47	77	zero	zero	NUM
cana-539	47	78	;	;	PUNCT
cana-539	47	79	to	to	PART
cana-539	47	80	:	:	PUNCT
cana-539	47	81	the	the	DET
cana-539	47	82	period	period	NOUN
cana-539	47	83	of	of	ADP
cana-539	47	84	time	time	NOUN
cana-539	47	85	in	in	ADP
cana-539	47	86	which	which	PRON
cana-539	47	87	ow	ow	INTJ
cana-539	47	88	inventory	inventory	NOUN
cana-539	47	89	level	level	NOUN
cana-539	47	90	drops	drop	VERB
cana-539	47	91	to	to	ADP
cana-539	47	92	zero	zero	NUM
cana-539	47	93	;	;	PUNCT
cana-539	47	94	t	t	NUM
cana-539	47	95	:	:	PUNCT
cana-539	47	96	cycle	cycle	NOUN
cana-539	47	97	length	length	NOUN
cana-539	47	98	;	;	PUNCT
cana-539	47	99	i1(t	i1(t	PROPN
cana-539	47	100	):	):	PUNCT
cana-539	47	101	stock	stock	NOUN
cana-539	47	102	level	level	NOUN
cana-539	47	103	in	in	ADP
cana-539	47	104	rw	rw	NOUN
cana-539	47	105	during	during	ADP
cana-539	47	106	[	[	X
cana-539	47	107	0	0	NUM
cana-539	47	108	,	,	PUNCT
cana-539	47	109	tr	tr	VERB
cana-539	47	110	]	]	PUNCT
cana-539	47	111	;	;	PUNCT
cana-539	47	112	i2(t	i2(t	PROPN
cana-539	47	113	):	):	PUNCT
cana-539	47	114	stock	stock	NOUN
cana-539	47	115	level	level	NOUN
cana-539	47	116	in	in	ADP
cana-539	47	117	ow	ow	INTJ
cana-539	47	118	during	during	ADP
cana-539	47	119	[	[	X
cana-539	47	120	0	0	NUM
cana-539	47	121	,	,	PUNCT
cana-539	47	122	tr	tr	VERB
cana-539	47	123	]	]	PUNCT
cana-539	47	124	;	;	PUNCT
cana-539	47	125	i3(t	i3(t	NUM
cana-539	47	126	):	):	PUNCT
cana-539	47	127	stock	stock	NOUN
cana-539	47	128	level	level	NOUN
cana-539	47	129	in	in	ADP
cana-539	47	130	ow	ow	INTJ
cana-539	47	131	during	during	ADP
cana-539	47	132	[	[	X
cana-539	47	133	tr	tr	VERB
cana-539	47	134	,	,	PUNCT
cana-539	47	135	to	to	ADP
cana-539	47	136	]	]	PUNCT
cana-539	47	137	;	;	PUNCT
cana-539	47	138	trc	trc	PROPN
cana-539	47	139	:	:	PUNCT
cana-539	47	140	total	total	ADJ
cana-539	47	141	relevant	relevant	ADJ
cana-539	47	142	cost	cost	NOUN
cana-539	47	143	;	;	PUNCT
cana-539	47	144	communications	communication	NOUN
cana-539	47	145	on	on	ADP
cana-539	47	146	applied	apply	VERB
cana-539	47	147	nonlinear	nonlinear	ADJ
cana-539	47	148	analysis	analysis	NOUN
cana-539	47	149	issn	issn	NOUN
cana-539	47	150	:	:	PUNCT
cana-539	47	151	1074	1074	NUM
cana-539	47	152	-	-	PUNCT
cana-539	47	153	133x	133x	NUM
cana-539	47	154	vol	vol	NOUN
cana-539	47	155	31	31	NUM
cana-539	47	156	no	no	NOUN
cana-539	47	157	.	.	NOUN
cana-539	47	158	2	2	NUM
cana-539	47	159	(	(	PUNCT
cana-539	47	160	2024	2024	NUM
cana-539	47	161	)	)	PUNCT
cana-539	47	162	242	242	NUM
cana-539	47	163	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	47	164	pc	pc	NOUN
cana-539	47	165	:	:	PUNCT
cana-539	47	166	purchasing	purchase	VERB
cana-539	47	167	cost	cost	NOUN
cana-539	47	168	;	;	PUNCT
cana-539	47	169	hc	hc	X
cana-539	47	170	:	:	PUNCT
cana-539	47	171	holding	hold	VERB
cana-539	47	172	cost	cost	NOUN
cana-539	47	173	;	;	PUNCT
cana-539	47	174	3	3	X
cana-539	47	175	.	.	NOUN
cana-539	47	176	assumptions	assumption	NOUN
cana-539	47	177	•	•	NUM
cana-539	47	178	rate	rate	NOUN
cana-539	47	179	of	of	ADP
cana-539	47	180	demand	demand	NOUN
cana-539	47	181	is	be	AUX
cana-539	47	182	time	time	NOUN
cana-539	47	183	dependent	dependent	ADJ
cana-539	47	184	&	&	CCONJ
cana-539	47	185	taken	take	VERB
cana-539	47	186	as	as	ADP
cana-539	47	187	𝑍(𝐼(𝑡	𝑍(𝐼(𝑡	PROPN
cana-539	47	188	)	)	PUNCT
cana-539	47	189	)	)	PUNCT
cana-539	48	1	=	=	PUNCT
cana-539	49	1	𝑎	𝑎	X
cana-539	49	2	+	+	NOUN
cana-539	49	3	𝑏𝑡	𝑏𝑡	NOUN
cana-539	49	4	•	•	NOUN
cana-539	49	5	no	no	DET
cana-539	49	6	shortages	shortage	NOUN
cana-539	49	7	are	be	AUX
cana-539	49	8	allowed	allow	VERB
cana-539	49	9	.	.	PUNCT
cana-539	50	1	•	•	NUM
cana-539	50	2	time	time	NOUN
cana-539	50	3	horizon	horizon	NOUN
cana-539	50	4	is	be	AUX
cana-539	50	5	taken	take	VERB
cana-539	50	6	as	as	ADP
cana-539	50	7	infinite	infinite	ADJ
cana-539	50	8	.	.	PUNCT
cana-539	51	1	•	•	PROPN
cana-539	51	2	preservation	preservation	NOUN
cana-539	51	3	technique	technique	NOUN
cana-539	51	4	is	be	AUX
cana-539	51	5	used	use	VERB
cana-539	51	6	for	for	ADP
cana-539	51	7	reducing	reduce	VERB
cana-539	51	8	deterioration	deterioration	NOUN
cana-539	51	9	.	.	PUNCT
cana-539	52	1	•	•	NUM
cana-539	52	2	lead	lead	NOUN
cana-539	52	3	time	time	NOUN
cana-539	52	4	is	be	AUX
cana-539	52	5	assumed	assume	VERB
cana-539	52	6	as	as	ADP
cana-539	52	7	zero	zero	NUM
cana-539	52	8	and	and	CCONJ
cana-539	52	9	replenishment	replenishment	NOUN
cana-539	52	10	rate	rate	NOUN
cana-539	52	11	is	be	AUX
cana-539	52	12	taken	take	VERB
cana-539	52	13	infinite	infinite	NOUN
cana-539	52	14	.	.	PUNCT
cana-539	53	1	•	•	NUM
cana-539	53	2	the	the	DET
cana-539	53	3	owned	own	VERB
cana-539	53	4	warehouse	warehouse	NOUN
cana-539	53	5	(	(	PUNCT
cana-539	53	6	ow	ow	INTJ
cana-539	53	7	)	)	PUNCT
cana-539	53	8	has	have	VERB
cana-539	53	9	only	only	ADV
cana-539	53	10	w2	w2	NOUN
cana-539	53	11	units	unit	NOUN
cana-539	53	12	of	of	ADP
cana-539	53	13	space	space	NOUN
cana-539	53	14	,	,	PUNCT
cana-539	53	15	and	and	CCONJ
cana-539	53	16	unlimited	unlimited	ADJ
cana-539	53	17	amount	amount	NOUN
cana-539	53	18	of	of	ADP
cana-539	53	19	space	space	NOUN
cana-539	53	20	in	in	ADP
cana-539	53	21	rented	rent	VERB
cana-539	53	22	warehouse	warehouse	NOUN
cana-539	53	23	.	.	PUNCT
cana-539	54	1	•	•	NUM
cana-539	54	2	because	because	SCONJ
cana-539	54	3	the	the	DET
cana-539	54	4	amount	amount	NOUN
cana-539	54	5	of	of	ADP
cana-539	54	6	holding	holding	NOUN
cana-539	54	7	(	(	PUNCT
cana-539	54	8	h1	h1	PROPN
cana-539	54	9	)	)	PUNCT
cana-539	54	10	of	of	ADP
cana-539	54	11	rw	rw	NOUN
cana-539	54	12	is	be	AUX
cana-539	54	13	greater	great	ADJ
cana-539	54	14	than	than	ADP
cana-539	54	15	cost	cost	NOUN
cana-539	54	16	of	of	ADP
cana-539	54	17	holding	hold	VERB
cana-539	54	18	(	(	PUNCT
cana-539	54	19	h2	h2	NOUN
cana-539	54	20	)	)	PUNCT
cana-539	54	21	of	of	ADP
cana-539	54	22	ow	ow	PROPN
cana-539	54	23	,	,	PUNCT
cana-539	54	24	utilization	utilization	NOUN
cana-539	54	25	of	of	ADP
cana-539	54	26	inventory	inventory	NOUN
cana-539	54	27	in	in	ADP
cana-539	54	28	ow	ow	INTJ
cana-539	54	29	begins	begin	VERB
cana-539	54	30	only	only	ADV
cana-539	54	31	when	when	SCONJ
cana-539	54	32	the	the	DET
cana-539	54	33	inventory	inventory	NOUN
cana-539	54	34	in	in	ADP
cana-539	54	35	rw	rw	PROPN
cana-539	54	36	reaches	reach	VERB
cana-539	54	37	zero	zero	NUM
cana-539	54	38	.	.	PUNCT
cana-539	55	1	•	•	NUM
cana-539	55	2	the	the	DET
cana-539	55	3	price	price	NOUN
cana-539	55	4	of	of	ADP
cana-539	55	5	transportation	transportation	NOUN
cana-539	55	6	and	and	CCONJ
cana-539	55	7	time	time	NOUN
cana-539	55	8	for	for	ADP
cana-539	55	9	both	both	CCONJ
cana-539	55	10	rw	rw	NOUN
cana-539	55	11	and	and	CCONJ
cana-539	55	12	ow	ow	INTJ
cana-539	55	13	are	be	AUX
cana-539	55	14	lesser	less	ADJ
cana-539	55	15	.	.	PUNCT
cana-539	56	1	4	4	X
cana-539	56	2	.	.	X
cana-539	56	3	formulation	formulation	NOUN
cana-539	56	4	of	of	ADP
cana-539	56	5	mathematical	mathematical	ADJ
cana-539	56	6	model	model	NOUN
cana-539	56	7	the	the	DET
cana-539	56	8	inventory	inventory	NOUN
cana-539	56	9	is	be	AUX
cana-539	56	10	s	s	NOUN
cana-539	56	11	at	at	ADP
cana-539	56	12	t	t	NOUN
cana-539	56	13	=	=	SYM
cana-539	56	14	0	0	NUM
cana-539	56	15	,	,	PUNCT
cana-539	56	16	with	with	SCONJ
cana-539	56	17	s2	s2	NOUN
cana-539	56	18	units	unit	NOUN
cana-539	56	19	kept	keep	VERB
cana-539	56	20	in	in	ADP
cana-539	56	21	ow	ow	PROPN
cana-539	56	22	&	&	CCONJ
cana-539	56	23	rest	rest	NOUN
cana-539	56	24	of	of	ADP
cana-539	56	25	s1	s1	PROPN
cana-539	56	26	units	unit	NOUN
cana-539	56	27	kept	keep	VERB
cana-539	56	28	in	in	ADP
cana-539	56	29	rw	rw	NOUN
cana-539	56	30	.	.	PUNCT
cana-539	57	1	because	because	SCONJ
cana-539	57	2	of	of	ADP
cana-539	57	3	demand	demand	NOUN
cana-539	57	4	&	&	CCONJ
cana-539	57	5	deterioration	deterioration	NOUN
cana-539	57	6	the	the	DET
cana-539	57	7	inventory	inventory	NOUN
cana-539	57	8	of	of	ADP
cana-539	57	9	rented	rent	VERB
cana-539	57	10	warehouse	warehouse	NOUN
cana-539	57	11	decreases	decrease	VERB
cana-539	57	12	in	in	ADP
cana-539	57	13	the	the	DET
cana-539	57	14	interval	interval	NOUN
cana-539	57	15	[	[	X
cana-539	57	16	o	o	X
cana-539	57	17	,	,	PUNCT
cana-539	57	18	tr	tr	VERB
cana-539	57	19	]	]	PUNCT
cana-539	57	20	and	and	CCONJ
cana-539	57	21	become	become	VERB
cana-539	57	22	zero	zero	NUM
cana-539	57	23	at	at	ADP
cana-539	57	24	t	t	NOUN
cana-539	57	25	=	=	PUNCT
cana-539	57	26	tr	tr	VERB
cana-539	57	27	.	.	VERB
cana-539	57	28	after	after	ADP
cana-539	57	29	time	time	NOUN
cana-539	57	30	tr	tr	VERB
cana-539	57	31	,	,	PUNCT
cana-539	57	32	the	the	DET
cana-539	57	33	demand	demand	NOUN
cana-539	57	34	for	for	ADP
cana-539	57	35	items	item	NOUN
cana-539	57	36	is	be	AUX
cana-539	57	37	met	meet	VERB
cana-539	57	38	by	by	ADP
cana-539	57	39	using	use	VERB
cana-539	57	40	ow	ow	INTJ
cana-539	57	41	inventory	inventory	NOUN
cana-539	57	42	at	at	ADP
cana-539	57	43	[	[	X
cana-539	57	44	tr	tr	VERB
cana-539	57	45	;	;	PUNCT
cana-539	57	46	to	to	ADP
cana-539	57	47	]	]	PUNCT
cana-539	57	48	.	.	PUNCT
cana-539	58	1	the	the	DET
cana-539	58	2	depletion	depletion	NOUN
cana-539	58	3	in	in	ADP
cana-539	58	4	level	level	NOUN
cana-539	58	5	of	of	ADP
cana-539	58	6	inventory	inventory	NOUN
cana-539	58	7	in	in	ADP
cana-539	58	8	rented	rent	VERB
cana-539	58	9	warehouse	warehouse	NOUN
cana-539	58	10	is	be	AUX
cana-539	58	11	defined	define	VERB
cana-539	58	12	via	via	ADP
cana-539	58	13	the	the	DET
cana-539	58	14	equation	equation	NOUN
cana-539	58	15	:	:	PUNCT
cana-539	58	16	𝑑(𝐼1(𝑡	𝑑(𝐼1(𝑡	NUM
cana-539	58	17	)	)	PUNCT
cana-539	58	18	)	)	PUNCT
cana-539	58	19	𝑑𝑡	𝑑𝑡	ADP
cana-539	58	20	+	+	NUM
cana-539	58	21	𝜎𝛳𝐼1(𝑡	𝜎𝛳𝐼1(𝑡	NOUN
cana-539	58	22	)	)	PUNCT
cana-539	58	23	=	=	SYM
cana-539	58	24	−(𝑎	−(𝑎	NOUN
cana-539	58	25	+	+	CCONJ
cana-539	58	26	𝑏𝑡	𝑏𝑡	NOUN
cana-539	58	27	)	)	PUNCT
cana-539	58	28	;	;	PUNCT
cana-539	58	29	0	0	NUM
cana-539	58	30	≤	≤	NUM
cana-539	58	31	𝑡	𝑡	PROPN
cana-539	58	32	≤	≤	NOUN
cana-539	58	33	𝑡𝑟	𝑡𝑟	NOUN
cana-539	58	34	(	(	PUNCT
cana-539	58	35	1	1	NUM
cana-539	58	36	)	)	PUNCT
cana-539	58	37	and	and	CCONJ
cana-539	58	38	working	work	VERB
cana-539	58	39	of	of	ADP
cana-539	58	40	inventory	inventory	NOUN
cana-539	58	41	in	in	ADP
cana-539	58	42	owned	own	VERB
cana-539	58	43	warehouse	warehouse	NOUN
cana-539	58	44	is	be	AUX
cana-539	58	45	give	give	VERB
cana-539	58	46	as	as	SCONJ
cana-539	58	47	follows	follow	VERB
cana-539	58	48	:	:	PUNCT
cana-539	58	49	𝑑(𝐼2(𝑡	𝑑(𝐼2(𝑡	X
cana-539	58	50	)	)	PUNCT
cana-539	58	51	)	)	PUNCT
cana-539	58	52	𝑑𝑡	𝑑𝑡	ADP
cana-539	58	53	+	+	ADJ
cana-539	58	54	𝜎𝜃𝐼2(𝑡	𝜎𝜃𝐼2(𝑡	NOUN
cana-539	58	55	)	)	PUNCT
cana-539	58	56	=	=	SYM
cana-539	58	57	0	0	NUM
cana-539	58	58	;	;	PUNCT
cana-539	58	59	0	0	NUM
cana-539	58	60	≤	≤	NUM
cana-539	58	61	𝑡	𝑡	PROPN
cana-539	58	62	≤	≤	NOUN
cana-539	58	63	𝑡𝑟	𝑡𝑟	NOUN
cana-539	58	64	(	(	PUNCT
cana-539	58	65	2	2	NUM
cana-539	58	66	)	)	PUNCT
cana-539	58	67	𝑑(𝐼3(𝑡	𝑑(𝐼3(𝑡	PROPN
cana-539	58	68	)	)	PUNCT
cana-539	58	69	)	)	PUNCT
cana-539	58	70	𝑑𝑡	𝑑𝑡	ADP
cana-539	58	71	+	+	ADJ
cana-539	58	72	𝜎𝜃𝐼3(𝑡	𝜎𝜃𝐼3(𝑡	PROPN
cana-539	58	73	)	)	PUNCT
cana-539	59	1	=	=	SYM
cana-539	59	2	−(𝑎	−(𝑎	NOUN
cana-539	59	3	+	+	CCONJ
cana-539	59	4	𝑏𝑡	𝑏𝑡	NOUN
cana-539	59	5	)	)	PUNCT
cana-539	59	6	;	;	PUNCT
cana-539	59	7	𝑡𝑟	𝑡𝑟	VERB
cana-539	59	8	≤	≤	NUM
cana-539	59	9	𝑡	𝑡	PROPN
cana-539	59	10	≤	≤	NOUN
cana-539	59	11	𝑡𝑜	𝑡𝑜	PROPN
cana-539	59	12	(	(	PUNCT
cana-539	59	13	3	3	X
cana-539	59	14	)	)	PUNCT
cana-539	59	15	now	now	ADV
cana-539	59	16	solving	solve	VERB
cana-539	59	17	the	the	DET
cana-539	59	18	equation	equation	NOUN
cana-539	59	19	(	(	PUNCT
cana-539	59	20	1	1	NUM
cana-539	59	21	)	)	PUNCT
cana-539	59	22	,	,	PUNCT
cana-539	59	23	(	(	PUNCT
cana-539	59	24	2	2	X
cana-539	59	25	)	)	PUNCT
cana-539	59	26	&	&	CCONJ
cana-539	59	27	(	(	PUNCT
cana-539	59	28	3	3	NUM
cana-539	59	29	)	)	PUNCT
cana-539	59	30	,	,	PUNCT
cana-539	59	31	we	we	PRON
cana-539	59	32	get	get	VERB
cana-539	59	33	𝐼1	𝐼1	ADJ
cana-539	59	34	=	=	NOUN
cana-539	59	35	−	−	PROPN
cana-539	60	1	𝑎	𝑎	DET
cana-539	60	2	𝜎𝜃	𝜎𝜃	NOUN
cana-539	60	3	−	−	PROPN
cana-539	60	4	𝑏𝑡	𝑏𝑡	NOUN
cana-539	60	5	𝜎𝜃	𝜎𝜃	NOUN
cana-539	60	6	+	+	CCONJ
cana-539	60	7	𝑏	𝑏	PROPN
cana-539	60	8	𝜎𝜃	𝜎𝜃	ADJ
cana-539	60	9	2	2	NUM
cana-539	60	10	+	+	NOUN
cana-539	60	11	𝑐1𝑒	𝑐1𝑒	NOUN
cana-539	60	12	−𝜎𝜃𝑡	−𝜎𝜃𝑡	NOUN
cana-539	60	13	(	(	PUNCT
cana-539	60	14	4	4	X
cana-539	60	15	)	)	PUNCT
cana-539	60	16	𝐼2	𝐼2	NOUN
cana-539	60	17	=	=	SYM
cana-539	60	18	𝑒−𝜎𝜃𝑡𝑐2	𝑒−𝜎𝜃𝑡𝑐2	PROPN
cana-539	60	19	(	(	PUNCT
cana-539	60	20	5	5	NUM
cana-539	60	21	)	)	PUNCT
cana-539	60	22	𝐼3	𝐼3	NOUN
cana-539	60	23	=	=	PUNCT
cana-539	60	24	−	−	PROPN
cana-539	60	25	𝑎	𝑎	DET
cana-539	60	26	𝜎𝜃	𝜎𝜃	NOUN
cana-539	60	27	−	−	PROPN
cana-539	60	28	𝑏𝑡	𝑏𝑡	NOUN
cana-539	60	29	𝜎𝜃	𝜎𝜃	NOUN
cana-539	60	30	+	+	CCONJ
cana-539	61	1	𝑏	𝑏	PROPN
cana-539	61	2	𝜎𝜃	𝜎𝜃	ADJ
cana-539	61	3	2	2	NUM
cana-539	61	4	+	+	CCONJ
cana-539	61	5	𝑐3𝑒	𝑐3𝑒	NOUN
cana-539	61	6	−𝜎𝜃𝑡	−𝜎𝜃𝑡	NOUN
cana-539	61	7	(	(	PUNCT
cana-539	61	8	6	6	NUM
cana-539	61	9	)	)	PUNCT
cana-539	61	10	now	now	ADV
cana-539	61	11	using	use	VERB
cana-539	61	12	the	the	DET
cana-539	61	13	boundary	boundary	ADJ
cana-539	61	14	conditions	condition	NOUN
cana-539	61	15	,	,	PUNCT
cana-539	61	16	𝐼1(𝑡	𝐼1(𝑡	X
cana-539	61	17	=	=	SYM
cana-539	61	18	0	0	NUM
cana-539	61	19	)	)	PUNCT
cana-539	61	20	=	=	NOUN
cana-539	61	21	𝑆1	𝑆1	NOUN
cana-539	61	22	,	,	PUNCT
cana-539	61	23	𝐼1(𝑡	𝐼1(𝑡	X
cana-539	61	24	=	=	SYM
cana-539	61	25	𝑡𝑟	𝑡𝑟	PROPN
cana-539	61	26	)	)	PUNCT
cana-539	61	27	=	=	SYM
cana-539	61	28	0	0	NUM
cana-539	61	29	,	,	PUNCT
cana-539	61	30	𝐼2(𝑡	𝐼2(𝑡	PUNCT
cana-539	61	31	=	=	PUNCT
cana-539	61	32	0	0	X
cana-539	61	33	)	)	PUNCT
cana-539	61	34	=	=	SYM
cana-539	61	35	𝑆2	𝑆2	PROPN
cana-539	61	36	,	,	PUNCT
cana-539	61	37	𝐼2(𝑡	𝐼2(𝑡	PUNCT
cana-539	61	38	=	=	PRON
cana-539	61	39	𝑡𝑟	𝑡𝑟	PROPN
cana-539	61	40	)	)	PUNCT
cana-539	61	41	=	=	SYM
cana-539	61	42	𝐼3(𝑡	𝐼3(𝑡	PROPN
cana-539	61	43	=	=	SYM
cana-539	61	44	𝑡𝑟	𝑡𝑟	PROPN
cana-539	61	45	)	)	PUNCT
cana-539	61	46	,	,	PUNCT
cana-539	61	47	𝐼3(𝑡	𝐼3(𝑡	PROPN
cana-539	61	48	=	=	PUNCT
cana-539	62	1	𝑡𝑜	𝑡𝑜	PROPN
cana-539	62	2	=	=	PUNCT
cana-539	62	3	𝑇	𝑇	PROPN
cana-539	62	4	)	)	PUNCT
cana-539	62	5	=	=	SYM
cana-539	62	6	0	0	NUM
cana-539	62	7	communications	communication	NOUN
cana-539	62	8	on	on	ADP
cana-539	62	9	applied	apply	VERB
cana-539	62	10	nonlinear	nonlinear	ADJ
cana-539	62	11	analysis	analysis	NOUN
cana-539	62	12	issn	issn	NOUN
cana-539	62	13	:	:	PUNCT
cana-539	62	14	1074	1074	NUM
cana-539	62	15	-	-	PUNCT
cana-539	62	16	133x	133x	NUM
cana-539	62	17	vol	vol	NOUN
cana-539	62	18	31	31	NUM
cana-539	62	19	no	no	NOUN
cana-539	62	20	.	.	NOUN
cana-539	62	21	2	2	NUM
cana-539	62	22	(	(	PUNCT
cana-539	62	23	2024	2024	NUM
cana-539	62	24	)	)	PUNCT
cana-539	62	25	243	243	NUM
cana-539	62	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	62	27	𝐼1	𝐼1	NOUN
cana-539	62	28	=	=	SYM
cana-539	62	29	𝑆1𝑒	𝑆1𝑒	NOUN
cana-539	62	30	−𝜎𝜃𝑡	−𝜎𝜃𝑡	NOUN
cana-539	63	1	+	+	CCONJ
cana-539	63	2	𝑎	𝑎	PRON
cana-539	63	3	𝜎𝜃	𝜎𝜃	NOUN
cana-539	63	4	(	(	PUNCT
cana-539	63	5	𝑒−𝜎𝜃𝑡	𝑒−𝜎𝜃𝑡	NOUN
cana-539	63	6	−	−	PROPN
cana-539	63	7	1	1	NUM
cana-539	63	8	)	)	PUNCT
cana-539	63	9	−	−	NOUN
cana-539	64	1	𝑏	𝑏	PROPN
cana-539	64	2	𝜎𝜃	𝜎𝜃	NOUN
cana-539	64	3	2	2	NUM
cana-539	64	4	(	(	PUNCT
cana-539	64	5	𝑒−𝜎𝜃𝑡	𝑒−𝜎𝜃𝑡	NOUN
cana-539	64	6	−	−	PROPN
cana-539	64	7	1	1	NUM
cana-539	64	8	)	)	PUNCT
cana-539	64	9	−	−	PROPN
cana-539	64	10	𝑏𝑡	𝑏𝑡	INTJ
cana-539	64	11	𝜎𝜃	𝜎𝜃	NOUN
cana-539	64	12	(	(	PUNCT
cana-539	64	13	7	7	X
cana-539	64	14	)	)	PUNCT
cana-539	64	15	𝐼2	𝐼2	NOUN
cana-539	64	16	=	=	SYM
cana-539	64	17	𝑒−𝜎𝜃𝑡𝑆2	𝑒−𝜎𝜃𝑡𝑆2	PROPN
cana-539	64	18	(	(	PUNCT
cana-539	64	19	8)	8)	NUM
cana-539	64	20	𝐼3	𝐼3	NOUN
cana-539	64	21	=	=	PUNCT
cana-539	64	22	−	−	PROPN
cana-539	64	23	𝑎	𝑎	DET
cana-539	64	24	𝜎𝜃	𝜎𝜃	NOUN
cana-539	64	25	−	−	PROPN
cana-539	64	26	𝑏𝑡	𝑏𝑡	NOUN
cana-539	64	27	𝜎𝜃	𝜎𝜃	NOUN
cana-539	64	28	+	+	CCONJ
cana-539	64	29	𝑏	𝑏	PROPN
cana-539	64	30	𝜎𝜃	𝜎𝜃	ADJ
cana-539	64	31	2	2	NUM
cana-539	64	32	+	+	CCONJ
cana-539	64	33	𝑆2𝑒	𝑆2𝑒	PROPN
cana-539	64	34	−𝜎𝜃𝑡	−𝜎𝜃𝑡	NOUN
cana-539	64	35	+	+	CCONJ
cana-539	64	36	𝑒−𝜎𝜃(𝑡+𝑡𝑟	𝑒−𝜎𝜃(𝑡+𝑡𝑟	NOUN
cana-539	64	37	)	)	PUNCT
cana-539	64	38	[	[	PUNCT
cana-539	64	39	𝑎	𝑎	NOUN
cana-539	64	40	𝜎𝜃	𝜎𝜃	NOUN
cana-539	64	41	+	+	CCONJ
cana-539	64	42	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	64	43	𝜎𝜃	𝜎𝜃	NOUN
cana-539	64	44	−	−	NOUN
cana-539	64	45	𝑏	𝑏	PROPN
cana-539	64	46	𝜎𝜃	𝜎𝜃	NOUN
cana-539	64	47	2	2	NUM
cana-539	64	48	]	]	PUNCT
cana-539	64	49	(	(	PUNCT
cana-539	64	50	9	9	X
cana-539	64	51	)	)	PUNCT
cana-539	64	52	𝑆1	𝑆1	NOUN
cana-539	64	53	=	=	PUNCT
cana-539	65	1	[	[	X
cana-539	65	2	−	−	X
cana-539	65	3	𝑎	𝑎	NOUN
cana-539	65	4	𝜎𝜃	𝜎𝜃	NOUN
cana-539	65	5	+	+	CCONJ
cana-539	65	6	𝑏	𝑏	NOUN
cana-539	65	7	𝜎𝜃	𝜎𝜃	NOUN
cana-539	65	8	2	2	NUM
cana-539	65	9	]	]	PUNCT
cana-539	65	10	(	(	PUNCT
cana-539	65	11	1	1	NUM
cana-539	65	12	−	−	PROPN
cana-539	65	13	𝑒𝜎𝜃𝑡𝑟	𝑒𝜎𝜃𝑡𝑟	NOUN
cana-539	65	14	)	)	PUNCT
cana-539	66	1	+	+	CCONJ
cana-539	66	2	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	66	3	𝜎𝜃	𝜎𝜃	PROPN
cana-539	66	4	𝑒𝜎𝜃𝑡𝑟	𝑒𝜎𝜃𝑡𝑟	NOUN
cana-539	66	5	(	(	PUNCT
cana-539	66	6	10	10	NUM
cana-539	66	7	)	)	PUNCT
cana-539	66	8	𝑆2	𝑆2	NOUN
cana-539	66	9	=	=	PUNCT
cana-539	66	10	𝑒𝜎𝜃𝑇	𝑒𝜎𝜃𝑇	NOUN
cana-539	66	11	[	[	PUNCT
cana-539	66	12	𝑎	𝑎	NOUN
cana-539	66	13	𝜎𝜃	𝜎𝜃	NOUN
cana-539	66	14	+	+	CCONJ
cana-539	66	15	𝑏𝑇	𝑏𝑇	NOUN
cana-539	66	16	𝜎𝜃	𝜎𝜃	NOUN
cana-539	66	17	−	−	PROPN
cana-539	66	18	𝑏	𝑏	PROPN
cana-539	66	19	𝜎𝜃	𝜎𝜃	NOUN
cana-539	66	20	2	2	NUM
cana-539	66	21	]	]	PUNCT
cana-539	66	22	−	−	PROPN
cana-539	66	23	𝑒𝜎𝜃𝑡𝑟	𝑒𝜎𝜃𝑡𝑟	NOUN
cana-539	66	24	[	[	PUNCT
cana-539	66	25	𝑎	𝑎	NOUN
cana-539	66	26	𝜎𝜃	𝜎𝜃	NOUN
cana-539	66	27	+	+	CCONJ
cana-539	66	28	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	66	29	𝜎𝜃	𝜎𝜃	NOUN
cana-539	66	30	−	−	NOUN
cana-539	66	31	𝑏	𝑏	PROPN
cana-539	66	32	𝜎𝜃	𝜎𝜃	NOUN
cana-539	66	33	2	2	NUM
cana-539	66	34	]	]	PUNCT
cana-539	66	35	(	(	PUNCT
cana-539	66	36	11	11	NUM
cana-539	66	37	)	)	PUNCT
cana-539	66	38	total	total	ADJ
cana-539	66	39	order	order	NOUN
cana-539	66	40	quantity	quantity	NOUN
cana-539	66	41	𝑞	𝑞	X
cana-539	66	42	=	=	NOUN
cana-539	66	43	𝑆1	𝑆1	PROPN
cana-539	66	44	+	+	CCONJ
cana-539	66	45	𝑆2	𝑆2	PROPN
cana-539	66	46	𝑞	𝑞	X
cana-539	66	47	=	=	PUNCT
cana-539	67	1	[	[	X
cana-539	67	2	−	−	X
cana-539	67	3	𝑎	𝑎	NOUN
cana-539	67	4	𝜎𝜃	𝜎𝜃	NOUN
cana-539	67	5	+	+	CCONJ
cana-539	67	6	𝑏	𝑏	NOUN
cana-539	67	7	𝜎𝜃	𝜎𝜃	NOUN
cana-539	67	8	2	2	NUM
cana-539	67	9	]	]	PUNCT
cana-539	67	10	(	(	PUNCT
cana-539	67	11	1	1	NUM
cana-539	67	12	−	−	PROPN
cana-539	67	13	𝑒𝜎𝜃𝑡𝑟	𝑒𝜎𝜃𝑡𝑟	NOUN
cana-539	67	14	)	)	PUNCT
cana-539	68	1	+	+	CCONJ
cana-539	68	2	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	68	3	𝜎𝜃	𝜎𝜃	NOUN
cana-539	68	4	𝑒𝜎𝜃𝑡𝑟	𝑒𝜎𝜃𝑡𝑟	NOUN
cana-539	68	5	+	+	CCONJ
cana-539	68	6	𝑒𝜎𝜃𝑇	𝑒𝜎𝜃𝑇	NOUN
cana-539	68	7	[	[	PUNCT
cana-539	68	8	𝑎	𝑎	NOUN
cana-539	68	9	𝜎𝜃	𝜎𝜃	NOUN
cana-539	68	10	+	+	CCONJ
cana-539	68	11	𝑏𝑇	𝑏𝑇	NOUN
cana-539	68	12	𝜎𝜃	𝜎𝜃	NOUN
cana-539	68	13	−	−	PROPN
cana-539	68	14	𝑏	𝑏	PROPN
cana-539	68	15	𝜎𝜃	𝜎𝜃	NOUN
cana-539	68	16	2	2	NUM
cana-539	68	17	]	]	PUNCT
cana-539	68	18	−	−	PROPN
cana-539	68	19	𝑒𝜎𝜃𝑡𝑟	𝑒𝜎𝜃𝑡𝑟	NOUN
cana-539	68	20	[	[	PUNCT
cana-539	68	21	𝑎	𝑎	NOUN
cana-539	68	22	𝜎𝜃	𝜎𝜃	NOUN
cana-539	68	23	+	+	CCONJ
cana-539	68	24	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	68	25	𝜎𝜃	𝜎𝜃	NOUN
cana-539	68	26	−	−	NOUN
cana-539	68	27	𝑏	𝑏	PROPN
cana-539	68	28	𝜎𝜃	𝜎𝜃	NOUN
cana-539	68	29	2	2	NUM
cana-539	68	30	]	]	PUNCT
cana-539	68	31	(	(	PUNCT
cana-539	68	32	12	12	NUM
cana-539	68	33	)	)	PUNCT
cana-539	68	34	the	the	DET
cana-539	68	35	following	follow	VERB
cana-539	68	36	cost	cost	NOUN
cana-539	68	37	parameters	parameter	NOUN
cana-539	68	38	are	be	AUX
cana-539	68	39	part	part	NOUN
cana-539	68	40	of	of	ADP
cana-539	68	41	the	the	DET
cana-539	68	42	overall	overall	ADJ
cana-539	68	43	relevant	relevant	ADJ
cana-539	68	44	cost	cost	NOUN
cana-539	68	45	:	:	PUNCT
cana-539	68	46	1	1	X
cana-539	68	47	.	.	X
cana-539	68	48	cost	cost	NOUN
cana-539	68	49	of	of	ADP
cana-539	68	50	ordering	order	VERB
cana-539	68	51	𝑂c	𝑂c	PROPN
cana-539	68	52	=	=	PUNCT
cana-539	69	1	𝑂𝑐	𝑂𝑐	PRON
cana-539	69	2	2	2	NUM
cana-539	69	3	.	.	PUNCT
cana-539	69	4	the	the	DET
cana-539	69	5	amount	amount	NOUN
cana-539	69	6	of	of	ADP
cana-539	69	7	carrying	carry	VERB
cana-539	69	8	cost	cost	NOUN
cana-539	69	9	is	be	AUX
cana-539	69	10	obtained	obtain	VERB
cana-539	69	11	by	by	ADP
cana-539	69	12	:	:	PUNCT
cana-539	69	13	𝐻𝐶	𝐻𝐶	PROPN
cana-539	69	14	=	=	PUNCT
cana-539	69	15	𝐻1	𝐻1	NOUN
cana-539	69	16	[	[	X
cana-539	69	17	∫	∫	X
cana-539	69	18	𝐼1	𝐼1	X
cana-539	69	19	𝑡𝑟	𝑡𝑟	PROPN
cana-539	69	20	0	0	NUM
cana-539	69	21	(	(	PUNCT
cana-539	69	22	𝑡)𝑑𝑡	𝑡)𝑑𝑡	PROPN
cana-539	69	23	]	]	X
cana-539	69	24	+	+	CCONJ
cana-539	69	25	𝐻2	𝐻2	ADJ
cana-539	69	26	[	[	X
cana-539	69	27	∫	∫	X
cana-539	69	28	𝐼2(𝑡)𝑑𝑡	𝐼2(𝑡)𝑑𝑡	NOUN
cana-539	69	29	𝑡𝑟	𝑡𝑟	PROPN
cana-539	69	30	0	0	NUM
cana-539	70	1	+	+	CCONJ
cana-539	70	2	∫	∫	PROPN
cana-539	70	3	𝐼3(𝑡	𝐼3(𝑡	PROPN
cana-539	70	4	)	)	PUNCT
cana-539	70	5	𝑇	𝑇	PROPN
cana-539	70	6	𝑡𝑟	𝑡𝑟	VERB
cana-539	70	7	𝑑𝑡	𝑑𝑡	ADP
cana-539	70	8	]	]	PUNCT
cana-539	70	9	𝐻𝐶	𝐻𝐶	PROPN
cana-539	70	10	=	=	PUNCT
cana-539	70	11	𝐻1	𝐻1	NOUN
cana-539	71	1	[	[	X
cana-539	71	2	(	(	PUNCT
cana-539	71	3	1	1	NUM
cana-539	71	4	−	−	NUM
cana-539	71	5	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NUM
cana-539	71	6	)	)	PUNCT
cana-539	71	7	[	[	PUNCT
cana-539	71	8	𝑆1	𝑆1	NOUN
cana-539	71	9	𝜎𝜃	𝜎𝜃	NOUN
cana-539	71	10	+	+	CCONJ
cana-539	71	11	𝑎	𝑎	PRON
cana-539	71	12	𝜎𝜃	𝜎𝜃	NOUN
cana-539	71	13	2	2	NUM
cana-539	71	14	−	−	NOUN
cana-539	71	15	𝑏	𝑏	PROPN
cana-539	71	16	𝜎𝜃	𝜎𝜃	NOUN
cana-539	71	17	3	3	NUM
cana-539	71	18	]	]	PUNCT
cana-539	71	19	−	−	PROPN
cana-539	71	20	𝑎𝑡𝑟	𝑎𝑡𝑟	PROPN
cana-539	71	21	𝜎𝜃	𝜎𝜃	PROPN
cana-539	71	22	+	+	CCONJ
cana-539	71	23	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	71	24	𝜎𝜃	𝜎𝜃	PROPN
cana-539	71	25	2	2	NUM
cana-539	71	26	−	−	NOUN
cana-539	71	27	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	71	28	2	2	NUM
cana-539	71	29	2𝜎𝜃	2𝜎𝜃	NOUN
cana-539	71	30	]	]	PUNCT
cana-539	72	1	+	+	CCONJ
cana-539	72	2	𝐻2	𝐻2	ADJ
cana-539	72	3	[	[	X
cana-539	72	4	[	[	PUNCT
cana-539	72	5	𝑆2	𝑆2	ADJ
cana-539	72	6	𝜎𝜃	𝜎𝜃	NOUN
cana-539	72	7	(	(	PUNCT
cana-539	72	8	1	1	NUM
cana-539	72	9	−	−	NUM
cana-539	72	10	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NOUN
cana-539	72	11	)	)	PUNCT
cana-539	72	12	]	]	PUNCT
cana-539	73	1	+	+	CCONJ
cana-539	73	2	𝑎	𝑎	DET
cana-539	73	3	𝜎𝜃	𝜎𝜃	NOUN
cana-539	73	4	(	(	PUNCT
cana-539	73	5	𝑡𝑟	𝑡𝑟	VERB
cana-539	73	6	−	−	PROPN
cana-539	73	7	𝑇	𝑇	PROPN
cana-539	73	8	)	)	PUNCT
cana-539	73	9	+	+	NOUN
cana-539	73	10	𝑏	𝑏	PRON
cana-539	73	11	2𝜎𝜃	2𝜎𝜃	ADJ
cana-539	73	12	(	(	PUNCT
cana-539	73	13	𝑡𝑟	𝑡𝑟	VERB
cana-539	73	14	2	2	NUM
cana-539	73	15	−	−	PROPN
cana-539	73	16	𝑇2	𝑇2	NOUN
cana-539	73	17	)	)	PUNCT
cana-539	73	18	−	−	NOUN
cana-539	74	1	𝑏	𝑏	NUM
cana-539	74	2	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	3	2	2	NUM
cana-539	74	4	(	(	PUNCT
cana-539	74	5	𝑡𝑟	𝑡𝑟	VERB
cana-539	74	6	−	−	PROPN
cana-539	74	7	𝑇	𝑇	PROPN
cana-539	74	8	)	)	PUNCT
cana-539	74	9	+	+	CCONJ
cana-539	74	10	𝑆2	𝑆2	PROPN
cana-539	74	11	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	12	(	(	PUNCT
cana-539	74	13	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	X
cana-539	74	14	−	−	NOUN
cana-539	74	15	𝑒−𝜎𝜃𝑇	𝑒−𝜎𝜃𝑇	NOUN
cana-539	74	16	)	)	PUNCT
cana-539	74	17	+	+	CCONJ
cana-539	74	18	[	[	PUNCT
cana-539	74	19	𝑎	𝑎	X
cana-539	74	20	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	21	2	2	NUM
cana-539	74	22	+	+	CCONJ
cana-539	74	23	𝑏𝑇	𝑏𝑇	NOUN
cana-539	74	24	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	25	2	2	NUM
cana-539	74	26	−	−	NOUN
cana-539	74	27	𝑏	𝑏	PROPN
cana-539	74	28	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	29	3	3	NUM
cana-539	74	30	]	]	PUNCT
cana-539	74	31	(	(	PUNCT
cana-539	74	32	𝑒−𝜎𝜃(𝑡𝑟+𝑇	𝑒−𝜎𝜃(𝑡𝑟+𝑇	PROPN
cana-539	74	33	)	)	PUNCT
cana-539	74	34	−	−	PROPN
cana-539	74	35	𝑒−2𝜎𝜃𝑇)](13	𝑒−2𝜎𝜃𝑇)](13	NOUN
cana-539	74	36	)	)	PUNCT
cana-539	74	37	now	now	ADV
cana-539	74	38	,	,	PUNCT
cana-539	74	39	the	the	DET
cana-539	74	40	complete	complete	ADJ
cana-539	74	41	relevant	relevant	ADJ
cana-539	74	42	cost	cost	NOUN
cana-539	74	43	is	be	AUX
cana-539	74	44	given	give	VERB
cana-539	74	45	by	by	ADP
cana-539	74	46	:	:	PUNCT
cana-539	74	47	𝑇𝑅𝐶	𝑇𝑅𝐶	NOUN
cana-539	74	48	=	=	SYM
cana-539	74	49	1	1	NUM
cana-539	74	50	𝑇	𝑇	NOUN
cana-539	74	51	[	[	X
cana-539	74	52	𝑂𝐶	𝑂𝐶	PROPN
cana-539	74	53	+	+	CCONJ
cana-539	74	54	𝐻𝐶	𝐻𝐶	PROPN
cana-539	74	55	]	]	X
cana-539	74	56	𝑇𝑅𝐶	𝑇𝑅𝐶	NOUN
cana-539	74	57	=	=	SYM
cana-539	74	58	1	1	NUM
cana-539	74	59	𝑇	𝑇	NOUN
cana-539	74	60	[	[	X
cana-539	74	61	o	o	X
cana-539	74	62	+	+	X
cana-539	74	63	𝐻1	𝐻1	NOUN
cana-539	74	64	[	[	X
cana-539	74	65	(	(	PUNCT
cana-539	74	66	1	1	NUM
cana-539	74	67	−	−	NUM
cana-539	74	68	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NUM
cana-539	74	69	)	)	PUNCT
cana-539	74	70	[	[	PUNCT
cana-539	74	71	𝑆1	𝑆1	NOUN
cana-539	74	72	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	73	+	+	CCONJ
cana-539	74	74	𝑎	𝑎	DET
cana-539	74	75	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	76	2	2	NUM
cana-539	74	77	−	−	NOUN
cana-539	74	78	𝑏	𝑏	PROPN
cana-539	74	79	𝜎𝜃	𝜎𝜃	NOUN
cana-539	74	80	3	3	NUM
cana-539	74	81	]	]	PUNCT
cana-539	74	82	−	−	PROPN
cana-539	74	83	𝑎𝑡𝑟	𝑎𝑡𝑟	PROPN
cana-539	74	84	𝜎𝜃	𝜎𝜃	PROPN
cana-539	74	85	+	+	CCONJ
cana-539	74	86	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	74	87	𝜎𝜃	𝜎𝜃	PROPN
cana-539	74	88	2	2	NUM
cana-539	74	89	−	−	NOUN
cana-539	74	90	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	74	91	2	2	NUM
cana-539	74	92	2𝜎𝜃	2𝜎𝜃	NOUN
cana-539	74	93	]	]	PUNCT
cana-539	75	1	+	+	CCONJ
cana-539	75	2	𝐻2	𝐻2	ADJ
cana-539	75	3	[	[	X
cana-539	75	4	[	[	PUNCT
cana-539	75	5	𝑆2	𝑆2	ADJ
cana-539	75	6	𝜎𝜃	𝜎𝜃	NOUN
cana-539	75	7	(	(	PUNCT
cana-539	75	8	1	1	NUM
cana-539	75	9	−	−	NUM
cana-539	75	10	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NOUN
cana-539	75	11	)	)	PUNCT
cana-539	75	12	]	]	PUNCT
cana-539	76	1	+	+	CCONJ
cana-539	76	2	𝑎	𝑎	DET
cana-539	76	3	𝜎𝜃	𝜎𝜃	NOUN
cana-539	76	4	(	(	PUNCT
cana-539	76	5	𝑡𝑟	𝑡𝑟	VERB
cana-539	76	6	−	−	PROPN
cana-539	76	7	𝑇	𝑇	PROPN
cana-539	76	8	)	)	PUNCT
cana-539	76	9	+	+	NOUN
cana-539	76	10	𝑏	𝑏	PRON
cana-539	76	11	2𝜎𝜃	2𝜎𝜃	ADJ
cana-539	76	12	(	(	PUNCT
cana-539	76	13	𝑡𝑟	𝑡𝑟	VERB
cana-539	76	14	2	2	NUM
cana-539	76	15	−	−	PROPN
cana-539	76	16	𝑇2	𝑇2	NOUN
cana-539	76	17	)	)	PUNCT
cana-539	76	18	−	−	NOUN
cana-539	77	1	𝑏	𝑏	NUM
cana-539	77	2	𝜎𝜃	𝜎𝜃	NOUN
cana-539	77	3	2	2	NUM
cana-539	77	4	(	(	PUNCT
cana-539	77	5	𝑡𝑟	𝑡𝑟	VERB
cana-539	77	6	−	−	PROPN
cana-539	77	7	𝑇	𝑇	PROPN
cana-539	77	8	)	)	PUNCT
cana-539	77	9	+	+	CCONJ
cana-539	77	10	𝑆2	𝑆2	PROPN
cana-539	77	11	𝜎𝜃	𝜎𝜃	NOUN
cana-539	77	12	(	(	PUNCT
cana-539	77	13	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	X
cana-539	77	14	−	−	NOUN
cana-539	77	15	𝑒−𝜎𝜃𝑇	𝑒−𝜎𝜃𝑇	NOUN
cana-539	77	16	)	)	PUNCT
cana-539	77	17	+	+	CCONJ
cana-539	77	18	[	[	PUNCT
cana-539	77	19	𝑎	𝑎	X
cana-539	77	20	𝜎𝜃	𝜎𝜃	NOUN
cana-539	77	21	2	2	NUM
cana-539	77	22	+	+	CCONJ
cana-539	77	23	𝑏𝑇	𝑏𝑇	NOUN
cana-539	77	24	𝜎𝜃	𝜎𝜃	NOUN
cana-539	77	25	2	2	NUM
cana-539	77	26	−	−	NOUN
cana-539	77	27	𝑏	𝑏	PROPN
cana-539	77	28	𝜎𝜃	𝜎𝜃	NOUN
cana-539	77	29	3	3	NUM
cana-539	77	30	]	]	PUNCT
cana-539	77	31	(	(	PUNCT
cana-539	77	32	𝑒−𝜎𝜃(𝑡𝑟+𝑇	𝑒−𝜎𝜃(𝑡𝑟+𝑇	PROPN
cana-539	77	33	)	)	PUNCT
cana-539	77	34	−	−	PROPN
cana-539	77	35	𝑒−2𝜎𝜃𝑇)]](14	𝑒−2𝜎𝜃𝑇)]](14	NOUN
cana-539	77	36	)	)	PUNCT
cana-539	77	37	next	next	ADV
cana-539	77	38	,	,	PUNCT
cana-539	77	39	we	we	PRON
cana-539	77	40	will	will	AUX
cana-539	77	41	differentiate	differentiate	VERB
cana-539	77	42	the	the	DET
cana-539	77	43	equation	equation	NOUN
cana-539	77	44	(	(	PUNCT
cana-539	77	45	14	14	NUM
cana-539	77	46	)	)	PUNCT
cana-539	77	47	with	with	ADP
cana-539	77	48	respect	respect	NOUN
cana-539	77	49	to	to	ADP
cana-539	77	50	𝑡1	𝑡1	NOUN
cana-539	77	51	,	,	PUNCT
cana-539	77	52	𝜉	𝜉	X
cana-539	77	53	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-539	77	54	𝑇	𝑇	PROPN
cana-539	77	55	,	,	PUNCT
cana-539	77	56	to	to	PART
cana-539	77	57	reduce	reduce	VERB
cana-539	77	58	the	the	DET
cana-539	77	59	overall	overall	ADJ
cana-539	77	60	relevant	relevant	ADJ
cana-539	77	61	cost	cost	NOUN
cana-539	77	62	.	.	PUNCT
cana-539	78	1	required	require	VERB
cana-539	78	2	conditions	condition	NOUN
cana-539	78	3	for	for	ADP
cana-539	78	4	ideal	ideal	ADJ
cana-539	78	5	values	value	NOUN
cana-539	78	6	are	be	AUX
cana-539	78	7	:	:	PUNCT
cana-539	78	8	𝜕𝑇𝑅𝐶(𝑡𝑟	𝜕𝑇𝑅𝐶(𝑡𝑟	NUM
cana-539	78	9	,	,	PUNCT
cana-539	78	10	𝜉	𝜉	X
cana-539	78	11	,	,	PUNCT
cana-539	78	12	𝑇	𝑇	PROPN
cana-539	78	13	)	)	PUNCT
cana-539	78	14	𝜕𝑡𝑟	𝜕𝑡𝑟	PUNCT
cana-539	79	1	=	=	SYM
cana-539	79	2	0	0	NUM
cana-539	79	3	,	,	PUNCT
cana-539	79	4	𝜕𝑇𝑅𝐶(𝑡𝑟	𝜕𝑇𝑅𝐶(𝑡𝑟	X
cana-539	79	5	,	,	PUNCT
cana-539	79	6	𝜉	𝜉	X
cana-539	79	7	,	,	PUNCT
cana-539	79	8	𝑇	𝑇	PROPN
cana-539	79	9	)	)	PUNCT
cana-539	79	10	𝜕𝜉	𝜕𝜉	VERB
cana-539	79	11	=	=	SYM
cana-539	79	12	0	0	NUM
cana-539	79	13	,	,	PUNCT
cana-539	79	14	communications	communication	NOUN
cana-539	79	15	on	on	ADP
cana-539	79	16	applied	apply	VERB
cana-539	79	17	nonlinear	nonlinear	ADJ
cana-539	79	18	analysis	analysis	NOUN
cana-539	79	19	issn	issn	NOUN
cana-539	79	20	:	:	PUNCT
cana-539	79	21	1074	1074	NUM
cana-539	79	22	-	-	PUNCT
cana-539	79	23	133x	133x	NUM
cana-539	79	24	vol	vol	NOUN
cana-539	79	25	31	31	NUM
cana-539	79	26	no	no	NOUN
cana-539	79	27	.	.	NOUN
cana-539	79	28	2	2	NUM
cana-539	79	29	(	(	PUNCT
cana-539	79	30	2024	2024	NUM
cana-539	79	31	)	)	PUNCT
cana-539	79	32	244	244	NUM
cana-539	79	33	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	79	34	𝜕𝑇𝑅𝐶(𝑡𝑟	𝜕𝑇𝑅𝐶(𝑡𝑟	PUNCT
cana-539	79	35	,	,	PUNCT
cana-539	79	36	𝜉	𝜉	X
cana-539	79	37	,	,	PUNCT
cana-539	79	38	𝑇	𝑇	PROPN
cana-539	79	39	)	)	PUNCT
cana-539	79	40	𝜕𝑇	𝜕𝑇	NOUN
cana-539	79	41	=	=	SYM
cana-539	79	42	0	0	NUM
cana-539	79	43	,	,	PUNCT
cana-539	79	44	these	these	DET
cana-539	79	45	values	value	NOUN
cana-539	79	46	give	give	VERB
cana-539	79	47	the	the	DET
cana-539	79	48	determinant	determinant	ADJ
cana-539	79	49	value	value	NOUN
cana-539	79	50	of	of	ADP
cana-539	79	51	principal	principal	ADJ
cana-539	79	52	minor	minor	ADJ
cana-539	79	53	of	of	ADP
cana-539	79	54	hessian	hessian	ADJ
cana-539	79	55	matrix	matrix	NOUN
cana-539	79	56	and	and	CCONJ
cana-539	79	57	det(h1	det(h1	PROPN
cana-539	79	58	)	)	PUNCT
cana-539	79	59	>	>	X
cana-539	79	60	0	0	PROPN
cana-539	79	61	,	,	PUNCT
cana-539	79	62	det(h2	det(h2	NOUN
cana-539	79	63	)	)	PUNCT
cana-539	79	64	>	>	X
cana-539	79	65	0	0	NUM
cana-539	79	66	,	,	PUNCT
cana-539	79	67	det(h3	det(h3	PROPN
cana-539	79	68	)	)	PUNCT
cana-539	79	69	>	>	X
cana-539	79	70	0	0	X
cana-539	79	71	.	.	PUNCT
cana-539	80	1	h1	h1	PROPN
cana-539	80	2	,	,	PUNCT
cana-539	80	3	h2	h2	PROPN
cana-539	80	4	&	&	CCONJ
cana-539	80	5	h3	h3	NOUN
cana-539	80	6	are	be	AUX
cana-539	80	7	the	the	DET
cana-539	80	8	principal	principal	ADJ
cana-539	80	9	minor	minor	ADJ
cana-539	80	10	of	of	ADP
cana-539	80	11	the	the	DET
cana-539	80	12	hessian	hessian	ADJ
cana-539	80	13	matrix	matrix	NOUN
cana-539	80	14	.	.	PUNCT
cana-539	81	1	the	the	DET
cana-539	81	2	total	total	ADJ
cana-539	81	3	function	function	NOUN
cana-539	81	4	as	as	ADP
cana-539	81	5	a	a	DET
cana-539	81	6	hessian	hessian	ADJ
cana-539	81	7	matrix	matrix	NOUN
cana-539	81	8	is	be	AUX
cana-539	81	9	as	as	SCONJ
cana-539	81	10	follows	follow	VERB
cana-539	81	11	:	:	PUNCT
cana-539	81	12	[	[	PUNCT
cana-539	81	13	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	X
cana-539	81	14	𝜕𝑡𝑟2	𝜕𝑡𝑟2	PRON
cana-539	81	15	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	X
cana-539	81	16	𝜕𝑡𝑟𝜕𝜉	𝜕𝑡𝑟𝜕𝜉	PROPN
cana-539	81	17	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	X
cana-539	81	18	𝜕𝑡𝑟𝜕𝑇	𝜕𝑡𝑟𝜕𝑇	PROPN
cana-539	81	19	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	SYM
cana-539	81	20	𝜕𝜉𝜕𝑡𝑟	𝜕𝜉𝜕𝑡𝑟	PROPN
cana-539	81	21	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	SYM
cana-539	81	22	𝜕𝜉2	𝜕𝜉2	NOUN
cana-539	81	23	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	NUM
cana-539	81	24	𝜕𝑇𝜕𝜉	𝜕𝑇𝜕𝜉	PUNCT
cana-539	81	25	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	X
cana-539	81	26	𝜕𝑇𝜕𝑡𝑟	𝜕𝑇𝜕𝑡𝑟	PROPN
cana-539	81	27	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	SYM
cana-539	81	28	𝜕𝜉𝜕𝑇	𝜕𝜉𝜕𝑇	PROPN
cana-539	81	29	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	SYM
cana-539	81	30	𝜕𝑇2	𝜕𝑇2	NOUN
cana-539	81	31	]	]	PUNCT
cana-539	81	32	from	from	ADP
cana-539	81	33	equation	equation	NOUN
cana-539	81	34	(	(	PUNCT
cana-539	81	35	14	14	NUM
cana-539	81	36	)	)	PUNCT
cana-539	81	37	we	we	PRON
cana-539	81	38	get	get	VERB
cana-539	81	39	𝜕𝑇𝑅𝐶(𝑡𝑟,𝜉,𝑇	𝜕𝑇𝑅𝐶(𝑡𝑟,𝜉,𝑇	ADJ
cana-539	81	40	)	)	PUNCT
cana-539	81	41	𝜕𝑡𝑟	𝜕𝑡𝑟	PUNCT
cana-539	82	1	=	=	SYM
cana-539	82	2	1	1	NUM
cana-539	82	3	𝑇	𝑇	PROPN
cana-539	82	4	[	[	X
cana-539	82	5	𝐻1	𝐻1	PRON
cana-539	83	1	[	[	X
cana-539	83	2	𝑆1𝑒	𝑆1𝑒	NOUN
cana-539	83	3	−𝜎𝜃𝑡𝑟	−𝜎𝜃𝑡𝑟	PROPN
cana-539	84	1	+	+	CCONJ
cana-539	84	2	𝑎	𝑎	PRON
cana-539	84	3	𝜎𝜃	𝜎𝜃	NOUN
cana-539	84	4	(	(	PUNCT
cana-539	84	5	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NOUN
cana-539	84	6	)	)	PUNCT
cana-539	85	1	+	+	CCONJ
cana-539	85	2	𝑏	𝑏	X
cana-539	85	3	𝜎𝜃	𝜎𝜃	ADJ
cana-539	85	4	2	2	NUM
cana-539	85	5	(	(	PUNCT
cana-539	85	6	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	X
cana-539	85	7	−	−	PROPN
cana-539	85	8	1	1	NUM
cana-539	85	9	)	)	PUNCT
cana-539	85	10	−	−	PROPN
cana-539	85	11	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	85	12	𝜎𝜃	𝜎𝜃	NOUN
cana-539	85	13	]	]	PUNCT
cana-539	86	1	+	+	CCONJ
cana-539	86	2	𝐻2	𝐻2	ADJ
cana-539	86	3	[	[	PUNCT
cana-539	86	4	𝑎	𝑎	NOUN
cana-539	86	5	𝜎𝜃	𝜎𝜃	NOUN
cana-539	86	6	+	+	CCONJ
cana-539	86	7	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	86	8	𝜎𝜃	𝜎𝜃	NOUN
cana-539	86	9	−	−	NOUN
cana-539	86	10	𝑏	𝑏	PROPN
cana-539	86	11	𝜎𝜃	𝜎𝜃	ADJ
cana-539	86	12	2	2	NUM
cana-539	86	13	−	−	NOUN
cana-539	86	14	𝑒−𝜎𝜃(𝑡𝑟+𝑇	𝑒−𝜎𝜃(𝑡𝑟+𝑇	PROPN
cana-539	86	15	)	)	PUNCT
cana-539	86	16	[	[	PUNCT
cana-539	86	17	𝑎	𝑎	NOUN
cana-539	86	18	𝜎𝜃	𝜎𝜃	NOUN
cana-539	86	19	+	+	CCONJ
cana-539	86	20	𝑏𝑇	𝑏𝑇	NOUN
cana-539	86	21	𝜎𝜃	𝜎𝜃	NOUN
cana-539	86	22	−	−	PROPN
cana-539	86	23	𝑏	𝑏	PROPN
cana-539	86	24	𝜎𝜃	𝜎𝜃	PROPN
cana-539	86	25	2]]](15	2]]](15	NUM
cana-539	86	26	)	)	PUNCT
cana-539	86	27	𝜕𝑇𝑅𝐶(𝑡𝑟,𝜉,𝑇	𝜕𝑇𝑅𝐶(𝑡𝑟,𝜉,𝑇	ADJ
cana-539	86	28	)	)	PUNCT
cana-539	86	29	𝜕𝑇	𝜕𝑇	NOUN
cana-539	86	30	=	=	PUNCT
cana-539	87	1	−	−	PROPN
cana-539	87	2	1	1	NUM
cana-539	87	3	𝑇2	𝑇2	NOUN
cana-539	88	1	[	[	X
cana-539	88	2	o	o	X
cana-539	88	3	+	+	X
cana-539	88	4	𝐻1	𝐻1	NOUN
cana-539	88	5	[	[	X
cana-539	88	6	(	(	PUNCT
cana-539	88	7	1	1	NUM
cana-539	88	8	−	−	NUM
cana-539	88	9	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NUM
cana-539	88	10	)	)	PUNCT
cana-539	88	11	[	[	PUNCT
cana-539	88	12	𝑆1	𝑆1	NOUN
cana-539	88	13	𝜎𝜃	𝜎𝜃	NOUN
cana-539	88	14	+	+	CCONJ
cana-539	88	15	𝑎	𝑎	DET
cana-539	88	16	𝜎𝜃	𝜎𝜃	NOUN
cana-539	88	17	2	2	NUM
cana-539	88	18	−	−	NOUN
cana-539	88	19	𝑏	𝑏	PROPN
cana-539	88	20	𝜎𝜃	𝜎𝜃	NOUN
cana-539	88	21	3	3	NUM
cana-539	88	22	]	]	PUNCT
cana-539	88	23	−	−	PROPN
cana-539	88	24	𝑎𝑡𝑟	𝑎𝑡𝑟	PROPN
cana-539	88	25	𝜎𝜃	𝜎𝜃	PROPN
cana-539	88	26	+	+	CCONJ
cana-539	88	27	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	88	28	𝜎𝜃	𝜎𝜃	PROPN
cana-539	88	29	2	2	NUM
cana-539	88	30	−	−	NOUN
cana-539	88	31	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	88	32	2	2	NUM
cana-539	88	33	2𝜎𝜃	2𝜎𝜃	NOUN
cana-539	88	34	]	]	X
cana-539	88	35	]	]	X
cana-539	88	36	+	+	CCONJ
cana-539	88	37	𝐻2	𝐻2	ADJ
cana-539	89	1	[	[	X
cana-539	89	2	−	−	X
cana-539	89	3	𝑆2	𝑆2	PROPN
cana-539	89	4	𝑇2𝜎𝜃	𝑇2𝜎𝜃	PROPN
cana-539	89	5	(	(	PUNCT
cana-539	89	6	1	1	NUM
cana-539	89	7	−	−	NUM
cana-539	89	8	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NUM
cana-539	89	9	)	)	PUNCT
cana-539	89	10	−	−	ADP
cana-539	89	11	𝑎𝑡𝑟	𝑎𝑡𝑟	NOUN
cana-539	89	12	𝜎𝜃𝑇2	𝜎𝜃𝑇2	NOUN
cana-539	89	13	−	−	ADP
cana-539	89	14	𝑏	𝑏	PRON
cana-539	89	15	2𝜎𝜃	2𝜎𝜃	ADJ
cana-539	89	16	(	(	PUNCT
cana-539	89	17	𝑡𝑟	𝑡𝑟	VERB
cana-539	89	18	2	2	NUM
cana-539	89	19	𝑇2	𝑇2	NOUN
cana-539	89	20	+	+	CCONJ
cana-539	89	21	1	1	NUM
cana-539	89	22	)	)	PUNCT
cana-539	89	23	+	+	CCONJ
cana-539	89	24	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	89	25	𝜎𝜃	𝜎𝜃	PROPN
cana-539	89	26	2𝑇2	2𝑇2	NUM
cana-539	89	27	−	−	NOUN
cana-539	89	28	𝑆2	𝑆2	PROPN
cana-539	89	29	𝑇2𝜎𝜃	𝑇2𝜎𝜃	PROPN
cana-539	89	30	2	2	NUM
cana-539	89	31	(	(	PUNCT
cana-539	89	32	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	X
cana-539	89	33	−	−	NOUN
cana-539	89	34	𝑒−𝜎𝜃𝑇	𝑒−𝜎𝜃𝑇	NOUN
cana-539	89	35	)	)	PUNCT
cana-539	89	36	+	+	CCONJ
cana-539	89	37	𝑆2𝑒−𝜎𝜃𝑇	𝑆2𝑒−𝜎𝜃𝑇	PROPN
cana-539	89	38	𝑇𝜎𝜃	𝑇𝜎𝜃	PROPN
cana-539	89	39	+	+	CCONJ
cana-539	89	40	𝑏	𝑏	PROPN
cana-539	89	41	𝜎𝜃	𝜎𝜃	ADJ
cana-539	89	42	2	2	NUM
cana-539	89	43	(	(	PUNCT
cana-539	89	44	𝑒−𝜎𝜃(𝑡𝑟+𝑇	𝑒−𝜎𝜃(𝑡𝑟+𝑇	NOUN
cana-539	89	45	)	)	PUNCT
cana-539	89	46	−	−	NOUN
cana-539	89	47	𝑒−2𝜎𝜃𝑇	𝑒−2𝜎𝜃𝑇	NUM
cana-539	89	48	)	)	PUNCT
cana-539	90	1	+	+	CCONJ
cana-539	90	2	[	[	PUNCT
cana-539	90	3	𝑎	𝑎	NOUN
cana-539	90	4	𝜎𝜃	𝜎𝜃	NOUN
cana-539	90	5	+	+	CCONJ
cana-539	90	6	𝑏𝑇	𝑏𝑇	NOUN
cana-539	90	7	𝜎𝜃	𝜎𝜃	NOUN
cana-539	90	8	−	−	PROPN
cana-539	90	9	𝑏	𝑏	PROPN
cana-539	90	10	𝜎𝜃	𝜎𝜃	NOUN
cana-539	90	11	2	2	NUM
cana-539	90	12	]	]	PUNCT
cana-539	90	13	(	(	PUNCT
cana-539	90	14	2𝑒−2𝜎𝜃𝑇	2𝑒−2𝜎𝜃𝑇	NUM
cana-539	90	15	−	−	PROPN
cana-539	90	16	𝑒−𝜎𝜃(𝑡𝑟+𝑇	𝑒−𝜎𝜃(𝑡𝑟+𝑇	PROPN
cana-539	90	17	)	)	PUNCT
cana-539	90	18	)	)	PUNCT
cana-539	90	19	]	]	PUNCT
cana-539	91	1	=	=	SYM
cana-539	91	2	0	0	PUNCT
cana-539	91	3	(	(	PUNCT
cana-539	91	4	16	16	NUM
cana-539	91	5	)	)	PUNCT
cana-539	91	6	and	and	CCONJ
cana-539	91	7	find	find	VERB
cana-539	91	8	also	also	ADV
cana-539	91	9	,	,	PUNCT
cana-539	91	10	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	X
cana-539	91	11	𝜕𝑡𝑟	𝜕𝑡𝑟	SYM
cana-539	91	12	2	2	NUM
cana-539	91	13	=	=	SYM
cana-539	91	14	1	1	NUM
cana-539	91	15	𝑇	𝑇	PROPN
cana-539	91	16	[	[	X
cana-539	91	17	𝐻1	𝐻1	PRON
cana-539	91	18	[	[	X
cana-539	91	19	−𝑆1𝜎𝜃𝑒−𝜎𝜃𝑡𝑟	−𝑆1𝜎𝜃𝑒−𝜎𝜃𝑡𝑟	NOUN
cana-539	91	20	−	−	NOUN
cana-539	92	1	𝑏	𝑏	PROPN
cana-539	92	2	𝜎𝜃	𝜎𝜃	NOUN
cana-539	92	3	[	[	X
cana-539	92	4	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	X
cana-539	92	5	+	+	X
cana-539	92	6	1	1	NUM
cana-539	92	7	]	]	PUNCT
cana-539	92	8	]	]	PUNCT
cana-539	93	1	+	+	CCONJ
cana-539	93	2	𝐻2	𝐻2	ADJ
cana-539	93	3	[	[	X
cana-539	93	4	−𝑆2𝜎𝜃𝑒−𝜎𝜃𝑡𝑟	−𝑆2𝜎𝜃𝑒−𝜎𝜃𝑡𝑟	X
cana-539	93	5	+	+	CCONJ
cana-539	93	6	𝑏	𝑏	PRON
cana-539	93	7	𝜎𝜃	𝜎𝜃	NOUN
cana-539	93	8	+	+	NUM
cana-539	93	9	𝑒−2𝜎𝜃𝑡𝑟(4𝑎	𝑒−2𝜎𝜃𝑡𝑟(4𝑎	PROPN
cana-539	93	10	+	+	CCONJ
cana-539	93	11	4𝑏𝑡𝑟	4𝑏𝑡𝑟	NOUN
cana-539	93	12	)	)	PUNCT
cana-539	93	13	−	−	PROPN
cana-539	93	14	𝑒−𝜎𝜃(𝑡𝑟+𝑇	𝑒−𝜎𝜃(𝑡𝑟+𝑇	PROPN
cana-539	93	15	)	)	PUNCT
cana-539	94	1	[	[	X
cana-539	94	2	𝑎	𝑎	X
cana-539	94	3	+	+	NOUN
cana-539	94	4	𝑏	𝑏	NOUN
cana-539	94	5	−	−	NOUN
cana-539	94	6	𝑏	𝑏	PROPN
cana-539	94	7	𝜎𝜃	𝜎𝜃	NOUN
cana-539	94	8	]	]	PUNCT
cana-539	94	9	]	]	X
cana-539	94	10	]	]	X
cana-539	94	11	(	(	PUNCT
cana-539	94	12	17	17	NUM
cana-539	94	13	)	)	PUNCT
cana-539	94	14	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	NUM
cana-539	94	15	𝜕𝑇2	𝜕𝑇2	PROPN
cana-539	94	16	=	=	SYM
cana-539	94	17	−	−	PROPN
cana-539	94	18	1	1	NUM
cana-539	94	19	𝑇2	𝑇2	NOUN
cana-539	95	1	[	[	X
cana-539	95	2	o	o	X
cana-539	95	3	+	+	X
cana-539	95	4	𝐻1	𝐻1	PROPN
cana-539	95	5	[	[	X
cana-539	95	6	−𝑆1	−𝑆1	X
cana-539	95	7	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NOUN
cana-539	95	8	𝜎𝜃	𝜎𝜃	NOUN
cana-539	95	9	−	−	PROPN
cana-539	95	10	𝑎	𝑎	DET
cana-539	95	11	𝜎𝜃	𝜎𝜃	NOUN
cana-539	95	12	(	(	PUNCT
cana-539	95	13	𝑒−𝜎𝜃	𝑒−𝜎𝜃	PROPN
cana-539	95	14	𝜎𝜃	𝜎𝜃	PROPN
cana-539	95	15	−	−	PROPN
cana-539	95	16	𝑡𝑟	𝑡𝑟	NOUN
cana-539	95	17	)	)	PUNCT
cana-539	95	18	+	+	CCONJ
cana-539	95	19	𝑏	𝑏	PROPN
cana-539	95	20	𝜎𝜃	𝜎𝜃	ADJ
cana-539	95	21	2	2	NUM
cana-539	95	22	(	(	PUNCT
cana-539	95	23	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	X
cana-539	95	24	𝜎𝜃	𝜎𝜃	NOUN
cana-539	95	25	−	−	PROPN
cana-539	95	26	𝑡𝑟	𝑡𝑟	NOUN
cana-539	95	27	)	)	PUNCT
cana-539	95	28	−	−	ADP
cana-539	95	29	𝑏𝑡𝑟	𝑏𝑡𝑟	VERB
cana-539	95	30	2	2	NUM
cana-539	95	31	2𝜎𝜃	2𝜎𝜃	NOUN
cana-539	95	32	]	]	X
cana-539	95	33	]	]	X
cana-539	96	1	+	+	CCONJ
cana-539	96	2	𝐻2	𝐻2	ADJ
cana-539	96	3	[	[	PUNCT
cana-539	96	4	−2	−2	NOUN
cana-539	96	5	𝑇3𝜎𝜃	𝑇3𝜎𝜃	PROPN
cana-539	96	6	(	(	PUNCT
cana-539	96	7	𝑆2𝑒	𝑆2𝑒	PROPN
cana-539	96	8	−𝜎𝜃𝑡𝑟	−𝜎𝜃𝑡𝑟	PROPN
cana-539	96	9	+	+	CCONJ
cana-539	96	10	𝑎𝑡𝑟	𝑎𝑡𝑟	PROPN
cana-539	96	11	)	)	PUNCT
cana-539	96	12	+	+	CCONJ
cana-539	96	13	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	96	14	𝑇3𝜎𝜃	𝑇3𝜎𝜃	PROPN
cana-539	96	15	2	2	NUM
cana-539	96	16	(	(	PUNCT
cana-539	96	17	𝑡𝑟	𝑡𝑟	VERB
cana-539	96	18	−	−	PROPN
cana-539	96	19	2	2	NUM
cana-539	96	20	)	)	PUNCT
cana-539	96	21	−	−	NOUN
cana-539	96	22	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	NOUN
cana-539	96	23	𝜎𝜃	𝜎𝜃	NOUN
cana-539	96	24	2	2	NUM
cana-539	96	25	[	[	X
cana-539	96	26	𝑎	𝑎	X
cana-539	96	27	+	+	NUM
cana-539	96	28	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	96	29	+	+	CCONJ
cana-539	96	30	𝑏	𝑏	NOUN
cana-539	96	31	𝜎𝜃	𝜎𝜃	NOUN
cana-539	96	32	]	]	PUNCT
cana-539	96	33	[	[	PUNCT
cana-539	96	34	2	2	NUM
cana-539	96	35	𝑇3	𝑇3	NOUN
cana-539	96	36	(	(	PUNCT
cana-539	96	37	𝑒−𝜎𝜃𝑡𝑟	𝑒−𝜎𝜃𝑡𝑟	X
cana-539	96	38	−	−	NOUN
cana-539	96	39	𝑒−𝜎𝜃𝑇	𝑒−𝜎𝜃𝑇	NOUN
cana-539	96	40	)	)	PUNCT
cana-539	96	41	−	−	PROPN
cana-539	96	42	𝜎𝜃𝑒−𝜎𝜃𝑇	𝜎𝜃𝑒−𝜎𝜃𝑇	PROPN
cana-539	96	43	𝑇	𝑇	PROPN
cana-539	96	44	[	[	PUNCT
cana-539	96	45	2	2	NUM
cana-539	96	46	𝑇	𝑇	PROPN
cana-539	96	47	−	−	PROPN
cana-539	96	48	𝜎𝜃	𝜎𝜃	NOUN
cana-539	96	49	]	]	PUNCT
cana-539	96	50	]	]	X
cana-539	96	51	]	]	X
cana-539	96	52	(	(	PUNCT
cana-539	96	53	18	18	NUM
cana-539	96	54	)	)	PUNCT
cana-539	96	55	communications	communication	NOUN
cana-539	96	56	on	on	ADP
cana-539	96	57	applied	apply	VERB
cana-539	96	58	nonlinear	nonlinear	ADJ
cana-539	96	59	analysis	analysis	NOUN
cana-539	96	60	issn	issn	NOUN
cana-539	96	61	:	:	PUNCT
cana-539	96	62	1074	1074	NUM
cana-539	96	63	-	-	PUNCT
cana-539	96	64	133x	133x	NUM
cana-539	96	65	vol	vol	NOUN
cana-539	96	66	31	31	NUM
cana-539	96	67	no	no	NOUN
cana-539	96	68	.	.	NOUN
cana-539	96	69	2	2	NUM
cana-539	96	70	(	(	PUNCT
cana-539	96	71	2024	2024	NUM
cana-539	96	72	)	)	PUNCT
cana-539	97	1	245	245	NUM
cana-539	97	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	97	3	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	X
cana-539	97	4	𝜕𝑡𝑟𝜕𝑇	𝜕𝑡𝑟𝜕𝑇	NOUN
cana-539	97	5	=	=	SYM
cana-539	97	6	𝜕2𝑇𝑅𝐶	𝜕2𝑇𝑅𝐶	SYM
cana-539	97	7	𝜕𝑇𝜕𝑡𝑟	𝜕𝑇𝜕𝑡𝑟	NOUN
cana-539	97	8	=	=	SYM
cana-539	97	9	−	−	PROPN
cana-539	97	10	1	1	NUM
cana-539	97	11	𝑇2	𝑇2	NOUN
cana-539	97	12	[	[	X
cana-539	97	13	𝐻1	𝐻1	X
cana-539	98	1	[	[	X
cana-539	98	2	𝑆1𝑒	𝑆1𝑒	NOUN
cana-539	98	3	−𝜎𝜃𝑡𝑟	−𝜎𝜃𝑡𝑟	PROPN
cana-539	99	1	+	+	CCONJ
cana-539	99	2	𝑎	𝑎	PRON
cana-539	99	3	𝜎𝜃	𝜎𝜃	NOUN
cana-539	99	4	+	+	CCONJ
cana-539	99	5	𝑏	𝑏	PROPN
cana-539	99	6	𝜎𝜃	𝜎𝜃	ADJ
cana-539	99	7	2	2	NUM
cana-539	99	8	(	(	PUNCT
cana-539	99	9	−𝑒𝜎𝜃𝑡𝑟	−𝑒𝜎𝜃𝑡𝑟	NOUN
cana-539	99	10	−	−	PROPN
cana-539	99	11	1	1	NUM
cana-539	99	12	)	)	PUNCT
cana-539	99	13	−	−	PROPN
cana-539	99	14	𝑏𝑡𝑟	𝑏𝑡𝑟	PROPN
cana-539	99	15	𝜎𝜃	𝜎𝜃	NOUN
cana-539	99	16	]	]	PUNCT
cana-539	100	1	+	+	CCONJ
cana-539	100	2	𝐻2	𝐻2	ADJ
cana-539	100	3	[	[	X
cana-539	100	4	−	−	X
cana-539	100	5	1	1	NUM
cana-539	100	6	𝑇2	𝑇2	NOUN
cana-539	101	1	[	[	X
cana-539	101	2	𝑆2𝑒	𝑆2𝑒	PROPN
cana-539	101	3	−𝜎𝜃𝑡𝑟	−𝜎𝜃𝑡𝑟	PROPN
cana-539	101	4	−	−	NUM
cana-539	102	1	𝑎	𝑎	DET
cana-539	102	2	𝜎𝜃	𝜎𝜃	NOUN
cana-539	102	3	+	+	CCONJ
cana-539	102	4	𝑏𝑡𝑟	𝑏𝑡𝑟	NOUN
cana-539	102	5	𝜎𝜃	𝜎𝜃	NOUN
cana-539	102	6	−	−	NOUN
cana-539	102	7	𝑏	𝑏	PROPN
cana-539	102	8	𝜎𝜃	𝜎𝜃	NOUN
cana-539	102	9	2	2	NUM
cana-539	102	10	+	+	NUM
cana-539	102	11	𝑒−2𝜎𝜃𝑡𝑟	𝑒−2𝜎𝜃𝑡𝑟	NOUN
cana-539	103	1	[	[	X
cana-539	103	2	−	−	NOUN
cana-539	103	3	2𝑎	2𝑎	NUM
cana-539	103	4	𝜎𝜃	𝜎𝜃	VERB
cana-539	103	5	−	−	PROPN
cana-539	103	6	2𝑏𝑡𝑟	2𝑏𝑡𝑟	NUM
cana-539	103	7	𝜎𝜃	𝜎𝜃	NOUN
cana-539	103	8	−	−	NOUN
cana-539	103	9	𝑏	𝑏	PROPN
cana-539	103	10	𝜎𝜃	𝜎𝜃	NOUN
cana-539	103	11	2	2	NUM
cana-539	103	12	]	]	PUNCT
cana-539	103	13	−	−	PROPN
cana-539	103	14	𝑒−𝜎𝜃(𝑡𝑟+𝑇	𝑒−𝜎𝜃(𝑡𝑟+𝑇	PROPN
cana-539	103	15	)	)	PUNCT
cana-539	103	16	𝑇	𝑇	NOUN
cana-539	104	1	[	[	X
cana-539	104	2	𝜎𝜃	𝜎𝜃	ADP
cana-539	104	3	+	+	NOUN
cana-539	104	4	1	1	NUM
cana-539	104	5	𝑇	𝑇	NOUN
cana-539	104	6	]	]	PUNCT
cana-539	104	7	]	]	X
cana-539	104	8	]	]	X
cana-539	104	9	]	]	X
cana-539	104	10	(	(	PUNCT
cana-539	104	11	19	19	NUM
cana-539	104	12	)	)	PUNCT
cana-539	104	13	5	5	NUM
cana-539	104	14	.	.	PUNCT
cana-539	104	15	effect	effect	NOUN
cana-539	104	16	of	of	ADP
cana-539	104	17	preservation	preservation	NOUN
cana-539	104	18	technology	technology	NOUN
cana-539	104	19	within	within	ADP
cana-539	104	20	this	this	DET
cana-539	104	21	framework	framework	NOUN
cana-539	104	22	,	,	PUNCT
cana-539	104	23	we	we	PRON
cana-539	104	24	have	have	AUX
cana-539	104	25	included	include	VERB
cana-539	104	26	preservation	preservation	NOUN
cana-539	104	27	technology	technology	NOUN
cana-539	104	28	in	in	ADP
cana-539	104	29	order	order	NOUN
cana-539	104	30	to	to	PART
cana-539	104	31	reduce	reduce	VERB
cana-539	104	32	the	the	DET
cana-539	104	33	deterioration	deterioration	NOUN
cana-539	104	34	rate	rate	NOUN
cana-539	104	35	.	.	PUNCT
cana-539	105	1	we	we	PRON
cana-539	105	2	have	have	AUX
cana-539	105	3	taken	take	VERB
cana-539	105	4	the	the	DET
cana-539	105	5	following	follow	VERB
cana-539	105	6	values	value	NOUN
cana-539	105	7	𝑎	𝑎	X
cana-539	105	8	=	=	SYM
cana-539	105	9	3	3	NUM
cana-539	105	10	;	;	PUNCT
cana-539	105	11	ξ	ξ	X
cana-539	105	12	=	=	SYM
cana-539	105	13	0.0136073	0.0136073	NUM
cana-539	105	14	;	;	PUNCT
cana-539	106	1	θ	θ	X
cana-539	106	2	=	=	SYM
cana-539	106	3	0.09	0.09	NUM
cana-539	106	4	we	we	PRON
cana-539	106	5	get	get	VERB
cana-539	106	6	the	the	DET
cana-539	106	7	value	value	NOUN
cana-539	106	8	of	of	ADP
cana-539	106	9	m(ξ	m(ξ	NOUN
cana-539	106	10	)	)	PUNCT
cana-539	106	11	=	=	SYM
cana-539	106	12	0.04	0.04	NUM
cana-539	106	13	&	&	CCONJ
cana-539	106	14	𝜎𝜃	𝜎𝜃	PROPN
cana-539	106	15	=	=	PROPN
cana-539	106	16	0.05	0.05	NUM
cana-539	106	17	6	6	NUM
cana-539	106	18	.	.	PUNCT
cana-539	107	1	numerical	numerical	ADJ
cana-539	107	2	illustration	illustration	NOUN
cana-539	107	3	in	in	ADP
cana-539	107	4	order	order	NOUN
cana-539	107	5	to	to	PART
cana-539	107	6	demonstrate	demonstrate	VERB
cana-539	107	7	the	the	DET
cana-539	107	8	model	model	NOUN
cana-539	107	9	,	,	PUNCT
cana-539	107	10	we	we	PRON
cana-539	107	11	have	have	AUX
cana-539	107	12	taken	take	VERB
cana-539	107	13	the	the	DET
cana-539	107	14	following	follow	VERB
cana-539	107	15	inventory	inventory	NOUN
cana-539	107	16	system	system	NOUN
cana-539	107	17	:	:	PUNCT
cana-539	107	18	𝑂	𝑂	NOUN
cana-539	107	19	=	=	NOUN
cana-539	107	20	600	600	NUM
cana-539	107	21	;	;	PUNCT
cana-539	108	1	𝑎	𝑎	PROPN
cana-539	108	2	=	=	SYM
cana-539	108	3	250	250	NUM
cana-539	108	4	;	;	PUNCT
cana-539	108	5	𝑏	𝑏	PROPN
cana-539	108	6	=	=	SYM
cana-539	108	7	25	25	NUM
cana-539	108	8	;	;	PUNCT
cana-539	108	9	𝐻1	𝐻1	NOUN
cana-539	108	10	=	=	NOUN
cana-539	108	11	0.75	0.75	NUM
cana-539	108	12	;	;	PUNCT
cana-539	108	13	𝐻2	𝐻2	PROPN
cana-539	108	14	=	=	NUM
cana-539	108	15	0.4	0.4	NUM
cana-539	108	16	;	;	PUNCT
cana-539	108	17	𝑆1	𝑆1	NOUN
cana-539	108	18	=	=	SYM
cana-539	108	19	500	500	NUM
cana-539	108	20	;	;	PUNCT
cana-539	108	21	𝑆2	𝑆2	PROPN
cana-539	108	22	=	=	SYM
cana-539	108	23	300	300	NUM
cana-539	108	24	;	;	PUNCT
cana-539	108	25	𝜎𝜃	𝜎𝜃	NOUN
cana-539	108	26	=	=	NOUN
cana-539	108	27	0.05	0.05	NUM
cana-539	108	28	we	we	PRON
cana-539	108	29	observed	observe	VERB
cana-539	108	30	the	the	DET
cana-539	108	31	optimal	optimal	ADJ
cana-539	108	32	solution	solution	NOUN
cana-539	108	33	as	as	ADP
cana-539	108	34	𝑡𝑟	𝑡𝑟	ADJ
cana-539	108	35	∗	∗	NOUN
cana-539	108	36	=	=	PUNCT
cana-539	108	37	2.97148	2.97148	NUM
cana-539	108	38	;	;	PUNCT
cana-539	108	39	𝑇∗	𝑇∗	X
cana-539	108	40	=	=	SYM
cana-539	108	41	10	10	NUM
cana-539	108	42	;	;	PUNCT
cana-539	109	1	𝑇𝑅𝐶∗	𝑇𝑅𝐶∗	NOUN
cana-539	109	2	=	=	PUNCT
cana-539	109	3	665.0132	665.0132	NUM
cana-539	109	4	7	7	NUM
cana-539	109	5	.	.	X
cana-539	109	6	sensitivity	sensitivity	NOUN
cana-539	109	7	analysis	analysis	NOUN
cana-539	109	8	to	to	PART
cana-539	109	9	analyse	analyse	VERB
cana-539	109	10	the	the	DET
cana-539	109	11	sensitivity	sensitivity	NOUN
cana-539	109	12	of	of	ADP
cana-539	109	13	the	the	DET
cana-539	109	14	model	model	NOUN
cana-539	109	15	,	,	PUNCT
cana-539	109	16	we	we	PRON
cana-539	109	17	execute	execute	VERB
cana-539	109	18	a	a	DET
cana-539	109	19	sensitivity	sensitivity	NOUN
cana-539	109	20	analysis	analysis	NOUN
cana-539	109	21	by	by	ADP
cana-539	109	22	changing	change	VERB
cana-539	109	23	the	the	DET
cana-539	109	24	values	value	NOUN
cana-539	109	25	of	of	ADP
cana-539	109	26	various	various	ADJ
cana-539	109	27	key	key	ADJ
cana-539	109	28	parameters	parameter	NOUN
cana-539	109	29	such	such	ADJ
cana-539	109	30	as	as	ADP
cana-539	109	31	demand	demand	NOUN
cana-539	109	32	parameters	parameter	NOUN
cana-539	109	33	&	&	CCONJ
cana-539	109	34	deterioration	deterioration	NOUN
cana-539	109	35	rate	rate	NOUN
cana-539	109	36	.	.	PUNCT
cana-539	110	1	table	table	NOUN
cana-539	110	2	1	1	NUM
cana-539	110	3	,	,	PUNCT
cana-539	110	4	table	table	NOUN
cana-539	110	5	2	2	NUM
cana-539	110	6	&	&	CCONJ
cana-539	110	7	table	table	NOUN
cana-539	110	8	3	3	NUM
cana-539	110	9	depicts	depict	VERB
cana-539	110	10	the	the	DET
cana-539	110	11	impact	impact	NOUN
cana-539	110	12	of	of	ADP
cana-539	110	13	parameter	parameter	NOUN
cana-539	110	14	changes	change	NOUN
cana-539	110	15	.	.	PUNCT
cana-539	111	1	table	table	NOUN
cana-539	111	2	1	1	NUM
cana-539	111	3	:	:	PUNCT
cana-539	111	4	sensitivity	sensitivity	NOUN
cana-539	111	5	analysis	analysis	NOUN
cana-539	111	6	of	of	ADP
cana-539	111	7	optimal	optimal	ADJ
cana-539	111	8	solution	solution	NOUN
cana-539	111	9	with	with	ADP
cana-539	111	10	respect	respect	NOUN
cana-539	111	11	to	to	ADP
cana-539	111	12	variation	variation	NOUN
cana-539	111	13	in	in	ADP
cana-539	111	14	parameter	parameter	NOUN
cana-539	111	15	‘	'	PUNCT
cana-539	111	16	a	a	DET
cana-539	111	17	’	'	PUNCT
cana-539	111	18	t	t	NOUN
cana-539	111	19	t	t	PROPN
cana-539	111	20	trc	trc	PROPN
cana-539	111	21	variation	variation	NOUN
cana-539	111	22	in	in	ADP
cana-539	111	23	parameter	parameter	NOUN
cana-539	111	24	‘	'	PUNCT
cana-539	111	25	a	a	DET
cana-539	111	26	’	'	PUNCT
cana-539	111	27	220	220	NUM
cana-539	111	28	2.03169	2.03169	NUM
cana-539	111	29	11.2	11.2	NUM
cana-539	111	30	925.9562	925.9562	NUM
cana-539	111	31	235	235	NUM
cana-539	111	32	2.50437	2.50437	NUM
cana-539	111	33	10.6	10.6	NUM
cana-539	111	34	793.9031	793.9031	NUM
cana-539	111	35	265	265	NUM
cana-539	111	36	3.43325	3.43325	NUM
cana-539	111	37	9.4	9.4	NUM
cana-539	111	38	531.157011	531.157011	NUM
cana-539	111	39	table	table	NOUN
cana-539	111	40	2	2	NUM
cana-539	111	41	:	:	PUNCT
cana-539	111	42	sensitivity	sensitivity	NOUN
cana-539	111	43	analysis	analysis	NOUN
cana-539	111	44	of	of	ADP
cana-539	111	45	optimal	optimal	ADJ
cana-539	111	46	solution	solution	NOUN
cana-539	111	47	with	with	ADP
cana-539	111	48	respect	respect	NOUN
cana-539	111	49	to	to	ADP
cana-539	111	50	variation	variation	NOUN
cana-539	111	51	in	in	ADP
cana-539	111	52	parameter	parameter	NOUN
cana-539	111	53	‘	'	PUNCT
cana-539	111	54	b	b	X
cana-539	111	55	’	'	PUNCT
cana-539	111	56	t	t	PROPN
cana-539	111	57	t	t	PROPN
cana-539	111	58	trc	trc	PROPN
cana-539	111	59	variation	variation	NOUN
cana-539	111	60	in	in	ADP
cana-539	111	61	parameter	parameter	NOUN
cana-539	111	62	‘	'	PUNCT
cana-539	111	63	b	b	X
cana-539	111	64	’	'	PUNCT
cana-539	111	65	20	20	NUM
cana-539	111	66	4.97261	4.97261	NUM
cana-539	111	67	7.5	7.5	NUM
cana-539	111	68	144.115	144.115	NUM
cana-539	111	69	30	30	NUM
cana-539	111	70	1.57538	1.57538	NUM
cana-539	111	71	11.6	11.6	NUM
cana-539	111	72	1207.225	1207.225	NUM
cana-539	111	73	35	35	NUM
cana-539	111	74	0.543249	0.543249	NUM
cana-539	111	75	12.8	12.8	NUM
cana-539	111	76	1781.7228	1781.7228	PROPN
cana-539	111	77	communications	communication	NOUN
cana-539	111	78	on	on	ADP
cana-539	111	79	applied	apply	VERB
cana-539	111	80	nonlinear	nonlinear	ADJ
cana-539	111	81	analysis	analysis	NOUN
cana-539	111	82	issn	issn	NOUN
cana-539	111	83	:	:	PUNCT
cana-539	111	84	1074	1074	NUM
cana-539	111	85	-	-	PUNCT
cana-539	111	86	133x	133x	NUM
cana-539	111	87	vol	vol	NOUN
cana-539	111	88	31	31	NUM
cana-539	111	89	no	no	NOUN
cana-539	111	90	.	.	NOUN
cana-539	111	91	2	2	NUM
cana-539	111	92	(	(	PUNCT
cana-539	111	93	2024	2024	NUM
cana-539	111	94	)	)	PUNCT
cana-539	111	95	246	246	NUM
cana-539	111	96	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	111	97	table	table	NOUN
cana-539	111	98	3	3	NUM
cana-539	111	99	:	:	PUNCT
cana-539	111	100	sensitivity	sensitivity	NOUN
cana-539	111	101	analysis	analysis	NOUN
cana-539	111	102	of	of	ADP
cana-539	111	103	optimal	optimal	ADJ
cana-539	111	104	solution	solution	NOUN
cana-539	111	105	with	with	ADP
cana-539	111	106	respect	respect	NOUN
cana-539	111	107	to	to	ADP
cana-539	111	108	variation	variation	NOUN
cana-539	111	109	in	in	ADP
cana-539	111	110	parameter	parameter	NOUN
cana-539	111	111	‘	'	PUNCT
cana-539	111	112	𝝈𝜽	𝝈𝜽	NOUN
cana-539	111	113	’	'	PUNCT
cana-539	111	114	because	because	SCONJ
cana-539	111	115	of	of	ADP
cana-539	111	116	modification	modification	NOUN
cana-539	111	117	in	in	ADP
cana-539	111	118	the	the	DET
cana-539	111	119	value	value	NOUN
cana-539	111	120	of	of	ADP
cana-539	111	121	m(𝜉	m(𝜉	PROPN
cana-539	111	122	)	)	PUNCT
cana-539	111	123	t	t	PROPN
cana-539	111	124	t	t	PROPN
cana-539	111	125	trc	trc	PROPN
cana-539	111	126	fluctuation	fluctuation	NOUN
cana-539	111	127	in	in	ADP
cana-539	111	128	the	the	DET
cana-539	111	129	value	value	NOUN
cana-539	111	130	of	of	ADP
cana-539	111	131	𝛏	𝛏	NOUN
cana-539	111	132	fluctuation	fluctuation	NOUN
cana-539	111	133	in	in	ADP
cana-539	111	134	the	the	DET
cana-539	111	135	value	value	NOUN
cana-539	111	136	of	of	ADP
cana-539	111	137	‘	'	PUNCT
cana-539	111	138	m(𝜉	m(𝜉	PROPN
cana-539	111	139	)	)	PUNCT
cana-539	111	140	’	'	PUNCT
cana-539	111	141	variation	variation	NOUN
cana-539	111	142	in	in	ADP
cana-539	111	143	value	value	NOUN
cana-539	111	144	of	of	ADP
cana-539	111	145	‘	'	PUNCT
cana-539	111	146	𝝈𝜽	𝝈𝜽	NOUN
cana-539	111	147	’	'	PUNCT
cana-539	111	148	0.0190654	0.0190654	NUM
cana-539	111	149	0.05	0.05	NUM
cana-539	111	150	0.04	0.04	NUM
cana-539	111	151	1.50836	1.50836	NUM
cana-539	111	152	15	15	NUM
cana-539	111	153	1501.65025	1501.65025	NUM
cana-539	111	154	0.010735	0.010735	NUM
cana-539	111	155	0.03	0.03	NUM
cana-539	111	156	0.06	0.06	NUM
cana-539	111	157	3.90582	3.90582	NUM
cana-539	111	158	6.66678	6.66678	NUM
cana-539	111	159	238.0357	238.0357	NUM
cana-539	111	160	•	•	NOUN
cana-539	111	161	from	from	ADP
cana-539	111	162	table	table	NOUN
cana-539	111	163	1	1	NUM
cana-539	111	164	we	we	PRON
cana-539	111	165	can	can	AUX
cana-539	111	166	see	see	VERB
cana-539	111	167	that	that	PRON
cana-539	111	168	on	on	ADP
cana-539	111	169	increasing	increase	VERB
cana-539	111	170	the	the	DET
cana-539	111	171	value	value	NOUN
cana-539	111	172	of	of	ADP
cana-539	111	173	‘	'	PUNCT
cana-539	111	174	a	a	PRON
cana-539	111	175	’	'	PUNCT
cana-539	111	176	,	,	PUNCT
cana-539	111	177	the	the	DET
cana-539	111	178	value	value	NOUN
cana-539	111	179	of	of	ADP
cana-539	111	180	‘	'	PUNCT
cana-539	111	181	t	t	NOUN
cana-539	111	182	’	'	PUNCT
cana-539	111	183	and	and	CCONJ
cana-539	111	184	‘	'	PUNCT
cana-539	111	185	trc	trc	NOUN
cana-539	111	186	’	'	PUNCT
cana-539	111	187	decreases	decrease	NOUN
cana-539	111	188	and	and	CCONJ
cana-539	111	189	the	the	DET
cana-539	111	190	value	value	NOUN
cana-539	111	191	of	of	ADP
cana-539	111	192	‘	'	PUNCT
cana-539	111	193	t	t	NOUN
cana-539	111	194	’	'	PUNCT
cana-539	111	195	increases	increase	NOUN
cana-539	111	196	.	.	PUNCT
cana-539	112	1	•	•	NUM
cana-539	112	2	from	from	ADP
cana-539	112	3	table	table	NOUN
cana-539	112	4	2	2	NUM
cana-539	112	5	we	we	PRON
cana-539	112	6	can	can	AUX
cana-539	112	7	see	see	VERB
cana-539	112	8	that	that	PRON
cana-539	112	9	on	on	ADP
cana-539	112	10	increasing	increase	VERB
cana-539	112	11	the	the	DET
cana-539	112	12	value	value	NOUN
cana-539	112	13	of	of	ADP
cana-539	112	14	‘	'	PUNCT
cana-539	112	15	b	b	X
cana-539	112	16	’	'	PUNCT
cana-539	112	17	,	,	PUNCT
cana-539	112	18	the	the	DET
cana-539	112	19	value	value	NOUN
cana-539	112	20	of	of	ADP
cana-539	112	21	‘	'	PUNCT
cana-539	112	22	t	t	NOUN
cana-539	112	23	’	'	PUNCT
cana-539	112	24	and	and	CCONJ
cana-539	112	25	‘	'	PUNCT
cana-539	112	26	trc	trc	NOUN
cana-539	112	27	’	'	PUNCT
cana-539	112	28	increases	increase	NOUN
cana-539	112	29	and	and	CCONJ
cana-539	112	30	the	the	DET
cana-539	112	31	value	value	NOUN
cana-539	112	32	of	of	ADP
cana-539	112	33	‘	'	PUNCT
cana-539	112	34	t	t	NOUN
cana-539	112	35	’	'	PUNCT
cana-539	112	36	decreases	decrease	NOUN
cana-539	112	37	.	.	PUNCT
cana-539	113	1	•	•	NOUN
cana-539	113	2	from	from	ADP
cana-539	113	3	table	table	NOUN
cana-539	113	4	3	3	NUM
cana-539	113	5	we	we	PRON
cana-539	113	6	can	can	AUX
cana-539	113	7	see	see	VERB
cana-539	113	8	that	that	SCONJ
cana-539	113	9	as	as	ADP
cana-539	113	10	the	the	DET
cana-539	113	11	value	value	NOUN
cana-539	113	12	of	of	ADP
cana-539	113	13	‘	'	PUNCT
cana-539	113	14	ξ	ξ	X
cana-539	113	15	’	'	PUNCT
cana-539	113	16	decreases	decrease	NOUN
cana-539	113	17	then	then	ADV
cana-539	113	18	value	value	NOUN
cana-539	113	19	of	of	ADP
cana-539	113	20	‘	'	PUNCT
cana-539	113	21	𝜎𝜃	𝜎𝜃	NOUN
cana-539	113	22	’	'	PUNCT
cana-539	113	23	increases	increase	NOUN
cana-539	113	24	which	which	PRON
cana-539	113	25	results	result	VERB
cana-539	113	26	in	in	ADP
cana-539	113	27	increase	increase	NOUN
cana-539	113	28	in	in	ADP
cana-539	113	29	the	the	DET
cana-539	113	30	value	value	NOUN
cana-539	113	31	of	of	ADP
cana-539	113	32	‘	'	PUNCT
cana-539	113	33	t	t	NOUN
cana-539	113	34	’	'	PUNCT
cana-539	113	35	and	and	CCONJ
cana-539	113	36	decrease	decrease	NOUN
cana-539	113	37	in	in	ADP
cana-539	113	38	the	the	DET
cana-539	113	39	value	value	NOUN
cana-539	113	40	of	of	ADP
cana-539	113	41	‘	'	PUNCT
cana-539	113	42	t	t	NOUN
cana-539	113	43	’	'	PUNCT
cana-539	113	44	and	and	CCONJ
cana-539	113	45	‘	'	PUNCT
cana-539	113	46	trc	trc	NOUN
cana-539	113	47	’	'	PUNCT
cana-539	113	48	.	.	PUNCT
cana-539	114	1	8	8	X
cana-539	114	2	.	.	X
cana-539	114	3	conclusion	conclusion	NOUN
cana-539	114	4	for	for	ADP
cana-539	114	5	the	the	DET
cana-539	114	6	dual	dual	ADJ
cana-539	114	7	warehouse	warehouse	NOUN
cana-539	114	8	model	model	NOUN
cana-539	114	9	for	for	ADP
cana-539	114	10	inventory	inventory	NOUN
cana-539	114	11	having	have	VERB
cana-539	114	12	demand	demand	NOUN
cana-539	114	13	as	as	ADP
cana-539	114	14	time	time	NOUN
cana-539	114	15	-	-	PUNCT
cana-539	114	16	dependent	dependent	ADJ
cana-539	114	17	and	and	CCONJ
cana-539	114	18	preservation	preservation	NOUN
cana-539	114	19	technology	technology	NOUN
cana-539	114	20	,	,	PUNCT
cana-539	114	21	we	we	PRON
cana-539	114	22	found	find	VERB
cana-539	114	23	that	that	SCONJ
cana-539	114	24	the	the	DET
cana-539	114	25	optimal	optimal	ADJ
cana-539	114	26	strategy	strategy	NOUN
cana-539	114	27	involves	involve	VERB
cana-539	114	28	dynamically	dynamically	ADV
cana-539	114	29	allocating	allocate	VERB
cana-539	114	30	inventory	inventory	NOUN
cana-539	114	31	among	among	ADP
cana-539	114	32	the	the	DET
cana-539	114	33	warehouses	warehouse	NOUN
cana-539	114	34	based	base	VERB
cana-539	114	35	on	on	ADP
cana-539	114	36	demand	demand	NOUN
cana-539	114	37	patterns	pattern	NOUN
cana-539	114	38	and	and	CCONJ
cana-539	114	39	the	the	DET
cana-539	114	40	effectiveness	effectiveness	NOUN
cana-539	114	41	of	of	ADP
cana-539	114	42	preservation	preservation	NOUN
cana-539	114	43	technology	technology	NOUN
cana-539	114	44	.	.	PUNCT
cana-539	115	1	we	we	PRON
cana-539	115	2	can	can	AUX
cana-539	115	3	see	see	VERB
cana-539	115	4	through	through	ADP
cana-539	115	5	the	the	DET
cana-539	115	6	numerical	numerical	ADJ
cana-539	115	7	illustration	illustration	NOUN
cana-539	115	8	and	and	CCONJ
cana-539	115	9	sensitivity	sensitivity	NOUN
cana-539	115	10	analysis	analysis	NOUN
cana-539	115	11	that	that	SCONJ
cana-539	115	12	how	how	SCONJ
cana-539	115	13	the	the	DET
cana-539	115	14	value	value	NOUN
cana-539	115	15	of	of	ADP
cana-539	115	16	total	total	ADJ
cana-539	115	17	relevant	relevant	ADJ
cana-539	115	18	cost	cost	NOUN
cana-539	115	19	fluctuates	fluctuate	NOUN
cana-539	115	20	for	for	ADP
cana-539	115	21	the	the	DET
cana-539	115	22	different	different	ADJ
cana-539	115	23	values	value	NOUN
cana-539	115	24	of	of	ADP
cana-539	115	25	parameters	parameter	NOUN
cana-539	115	26	.	.	PUNCT
cana-539	116	1	we	we	PRON
cana-539	116	2	can	can	AUX
cana-539	116	3	also	also	ADV
cana-539	116	4	see	see	VERB
cana-539	116	5	that	that	SCONJ
cana-539	116	6	by	by	ADP
cana-539	116	7	using	use	VERB
cana-539	116	8	the	the	DET
cana-539	116	9	preservation	preservation	NOUN
cana-539	116	10	technology	technology	NOUN
cana-539	116	11	we	we	PRON
cana-539	116	12	can	can	AUX
cana-539	116	13	reduce	reduce	VERB
cana-539	116	14	the	the	DET
cana-539	116	15	rate	rate	NOUN
cana-539	116	16	of	of	ADP
cana-539	116	17	deterioration	deterioration	NOUN
cana-539	116	18	and	and	CCONJ
cana-539	116	19	preserves	preserve	VERB
cana-539	116	20	the	the	DET
cana-539	116	21	products	product	NOUN
cana-539	116	22	for	for	ADP
cana-539	116	23	the	the	DET
cana-539	116	24	longer	long	ADJ
cana-539	116	25	time	time	NOUN
cana-539	116	26	.	.	PUNCT
cana-539	117	1	we	we	PRON
cana-539	117	2	have	have	AUX
cana-539	117	3	also	also	ADV
cana-539	117	4	drawn	draw	VERB
cana-539	117	5	the	the	DET
cana-539	117	6	graphs	graph	NOUN
cana-539	117	7	showing	show	VERB
cana-539	117	8	the	the	DET
cana-539	117	9	variation	variation	NOUN
cana-539	117	10	in	in	ADP
cana-539	117	11	total	total	ADJ
cana-539	117	12	cost	cost	NOUN
cana-539	117	13	with	with	ADP
cana-539	117	14	respect	respect	NOUN
cana-539	117	15	to	to	ADP
cana-539	117	16	the	the	DET
cana-539	117	17	demand	demand	NOUN
cana-539	117	18	parameters	parameter	NOUN
cana-539	117	19	.	.	PUNCT
cana-539	118	1	this	this	DET
cana-539	118	2	approach	approach	NOUN
cana-539	118	3	maximizes	maximize	VERB
cana-539	118	4	the	the	DET
cana-539	118	5	service	service	NOUN
cana-539	118	6	levels	level	NOUN
cana-539	118	7	while	while	SCONJ
cana-539	118	8	reducing	reduce	VERB
cana-539	118	9	the	the	DET
cana-539	118	10	costs	cost	NOUN
cana-539	118	11	,	,	PUNCT
cana-539	118	12	ensuring	ensure	VERB
cana-539	118	13	that	that	SCONJ
cana-539	118	14	products	product	NOUN
cana-539	118	15	will	will	AUX
cana-539	118	16	be	be	AUX
cana-539	118	17	available	available	ADJ
cana-539	118	18	when	when	SCONJ
cana-539	118	19	needed	need	VERB
cana-539	118	20	fig	fig	NOUN
cana-539	118	21	(	(	PUNCT
cana-539	118	22	a	a	PRON
cana-539	118	23	)	)	PUNCT
cana-539	118	24	fig	fig	NOUN
cana-539	118	25	(	(	PUNCT
cana-539	118	26	b	b	NOUN
cana-539	118	27	)	)	PUNCT
cana-539	118	28	communications	communication	NOUN
cana-539	118	29	on	on	ADP
cana-539	118	30	applied	apply	VERB
cana-539	118	31	nonlinear	nonlinear	ADJ
cana-539	118	32	analysis	analysis	NOUN
cana-539	118	33	issn	issn	NOUN
cana-539	118	34	:	:	PUNCT
cana-539	118	35	1074	1074	NUM
cana-539	118	36	-	-	PUNCT
cana-539	118	37	133x	133x	NUM
cana-539	118	38	vol	vol	NOUN
cana-539	118	39	31	31	NUM
cana-539	118	40	no	no	NOUN
cana-539	118	41	.	.	NOUN
cana-539	118	42	2	2	NUM
cana-539	118	43	(	(	PUNCT
cana-539	118	44	2024	2024	NUM
cana-539	118	45	)	)	PUNCT
cana-539	118	46	247	247	NUM
cana-539	118	47	https://internationalpubls.com	https://internationalpubls.com	X
cana-539	118	48	with	with	ADP
cana-539	118	49	minimizing	minimize	VERB
cana-539	118	50	the	the	DET
cana-539	118	51	risk	risk	NOUN
cana-539	118	52	of	of	ADP
cana-539	118	53	obsolescence	obsolescence	NOUN
cana-539	118	54	.	.	PUNCT
cana-539	119	1	this	this	DET
cana-539	119	2	model	model	NOUN
cana-539	119	3	can	can	AUX
cana-539	119	4	be	be	AUX
cana-539	119	5	applicable	applicable	ADJ
cana-539	119	6	for	for	ADP
cana-539	119	7	the	the	DET
cana-539	119	8	items	item	NOUN
cana-539	119	9	having	have	VERB
cana-539	119	10	linear	linear	ADJ
cana-539	119	11	time	time	NOUN
cana-539	119	12	-	-	PUNCT
cana-539	119	13	dependent	dependent	ADJ
cana-539	119	14	demand	demand	NOUN
cana-539	119	15	such	such	ADJ
cana-539	119	16	as	as	ADP
cana-539	119	17	food	food	NOUN
cana-539	119	18	items	item	NOUN
cana-539	119	19	,	,	PUNCT
cana-539	119	20	raw	raw	ADJ
cana-539	119	21	materials	material	NOUN
cana-539	119	22	and	and	CCONJ
cana-539	119	23	many	many	ADJ
cana-539	119	24	more	more	ADJ
cana-539	119	25	.	.	PUNCT
cana-539	120	1	references	reference	NOUN
cana-539	120	2	[	[	X
cana-539	120	3	1	1	NUM
cana-539	120	4	]	]	X
cana-539	120	5	hartley	hartley	PROPN
cana-539	120	6	,	,	PUNCT
cana-539	120	7	r.v	r.v	PROPN
cana-539	120	8	.	.	PROPN
cana-539	120	9	,	,	PUNCT
cana-539	120	10	(	(	PUNCT
cana-539	120	11	1976	1976	NUM
cana-539	120	12	)	)	PUNCT
cana-539	120	13	.	.	PUNCT
cana-539	121	1	operations	operation	NOUN
cana-539	121	2	researcha	researcha	ADJ
cana-539	121	3	managerial	managerial	ADJ
cana-539	121	4	emphasis	emphasis	NOUN
cana-539	121	5	,	,	PUNCT
cana-539	121	6	california	california	PROPN
cana-539	121	7	:	:	PUNCT
cana-539	121	8	good	good	ADJ
cana-539	121	9	year	year	NOUN
cana-539	121	10	publishing	publish	VERB
cana-539	121	11	company	company	NOUN
cana-539	121	12	.	.	PUNCT
cana-539	122	1	[	[	X
cana-539	122	2	2	2	NUM
cana-539	122	3	]	]	PUNCT
cana-539	122	4	sarma	sarma	NOUN
cana-539	122	5	,	,	PUNCT
cana-539	122	6	k.	k.	PROPN
cana-539	122	7	v.	v.	PROPN
cana-539	122	8	s.	s.	PROPN
cana-539	122	9	(	(	PUNCT
cana-539	122	10	1987	1987	NUM
cana-539	122	11	)	)	PUNCT
cana-539	122	12	.	.	PUNCT
cana-539	123	1	a	a	DET
cana-539	123	2	deterministic	deterministic	ADJ
cana-539	123	3	order	order	NOUN
cana-539	123	4	level	level	NOUN
cana-539	123	5	inventory	inventory	NOUN
cana-539	123	6	model	model	NOUN
cana-539	123	7	for	for	ADP
cana-539	123	8	deteriorating	deteriorate	VERB
cana-539	123	9	items	item	NOUN
cana-539	123	10	with	with	ADP
cana-539	123	11	two	two	NUM
cana-539	123	12	storage	storage	NOUN
cana-539	123	13	facilities	facility	NOUN
cana-539	123	14	.	.	PUNCT
cana-539	124	1	european	european	ADJ
cana-539	124	2	journal	journal	PROPN
cana-539	124	3	of	of	ADP
cana-539	124	4	operational	operational	ADJ
cana-539	124	5	research	research	NOUN
cana-539	124	6	,	,	PUNCT
cana-539	124	7	29(1	29(1	NUM
cana-539	124	8	)	)	PUNCT
cana-539	124	9	,	,	PUNCT
cana-539	124	10	70	70	NUM
cana-539	124	11	-	-	SYM
cana-539	124	12	73	73	NUM
cana-539	124	13	.	.	PUNCT
cana-539	125	1	[	[	X
cana-539	125	2	3	3	NUM
cana-539	125	3	]	]	X
cana-539	125	4	singh	singh	PROPN
cana-539	125	5	,	,	PUNCT
cana-539	125	6	s.	s.	PROPN
cana-539	125	7	r.	r.	PROPN
cana-539	125	8	,	,	PUNCT
cana-539	125	9	&	&	CCONJ
cana-539	125	10	rathore	rathore	PROPN
cana-539	125	11	,	,	PUNCT
cana-539	125	12	h.	h.	PROPN
cana-539	125	13	(	(	PUNCT
cana-539	125	14	2015	2015	NUM
cana-539	125	15	)	)	PUNCT
cana-539	125	16	.	.	PUNCT
cana-539	126	1	two	two	NUM
cana-539	126	2	-	-	PUNCT
cana-539	126	3	warehouse	warehouse	NOUN
cana-539	126	4	reverse	reverse	ADJ
cana-539	126	5	logistic	logistic	ADJ
cana-539	126	6	inventory	inventory	NOUN
cana-539	126	7	model	model	NOUN
cana-539	126	8	for	for	ADP
cana-539	126	9	deteriorating	deteriorate	VERB
cana-539	126	10	item	item	NOUN
cana-539	126	11	under	under	ADP
cana-539	126	12	learning	learn	VERB
cana-539	126	13	effect	effect	NOUN
cana-539	126	14	.	.	PUNCT
cana-539	127	1	in	in	ADP
cana-539	127	2	proceedings	proceeding	NOUN
cana-539	127	3	of	of	ADP
cana-539	127	4	fourth	fourth	ADJ
cana-539	127	5	international	international	ADJ
cana-539	127	6	conference	conference	NOUN
cana-539	127	7	on	on	ADP
cana-539	127	8	soft	soft	ADJ
cana-539	127	9	computing	computing	NOUN
cana-539	127	10	for	for	ADP
cana-539	127	11	problem	problem	NOUN
cana-539	127	12	solving	solve	VERB
cana-539	127	13	:	:	PUNCT
cana-539	127	14	socpros	socpro	NOUN
cana-539	127	15	2014	2014	NUM
cana-539	127	16	,	,	PUNCT
cana-539	127	17	volume	volume	NOUN
cana-539	127	18	1	1	NUM
cana-539	127	19	(	(	PUNCT
cana-539	127	20	pp	pp	ADJ
cana-539	127	21	.	.	PUNCT
cana-539	128	1	45	45	NUM
cana-539	128	2	-	-	SYM
cana-539	128	3	57	57	NUM
cana-539	128	4	)	)	PUNCT
cana-539	128	5	.	.	PUNCT
cana-539	129	1	springer	springer	PROPN
cana-539	129	2	india	india	PROPN
cana-539	129	3	.	.	PUNCT
cana-539	130	1	[	[	X
cana-539	130	2	4	4	NUM
cana-539	130	3	]	]	X
cana-539	130	4	kumar	kumar	PROPN
cana-539	130	5	,	,	PUNCT
cana-539	130	6	n.	n.	PROPN
cana-539	130	7	,	,	PUNCT
cana-539	130	8	singh	singh	PROPN
cana-539	130	9	,	,	PUNCT
cana-539	130	10	s.	s.	PROPN
cana-539	130	11	,	,	PUNCT
cana-539	130	12	&	&	CCONJ
cana-539	130	13	kumari	kumari	PROPN
cana-539	130	14	,	,	PUNCT
cana-539	130	15	r.	r.	PROPN
cana-539	130	16	(	(	PUNCT
cana-539	130	17	2013	2013	NUM
cana-539	130	18	)	)	PUNCT
cana-539	130	19	.	.	PUNCT
cana-539	130	20	two	two	NUM
cana-539	130	21	-	-	PUNCT
cana-539	130	22	warehouse	warehouse	NOUN
cana-539	130	23	inventory	inventory	NOUN
cana-539	130	24	model	model	NOUN
cana-539	130	25	of	of	ADP
cana-539	130	26	deteriorating	deteriorate	VERB
cana-539	130	27	items	item	NOUN
cana-539	130	28	with	with	ADP
cana-539	130	29	three	three	NUM
cana-539	130	30	-	-	PUNCT
cana-539	130	31	component	component	NOUN
cana-539	130	32	demand	demand	NOUN
cana-539	130	33	rate	rate	NOUN
cana-539	130	34	and	and	CCONJ
cana-539	130	35	time	time	NOUN
cana-539	130	36	-	-	PUNCT
cana-539	130	37	proportional	proportional	ADJ
cana-539	130	38	backlogging	backlogge	VERB
cana-539	130	39	rate	rate	NOUN
cana-539	130	40	in	in	ADP
cana-539	130	41	fuzzy	fuzzy	ADJ
cana-539	130	42	environment	environment	NOUN
cana-539	130	43	.	.	PUNCT
cana-539	131	1	international	international	ADJ
cana-539	131	2	journal	journal	PROPN
cana-539	131	3	of	of	ADP
cana-539	131	4	industrial	industrial	ADJ
cana-539	131	5	engineering	engineering	NOUN
cana-539	131	6	computations	computation	NOUN
cana-539	131	7	,	,	PUNCT
cana-539	131	8	4(4	4(4	NUM
cana-539	131	9	)	)	PUNCT
cana-539	131	10	,	,	PUNCT
cana-539	131	11	587	587	NUM
cana-539	131	12	-	-	SYM
cana-539	131	13	598	598	NUM
cana-539	131	14	.	.	PUNCT
cana-539	132	1	[	[	X
cana-539	132	2	5	5	NUM
cana-539	132	3	]	]	X
cana-539	132	4	singh	singh	PROPN
cana-539	132	5	,	,	PUNCT
cana-539	132	6	s.	s.	PROPN
cana-539	132	7	r.	r.	PROPN
cana-539	132	8	,	,	PUNCT
cana-539	132	9	&	&	CCONJ
cana-539	132	10	rathore	rathore	PROPN
cana-539	132	11	,	,	PUNCT
cana-539	132	12	h.	h.	PROPN
cana-539	132	13	(	(	PUNCT
cana-539	132	14	2014	2014	NUM
cana-539	132	15	,	,	PUNCT
cana-539	132	16	august	august	PROPN
cana-539	132	17	)	)	PUNCT
cana-539	132	18	.	.	PUNCT
cana-539	133	1	a	a	DET
cana-539	133	2	two	two	NUM
cana-539	133	3	warehouse	warehouse	NOUN
cana-539	133	4	inventory	inventory	NOUN
cana-539	133	5	model	model	NOUN
cana-539	133	6	with	with	ADP
cana-539	133	7	non	non	ADJ
cana-539	133	8	-	-	ADJ
cana-539	133	9	instantaneous	instantaneous	ADJ
cana-539	133	10	deterioration	deterioration	NOUN
cana-539	133	11	and	and	CCONJ
cana-539	133	12	partial	partial	ADJ
cana-539	133	13	backlogging	backlogging	NOUN
cana-539	133	14	.	.	PUNCT
cana-539	134	1	in	in	ADP
cana-539	134	2	2014	2014	NUM
cana-539	134	3	seventh	seventh	ADJ
cana-539	134	4	international	international	ADJ
cana-539	134	5	conference	conference	NOUN
cana-539	134	6	on	on	ADP
cana-539	134	7	contemporary	contemporary	ADJ
cana-539	134	8	computing	computing	PROPN
cana-539	134	9	(	(	PUNCT
cana-539	134	10	ic3	ic3	PROPN
cana-539	134	11	)	)	PUNCT
cana-539	134	12	(	(	PUNCT
cana-539	134	13	pp	pp	ADJ
cana-539	134	14	.	.	PUNCT
cana-539	135	1	431	431	NUM
cana-539	135	2	-	-	SYM
cana-539	135	3	436	436	NUM
cana-539	135	4	)	)	PUNCT
cana-539	135	5	.	.	PUNCT
cana-539	136	1	ieee	ieee	NOUN
cana-539	136	2	.	.	PUNCT
cana-539	137	1	[	[	X
cana-539	137	2	6	6	NUM
cana-539	137	3	]	]	X
cana-539	137	4	sharma	sharma	NOUN
cana-539	137	5	,	,	PUNCT
cana-539	137	6	v.	v.	PROPN
cana-539	137	7	,	,	PUNCT
cana-539	137	8	&	&	CCONJ
cana-539	137	9	chaudhary	chaudhary	PROPN
cana-539	137	10	,	,	PUNCT
cana-539	137	11	r.	r.	PROPN
cana-539	137	12	(	(	PUNCT
cana-539	137	13	2016	2016	NUM
cana-539	137	14	)	)	PUNCT
cana-539	137	15	.	.	PUNCT
cana-539	138	1	two	two	NUM
cana-539	138	2	-	-	PUNCT
cana-539	138	3	warehouse	warehouse	NOUN
cana-539	138	4	optimized	optimize	VERB
cana-539	138	5	inventory	inventory	NOUN
cana-539	138	6	model	model	NOUN
cana-539	138	7	for	for	ADP
cana-539	138	8	time	time	NOUN
cana-539	138	9	dependent	dependent	ADJ
cana-539	138	10	decaying	decay	VERB
cana-539	138	11	items	item	NOUN
cana-539	138	12	with	with	ADP
cana-539	138	13	ramp	ramp	NOUN
cana-539	138	14	type	type	NOUN
cana-539	138	15	demand	demand	NOUN
cana-539	138	16	rate	rate	NOUN
cana-539	138	17	under	under	ADP
cana-539	138	18	inflation	inflation	NOUN
cana-539	138	19	.	.	PUNCT
cana-539	139	1	uncertain	uncertain	ADJ
cana-539	139	2	supply	supply	NOUN
cana-539	139	3	chain	chain	NOUN
cana-539	139	4	management	management	NOUN
cana-539	139	5	,	,	PUNCT
cana-539	139	6	4(4	4(4	NUM
cana-539	139	7	)	)	PUNCT
cana-539	139	8	,	,	PUNCT
cana-539	139	9	287	287	NUM
cana-539	139	10	-	-	SYM
cana-539	139	11	306	306	NUM
cana-539	139	12	.	.	PUNCT
cana-539	140	1	[	[	X
cana-539	140	2	7	7	NUM
cana-539	140	3	]	]	X
cana-539	140	4	agrawal	agrawal	PROPN
cana-539	140	5	,	,	PUNCT
cana-539	140	6	s.	s.	PROPN
cana-539	140	7	,	,	PUNCT
cana-539	140	8	&	&	CCONJ
cana-539	140	9	banerjee	banerjee	PROPN
cana-539	140	10	,	,	PUNCT
cana-539	140	11	s.	s.	PROPN
cana-539	140	12	(	(	PUNCT
cana-539	140	13	2011	2011	NUM
cana-539	140	14	)	)	PUNCT
cana-539	140	15	.	.	PUNCT
cana-539	141	1	two	two	NUM
cana-539	141	2	-	-	PUNCT
cana-539	141	3	warehouse	warehouse	NOUN
cana-539	141	4	inventory	inventory	NOUN
cana-539	141	5	model	model	NOUN
cana-539	141	6	with	with	ADP
cana-539	141	7	ramp	ramp	NOUN
cana-539	141	8	-	-	PUNCT
cana-539	141	9	type	type	NOUN
cana-539	141	10	demand	demand	NOUN
cana-539	141	11	and	and	CCONJ
cana-539	141	12	partially	partially	ADV
cana-539	141	13	backlogged	backlogge	VERB
cana-539	141	14	shortages	shortage	NOUN
cana-539	141	15	.	.	PUNCT
cana-539	142	1	international	international	ADJ
cana-539	142	2	journal	journal	PROPN
cana-539	142	3	of	of	ADP
cana-539	142	4	systems	system	NOUN
cana-539	142	5	science	science	NOUN
cana-539	142	6	,	,	PUNCT
cana-539	142	7	42(7	42(7	NOUN
cana-539	142	8	)	)	PUNCT
cana-539	142	9	,	,	PUNCT
cana-539	142	10	1115	1115	NUM
cana-539	142	11	-	-	SYM
cana-539	142	12	1126	1126	NUM
cana-539	142	13	.	.	PUNCT
cana-539	143	1	[	[	X
cana-539	143	2	8	8	NUM
cana-539	143	3	]	]	X
cana-539	143	4	singh	singh	PROPN
cana-539	143	5	,	,	PUNCT
cana-539	143	6	s.	s.	PROPN
cana-539	143	7	r.	r.	PROPN
cana-539	143	8	,	,	PUNCT
cana-539	143	9	kumari	kumari	PROPN
cana-539	143	10	,	,	PUNCT
cana-539	143	11	r.	r.	PROPN
cana-539	143	12	,	,	PUNCT
cana-539	143	13	&	&	CCONJ
cana-539	143	14	kumar	kumar	PROPN
cana-539	143	15	,	,	PUNCT
cana-539	143	16	n.	n.	PROPN
cana-539	143	17	(	(	PUNCT
cana-539	143	18	2011	2011	NUM
cana-539	143	19	)	)	PUNCT
cana-539	143	20	.	.	PUNCT
cana-539	144	1	a	a	DET
cana-539	144	2	deterministic	deterministic	ADJ
cana-539	144	3	two	two	NUM
cana-539	144	4	warehouse	warehouse	NOUN
cana-539	144	5	inventory	inventory	NOUN
cana-539	144	6	model	model	NOUN
cana-539	144	7	for	for	ADP
cana-539	144	8	deteriorating	deteriorate	VERB
cana-539	144	9	items	item	NOUN
cana-539	144	10	with	with	ADP
cana-539	144	11	stock	stock	NOUN
cana-539	144	12	-	-	PUNCT
cana-539	144	13	dependent	dependent	ADJ
cana-539	144	14	demand	demand	NOUN
cana-539	144	15	and	and	CCONJ
cana-539	144	16	shortages	shortage	NOUN
cana-539	144	17	under	under	ADP
cana-539	144	18	the	the	DET
cana-539	144	19	conditions	condition	NOUN
cana-539	144	20	of	of	ADP
cana-539	144	21	permissible	permissible	ADJ
cana-539	144	22	delay	delay	NOUN
cana-539	144	23	.	.	PUNCT
cana-539	145	1	international	international	ADJ
cana-539	145	2	journal	journal	PROPN
cana-539	145	3	of	of	ADP
cana-539	145	4	mathematical	mathematical	ADJ
cana-539	145	5	modelling	modelling	NOUN
cana-539	145	6	and	and	CCONJ
cana-539	145	7	numerical	numerical	ADJ
cana-539	145	8	optimisation	optimisation	NOUN
cana-539	145	9	,	,	PUNCT
cana-539	145	10	2(4	2(4	NUM
cana-539	145	11	)	)	PUNCT
cana-539	145	12	,	,	PUNCT
cana-539	145	13	357	357	NUM
cana-539	145	14	-	-	SYM
cana-539	145	15	375	375	NUM
cana-539	145	16	.	.	PUNCT
cana-539	146	1	[	[	X
cana-539	146	2	9	9	NUM
cana-539	146	3	]	]	X
cana-539	146	4	zhou	zhou	X
cana-539	146	5	,	,	PUNCT
cana-539	146	6	y.	y.	PROPN
cana-539	146	7	w.	w.	PROPN
cana-539	146	8	,	,	PUNCT
cana-539	146	9	&	&	CCONJ
cana-539	146	10	yang	yang	PROPN
cana-539	146	11	,	,	PUNCT
cana-539	146	12	s.	s.	PROPN
cana-539	146	13	l.	l.	PROPN
cana-539	146	14	(	(	PUNCT
cana-539	146	15	2005	2005	NUM
cana-539	146	16	)	)	PUNCT
cana-539	146	17	.	.	PUNCT
cana-539	147	1	a	a	DET
cana-539	147	2	two	two	NUM
cana-539	147	3	-	-	PUNCT
cana-539	147	4	warehouse	warehouse	NOUN
cana-539	147	5	inventory	inventory	NOUN
cana-539	147	6	model	model	NOUN
cana-539	147	7	for	for	ADP
cana-539	147	8	items	item	NOUN
cana-539	147	9	with	with	ADP
cana-539	147	10	stock	stock	NOUN
cana-539	147	11	-	-	PUNCT
cana-539	147	12	leveldependent	leveldependent	NOUN
cana-539	147	13	demand	demand	NOUN
cana-539	147	14	rate	rate	NOUN
cana-539	147	15	.	.	PUNCT
cana-539	148	1	international	international	ADJ
cana-539	148	2	journal	journal	PROPN
cana-539	148	3	of	of	ADP
cana-539	148	4	production	production	NOUN
cana-539	148	5	economics	economic	NOUN
cana-539	148	6	,	,	PUNCT
cana-539	148	7	95(2	95(2	NOUN
cana-539	148	8	)	)	PUNCT
cana-539	148	9	,	,	PUNCT
cana-539	148	10	215	215	NUM
cana-539	148	11	-	-	SYM
cana-539	148	12	228	228	NUM
cana-539	148	13	.	.	PUNCT
cana-539	149	1	[	[	X
cana-539	149	2	10	10	NUM
cana-539	149	3	]	]	X
cana-539	149	4	gupta	gupta	PROPN
cana-539	149	5	,	,	PUNCT
cana-539	149	6	c.	c.	PROPN
cana-539	149	7	,	,	PUNCT
cana-539	149	8	kumar	kumar	PROPN
cana-539	149	9	,	,	PUNCT
cana-539	149	10	v.	v.	PROPN
cana-539	149	11	,	,	PUNCT
cana-539	149	12	&	&	CCONJ
cana-539	149	13	gola	gola	PROPN
cana-539	149	14	,	,	PUNCT
cana-539	149	15	k.	k.	PROPN
cana-539	149	16	k.	k.	PROPN
cana-539	149	17	(	(	PUNCT
cana-539	149	18	2022	2022	NUM
cana-539	149	19	,	,	PUNCT
cana-539	149	20	december	december	PROPN
cana-539	149	21	)	)	PUNCT
cana-539	149	22	.	.	PUNCT
cana-539	150	1	implementation	implementation	NOUN
cana-539	150	2	analysis	analysis	NOUN
cana-539	150	3	for	for	ADP
cana-539	150	4	the	the	DET
cana-539	150	5	applications	application	NOUN
cana-539	150	6	of	of	ADP
cana-539	150	7	warehouse	warehouse	NOUN
cana-539	150	8	model	model	NOUN
cana-539	150	9	under	under	ADP
cana-539	150	10	linear	linear	ADJ
cana-539	150	11	integer	integer	NOUN
cana-539	150	12	problems	problem	NOUN
cana-539	150	13	.	.	PUNCT
cana-539	151	1	in	in	ADP
cana-539	151	2	international	international	ADJ
cana-539	151	3	conference	conference	NOUN
cana-539	151	4	on	on	ADP
cana-539	151	5	intelligent	intelligent	ADJ
cana-539	151	6	systems	system	NOUN
cana-539	151	7	design	design	NOUN
cana-539	151	8	and	and	CCONJ
cana-539	151	9	applications	application	NOUN
cana-539	151	10	(	(	PUNCT
cana-539	151	11	pp	pp	ADJ
cana-539	151	12	.	.	PUNCT
cana-539	151	13	239	239	NUM
cana-539	151	14	-	-	SYM
cana-539	151	15	247	247	NUM
cana-539	151	16	)	)	PUNCT
cana-539	151	17	.	.	PUNCT
cana-539	152	1	cham	cham	PROPN
cana-539	152	2	:	:	PUNCT
cana-539	152	3	springer	springer	NOUN
cana-539	152	4	nature	nature	PROPN
cana-539	152	5	switzerland	switzerland	PROPN
cana-539	152	6	.	.	PUNCT
cana-539	153	1	[	[	X
cana-539	153	2	11	11	NUM
cana-539	153	3	]	]	X
cana-539	153	4	gupta	gupta	PROPN
cana-539	153	5	,	,	PUNCT
cana-539	153	6	c.	c.	PROPN
cana-539	153	7	,	,	PUNCT
cana-539	153	8	kumar	kumar	PROPN
cana-539	153	9	,	,	PUNCT
cana-539	153	10	v.	v.	PROPN
cana-539	153	11	,	,	PUNCT
cana-539	153	12	&	&	CCONJ
cana-539	153	13	kumar	kumar	PROPN
cana-539	153	14	,	,	PUNCT
cana-539	153	15	k.	k.	PROPN
cana-539	153	16	(	(	PUNCT
cana-539	153	17	2022	2022	NUM
cana-539	153	18	,	,	PUNCT
cana-539	153	19	december	december	PROPN
cana-539	153	20	)	)	PUNCT
cana-539	153	21	.	.	PUNCT
cana-539	154	1	a	a	DET
cana-539	154	2	study	study	NOUN
cana-539	154	3	on	on	ADP
cana-539	154	4	the	the	DET
cana-539	154	5	applications	application	NOUN
cana-539	154	6	of	of	ADP
cana-539	154	7	supply	supply	NOUN
cana-539	154	8	chain	chain	NOUN
cana-539	154	9	management	management	NOUN
cana-539	154	10	.	.	PUNCT
cana-539	155	1	in	in	ADP
cana-539	155	2	2022	2022	NUM
cana-539	155	3	11th	11th	ADJ
cana-539	155	4	international	international	ADJ
cana-539	155	5	conference	conference	NOUN
cana-539	155	6	on	on	ADP
cana-539	155	7	system	system	NOUN
cana-539	155	8	modeling	modeling	NOUN
cana-539	155	9	&	&	CCONJ
cana-539	155	10	advancement	advancement	NOUN
cana-539	155	11	in	in	ADP
cana-539	155	12	research	research	NOUN
cana-539	155	13	trends	trend	NOUN
cana-539	155	14	(	(	PUNCT
cana-539	155	15	smart	smart	ADJ
cana-539	155	16	)	)	PUNCT
cana-539	155	17	(	(	PUNCT
cana-539	155	18	pp	pp	ADV
cana-539	155	19	.	.	PUNCT
cana-539	156	1	737	737	NUM
cana-539	156	2	-	-	SYM
cana-539	156	3	741	741	NUM
cana-539	156	4	)	)	PUNCT
cana-539	156	5	.	.	PUNCT
cana-539	157	1	ieee	ieee	NOUN
cana-539	157	2	.	.	PUNCT
cana-539	158	1	[	[	X
cana-539	158	2	12	12	NUM
cana-539	158	3	]	]	X
cana-539	158	4	saxena	saxena	PROPN
cana-539	158	5	,	,	PUNCT
cana-539	158	6	a.	a.	PROPN
cana-539	158	7	k.	k.	PROPN
cana-539	158	8	(	(	PUNCT
cana-539	158	9	2022	2022	NUM
cana-539	158	10	,	,	PUNCT
cana-539	158	11	december	december	PROPN
cana-539	158	12	)	)	PUNCT
cana-539	158	13	.	.	PUNCT
cana-539	159	1	an	an	DET
cana-539	159	2	eoq	eoq	NOUN
cana-539	159	3	model	model	NOUN
cana-539	159	4	for	for	ADP
cana-539	159	5	deteriorating	deteriorate	VERB
cana-539	159	6	items	item	NOUN
cana-539	159	7	with	with	ADP
cana-539	159	8	time	time	NOUN
cana-539	159	9	dependent	dependent	ADJ
cana-539	159	10	demand	demand	NOUN
cana-539	159	11	.	.	PUNCT
cana-539	160	1	in	in	ADP
cana-539	160	2	2022	2022	NUM
cana-539	160	3	11th	11th	ADJ
cana-539	160	4	international	international	ADJ
cana-539	160	5	conference	conference	NOUN
cana-539	160	6	on	on	ADP
cana-539	160	7	system	system	NOUN
cana-539	160	8	modeling	modeling	NOUN
cana-539	160	9	&	&	CCONJ
cana-539	160	10	advancement	advancement	NOUN
cana-539	160	11	in	in	ADP
cana-539	160	12	research	research	NOUN
cana-539	160	13	trends	trend	NOUN
cana-539	160	14	(	(	PUNCT
cana-539	160	15	smart	smart	ADJ
cana-539	160	16	)	)	PUNCT
cana-539	160	17	(	(	PUNCT
cana-539	160	18	pp	pp	ADJ
cana-539	160	19	.	.	PUNCT
cana-539	160	20	926	926	NUM
cana-539	160	21	-	-	SYM
cana-539	160	22	930	930	NUM
cana-539	160	23	)	)	PUNCT
cana-539	160	24	.	.	PUNCT
cana-539	161	1	ieee	ieee	PROPN
cana-539	161	2	.	.	PUNCT
cana-539	162	1	[	[	X
cana-539	162	2	13	13	NUM
cana-539	162	3	]	]	X
cana-539	162	4	saxena	saxena	PROPN
cana-539	162	5	,	,	PUNCT
cana-539	162	6	a.	a.	PROPN
cana-539	162	7	k.	k.	PROPN
cana-539	162	8	(	(	PUNCT
cana-539	162	9	2021	2021	NUM
cana-539	162	10	,	,	PUNCT
cana-539	162	11	december	december	PROPN
cana-539	162	12	)	)	PUNCT
cana-539	162	13	.	.	PUNCT
cana-539	163	1	review	review	NOUN
cana-539	163	2	on	on	ADP
cana-539	163	3	eoq	eoq	NOUN
cana-539	163	4	models	model	NOUN
cana-539	163	5	for	for	ADP
cana-539	163	6	instanteneous	instanteneous	ADJ
cana-539	163	7	and	and	CCONJ
cana-539	163	8	non	non	ADJ
cana-539	163	9	-	-	ADJ
cana-539	163	10	instanteneous	instanteneous	ADJ
cana-539	163	11	deteriorating	deteriorating	ADJ
cana-539	163	12	items	item	NOUN
cana-539	163	13	.	.	PUNCT
cana-539	164	1	in	in	ADP
cana-539	164	2	2021	2021	NUM
cana-539	164	3	10th	10th	ADJ
cana-539	164	4	international	international	ADJ
cana-539	164	5	conference	conference	NOUN
cana-539	164	6	on	on	ADP
cana-539	164	7	system	system	NOUN
cana-539	164	8	modeling	modeling	NOUN
cana-539	164	9	&	&	CCONJ
cana-539	164	10	advancement	advancement	NOUN
cana-539	164	11	in	in	ADP
cana-539	164	12	research	research	NOUN
cana-539	164	13	trends	trend	NOUN
cana-539	164	14	(	(	PUNCT
cana-539	164	15	smart	smart	ADJ
cana-539	164	16	)	)	PUNCT
cana-539	164	17	(	(	PUNCT
cana-539	164	18	pp	pp	X
cana-539	164	19	.	.	PUNCT
cana-539	165	1	312	312	NUM
cana-539	165	2	-	-	SYM
cana-539	165	3	315	315	NUM
cana-539	165	4	)	)	PUNCT
cana-539	165	5	.	.	PUNCT
cana-539	166	1	ieee	ieee	NOUN
cana-539	166	2	.	.	PUNCT
cana-539	167	1	[	[	X
cana-539	167	2	14	14	NUM
cana-539	167	3	]	]	PUNCT
cana-539	167	4	rastogi	rastogi	NOUN
cana-539	167	5	,	,	PUNCT
cana-539	167	6	m.	m.	NOUN
cana-539	167	7	,	,	PUNCT
cana-539	167	8	singh	singh	PROPN
cana-539	167	9	,	,	PUNCT
cana-539	167	10	s.	s.	PROPN
cana-539	167	11	,	,	PUNCT
cana-539	167	12	kushwah	kushwah	PROPN
cana-539	167	13	,	,	PUNCT
cana-539	167	14	p.	p.	PROPN
cana-539	167	15	,	,	PUNCT
cana-539	167	16	&	&	CCONJ
cana-539	167	17	tayal	tayal	NOUN
cana-539	167	18	,	,	PUNCT
cana-539	167	19	s.	s.	PROPN
cana-539	167	20	(	(	PUNCT
cana-539	167	21	2017	2017	NUM
cana-539	167	22	)	)	PUNCT
cana-539	167	23	.	.	PUNCT
cana-539	168	1	two	two	NUM
cana-539	168	2	warehouse	warehouse	NOUN
cana-539	168	3	inventory	inventory	NOUN
cana-539	168	4	policy	policy	NOUN
cana-539	168	5	with	with	ADP
cana-539	168	6	price	price	NOUN
cana-539	168	7	dependent	dependent	ADJ
cana-539	168	8	demand	demand	NOUN
cana-539	168	9	and	and	CCONJ
cana-539	168	10	deterioration	deterioration	NOUN
cana-539	168	11	under	under	ADP
cana-539	168	12	partial	partial	ADJ
cana-539	168	13	backlogging	backlogging	NOUN
cana-539	168	14	.	.	PUNCT
cana-539	169	1	decision	decision	NOUN
cana-539	169	2	science	science	NOUN
cana-539	169	3	letters	letter	NOUN
cana-539	169	4	,	,	PUNCT
cana-539	169	5	6(1	6(1	NUM
cana-539	169	6	)	)	PUNCT
cana-539	169	7	,	,	PUNCT
cana-539	169	8	11	11	NUM
cana-539	169	9	-	-	SYM
cana-539	169	10	22	22	NUM
cana-539	169	11	.	.	PUNCT
cana-539	170	1	[	[	X
cana-539	170	2	15	15	NUM
cana-539	170	3	]	]	X
cana-539	170	4	mandal	mandal	PROPN
cana-539	170	5	,	,	PUNCT
cana-539	170	6	b.	b.	PROPN
cana-539	170	7	a.	a.	PROPN
cana-539	170	8	,	,	PUNCT
cana-539	170	9	&	&	CCONJ
cana-539	170	10	phaujdar	phaujdar	PROPN
cana-539	170	11	,	,	PUNCT
cana-539	170	12	s.	s.	PROPN
cana-539	170	13	(	(	PUNCT
cana-539	170	14	1989	1989	NUM
cana-539	170	15	)	)	PUNCT
cana-539	170	16	.	.	PUNCT
cana-539	171	1	an	an	DET
cana-539	171	2	inventory	inventory	NOUN
cana-539	171	3	model	model	NOUN
cana-539	171	4	for	for	ADP
cana-539	171	5	deteriorating	deteriorate	VERB
cana-539	171	6	items	item	NOUN
cana-539	171	7	and	and	CCONJ
cana-539	171	8	stock	stock	NOUN
cana-539	171	9	-	-	PUNCT
cana-539	171	10	dependent	dependent	ADJ
cana-539	171	11	consumption	consumption	NOUN
cana-539	171	12	rate	rate	NOUN
cana-539	171	13	.	.	PUNCT
cana-539	172	1	journal	journal	NOUN
cana-539	172	2	of	of	ADP
cana-539	172	3	the	the	DET
cana-539	172	4	operational	operational	ADJ
cana-539	172	5	research	research	NOUN
cana-539	172	6	society	society	NOUN
cana-539	172	7	,	,	PUNCT
cana-539	172	8	40(5	40(5	NOUN
cana-539	172	9	)	)	PUNCT
cana-539	172	10	,	,	PUNCT
cana-539	172	11	483	483	NUM
cana-539	172	12	-	-	SYM
cana-539	172	13	488	488	NUM
cana-539	172	14	.	.	PUNCT