id sid tid token lemma pos cana-380 1 1 communications communication NOUN cana-380 1 2 on on ADP cana-380 1 3 applied apply VERB cana-380 1 4 nonlinear nonlinear ADJ cana-380 1 5 analysis analysis NOUN cana-380 1 6 issn issn NOUN cana-380 1 7 : : PUNCT cana-380 1 8 1074 1074 NUM cana-380 1 9 - - PUNCT cana-380 1 10 133x 133x NUM cana-380 1 11 vol vol NOUN cana-380 1 12 31 31 NUM cana-380 1 13 no no NOUN cana-380 1 14 . . NOUN cana-380 1 15 1 1 NUM cana-380 1 16 ( ( PUNCT cana-380 1 17 2024 2024 NUM cana-380 1 18 ) ) PUNCT cana-380 1 19 177 177 NUM cana-380 1 20 https://internationalpubls.com https://internationalpubls.com X cana-380 1 21 an an DET cana-380 1 22 inventory inventory NOUN cana-380 1 23 model model NOUN cana-380 1 24 with with ADP cana-380 1 25 fluctuate fluctuate NOUN cana-380 1 26 ordering ordering NOUN cana-380 1 27 and and CCONJ cana-380 1 28 holding hold VERB cana-380 1 29 cost cost NOUN cana-380 1 30 with with ADP cana-380 1 31 salvage salvage NOUN cana-380 1 32 value value NOUN cana-380 1 33 for for ADP cana-380 1 34 time time NOUN cana-380 1 35 sensitive sensitive ADJ cana-380 1 36 demand demand NOUN cana-380 1 37 and and CCONJ cana-380 1 38 partial partial ADJ cana-380 1 39 backlogging backlogge VERB cana-380 1 40 garima garima PROPN cana-380 2 1 khare1 khare1 PROPN cana-380 2 2 , , PUNCT cana-380 2 3 garima garima PROPN cana-380 2 4 sharma1 sharma1 PROPN cana-380 2 5 1department 1department NUM cana-380 2 6 of of ADP cana-380 2 7 mathematics mathematic NOUN cana-380 2 8 , , PUNCT cana-380 2 9 school school NOUN cana-380 2 10 of of ADP cana-380 2 11 liberal liberal ADJ cana-380 2 12 arts art NOUN cana-380 2 13 and and CCONJ cana-380 2 14 sciences science NOUN cana-380 2 15 , , PUNCT cana-380 2 16 mody mody PROPN cana-380 2 17 university university PROPN cana-380 2 18 of of ADP cana-380 2 19 science science NOUN cana-380 2 20 and and CCONJ cana-380 2 21 technology technology NOUN cana-380 2 22 , , PUNCT cana-380 2 23 lakshmangarh-332311 lakshmangarh-332311 NOUN cana-380 2 24 , , PUNCT cana-380 2 25 rajasthan rajasthan PROPN cana-380 2 26 , , PUNCT cana-380 2 27 india india PROPN cana-380 2 28 corresponding corresponding ADJ cana-380 2 29 author author NOUN cana-380 2 30 : : PUNCT cana-380 2 31 garimashish188@gmail.com garimashish188@gmail.com X cana-380 3 1 contributing contribute VERB cana-380 3 2 author author NOUN cana-380 3 3 : : PUNCT cana-380 3 4 garimasharma.slas@modyuniversity.ac.in garimasharma.slas@modyuniversity.ac.in NUM cana-380 3 5 article article NOUN cana-380 3 6 history history NOUN cana-380 3 7 : : PUNCT cana-380 3 8 received receive VERB cana-380 3 9 : : PUNCT cana-380 3 10 12 12 NUM cana-380 3 11 - - SYM cana-380 3 12 10 10 NUM cana-380 3 13 - - PUNCT cana-380 3 14 2023 2023 NUM cana-380 3 15 revised revise VERB cana-380 3 16 : : PUNCT cana-380 3 17 24 24 NUM cana-380 3 18 - - SYM cana-380 3 19 11 11 NUM cana-380 3 20 - - SYM cana-380 3 21 2023 2023 NUM cana-380 3 22 accepted accept VERB cana-380 3 23 : : PUNCT cana-380 3 24 10 10 NUM cana-380 3 25 - - SYM cana-380 3 26 12 12 NUM cana-380 3 27 - - PUNCT cana-380 3 28 2023 2023 NUM cana-380 3 29 abstract abstract NOUN cana-380 3 30 : : PUNCT cana-380 3 31 inventory inventory NOUN cana-380 3 32 models model NOUN cana-380 3 33 are be AUX cana-380 3 34 essential essential ADJ cana-380 3 35 in in ADP cana-380 3 36 evaluating evaluate VERB cana-380 3 37 a a DET cana-380 3 38 wide wide ADJ cana-380 3 39 range range NOUN cana-380 3 40 of of ADP cana-380 3 41 genuine genuine ADJ cana-380 3 42 situations situation NOUN cana-380 3 43 that that PRON cana-380 3 44 occur occur VERB cana-380 3 45 in in ADP cana-380 3 46 locations location NOUN cana-380 3 47 , , PUNCT cana-380 3 48 including include VERB cana-380 3 49 grocery grocery NOUN cana-380 3 50 and and CCONJ cana-380 3 51 vegetable vegetable NOUN cana-380 3 52 markets market NOUN cana-380 3 53 , , PUNCT cana-380 3 54 market market NOUN cana-380 3 55 yards yard NOUN cana-380 3 56 , , PUNCT cana-380 3 57 petroleum petroleum NOUN cana-380 3 58 exploration exploration NOUN cana-380 3 59 businesses business NOUN cana-380 3 60 , , PUNCT cana-380 3 61 etc etc X cana-380 3 62 . . X cana-380 4 1 this this DET cana-380 4 2 article article NOUN cana-380 4 3 introduces introduce VERB cana-380 4 4 an an DET cana-380 4 5 economic economic ADJ cana-380 4 6 order order NOUN cana-380 4 7 quantity quantity NOUN cana-380 4 8 ( ( PUNCT cana-380 4 9 eoq eoq NOUN cana-380 4 10 ) ) PUNCT cana-380 4 11 profit profit NOUN cana-380 4 12 optimization optimization NOUN cana-380 4 13 for for ADP cana-380 4 14 degrading degrade VERB cana-380 4 15 products product NOUN cana-380 4 16 . . PUNCT cana-380 5 1 it it PRON cana-380 5 2 analyzes analyze VERB cana-380 5 3 how how SCONJ cana-380 5 4 variable variable ADJ cana-380 5 5 ordering ordering NOUN cana-380 5 6 prices price NOUN cana-380 5 7 and and CCONJ cana-380 5 8 holding hold VERB cana-380 5 9 charges charge NOUN cana-380 5 10 affect affect VERB cana-380 5 11 profit profit NOUN cana-380 5 12 margins margin NOUN cana-380 5 13 within within ADP cana-380 5 14 restricted restricted ADJ cana-380 5 15 planning planning NOUN cana-380 5 16 horizons horizon NOUN cana-380 5 17 . . PUNCT cana-380 6 1 here here ADV cana-380 6 2 demand demand NOUN cana-380 6 3 rate rate NOUN cana-380 6 4 is be AUX cana-380 6 5 projected project VERB cana-380 6 6 to to PART cana-380 6 7 be be AUX cana-380 6 8 time time NOUN cana-380 6 9 sensitive sensitive ADJ cana-380 6 10 , , PUNCT cana-380 6 11 and and CCONJ cana-380 6 12 the the DET cana-380 6 13 worsening worsen VERB cana-380 6 14 price price NOUN cana-380 6 15 is be AUX cana-380 6 16 proportional proportional ADJ cana-380 6 17 to to ADP cana-380 6 18 time time NOUN cana-380 6 19 . . PUNCT cana-380 7 1 models model NOUN cana-380 7 2 of of ADP cana-380 7 3 inventories inventory NOUN cana-380 7 4 for for ADP cana-380 7 5 decaying decay VERB cana-380 7 6 objects object NOUN cana-380 7 7 are be AUX cana-380 7 8 established establish VERB cana-380 7 9 . . PUNCT cana-380 8 1 the the DET cana-380 8 2 dilemma dilemma NOUN cana-380 8 3 is be AUX cana-380 8 4 solved solve VERB cana-380 8 5 when when SCONJ cana-380 8 6 shortages shortage NOUN cana-380 8 7 are be AUX cana-380 8 8 considered consider VERB cana-380 8 9 acceptable acceptable ADJ cana-380 8 10 and and CCONJ cana-380 8 11 partially partially ADV cana-380 8 12 backordered backordere VERB cana-380 8 13 . . PUNCT cana-380 9 1 the the DET cana-380 9 2 holding hold VERB cana-380 9 3 and and CCONJ cana-380 9 4 ordering ordering NOUN cana-380 9 5 expenses expense NOUN cana-380 9 6 tend tend VERB cana-380 9 7 to to PART cana-380 9 8 fluctuate fluctuate VERB cana-380 9 9 . . PUNCT cana-380 10 1 the the DET cana-380 10 2 salvage salvage NOUN cana-380 10 3 value value NOUN cana-380 10 4 is be AUX cana-380 10 5 allocated allocate VERB cana-380 10 6 to to ADP cana-380 10 7 items item NOUN cana-380 10 8 in in ADP cana-380 10 9 the the DET cana-380 10 10 system system NOUN cana-380 10 11 that that PRON cana-380 10 12 have have AUX cana-380 10 13 deteriorated deteriorate VERB cana-380 10 14 . . PUNCT cana-380 11 1 a a DET cana-380 11 2 numerical numerical ADJ cana-380 11 3 example example NOUN cana-380 11 4 is be AUX cana-380 11 5 used use VERB cana-380 11 6 to to PART cana-380 11 7 discuss discuss VERB cana-380 11 8 the the DET cana-380 11 9 sensitivity sensitivity NOUN cana-380 11 10 of of ADP cana-380 11 11 the the DET cana-380 11 12 models model NOUN cana-380 11 13 . . PUNCT cana-380 12 1 further far ADV cana-380 12 2 , , PUNCT cana-380 12 3 we we PRON cana-380 12 4 exemplify exemplify VERB cana-380 12 5 that that SCONJ cana-380 12 6 the the DET cana-380 12 7 significantly significantly ADV cana-380 12 8 reduced reduce VERB cana-380 12 9 cost cost NOUN cana-380 12 10 coefficient coefficient NOUN cana-380 12 11 is be AUX cana-380 12 12 convex convex ADJ cana-380 12 13 if if SCONJ cana-380 12 14 evaluated evaluate VERB cana-380 12 15 simultaneously simultaneously ADV cana-380 12 16 and and CCONJ cana-380 12 17 finds find VERB cana-380 12 18 the the DET cana-380 12 19 most most ADV cana-380 12 20 efficient efficient ADJ cana-380 12 21 solution solution NOUN cana-380 12 22 . . PUNCT cana-380 13 1 the the DET cana-380 13 2 statistical statistical ADJ cana-380 13 3 analysis analysis NOUN cana-380 13 4 reveals reveal VERB cana-380 13 5 that that SCONJ cana-380 13 6 a a DET cana-380 13 7 suitable suitable ADJ cana-380 13 8 policy policy NOUN cana-380 13 9 can can AUX cana-380 13 10 benefit benefit VERB cana-380 13 11 the the DET cana-380 13 12 retailer retailer NOUN cana-380 13 13 , , PUNCT cana-380 13 14 especially especially ADV cana-380 13 15 for for ADP cana-380 13 16 worsening worsen VERB cana-380 13 17 products product NOUN cana-380 13 18 . . PUNCT cana-380 14 1 keywords keyword NOUN cana-380 14 2 : : PUNCT cana-380 14 3 partial partial ADJ cana-380 14 4 backlogging backlogging NOUN cana-380 14 5 , , PUNCT cana-380 14 6 deterioration deterioration NOUN cana-380 14 7 rate rate NOUN cana-380 14 8 , , PUNCT cana-380 14 9 salvage salvage NOUN cana-380 14 10 value value NOUN cana-380 14 11 , , PUNCT cana-380 14 12 shortages shortage NOUN cana-380 14 13 , , PUNCT cana-380 14 14 variable variable ADJ cana-380 14 15 ordering ordering NOUN cana-380 14 16 , , PUNCT cana-380 14 17 and and CCONJ cana-380 14 18 holding hold VERB cana-380 14 19 cost cost NOUN cana-380 14 20 . . PUNCT cana-380 15 1 1 1 X cana-380 15 2 . . X cana-380 15 3 introduction introduction NOUN cana-380 15 4 change change NOUN cana-380 15 5 , , PUNCT cana-380 15 6 decay decay NOUN cana-380 15 7 , , PUNCT cana-380 15 8 damage damage NOUN cana-380 15 9 , , PUNCT cana-380 15 10 obsolescence obsolescence NOUN cana-380 15 11 , , PUNCT cana-380 15 12 spoilage spoilage NOUN cana-380 15 13 , , PUNCT cana-380 15 14 and and CCONJ cana-380 15 15 pilferage pilferage NOUN cana-380 15 16 all all PRON cana-380 15 17 contribute contribute VERB cana-380 15 18 to to ADP cana-380 15 19 the the DET cana-380 15 20 loss loss NOUN cana-380 15 21 of of ADP cana-380 15 22 a a DET cana-380 15 23 stock stock NOUN cana-380 15 24 's 's PART cana-380 15 25 usability usability NOUN cana-380 15 26 or or CCONJ cana-380 15 27 marginal marginal ADJ cana-380 15 28 value value NOUN cana-380 15 29 . . PUNCT cana-380 16 1 medicine medicine NOUN cana-380 16 2 , , PUNCT cana-380 16 3 blood blood NOUN cana-380 16 4 , , PUNCT cana-380 16 5 seafood seafood NOUN cana-380 16 6 , , PUNCT cana-380 16 7 liquor liquor NOUN cana-380 16 8 , , PUNCT cana-380 16 9 gas gas NOUN cana-380 16 10 , , PUNCT cana-380 16 11 food food NOUN cana-380 16 12 , , PUNCT cana-380 16 13 and and CCONJ cana-380 16 14 radioactive radioactive ADJ cana-380 16 15 substances substance NOUN cana-380 16 16 all all PRON cana-380 16 17 have have VERB cana-380 16 18 a a DET cana-380 16 19 limited limited ADJ cana-380 16 20 shelf shelf NOUN cana-380 16 21 life life NOUN cana-380 16 22 and and CCONJ cana-380 16 23 begin begin VERB cana-380 16 24 to to PART cana-380 16 25 degrade degrade VERB cana-380 16 26 immediately immediately ADV cana-380 16 27 after after SCONJ cana-380 16 28 they they PRON cana-380 16 29 are be AUX cana-380 16 30 received receive VERB cana-380 16 31 . . PUNCT cana-380 17 1 as as ADP cana-380 17 2 a a DET cana-380 17 3 result result NOUN cana-380 17 4 , , PUNCT cana-380 17 5 the the DET cana-380 17 6 deterioration deterioration NOUN cana-380 17 7 of of ADP cana-380 17 8 the the DET cana-380 17 9 product product NOUN cana-380 17 10 can can AUX cana-380 17 11 not not PART cana-380 17 12 be be AUX cana-380 17 13 overlooked overlook VERB cana-380 17 14 . . PUNCT cana-380 18 1 during during ADP cana-380 18 2 stockouts stockout NOUN cana-380 18 3 , , PUNCT cana-380 18 4 most most ADJ cana-380 18 5 inventory inventory NOUN cana-380 18 6 models model NOUN cana-380 18 7 incorrectly incorrectly ADV cana-380 18 8 assume assume VERB cana-380 18 9 that that SCONJ cana-380 18 10 all all DET cana-380 18 11 demand demand NOUN cana-380 18 12 is be AUX cana-380 18 13 lost lose VERB cana-380 18 14 or or CCONJ cana-380 18 15 backlogged backlogge VERB cana-380 18 16 . . PUNCT cana-380 19 1 in in ADP cana-380 19 2 reality reality NOUN cana-380 19 3 , , PUNCT cana-380 19 4 some some DET cana-380 19 5 customers customer NOUN cana-380 19 6 wait wait VERB cana-380 19 7 for for ADP cana-380 19 8 replenishment replenishment NOUN cana-380 19 9 , , PUNCT cana-380 19 10 particularly particularly ADV cana-380 19 11 if if SCONJ cana-380 19 12 the the DET cana-380 19 13 delay delay NOUN cana-380 19 14 is be AUX cana-380 19 15 brief brief ADJ cana-380 19 16 , , PUNCT cana-380 19 17 while while SCONJ cana-380 19 18 others other NOUN cana-380 19 19 become become VERB cana-380 19 20 agitated agitated ADJ cana-380 19 21 and and CCONJ cana-380 19 22 leave leave VERB cana-380 19 23 because because SCONJ cana-380 19 24 of of ADP cana-380 19 25 these these DET cana-380 19 26 stockouts stockout NOUN cana-380 19 27 , , PUNCT cana-380 19 28 backlogging backlogge VERB cana-380 19 29 , , PUNCT cana-380 19 30 in in ADP cana-380 19 31 part part NOUN cana-380 19 32 has have AUX cana-380 19 33 been be AUX cana-380 19 34 implemented implement VERB cana-380 19 35 in in ADP cana-380 19 36 this this DET cana-380 19 37 investigation investigation NOUN cana-380 19 38 . . PUNCT cana-380 20 1 most most ADJ cana-380 20 2 academics academic NOUN cana-380 20 3 believe believe VERB cana-380 20 4 that that SCONJ cana-380 20 5 scarcity scarcity NOUN cana-380 20 6 is be AUX cana-380 20 7 entirely entirely ADV cana-380 20 8 accumulated accumulate VERB cana-380 20 9 . . PUNCT cana-380 21 1 some some DET cana-380 21 2 clients client NOUN cana-380 21 3 choose choose VERB cana-380 21 4 to to PART cana-380 21 5 wait wait VERB cana-380 21 6 patiently patiently ADV cana-380 21 7 for for ADP cana-380 21 8 delays delay NOUN cana-380 21 9 amid amid ADP cana-380 21 10 a a DET cana-380 21 11 scarcity scarcity NOUN cana-380 21 12 , , PUNCT cana-380 21 13 while while SCONJ cana-380 21 14 others other NOUN cana-380 21 15 do do VERB cana-380 21 16 not not PART cana-380 21 17 . . PUNCT cana-380 22 1 the the DET cana-380 22 2 financial financial ADJ cana-380 22 3 burden burden NOUN cana-380 22 4 of of ADP cana-380 22 5 missing miss VERB cana-380 22 6 out out ADP cana-380 22 7 on on ADP cana-380 22 8 sales sale NOUN cana-380 22 9 should should AUX cana-380 22 10 be be AUX cana-380 22 11 taken take VERB cana-380 22 12 into into ADP cana-380 22 13 consideration consideration NOUN cana-380 22 14 in in ADP cana-380 22 15 the the DET cana-380 22 16 modelling modelling NOUN cana-380 22 17 methodologies methodology NOUN cana-380 22 18 . . PUNCT cana-380 23 1 decaying decay VERB cana-380 23 2 models model NOUN cana-380 23 3 of of ADP cana-380 23 4 stocks stock NOUN cana-380 23 5 have have AUX cana-380 23 6 received receive VERB cana-380 23 7 significant significant ADJ cana-380 23 8 attention attention NOUN cana-380 23 9 in in ADP cana-380 23 10 the the DET cana-380 23 11 last last ADJ cana-380 23 12 couple couple NOUN cana-380 23 13 of of ADP cana-380 23 14 decades decade NOUN cana-380 23 15 . . PUNCT cana-380 24 1 for for ADP cana-380 24 2 a a DET cana-380 24 3 constant constant ADJ cana-380 24 4 demand demand NOUN cana-380 24 5 , , PUNCT cana-380 24 6 ghare ghare NOUN cana-380 24 7 and and CCONJ cana-380 24 8 schrader schrader NOUN cana-380 24 9 [ [ X cana-380 24 10 1 1 NUM cana-380 24 11 ] ] PUNCT cana-380 24 12 became become VERB cana-380 24 13 the the DET cana-380 24 14 first first ADJ cana-380 24 15 to to PART cana-380 24 16 acquire acquire VERB cana-380 24 17 a a DET cana-380 24 18 continuously continuously ADV cana-380 24 19 depleting deplete VERB cana-380 24 20 inventory inventory NOUN cana-380 24 21 . . PUNCT cana-380 25 1 through through ADP cana-380 25 2 rectifying rectifying NOUN cana-380 25 3 and and CCONJ cana-380 25 4 altering alter VERB cana-380 25 5 the the DET cana-380 25 6 error error NOUN cana-380 25 7 in in ADP cana-380 25 8 shah shah PROPN cana-380 25 9 and and CCONJ cana-380 25 10 jaiswal jaiswal PROPN cana-380 25 11 's 's PART cana-380 25 12 analysis analysis NOUN cana-380 25 13 [ [ X cana-380 25 14 3 3 NUM cana-380 25 15 ] ] PUNCT cana-380 25 16 , , PUNCT cana-380 25 17 in in ADP cana-380 25 18 determining determine VERB cana-380 25 19 the the DET cana-380 25 20 mean mean ADJ cana-380 25 21 quantity quantity NOUN cana-380 25 22 of of ADP cana-380 25 23 inventory inventory NOUN cana-380 25 24 storage storage NOUN cana-380 25 25 cost cost NOUN cana-380 25 26 , , PUNCT cana-380 25 27 aggarwal aggarwal NOUN cana-380 25 28 [ [ X cana-380 25 29 2 2 NUM cana-380 25 30 ] ] PUNCT cana-380 25 31 , , PUNCT cana-380 25 32 created create VERB cana-380 25 33 an an DET cana-380 25 34 order order NOUN cana-380 25 35 - - PUNCT cana-380 25 36 specific specific ADJ cana-380 25 37 stock stock NOUN cana-380 25 38 model model NOUN cana-380 25 39 . . PUNCT cana-380 26 1 mailto:garimashish188@gmail.com mailto:garimashish188@gmail.com PROPN cana-380 26 2 mailto:garimasharma.slas@modyuniversity.ac.in mailto:garimasharma.slas@modyuniversity.ac.in PROPN cana-380 26 3 communications communication NOUN cana-380 26 4 on on ADP cana-380 26 5 applied apply VERB cana-380 26 6 nonlinear nonlinear ADJ cana-380 26 7 analysis analysis NOUN cana-380 26 8 issn issn NOUN cana-380 26 9 : : PUNCT cana-380 26 10 1074 1074 NUM cana-380 26 11 - - PUNCT cana-380 26 12 133x 133x NUM cana-380 26 13 vol vol NOUN cana-380 26 14 31 31 NUM cana-380 26 15 no no NOUN cana-380 26 16 . . NOUN cana-380 26 17 1 1 NUM cana-380 26 18 ( ( PUNCT cana-380 26 19 2024 2024 NUM cana-380 26 20 ) ) PUNCT cana-380 26 21 178 178 NUM cana-380 26 22 https://internationalpubls.com https://internationalpubls.com X cana-380 26 23 goyal goyal PROPN cana-380 26 24 and and CCONJ cana-380 26 25 giri giri PROPN cana-380 27 1 [ [ X cana-380 27 2 4 4 NUM cana-380 27 3 ] ] PUNCT cana-380 27 4 , , PUNCT cana-380 27 5 have have AUX cana-380 27 6 recently recently ADV cana-380 27 7 released release VERB cana-380 27 8 a a DET cana-380 27 9 comprehensive comprehensive ADJ cana-380 27 10 review review NOUN cana-380 27 11 of of ADP cana-380 27 12 research research NOUN cana-380 27 13 on on ADP cana-380 27 14 deteriorating deteriorate VERB cana-380 27 15 inventories inventory NOUN cana-380 27 16 . . PUNCT cana-380 28 1 they they PRON cana-380 28 2 asserted assert VERB cana-380 28 3 that that SCONJ cana-380 28 4 due due ADP cana-380 28 5 to to ADP cana-380 28 6 the the DET cana-380 28 7 fact fact NOUN cana-380 28 8 that that SCONJ cana-380 28 9 numerous numerous ADJ cana-380 28 10 inventory inventory NOUN cana-380 28 11 items item NOUN cana-380 28 12 , , PUNCT cana-380 28 13 such such ADJ cana-380 28 14 as as ADP cana-380 28 15 technological technological ADJ cana-380 28 16 goods good NOUN cana-380 28 17 and and CCONJ cana-380 28 18 trendy trendy ADJ cana-380 28 19 clothing clothing NOUN cana-380 28 20 , , PUNCT cana-380 28 21 experience experience NOUN cana-380 28 22 demand demand NOUN cana-380 28 23 rate rate NOUN cana-380 28 24 swings swing NOUN cana-380 28 25 , , PUNCT cana-380 28 26 applying apply VERB cana-380 28 27 the the DET cana-380 28 28 concept concept NOUN cana-380 28 29 of of ADP cana-380 28 30 a a DET cana-380 28 31 consistent consistent ADJ cana-380 28 32 rate rate NOUN cana-380 28 33 of of ADP cana-380 28 34 demand demand NOUN cana-380 28 35 to to ADP cana-380 28 36 them they PRON cana-380 28 37 is be AUX cana-380 28 38 not not PART cana-380 28 39 invariably invariably ADV cana-380 28 40 suitable suitable ADJ cana-380 28 41 . . PUNCT cana-380 29 1 many many ADJ cana-380 29 2 items item NOUN cana-380 29 3 experience experience NOUN cana-380 29 4 increased increase VERB cana-380 29 5 necessitate necessitate ADJ cana-380 29 6 throughout throughout ADP cana-380 29 7 the the DET cana-380 29 8 expansion expansion NOUN cana-380 29 9 phase phase NOUN cana-380 29 10 during during ADP cana-380 29 11 which which PRON cana-380 29 12 the the DET cana-380 29 13 item item NOUN cana-380 29 14 they they PRON cana-380 29 15 produce produce VERB cana-380 29 16 endures endure NOUN cana-380 29 17 . . PUNCT cana-380 30 1 alamri alamri PROPN cana-380 30 2 and and CCONJ cana-380 30 3 balkhi balkhi VERB cana-380 30 4 [ [ X cana-380 30 5 5 5 NUM cana-380 30 6 ] ] PUNCT cana-380 30 7 , , PUNCT cana-380 30 8 investigated investigate VERB cana-380 30 9 the the DET cana-380 30 10 appropriate appropriate ADJ cana-380 30 11 measure measure NOUN cana-380 30 12 of of ADP cana-380 30 13 a a DET cana-380 30 14 production production NOUN cana-380 30 15 order order NOUN cana-380 30 16 for for ADP cana-380 30 17 perishable perishable ADJ cana-380 30 18 goods good NOUN cana-380 30 19 with with ADP cana-380 30 20 cyclical cyclical ADJ cana-380 30 21 demand demand NOUN cana-380 30 22 and and CCONJ cana-380 30 23 also also ADV cana-380 30 24 deterioration deterioration NOUN cana-380 30 25 rates rate NOUN cana-380 30 26 in in ADP cana-380 30 27 connection connection NOUN cana-380 30 28 to to ADP cana-380 30 29 memory memory NOUN cana-380 30 30 loss loss NOUN cana-380 30 31 and and CCONJ cana-380 30 32 learning learning NOUN cana-380 30 33 . . PUNCT cana-380 31 1 dye dye VERB cana-380 31 2 et et PROPN cana-380 31 3 al al PROPN cana-380 31 4 . . PUNCT cana-380 32 1 [ [ X cana-380 32 2 6 6 NUM cana-380 32 3 ] ] PUNCT cana-380 32 4 , , PUNCT cana-380 32 5 estimated estimate VERB cana-380 32 6 the the DET cana-380 32 7 optimal optimal ADJ cana-380 32 8 lot lot NOUN cana-380 32 9 size size NOUN cana-380 32 10 and and CCONJ cana-380 32 11 selling sell VERB cana-380 32 12 price price NOUN cana-380 32 13 given give VERB cana-380 32 14 an an DET cana-380 32 15 exponential exponential ADJ cana-380 32 16 partial partial ADJ cana-380 32 17 backlog backlog NOUN cana-380 32 18 and and CCONJ cana-380 32 19 a a DET cana-380 32 20 variable variable ADJ cana-380 32 21 rate rate NOUN cana-380 32 22 of of ADP cana-380 32 23 deterioration deterioration NOUN cana-380 32 24 . . PUNCT cana-380 33 1 according accord VERB cana-380 33 2 to to ADP cana-380 33 3 them they PRON cana-380 33 4 , , PUNCT cana-380 33 5 the the DET cana-380 33 6 proportion proportion NOUN cana-380 33 7 of of ADP cana-380 33 8 client client NOUN cana-380 33 9 backlogs backlog NOUN cana-380 33 10 in in ADP cana-380 33 11 their their PRON cana-380 33 12 purchases purchase NOUN cana-380 33 13 augments augment VERB cana-380 33 14 as as SCONJ cana-380 33 15 the the DET cana-380 33 16 time time NOUN cana-380 33 17 between between ADP cana-380 33 18 replenishments replenishment NOUN cana-380 33 19 decreases decrease VERB cana-380 33 20 . . PUNCT cana-380 34 1 this this DET cana-380 34 2 investigation investigation NOUN cana-380 34 3 predicts predict VERB cana-380 34 4 a a DET cana-380 34 5 conceptual conceptual ADJ cana-380 34 6 framework framework NOUN cana-380 34 7 for for ADP cana-380 34 8 eoq eoq NOUN cana-380 34 9 inventories inventory NOUN cana-380 34 10 that that PRON cana-380 34 11 accounts account VERB cana-380 34 12 for for ADP cana-380 34 13 decaying decay VERB cana-380 34 14 objects object NOUN cana-380 34 15 and and CCONJ cana-380 34 16 demand demand NOUN cana-380 34 17 that that PRON cana-380 34 18 decreases decrease VERB cana-380 34 19 exponentially exponentially ADV cana-380 34 20 . . PUNCT cana-380 35 1 v. v. PROPN cana-380 35 2 k. k. PROPN cana-380 35 3 mishra mishra PROPN cana-380 36 1 [ [ X cana-380 36 2 7 7 NUM cana-380 36 3 ] ] PUNCT cana-380 36 4 developed develop VERB cana-380 36 5 an an DET cana-380 36 6 a a DET cana-380 36 7 stock stock NOUN cana-380 36 8 approach approach NOUN cana-380 36 9 that that PRON cana-380 36 10 incorporates incorporate VERB cana-380 36 11 time time NOUN cana-380 36 12 - - PUNCT cana-380 36 13 dependent dependent ADJ cana-380 36 14 variables variable NOUN cana-380 36 15 storage storage NOUN cana-380 36 16 costs cost NOUN cana-380 36 17 , , PUNCT cana-380 36 18 deterioration deterioration NOUN cana-380 36 19 , , PUNCT cana-380 36 20 salvage salvage NOUN cana-380 36 21 value value NOUN cana-380 36 22 , , PUNCT cana-380 36 23 and and CCONJ cana-380 36 24 scarcity scarcity NOUN cana-380 36 25 . . PUNCT cana-380 37 1 vinod vinod PROPN cana-380 37 2 kumar kumar PROPN cana-380 37 3 et et PROPN cana-380 37 4 al.[8 al.[8 PROPN cana-380 37 5 ] ] PUNCT cana-380 37 6 , , PUNCT cana-380 37 7 regarded regard VERB cana-380 37 8 as as ADP cana-380 37 9 an an DET cana-380 37 10 inventory inventory NOUN cana-380 37 11 framework framework NOUN cana-380 37 12 for for ADP cana-380 37 13 degrading degrade VERB cana-380 37 14 goods good NOUN cana-380 37 15 under under ADP cana-380 37 16 a a DET cana-380 37 17 partial partial ADJ cana-380 37 18 stockpile stockpile NOUN cana-380 37 19 with with ADP cana-380 37 20 holding hold VERB cana-380 37 21 costs cost NOUN cana-380 37 22 that that DET cana-380 37 23 fluctuate fluctuate NOUN cana-380 37 24 with with ADP cana-380 37 25 time time NOUN cana-380 37 26 and and CCONJ cana-380 37 27 demand demand NOUN cana-380 37 28 . . PUNCT cana-380 38 1 the the DET cana-380 38 2 concept concept NOUN cana-380 38 3 of of ADP cana-380 38 4 quadratic quadratic ADJ cana-380 38 5 demand demand NOUN cana-380 38 6 , , PUNCT cana-380 38 7 time time NOUN cana-380 38 8 - - PUNCT cana-380 38 9 dependent dependent ADJ cana-380 38 10 deterioration deterioration NOUN cana-380 38 11 without without ADP cana-380 38 12 shortages shortage NOUN cana-380 38 13 , , PUNCT cana-380 38 14 and and CCONJ cana-380 38 15 salvage salvage NOUN cana-380 38 16 value value NOUN cana-380 38 17 was be AUX cana-380 38 18 proposed propose VERB cana-380 38 19 by by ADP cana-380 38 20 mohan mohan PROPN cana-380 38 21 and and CCONJ cana-380 38 22 r. r. PROPN cana-380 38 23 venkateswarlu venkateswarlu NOUN cana-380 39 1 [ [ X cana-380 39 2 9 9 NUM cana-380 39 3 ] ] PUNCT cana-380 39 4 . . PUNCT cana-380 40 1 kavitha kavitha PROPN cana-380 40 2 priya priya PROPN cana-380 40 3 and and CCONJ cana-380 40 4 k. k. PROPN cana-380 40 5 senbagam senbagam VERB cana-380 41 1 [ [ X cana-380 41 2 10 10 NUM cana-380 41 3 ] ] PUNCT cana-380 41 4 proposed propose VERB cana-380 41 5 a a DET cana-380 41 6 method method NOUN cana-380 41 7 for for ADP cana-380 41 8 time time NOUN cana-380 41 9 - - PUNCT cana-380 41 10 dependently dependently ADV cana-380 41 11 deteriorating deteriorate VERB cana-380 41 12 goods good NOUN cana-380 41 13 with with ADP cana-380 41 14 quadratic quadratic ADJ cana-380 41 15 time time NOUN cana-380 41 16 - - PUNCT cana-380 41 17 varying vary VERB cana-380 41 18 demand demand NOUN cana-380 41 19 and and CCONJ cana-380 41 20 a a DET cana-380 41 21 partial partial ADJ cana-380 41 22 backlog backlog NOUN cana-380 41 23 . . PUNCT cana-380 42 1 numerous numerous ADJ cana-380 42 2 academics academic NOUN cana-380 42 3 developed develop VERB cana-380 42 4 alternative alternative ADJ cana-380 42 5 inventory inventory NOUN cana-380 42 6 models model NOUN cana-380 42 7 based base VERB cana-380 42 8 on on ADP cana-380 42 9 different different ADJ cana-380 42 10 patterns pattern NOUN cana-380 42 11 of of ADP cana-380 42 12 demand demand NOUN cana-380 42 13 . . PUNCT cana-380 43 1 pervin pervin NOUN cana-380 43 2 et et PROPN cana-380 43 3 al al PROPN cana-380 43 4 . . PUNCT cana-380 44 1 [ [ X cana-380 44 2 11 11 NUM cana-380 44 3 ] ] PUNCT cana-380 44 4 created create VERB cana-380 44 5 an an DET cana-380 44 6 inventory inventory NOUN cana-380 44 7 model model NOUN cana-380 44 8 with with ADP cana-380 44 9 time time NOUN cana-380 44 10 - - PUNCT cana-380 44 11 based base VERB cana-380 44 12 demand demand NOUN cana-380 44 13 and and CCONJ cana-380 44 14 a a DET cana-380 44 15 stochastic stochastic ADJ cana-380 44 16 deterioration deterioration NOUN cana-380 44 17 rate rate NOUN cana-380 44 18 . . PUNCT cana-380 45 1 singh singh PROPN cana-380 45 2 and and CCONJ cana-380 45 3 mishra mishra PROPN cana-380 46 1 [ [ X cana-380 46 2 12 12 NUM cana-380 46 3 ] ] PUNCT cana-380 46 4 proposed propose VERB cana-380 46 5 a a DET cana-380 46 6 green green ADJ cana-380 46 7 inventory inventory NOUN cana-380 46 8 model model NOUN cana-380 46 9 for for ADP cana-380 46 10 non non ADJ cana-380 46 11 - - ADJ cana-380 46 12 instantaneous instantaneous ADJ cana-380 46 13 substitutable substitutable ADJ cana-380 46 14 degrading degrading ADJ cana-380 46 15 products product NOUN cana-380 46 16 that that PRON cana-380 46 17 employ employ VERB cana-380 46 18 a a DET cana-380 46 19 combined combine VERB cana-380 46 20 ordering ordering NOUN cana-380 46 21 strategy strategy NOUN cana-380 46 22 and and CCONJ cana-380 46 23 carbon carbon NOUN cana-380 46 24 emissions emission NOUN cana-380 46 25 . . PUNCT cana-380 47 1 s. s. PROPN cana-380 47 2 fatma fatma PROPN cana-380 47 3 , , PUNCT cana-380 47 4 v. v. PROPN cana-380 47 5 k. k. PROPN cana-380 47 6 mishra mishra PROPN cana-380 47 7 , , PUNCT cana-380 47 8 and and CCONJ cana-380 47 9 r. r. PROPN cana-380 47 10 singh singh PROPN cana-380 48 1 [ [ X cana-380 48 2 13 13 NUM cana-380 48 3 ] ] PUNCT cana-380 48 4 , , PUNCT cana-380 48 5 model model NOUN cana-380 48 6 of of ADP cana-380 48 7 inventory inventory NOUN cana-380 48 8 for for ADP cana-380 48 9 immediate immediate ADJ cana-380 48 10 deterioration deterioration NOUN cana-380 48 11 goods good NOUN cana-380 48 12 with with ADP cana-380 48 13 time time NOUN cana-380 48 14 sensitive sensitive ADJ cana-380 48 15 demand demand NOUN cana-380 48 16 for for ADP cana-380 48 17 post post NOUN cana-380 48 18 covid-19 covid-19 PROPN cana-380 48 19 recovery recovery NOUN cana-380 48 20 . . PUNCT cana-380 49 1 this this DET cana-380 49 2 paper paper NOUN cana-380 49 3 contains contain VERB cana-380 49 4 , , PUNCT cana-380 49 5 it it PRON cana-380 49 6 is be AUX cana-380 49 7 anticipated anticipate VERB cana-380 49 8 that that SCONJ cana-380 49 9 the the DET cana-380 49 10 demand demand NOUN cana-380 49 11 rate rate NOUN cana-380 49 12 will will AUX cana-380 49 13 be be AUX cana-380 49 14 time time NOUN cana-380 49 15 sensitive sensitive ADJ cana-380 49 16 and and CCONJ cana-380 49 17 that that SCONJ cana-380 49 18 the the DET cana-380 49 19 rate rate NOUN cana-380 49 20 of of ADP cana-380 49 21 worsening worsening NOUN cana-380 49 22 will will AUX cana-380 49 23 be be AUX cana-380 49 24 proportionate proportionate ADJ cana-380 49 25 to to ADP cana-380 49 26 time time NOUN cana-380 49 27 , , PUNCT cana-380 49 28 a a DET cana-380 49 29 model model NOUN cana-380 49 30 of of ADP cana-380 49 31 stock stock NOUN cana-380 49 32 for for ADP cana-380 49 33 items item NOUN cana-380 49 34 that that PRON cana-380 49 35 are be AUX cana-380 49 36 degrading degrade VERB cana-380 49 37 will will AUX cana-380 49 38 be be AUX cana-380 49 39 created create VERB cana-380 49 40 . . PUNCT cana-380 50 1 when when SCONJ cana-380 50 2 shortages shortage NOUN cana-380 50 3 are be AUX cana-380 50 4 acceptable acceptable ADJ cana-380 50 5 and and CCONJ cana-380 50 6 partially partially ADV cana-380 50 7 backordered backordere VERB cana-380 50 8 , , PUNCT cana-380 50 9 the the DET cana-380 50 10 problem problem NOUN cana-380 50 11 is be AUX cana-380 50 12 resolved resolve VERB cana-380 50 13 . . PUNCT cana-380 51 1 costs cost NOUN cana-380 51 2 of of ADP cana-380 51 3 holding hold VERB cana-380 51 4 and and CCONJ cana-380 51 5 ordering ordering NOUN cana-380 51 6 are be AUX cana-380 51 7 variables variable NOUN cana-380 51 8 . . PUNCT cana-380 52 1 items item NOUN cana-380 52 2 in in ADP cana-380 52 3 the the DET cana-380 52 4 system system NOUN cana-380 52 5 that that PRON cana-380 52 6 have have AUX cana-380 52 7 deteriorated deteriorate VERB cana-380 52 8 are be AUX cana-380 52 9 given give VERB cana-380 52 10 the the DET cana-380 52 11 salvage salvage NOUN cana-380 52 12 value value NOUN cana-380 52 13 . . PUNCT cana-380 53 1 an an DET cana-380 53 2 example example NOUN cana-380 53 3 utilizing utilize VERB cana-380 53 4 numbers number NOUN cana-380 53 5 is be AUX cana-380 53 6 used use VERB cana-380 53 7 to to PART cana-380 53 8 discuss discuss VERB cana-380 53 9 the the DET cana-380 53 10 models model NOUN cana-380 53 11 ' ' PART cana-380 53 12 sensitivity sensitivity NOUN cana-380 53 13 . . PUNCT cana-380 54 1 the the DET cana-380 54 2 goal goal NOUN cana-380 54 3 of of ADP cana-380 54 4 this this DET cana-380 54 5 modelling modelling NOUN cana-380 54 6 is be AUX cana-380 54 7 to to PART cana-380 54 8 examine examine VERB cana-380 54 9 the the DET cana-380 54 10 influence influence NOUN cana-380 54 11 of of ADP cana-380 54 12 variable variable ADJ cana-380 54 13 ordering ordering NOUN cana-380 54 14 and and CCONJ cana-380 54 15 holding hold VERB cana-380 54 16 costs cost NOUN cana-380 54 17 with with ADP cana-380 54 18 salvage salvage NOUN cana-380 54 19 values value NOUN cana-380 54 20 on on ADP cana-380 54 21 the the DET cana-380 54 22 partially partially ADV cana-380 54 23 backlogged backlogge VERB cana-380 54 24 problem problem NOUN cana-380 54 25 's 's PART cana-380 54 26 overall overall ADJ cana-380 54 27 inventory inventory NOUN cana-380 54 28 cost cost NOUN cana-380 54 29 . . PUNCT cana-380 55 1 2 2 X cana-380 55 2 . . X cana-380 55 3 presumptions presumption NOUN cana-380 55 4 and and CCONJ cana-380 55 5 annotations annotation NOUN cana-380 55 6 2.1 2.1 NUM cana-380 55 7 presumptions presumption NOUN cana-380 55 8 this this DET cana-380 55 9 mathematical mathematical ADJ cana-380 55 10 model model NOUN cana-380 55 11 is be AUX cana-380 55 12 described describe VERB cana-380 55 13 by by ADP cana-380 55 14 considering consider VERB cana-380 55 15 the the DET cana-380 55 16 subsequent subsequent ADJ cana-380 55 17 presumptions presumption NOUN cana-380 55 18 and and CCONJ cana-380 55 19 notations notation NOUN cana-380 55 20 . . PUNCT cana-380 56 1 assumptions assumption NOUN cana-380 56 2 are be AUX cana-380 56 3 , , PUNCT cana-380 56 4 1 1 X cana-380 56 5 . . PUNCT cana-380 57 1 the the DET cana-380 57 2 demand demand NOUN cana-380 57 3 rate rate NOUN cana-380 57 4 𝑓(𝑑 𝑓(𝑑 NOUN cana-380 57 5 ) ) PUNCT cana-380 57 6 at at ADP cana-380 57 7 times time NOUN cana-380 57 8 it it PRON cana-380 57 9 is be AUX cana-380 57 10 assumed assume VERB cana-380 57 11 as as ADP cana-380 57 12 𝑓(𝑑 𝑓(𝑑 NOUN cana-380 57 13 ) ) PUNCT cana-380 58 1 = = SYM cana-380 58 2 πœ”1 πœ”1 NOUN cana-380 58 3 + + X cana-380 58 4 πœ”2𝑑 πœ”2𝑑 NOUN cana-380 58 5 ; ; PUNCT cana-380 58 6 πœ”1 πœ”1 ADJ cana-380 58 7 , , PUNCT cana-380 58 8 πœ”2 πœ”2 PROPN cana-380 58 9 are be AUX cana-380 58 10 constants constant NOUN cana-380 58 11 . . PUNCT cana-380 59 1 2 2 X cana-380 59 2 . . X cana-380 59 3 replenishment replenishment NOUN cana-380 59 4 occurs occur VERB cana-380 59 5 . . PUNCT cana-380 60 1 3 3 X cana-380 60 2 . . X cana-380 60 3 shortages shortage NOUN cana-380 60 4 are be AUX cana-380 60 5 allowed allow VERB cana-380 60 6 . . PUNCT cana-380 61 1 4 4 X cana-380 61 2 . . X cana-380 61 3 πœƒ(𝑑 πœƒ(𝑑 PROPN cana-380 61 4 ) ) PUNCT cana-380 62 1 = = PRON cana-380 62 2 πœƒπ‘‘ πœƒπ‘‘ X cana-380 62 3 is be VERB cana-380 62 4 the the DET cana-380 62 5 deterioration deterioration NOUN cana-380 62 6 rate rate NOUN cana-380 62 7 . . PUNCT cana-380 63 1 5 5 X cana-380 63 2 . . X cana-380 63 3 both both CCONJ cana-380 63 4 the the DET cana-380 63 5 storage storage NOUN cana-380 63 6 cost cost NOUN cana-380 63 7 and and CCONJ cana-380 63 8 purchasing purchase VERB cana-380 63 9 cost cost NOUN cana-380 63 10 are be AUX cana-380 63 11 variable variable ADJ cana-380 63 12 6 6 NUM cana-380 63 13 . . PUNCT cana-380 64 1 here here ADV cana-380 64 2 , , PUNCT cana-380 64 3 holding hold VERB cana-380 64 4 cost cost NOUN cana-380 64 5 is be AUX cana-380 64 6 time time NOUN cana-380 64 7 sensitive sensitive ADJ cana-380 64 8 i.e. i.e. ADV cana-380 64 9 , , PUNCT cana-380 64 10 where where SCONJ cana-380 64 11 𝛼 𝛼 X cana-380 64 12 > > X cana-380 64 13 0 0 NUM cana-380 64 14 , , PUNCT cana-380 64 15 𝛽 𝛽 NOUN cana-380 64 16 > > X cana-380 64 17 0 0 NUM cana-380 64 18 7 7 NUM cana-380 64 19 . . PUNCT cana-380 64 20 here here ADV cana-380 64 21 ordering order VERB cana-380 64 22 cost cost NOUN cana-380 64 23 is be AUX cana-380 64 24 πΆπ‘œ πΆπ‘œ PROPN cana-380 64 25 = = PROPN cana-380 64 26 π‘žπ›Ύβˆ’1 π‘žπ›Ύβˆ’1 PROPN cana-380 64 27 where where SCONJ cana-380 64 28 π‘ž π‘ž X cana-380 64 29 > > X cana-380 64 30 0 0 PROPN cana-380 64 31 , , PUNCT cana-380 64 32 𝛾 𝛾 ADP cana-380 64 33 > > X cana-380 64 34 0 0 X cana-380 64 35 . . PUNCT cana-380 65 1 communications communication NOUN cana-380 65 2 on on ADP cana-380 65 3 applied apply VERB cana-380 65 4 nonlinear nonlinear ADJ cana-380 65 5 analysis analysis NOUN cana-380 65 6 issn issn NOUN cana-380 65 7 : : PUNCT cana-380 65 8 1074 1074 NUM cana-380 65 9 - - PUNCT cana-380 65 10 133x 133x NUM cana-380 65 11 vol vol NOUN cana-380 65 12 31 31 NUM cana-380 65 13 no no NOUN cana-380 65 14 . . NOUN cana-380 65 15 1 1 NUM cana-380 65 16 ( ( PUNCT cana-380 65 17 2024 2024 NUM cana-380 65 18 ) ) PUNCT cana-380 65 19 179 179 NUM cana-380 65 20 https://internationalpubls.com https://internationalpubls.com X cana-380 65 21 units unit NOUN cana-380 65 22 that that PRON cana-380 65 23 have have AUX cana-380 65 24 deteriorated deteriorate VERB cana-380 65 25 over over ADP cana-380 65 26 the the DET cana-380 65 27 period period NOUN cana-380 65 28 of of ADP cana-380 65 29 a a DET cana-380 65 30 cycle cycle NOUN cana-380 65 31 are be AUX cana-380 65 32 related relate VERB cana-380 65 33 with with ADP cana-380 65 34 the the DET cana-380 65 35 salvage salvage NOUN cana-380 65 36 value value NOUN cana-380 65 37 𝛿 𝛿 NOUN cana-380 65 38 , , PUNCT cana-380 65 39 0 0 NUM cana-380 65 40 ≀ ≀ NOUN cana-380 65 41 𝛿 𝛿 PRON cana-380 65 42 < < X cana-380 65 43 1 1 NUM cana-380 65 44 . . PUNCT cana-380 65 45 unmet unmet NOUN cana-380 65 46 demand demand NOUN cana-380 65 47 fulfilled fulfil VERB cana-380 65 48 have have AUX cana-380 65 49 been be AUX cana-380 65 50 described describe VERB cana-380 65 51 as as ADP cana-380 65 52 partially partially ADV cana-380 65 53 backlogged backlogge VERB cana-380 65 54 . . PUNCT cana-380 66 1 as as SCONJ cana-380 66 2 consumers consumer NOUN cana-380 66 3 ' ' PART cana-380 66 4 waiting waiting NOUN cana-380 66 5 period period NOUN cana-380 66 6 , , PUNCT cana-380 66 7 ( ( PUNCT cana-380 66 8 𝑇 𝑇 PROPN cana-380 66 9 βˆ’ βˆ’ PUNCT cana-380 66 10 𝑑 𝑑 NOUN cana-380 66 11 ) ) PUNCT cana-380 66 12 reduces reduce VERB cana-380 66 13 , , PUNCT cana-380 66 14 the the DET cana-380 66 15 percentage percentage NOUN cana-380 66 16 of of ADP cana-380 66 17 backorders backorder NOUN cana-380 66 18 increases increase NOUN cana-380 66 19 . . PUNCT cana-380 67 1 the the DET cana-380 67 2 partial partial ADJ cana-380 67 3 reserve reserve NOUN cana-380 67 4 rate rate NOUN cana-380 67 5 is be AUX cana-380 67 6 equals equal VERB cana-380 67 7 to to ADP cana-380 67 8 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘ π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘ NOUN cana-380 67 9 ) ) PUNCT cana-380 67 10 . . PUNCT cana-380 68 1 where where SCONJ cana-380 68 2 πœ‡ πœ‡ ADV cana-380 68 3 is be AUX cana-380 68 4 the the DET cana-380 68 5 parameter parameter NOUN cana-380 68 6 for for ADP cana-380 68 7 positive positive ADJ cana-380 68 8 backlogging backlogging NOUN cana-380 68 9 . . PUNCT cana-380 69 1 2.2 2.2 NUM cana-380 69 2 notations notation NOUN cana-380 69 3 notation notation NOUN cana-380 69 4 description description NOUN cana-380 69 5 𝐢𝑆 𝐢𝑆 INTJ cana-380 70 1 πΆπ‘œ πΆπ‘œ SCONJ cana-380 70 2 𝐢𝐷 𝐢𝐷 PROPN cana-380 70 3 π‘Š π‘Š PROPN cana-380 70 4 𝑆 𝑆 PROPN cana-380 70 5 𝑄 𝑄 PROPN cana-380 70 6 𝐼(𝑑 𝐼(𝑑 NOUN cana-380 70 7 ) ) PUNCT cana-380 70 8 𝑑1 𝑑1 NOUN cana-380 70 9 𝑇 𝑇 PROPN cana-380 70 10 𝑇𝐢 𝑇𝐢 PROPN cana-380 70 11 𝛼 𝛼 X cana-380 70 12 Ξ² Ξ² NOUN cana-380 70 13 𝛿 𝛿 ADJ cana-380 70 14 shortage shortage NOUN cana-380 70 15 cost cost NOUN cana-380 70 16 per per ADP cana-380 70 17 unit unit NOUN cana-380 70 18 of of ADP cana-380 70 19 time time NOUN cana-380 70 20 . . PUNCT cana-380 71 1 ordering order VERB cana-380 71 2 cost cost NOUN cana-380 71 3 per per ADP cana-380 71 4 order order NOUN cana-380 71 5 . . PUNCT cana-380 72 1 deterioration deterioration NOUN cana-380 72 2 cost cost VERB cana-380 72 3 the the DET cana-380 72 4 maximal maximal ADJ cana-380 72 5 storage storage NOUN cana-380 72 6 amount amount NOUN cana-380 72 7 for for ADP cana-380 72 8 every every DET cana-380 72 9 procurement procurement NOUN cana-380 72 10 period period NOUN cana-380 72 11 . . PUNCT cana-380 73 1 the the DET cana-380 73 2 highest high ADJ cana-380 73 3 quantity quantity NOUN cana-380 73 4 of of ADP cana-380 73 5 inventory inventory NOUN cana-380 73 6 the the DET cana-380 73 7 amount amount NOUN cana-380 73 8 of of ADP cana-380 73 9 the the DET cana-380 73 10 order order NOUN cana-380 73 11 ( ( PUNCT cana-380 73 12 𝑄 𝑄 NOUN cana-380 73 13 = = SYM cana-380 73 14 π‘Š π‘Š PROPN cana-380 73 15 + + CCONJ cana-380 73 16 𝑆 𝑆 PROPN cana-380 73 17 ) ) PUNCT cana-380 73 18 . . PUNCT cana-380 74 1 inventory inventory NOUN cana-380 74 2 level level NOUN cana-380 74 3 at at ADP cana-380 74 4 time time NOUN cana-380 74 5 t. t. NOUN cana-380 74 6 time time NOUN cana-380 74 7 when when SCONJ cana-380 74 8 shortage shortage NOUN cana-380 74 9 start start VERB cana-380 74 10 . . PUNCT cana-380 75 1 total total ADJ cana-380 75 2 length length NOUN cana-380 75 3 of of ADP cana-380 75 4 each each DET cana-380 75 5 ordering order VERB cana-380 75 6 cycle cycle NOUN cana-380 75 7 . . PUNCT cana-380 76 1 the the DET cana-380 76 2 total total ADJ cana-380 76 3 price price NOUN cana-380 76 4 of of ADP cana-380 76 5 the the DET cana-380 76 6 stock stock NOUN cana-380 76 7 for for ADP cana-380 76 8 each each DET cana-380 76 9 purchase purchase NOUN cana-380 76 10 period period NOUN cana-380 76 11 ( ( PUNCT cana-380 76 12 0 0 NUM cana-380 76 13 , , PUNCT cana-380 76 14 𝑇 𝑇 PROPN cana-380 76 15 ) ) PUNCT cana-380 76 16 . . PUNCT cana-380 77 1 holding hold VERB cana-380 77 2 cost cost NOUN cana-380 77 3 parameter parameter NOUN cana-380 77 4 . . PUNCT cana-380 78 1 holding hold VERB cana-380 78 2 cost cost NOUN cana-380 78 3 parameter parameter NOUN cana-380 78 4 . . PUNCT cana-380 79 1 salvage salvage NOUN cana-380 79 2 value value NOUN cana-380 79 3 3 3 NUM cana-380 79 4 . . PUNCT cana-380 79 5 model model NOUN cana-380 79 6 formulation formulation NOUN cana-380 79 7 this this DET cana-380 79 8 study study NOUN cana-380 79 9 makes make VERB cana-380 79 10 the the DET cana-380 79 11 assumption assumption NOUN cana-380 79 12 that that SCONJ cana-380 79 13 a a DET cana-380 79 14 depreciating depreciate VERB cana-380 79 15 product product NOUN cana-380 79 16 will will AUX cana-380 79 17 need need VERB cana-380 79 18 to to PART cana-380 79 19 be be AUX cana-380 79 20 replenished replenish VERB cana-380 79 21 with with ADP cana-380 79 22 variable variable ADJ cana-380 79 23 holding holding NOUN cana-380 79 24 and and CCONJ cana-380 79 25 ordering ordering NOUN cana-380 79 26 costs cost NOUN cana-380 79 27 . . PUNCT cana-380 80 1 we we PRON cana-380 80 2 provide provide VERB cana-380 80 3 the the DET cana-380 80 4 appropriate appropriate ADJ cana-380 80 5 order order NOUN cana-380 80 6 quantity quantity NOUN cana-380 80 7 , , PUNCT cana-380 80 8 𝑄 𝑄 PROPN cana-380 80 9 , , PUNCT cana-380 80 10 and and CCONJ cana-380 80 11 the the DET cana-380 80 12 ideal ideal ADJ cana-380 80 13 total total ADJ cana-380 80 14 cost cost NOUN cana-380 80 15 of of ADP cana-380 80 16 inventory inventory NOUN cana-380 80 17 . . PUNCT cana-380 81 1 fig fig NOUN cana-380 81 2 . . PUNCT cana-380 82 1 1 1 NUM cana-380 82 2 inventory inventory NOUN cana-380 82 3 level level NOUN cana-380 82 4 i(t i(t NOUN cana-380 82 5 ) ) PUNCT cana-380 82 6 vs. vs. ADP cana-380 82 7 time time NOUN cana-380 82 8 communications communication NOUN cana-380 82 9 on on ADP cana-380 82 10 applied apply VERB cana-380 82 11 nonlinear nonlinear ADJ cana-380 82 12 analysis analysis NOUN cana-380 82 13 issn issn NOUN cana-380 82 14 : : PUNCT cana-380 82 15 1074 1074 NUM cana-380 82 16 - - PUNCT cana-380 82 17 133x 133x NUM cana-380 82 18 vol vol NOUN cana-380 82 19 31 31 NUM cana-380 82 20 no no NOUN cana-380 82 21 . . NOUN cana-380 82 22 1 1 NUM cana-380 82 23 ( ( PUNCT cana-380 82 24 2024 2024 NUM cana-380 82 25 ) ) PUNCT cana-380 82 26 180 180 NUM cana-380 82 27 https://internationalpubls.com https://internationalpubls.com X cana-380 82 28 the the DET cana-380 82 29 inventory inventory NOUN cana-380 82 30 level level NOUN cana-380 82 31 𝐼(𝑑 𝐼(𝑑 PROPN cana-380 82 32 ) ) PUNCT cana-380 82 33 falls fall VERB cana-380 82 34 to to ADP cana-380 82 35 zero zero NUM cana-380 82 36 at at ADP cana-380 82 37 𝑑 𝑑 NOUN cana-380 82 38 = = NOUN cana-380 82 39 𝑑1 𝑑1 NOUN cana-380 82 40 due due ADP cana-380 82 41 to to ADP cana-380 82 42 both both DET cana-380 82 43 demand demand NOUN cana-380 82 44 and and CCONJ cana-380 82 45 deterioration deterioration NOUN cana-380 82 46 throughout throughout ADP cana-380 82 47 the the DET cana-380 82 48 period period NOUN cana-380 82 49 [ [ X cana-380 82 50 0 0 NUM cana-380 82 51 , , PUNCT cana-380 82 52 𝑑1 𝑑1 PROPN cana-380 82 53 ] ] PUNCT cana-380 82 54 , , PUNCT cana-380 82 55 whilst whilst SCONJ cana-380 82 56 shortages shortage NOUN cana-380 82 57 occur occur VERB cana-380 82 58 during during ADP cana-380 82 59 the the DET cana-380 82 60 period period NOUN cana-380 82 61 [ [ X cana-380 82 62 𝑑1 𝑑1 NOUN cana-380 82 63 , , PUNCT cana-380 82 64 𝑇 𝑇 PROPN cana-380 82 65 ] ] PUNCT cana-380 82 66 due due ADP cana-380 82 67 to to ADP cana-380 82 68 demand demand NOUN cana-380 82 69 and and CCONJ cana-380 82 70 a a DET cana-380 82 71 portion portion NOUN cana-380 82 72 of of ADP cana-380 82 73 requirements requirement NOUN cana-380 82 74 are be AUX cana-380 82 75 backlogged backlogge VERB cana-380 82 76 . . PUNCT cana-380 83 1 𝑑𝐼1(𝑑 𝑑𝐼1(𝑑 NOUN cana-380 83 2 ) ) PUNCT cana-380 83 3 𝑑𝑑 𝑑𝑑 ADP cana-380 83 4 + + ADJ cana-380 83 5 πœƒπ‘‘πΌ1(𝑑 πœƒπ‘‘πΌ1(𝑑 NOUN cana-380 83 6 ) ) PUNCT cana-380 83 7 = = SYM cana-380 83 8 βˆ’(πœ”1 βˆ’(πœ”1 NUM cana-380 83 9 + + CCONJ cana-380 83 10 πœ”2𝑑 πœ”2𝑑 PROPN cana-380 83 11 ) ) PUNCT cana-380 83 12 ; ; PUNCT cana-380 83 13 0 0 NUM cana-380 83 14 ≀ ≀ NUM cana-380 83 15 𝑑 𝑑 PROPN cana-380 83 16 ≀ ≀ ADJ cana-380 83 17 𝑑1 𝑑1 NOUN cana-380 83 18 ( ( PUNCT cana-380 83 19 1 1 NUM cana-380 83 20 ) ) PUNCT cana-380 83 21 and and CCONJ cana-380 83 22 during during ADP cana-380 83 23 the the DET cana-380 83 24 interval interval NOUN cana-380 83 25 [ [ X cana-380 83 26 𝑑1 𝑑1 NOUN cana-380 83 27 , , PUNCT cana-380 83 28 𝑇 𝑇 PROPN cana-380 83 29 ] ] X cana-380 83 30 the the DET cana-380 83 31 shortage shortage NOUN cana-380 83 32 occurs occur VERB cana-380 83 33 , , PUNCT cana-380 83 34 so so CCONJ cana-380 83 35 the the DET cana-380 83 36 differential differential ADJ cana-380 83 37 equation equation NOUN cana-380 83 38 is be AUX cana-380 83 39 given give VERB cana-380 83 40 by by ADP cana-380 83 41 : : PUNCT cana-380 83 42 𝑑𝐼2(𝑑 𝑑𝐼2(𝑑 NOUN cana-380 83 43 ) ) PUNCT cana-380 83 44 𝑑𝑑 𝑑𝑑 ADP cana-380 83 45 = = NOUN cana-380 83 46 = = NOUN cana-380 83 47 βˆ’(πœ”1 βˆ’(πœ”1 NUM cana-380 83 48 + + NOUN cana-380 83 49 πœ”2𝑑)π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 πœ”2𝑑)π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 NUM cana-380 83 50 ) ) PUNCT cana-380 83 51 ; ; PUNCT cana-380 83 52 𝑑1 𝑑1 NOUN cana-380 83 53 ≀ ≀ NUM cana-380 83 54 𝑑 𝑑 VERB cana-380 83 55 ≀ ≀ ADJ cana-380 83 56 𝑇 𝑇 PROPN cana-380 83 57 ( ( PUNCT cana-380 83 58 2 2 NUM cana-380 83 59 ) ) PUNCT cana-380 83 60 with with ADP cana-380 83 61 the the DET cana-380 83 62 boundary boundary ADJ cana-380 83 63 conditions condition NOUN cana-380 83 64 : : PUNCT cana-380 83 65 𝑑 𝑑 X cana-380 83 66 = = SYM cana-380 83 67 0 0 NUM cana-380 83 68 , , PUNCT cana-380 83 69 𝐼(0 𝐼(0 X cana-380 83 70 ) ) PUNCT cana-380 83 71 = = SYM cana-380 83 72 π‘Š π‘Š PROPN cana-380 83 73 , , PUNCT cana-380 83 74 𝑑 𝑑 X cana-380 83 75 = = SYM cana-380 83 76 𝑑1 𝑑1 NOUN cana-380 83 77 ; ; PUNCT cana-380 83 78 𝐼(𝑑1 𝐼(𝑑1 X cana-380 83 79 ) ) PUNCT cana-380 83 80 = = SYM cana-380 83 81 0 0 NUM cana-380 83 82 𝑑 𝑑 PROPN cana-380 83 83 = = SYM cana-380 83 84 𝑇 𝑇 PROPN cana-380 83 85 ; ; PUNCT cana-380 83 86 i(𝑇 i(𝑇 NOUN cana-380 83 87 ) ) PUNCT cana-380 84 1 = = PUNCT cana-380 84 2 𝑆 𝑆 PROPN cana-380 84 3 now now ADV cana-380 84 4 by by ADP cana-380 84 5 solving solve VERB cana-380 84 6 equation equation NOUN cana-380 84 7 ( ( PUNCT cana-380 84 8 1 1 NUM cana-380 84 9 ) ) PUNCT cana-380 84 10 , , PUNCT cana-380 84 11 we we PRON cana-380 84 12 get get VERB cana-380 84 13 , , PUNCT cana-380 84 14 𝐼1(𝑑 𝐼1(𝑑 X cana-380 84 15 ) ) PUNCT cana-380 84 16 = = PRON cana-380 85 1 ( ( PUNCT cana-380 85 2 πœ”1+πœ”2𝑑 πœ”1+πœ”2𝑑 ADP cana-380 85 3 πœƒ πœƒ NUM cana-380 85 4 βˆ’ βˆ’ NOUN cana-380 85 5 πœ”2 πœ”2 PROPN cana-380 85 6 πœƒ2 πœƒ2 PROPN cana-380 85 7 ) ) PUNCT cana-380 85 8 π‘’πœƒ(𝑑1βˆ’π‘‘ π‘’πœƒ(𝑑1βˆ’π‘‘ NOUN cana-380 85 9 ) ) PUNCT cana-380 86 1 βˆ’ βˆ’ PROPN cana-380 87 1 ( ( PUNCT cana-380 87 2 πœ”1+πœ”2𝑑 πœ”1+πœ”2𝑑 ADP cana-380 87 3 πœƒ πœƒ NUM cana-380 87 4 βˆ’ βˆ’ NOUN cana-380 87 5 πœ”2 πœ”2 PROPN cana-380 87 6 πœƒ2 πœƒ2 PROPN cana-380 87 7 ) ) PUNCT cana-380 87 8 ( ( PUNCT cana-380 87 9 3 3 X cana-380 87 10 ) ) PUNCT cana-380 87 11 by by ADP cana-380 87 12 solving solve VERB cana-380 87 13 equation equation NOUN cana-380 87 14 ( ( PUNCT cana-380 87 15 2 2 NUM cana-380 87 16 ) ) PUNCT cana-380 87 17 , , PUNCT cana-380 87 18 we we PRON cana-380 87 19 get get VERB cana-380 87 20 : : PUNCT cana-380 87 21 𝐼2(𝑑 𝐼2(𝑑 X cana-380 87 22 ) ) PUNCT cana-380 87 23 = = SYM cana-380 87 24 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 PROPN cana-380 87 25 ) ) PUNCT cana-380 87 26 ( ( PUNCT cana-380 87 27 πœ”1+πœ”2𝑑 πœ”1+πœ”2𝑑 ADP cana-380 87 28 πœ‡ πœ‡ ADP cana-380 87 29 βˆ’ βˆ’ NOUN cana-380 87 30 πœ”2 πœ”2 ADJ cana-380 87 31 πœ‡2 πœ‡2 NOUN cana-380 87 32 ) ) PUNCT cana-380 88 1 βˆ’ βˆ’ PROPN cana-380 88 2 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘ π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘ PROPN cana-380 88 3 ) ) PUNCT cana-380 88 4 ( ( PUNCT cana-380 88 5 πœ”1+πœ”2𝑑 πœ”1+πœ”2𝑑 ADP cana-380 88 6 πœ‡ πœ‡ ADP cana-380 88 7 βˆ’ βˆ’ NOUN cana-380 88 8 πœ”2 πœ”2 ADJ cana-380 88 9 πœ‡2 πœ‡2 NOUN cana-380 88 10 ) ) PUNCT cana-380 88 11 ( ( PUNCT cana-380 88 12 4 4 X cana-380 88 13 ) ) PUNCT cana-380 88 14 now now ADV cana-380 88 15 , , PUNCT cana-380 88 16 at at ADP cana-380 88 17 𝑑 𝑑 X cana-380 88 18 = = SYM cana-380 88 19 0 0 NUM cana-380 88 20 the the DET cana-380 88 21 maximal maximal ADJ cana-380 88 22 storage storage NOUN cana-380 88 23 amount amount NOUN cana-380 88 24 for for ADP cana-380 88 25 every every DET cana-380 88 26 period period NOUN cana-380 88 27 is be AUX cana-380 88 28 given give VERB cana-380 88 29 by by ADP cana-380 88 30 𝐼1(0 𝐼1(0 NOUN cana-380 88 31 ) ) PUNCT cana-380 88 32 = = SYM cana-380 88 33 π‘Š π‘Š PROPN cana-380 88 34 , , PUNCT cana-380 88 35 𝑑 𝑑 X cana-380 88 36 = = SYM cana-380 88 37 0 0 NUM cana-380 88 38 π‘Š π‘Š PROPN cana-380 88 39 = = SYM cana-380 88 40 𝐼1(0 𝐼1(0 NOUN cana-380 88 41 ) ) PUNCT cana-380 88 42 = = PUNCT cana-380 88 43 ( ( PUNCT cana-380 88 44 πœ”1 πœ”1 NOUN cana-380 88 45 + + CCONJ cana-380 88 46 πœ”2𝑑 πœ”2𝑑 PROPN cana-380 88 47 πœƒ πœƒ NUM cana-380 88 48 βˆ’ βˆ’ NOUN cana-380 88 49 πœ”2 πœ”2 ADJ cana-380 88 50 πœƒ2 πœƒ2 NOUN cana-380 88 51 ) ) PUNCT cana-380 88 52 π‘’πœƒπ‘‘1 π‘’πœƒπ‘‘1 PROPN cana-380 88 53 βˆ’ βˆ’ PROPN cana-380 89 1 ( ( PUNCT cana-380 89 2 πœ”1 πœ”1 ADJ cana-380 89 3 πœƒ πœƒ PRON cana-380 89 4 βˆ’ βˆ’ NOUN cana-380 89 5 πœ”2 πœ”2 ADJ cana-380 89 6 πœƒ2 πœƒ2 PROPN cana-380 89 7 ) ) PUNCT cana-380 89 8 and and CCONJ cana-380 89 9 at at ADP cana-380 89 10 𝑑 𝑑 PROPN cana-380 89 11 = = SYM cana-380 89 12 𝑇 𝑇 PROPN cana-380 89 13 the the DET cana-380 89 14 maximum maximum ADJ cana-380 89 15 cycle cycle NOUN cana-380 89 16 - - PUNCT cana-380 89 17 level level NOUN cana-380 89 18 quadratic quadratic ADJ cana-380 89 19 demand demand NOUN cana-380 89 20 is be AUX cana-380 89 21 given give VERB cana-380 89 22 by by ADP cana-380 89 23 𝑑 𝑑 PROPN cana-380 89 24 = = PROPN cana-380 89 25 𝑇 𝑇 PROPN cana-380 89 26 , , PUNCT cana-380 89 27 𝐼2(𝑑 𝐼2(𝑑 PROPN cana-380 89 28 ) ) PUNCT cana-380 89 29 = = SYM cana-380 90 1 βˆ’π‘† βˆ’π‘† ADJ cana-380 90 2 𝑆 𝑆 PROPN cana-380 90 3 = = SYM cana-380 90 4 ( ( PUNCT cana-380 90 5 πœ”1 πœ”1 PROPN cana-380 90 6 + + X cana-380 90 7 πœ”2𝑑 πœ”2𝑑 ADP cana-380 90 8 πœ‡ πœ‡ ADP cana-380 90 9 βˆ’ βˆ’ PROPN cana-380 90 10 πœ”2 πœ”2 PROPN cana-380 90 11 πœ‡2 πœ‡2 PROPN cana-380 90 12 ) ) PUNCT cana-380 90 13 βˆ’ βˆ’ ADP cana-380 90 14 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 PROPN cana-380 90 15 ) ) PUNCT cana-380 90 16 ( ( PUNCT cana-380 90 17 πœ”1 πœ”1 NOUN cana-380 90 18 + + CCONJ cana-380 90 19 πœ”2𝑑 πœ”2𝑑 ADP cana-380 90 20 πœ‡ πœ‡ ADP cana-380 90 21 βˆ’ βˆ’ PROPN cana-380 90 22 πœ”2 πœ”2 PROPN cana-380 90 23 πœ‡2 πœ‡2 PROPN cana-380 90 24 ) ) PUNCT cana-380 90 25 now now ADV cana-380 90 26 the the DET cana-380 90 27 amount amount NOUN cana-380 90 28 purchased purchase VERB cana-380 90 29 per per ADP cana-380 90 30 round round NOUN cana-380 90 31 is be AUX cana-380 90 32 , , PUNCT cana-380 90 33 𝑄 𝑄 PROPN cana-380 90 34 = = SYM cana-380 90 35 π‘Š π‘Š PROPN cana-380 90 36 + + NOUN cana-380 90 37 𝑆 𝑆 PROPN cana-380 90 38 = = SYM cana-380 90 39 ( ( PUNCT cana-380 90 40 πœ”1+πœ”2𝑑 πœ”1+πœ”2𝑑 ADP cana-380 90 41 πœƒ πœƒ NUM cana-380 90 42 βˆ’ βˆ’ NOUN cana-380 90 43 πœ”2 πœ”2 PROPN cana-380 90 44 πœƒ2 πœƒ2 PROPN cana-380 90 45 ) ) PUNCT cana-380 90 46 π‘’πœƒπ‘‘1 π‘’πœƒπ‘‘1 NOUN cana-380 90 47 βˆ’ βˆ’ PROPN cana-380 91 1 ( ( PUNCT cana-380 91 2 πœ”1 πœ”1 ADJ cana-380 91 3 πœƒ πœƒ PRON cana-380 91 4 βˆ’ βˆ’ NOUN cana-380 91 5 πœ”2 πœ”2 PROPN cana-380 91 6 πœƒ2 πœƒ2 PROPN cana-380 91 7 ) ) PUNCT cana-380 91 8 + + CCONJ cana-380 91 9 ( ( PUNCT cana-380 91 10 πœ”1+πœ”2𝑑 πœ”1+πœ”2𝑑 ADP cana-380 91 11 πœ‡ πœ‡ ADP cana-380 91 12 βˆ’ βˆ’ NOUN cana-380 91 13 πœ”2 πœ”2 ADJ cana-380 91 14 πœ‡2 πœ‡2 NOUN cana-380 91 15 ) ) PUNCT cana-380 91 16 βˆ’ βˆ’ PROPN cana-380 91 17 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 PROPN cana-380 91 18 ) ) PUNCT cana-380 91 19 ( ( PUNCT cana-380 91 20 πœ”1+πœ”2𝑑 πœ”1+πœ”2𝑑 ADP cana-380 91 21 πœ‡ πœ‡ ADP cana-380 91 22 βˆ’ βˆ’ NOUN cana-380 91 23 πœ”2 πœ”2 ADJ cana-380 91 24 πœ‡2 πœ‡2 NOUN cana-380 91 25 ) ) PUNCT cana-380 91 26 ( ( PUNCT cana-380 91 27 5 5 X cana-380 91 28 ) ) PUNCT cana-380 91 29 the the DET cana-380 91 30 price price NOUN cana-380 91 31 of of ADP cana-380 91 32 holding hold VERB cana-380 91 33 per per ADP cana-380 91 34 unit unit NOUN cana-380 91 35 time time NOUN cana-380 91 36 originates originate NOUN cana-380 91 37 by by ADP cana-380 91 38 , , PUNCT cana-380 91 39 𝐻𝐢 𝐻𝐢 PROPN cana-380 91 40 = = SYM cana-380 91 41 ∫ ∫ PROPN cana-380 91 42 ( ( PUNCT cana-380 91 43 𝛼 𝛼 NOUN cana-380 91 44 + + X cana-380 91 45 𝛽𝑑)𝐼1 𝛽𝑑)𝐼1 ADJ cana-380 91 46 𝑑1 𝑑1 NOUN cana-380 91 47 0 0 NUM cana-380 91 48 ( ( PUNCT cana-380 91 49 𝑑 𝑑 NOUN cana-380 91 50 ) ) PUNCT cana-380 91 51 𝐻𝐢 𝐻𝐢 PROPN cana-380 91 52 = = SYM cana-380 91 53 1 1 NUM cana-380 91 54 2πœƒ4 2πœƒ4 NUM cana-380 92 1 [ [ X cana-380 92 2 { { PUNCT cana-380 92 3 2πœƒ2(𝛽(2πœ”2𝑑1 2πœƒ2(𝛽(2πœ”2𝑑1 NUM cana-380 92 4 2 2 NUM cana-380 92 5 + + CCONJ cana-380 92 6 2πœ”1𝑑1 2πœ”1𝑑1 NUM cana-380 92 7 ) ) PUNCT cana-380 92 8 + + CCONJ cana-380 92 9 𝛼(2πœ”2𝑑1 𝛼(2πœ”2𝑑1 PROPN cana-380 92 10 + + NUM cana-380 92 11 2πœ”1 2πœ”1 NUM cana-380 92 12 ) ) PUNCT cana-380 92 13 } } PUNCT cana-380 93 1 + + CCONJ cana-380 93 2 πœƒ(𝛽(βˆ’6πœ”2𝑑1 πœƒ(𝛽(βˆ’6πœ”2𝑑1 ADJ cana-380 93 3 βˆ’ βˆ’ NOUN cana-380 93 4 2πœ”1 2πœ”1 NUM cana-380 93 5 ) ) PUNCT cana-380 93 6 βˆ’ βˆ’ NOUN cana-380 93 7 4πœ”2𝛼 4πœ”2𝛼 NOUN cana-380 93 8 ) ) PUNCT cana-380 94 1 + + CCONJ cana-380 94 2 6πœ”2𝛽)(1 6πœ”2𝛽)(1 NOUN cana-380 94 3 βˆ’ βˆ’ NOUN cana-380 94 4 πœƒπ‘‘1 πœƒπ‘‘1 NOUN cana-380 94 5 ) ) PUNCT cana-380 94 6 + + NUM cana-380 94 7 πœƒ2(πœ”2𝛽𝑑1 πœƒ2(πœ”2𝛽𝑑1 NOUN cana-380 94 8 2 2 NUM cana-380 94 9 + + NOUN cana-380 94 10 2πœ”2𝛼𝑑1 2πœ”2𝛼𝑑1 NUM cana-380 94 11 ) ) PUNCT cana-380 94 12 + + NUM cana-380 94 13 πœƒ3(βˆ’πœ”1𝛽𝑑1 πœƒ3(βˆ’πœ”1𝛽𝑑1 NUM cana-380 94 14 2 2 NUM cana-380 94 15 βˆ’ βˆ’ PROPN cana-380 94 16 2πœ”1𝛼𝑑1 2πœ”1𝛼𝑑1 NUM cana-380 94 17 ) ) PUNCT cana-380 94 18 ] ] PUNCT cana-380 95 1 βˆ’ βˆ’ PROPN cana-380 95 2 { { PUNCT cana-380 95 3 πœ”1π›Όπœƒ4+(βˆ’πœ”1π›½βˆ’2πœ”2𝛼)πœƒ+3πœ”2𝛽 πœ”1π›Όπœƒ4+(βˆ’πœ”1π›½βˆ’2πœ”2𝛼)πœƒ+3πœ”2𝛽 NUM cana-380 95 4 πœƒ4 πœƒ4 PROPN cana-380 95 5 } } PUNCT cana-380 95 6 ( ( PUNCT cana-380 95 7 6 6 X cana-380 95 8 ) ) PUNCT cana-380 95 9 communications communication NOUN cana-380 95 10 on on ADP cana-380 95 11 applied apply VERB cana-380 95 12 nonlinear nonlinear ADJ cana-380 95 13 analysis analysis NOUN cana-380 95 14 issn issn NOUN cana-380 95 15 : : PUNCT cana-380 95 16 1074 1074 NUM cana-380 95 17 - - PUNCT cana-380 95 18 133x 133x NUM cana-380 95 19 vol vol NOUN cana-380 95 20 31 31 NUM cana-380 95 21 no no NOUN cana-380 95 22 . . NOUN cana-380 95 23 1 1 NUM cana-380 95 24 ( ( PUNCT cana-380 95 25 2024 2024 NUM cana-380 95 26 ) ) PUNCT cana-380 95 27 181 181 NUM cana-380 95 28 https://internationalpubls.com https://internationalpubls.com X cana-380 95 29 the the DET cana-380 95 30 cost cost NOUN cana-380 95 31 of of ADP cana-380 95 32 ordering order VERB cana-380 95 33 per per ADP cana-380 95 34 order order NOUN cana-380 95 35 is be AUX cana-380 95 36 calculated calculate VERB cana-380 95 37 by by ADP cana-380 95 38 𝑂𝐢 𝑂𝐢 PROPN cana-380 95 39 = = SYM cana-380 95 40 πΆπ‘œ πΆπ‘œ PROPN cana-380 95 41 = = PUNCT cana-380 95 42 π‘žπ›Ύβˆ’1 π‘žπ›Ύβˆ’1 PROPN cana-380 95 43 ( ( PUNCT cana-380 95 44 7 7 NUM cana-380 95 45 ) ) PUNCT cana-380 95 46 now now ADV cana-380 95 47 , , PUNCT cana-380 95 48 the the DET cana-380 95 49 deteriorating deteriorate VERB cana-380 95 50 cost cost NOUN cana-380 95 51 is be AUX cana-380 95 52 given give VERB cana-380 95 53 by by ADP cana-380 95 54 , , PUNCT cana-380 95 55 𝐷𝐢 𝐷𝐢 PROPN cana-380 95 56 = = PUNCT cana-380 95 57 𝐢𝐷 𝐢𝐷 PROPN cana-380 95 58 [ [ X cana-380 95 59 π‘Š π‘Š PROPN cana-380 95 60 βˆ’ βˆ’ PROPN cana-380 95 61 ∫ ∫ NOUN cana-380 95 62 𝑓(𝑑)𝑑𝑑 𝑓(𝑑)𝑑𝑑 NOUN cana-380 95 63 𝑑1 𝑑1 NOUN cana-380 95 64 0 0 PUNCT cana-380 95 65 ] ] PUNCT cana-380 95 66 𝐷𝐢 𝐷𝐢 PROPN cana-380 95 67 = = PUNCT cana-380 95 68 𝐢𝐷 𝐢𝐷 PROPN cana-380 95 69 [ [ X cana-380 95 70 ( ( PUNCT cana-380 95 71 πœ”1+πœ”2𝑑1 πœ”1+πœ”2𝑑1 PROPN cana-380 95 72 πœƒ πœƒ NOUN cana-380 95 73 βˆ’ βˆ’ PROPN cana-380 95 74 πœ”2 πœ”2 PROPN cana-380 95 75 πœƒ2 πœƒ2 PROPN cana-380 95 76 ) ) PUNCT cana-380 95 77 π‘’πœƒπ‘‘1 π‘’πœƒπ‘‘1 NOUN cana-380 95 78 βˆ’ βˆ’ PROPN cana-380 96 1 ( ( PUNCT cana-380 96 2 πœ”1 πœ”1 ADJ cana-380 96 3 πœƒ πœƒ PRON cana-380 96 4 βˆ’ βˆ’ X cana-380 96 5 πœ”2 πœ”2 PROPN cana-380 96 6 πœƒ2 πœƒ2 PROPN cana-380 96 7 ) ) PUNCT cana-380 96 8 βˆ’ βˆ’ PROPN cana-380 96 9 ( ( PUNCT cana-380 96 10 πœ”1𝑑1 πœ”1𝑑1 PUNCT cana-380 96 11 + + CCONJ cana-380 96 12 πœ”2𝑑1 πœ”2𝑑1 X cana-380 96 13 2 2 NUM cana-380 96 14 2 2 NUM cana-380 96 15 ) ) PUNCT cana-380 96 16 ] ] PUNCT cana-380 96 17 ( ( PUNCT cana-380 96 18 8) 8) NUM cana-380 96 19 shortages shortage NOUN cana-380 96 20 incur incur NOUN cana-380 96 21 costs cost NOUN cana-380 96 22 over over ADP cana-380 96 23 time time NOUN cana-380 96 24 is be AUX cana-380 96 25 given give VERB cana-380 96 26 by by ADP cana-380 96 27 𝑆𝐢 𝑆𝐢 PROPN cana-380 96 28 = = PUNCT cana-380 96 29 βˆ’πΆπ‘† βˆ’πΆπ‘† VERB cana-380 96 30 ∫ ∫ PROPN cana-380 96 31 𝐼2(𝑑 𝐼2(𝑑 PROPN cana-380 96 32 ) ) PUNCT cana-380 96 33 𝑇 𝑇 PROPN cana-380 96 34 𝑑1 𝑑1 NOUN cana-380 96 35 𝑆𝐢 𝑆𝐢 PROPN cana-380 96 36 = = PUNCT cana-380 96 37 βˆ’πΆπ‘† βˆ’πΆπ‘† PROPN cana-380 96 38 [ [ PUNCT cana-380 96 39 ( ( PUNCT cana-380 96 40 πœ”1+πœ”2𝑇 πœ”1+πœ”2𝑇 X cana-380 96 41 πœ‡2 πœ‡2 VERB cana-380 96 42 βˆ’ βˆ’ PROPN cana-380 96 43 2πœ”2 2πœ”2 NUM cana-380 96 44 πœ‡3 πœ‡3 NOUN cana-380 96 45 ) ) PUNCT cana-380 97 1 βˆ’ βˆ’ PROPN cana-380 98 1 ( ( PUNCT cana-380 98 2 πœ”1+πœ”2𝑑1 πœ”1+πœ”2𝑑1 PROPN cana-380 98 3 πœ‡2 πœ‡2 PROPN cana-380 98 4 βˆ’ βˆ’ PROPN cana-380 98 5 2πœ”2 2πœ”2 NUM cana-380 98 6 πœ‡3 πœ‡3 NOUN cana-380 98 7 ) ) PUNCT cana-380 99 1 + + CCONJ cana-380 99 2 ( ( PUNCT cana-380 99 3 𝑇 𝑇 PROPN cana-380 99 4 βˆ’ βˆ’ PROPN cana-380 99 5 𝑑1 𝑑1 NOUN cana-380 99 6 ) ) PUNCT cana-380 99 7 ( ( PUNCT cana-380 99 8 πœ”1+πœ”2𝑑1 πœ”1+πœ”2𝑑1 PROPN cana-380 99 9 πœ‡2 πœ‡2 PROPN cana-380 99 10 βˆ’ βˆ’ PROPN cana-380 100 1 πœ”2 πœ”2 PROPN cana-380 100 2 πœ‡3 πœ‡3 PROPN cana-380 100 3 ) ) PUNCT cana-380 100 4 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 PROPN cana-380 100 5 ) ) PUNCT cana-380 100 6 ] ] PUNCT cana-380 101 1 ( ( PUNCT cana-380 101 2 9 9 X cana-380 101 3 ) ) PUNCT cana-380 101 4 the the DET cana-380 101 5 salvage salvage NOUN cana-380 101 6 value value NOUN cana-380 101 7 πœ• πœ• PROPN cana-380 101 8 , , PUNCT cana-380 101 9 0 0 NUM cana-380 101 10 ≀ ≀ NUM cana-380 101 11 πœ• πœ• VERB cana-380 101 12 < < SYM cana-380 101 13 1 1 NUM cana-380 101 14 𝑆𝑉 𝑆𝑉 PROPN cana-380 101 15 = = SYM cana-380 101 16 𝛿(𝐢𝐷 𝛿(𝐢𝐷 PROPN cana-380 101 17 ) ) PUNCT cana-380 101 18 ( ( PUNCT cana-380 101 19 10 10 NUM cana-380 101 20 ) ) PUNCT cana-380 101 21 therefore therefore ADV cana-380 101 22 , , PUNCT cana-380 101 23 the the DET cana-380 101 24 entire entire ADJ cana-380 101 25 cost cost NOUN cana-380 101 26 per per ADP cana-380 101 27 unit unit NOUN cana-380 101 28 time time NOUN cana-380 101 29 per per ADP cana-380 101 30 unit unit NOUN cana-380 101 31 cycle cycle NOUN cana-380 101 32 is be AUX cana-380 101 33 provided provide VERB cana-380 101 34 by by ADP cana-380 101 35 , , PUNCT cana-380 101 36 𝑇𝐢 𝑇𝐢 ADJ cana-380 101 37 = = SYM cana-380 101 38 1 1 NUM cana-380 101 39 𝑇 𝑇 PROPN cana-380 101 40 ( ( PUNCT cana-380 101 41 𝐻𝐢 𝐻𝐢 PROPN cana-380 101 42 + + CCONJ cana-380 101 43 𝑆𝐢 𝑆𝐢 PROPN cana-380 101 44 + + CCONJ cana-380 101 45 𝑂𝐢 𝑂𝐢 PROPN cana-380 101 46 + + CCONJ cana-380 101 47 𝐷𝐢 𝐷𝐢 PROPN cana-380 101 48 βˆ’ βˆ’ PROPN cana-380 101 49 𝑆𝑉 𝑆𝑉 PROPN cana-380 101 50 ) ) PUNCT cana-380 101 51 = = SYM cana-380 101 52 1 1 NUM cana-380 101 53 𝑇 𝑇 PROPN cana-380 101 54 [ [ PUNCT cana-380 101 55 1 1 NUM cana-380 101 56 2πœƒ4 2πœƒ4 NUM cana-380 101 57 [ [ X cana-380 101 58 { { PUNCT cana-380 101 59 2πœƒ2(𝛽(2πœ”2𝑑1 2πœƒ2(𝛽(2πœ”2𝑑1 NUM cana-380 101 60 2 2 NUM cana-380 101 61 + + CCONJ cana-380 101 62 2πœ”1𝑑1 2πœ”1𝑑1 NUM cana-380 101 63 ) ) PUNCT cana-380 101 64 + + CCONJ cana-380 101 65 𝛼(2πœ”2𝑑1 𝛼(2πœ”2𝑑1 PROPN cana-380 101 66 + + NUM cana-380 101 67 2πœ”1 2πœ”1 NUM cana-380 101 68 ) ) PUNCT cana-380 101 69 } } PUNCT cana-380 101 70 + + CCONJ cana-380 101 71 πœƒ(𝛽(βˆ’6πœ”2𝑑1 πœƒ(𝛽(βˆ’6πœ”2𝑑1 ADJ cana-380 101 72 βˆ’ βˆ’ NOUN cana-380 101 73 2πœ”1 2πœ”1 NUM cana-380 101 74 ) ) PUNCT cana-380 101 75 βˆ’ βˆ’ NOUN cana-380 101 76 4πœ”2𝛼 4πœ”2𝛼 NOUN cana-380 101 77 ) ) PUNCT cana-380 102 1 + + CCONJ cana-380 102 2 6πœ”2𝛽)(1 6πœ”2𝛽)(1 NOUN cana-380 102 3 βˆ’ βˆ’ NOUN cana-380 102 4 πœƒπ‘‘1 πœƒπ‘‘1 NOUN cana-380 102 5 ) ) PUNCT cana-380 102 6 + + NUM cana-380 102 7 πœƒ2(πœ”2𝛽𝑑1 πœƒ2(πœ”2𝛽𝑑1 NOUN cana-380 102 8 2 2 NUM cana-380 102 9 + + NOUN cana-380 102 10 2πœ”2𝛼𝑑1 2πœ”2𝛼𝑑1 NUM cana-380 102 11 ) ) PUNCT cana-380 102 12 + + NUM cana-380 102 13 πœƒ3(βˆ’πœ”1𝛽𝑑1 πœƒ3(βˆ’πœ”1𝛽𝑑1 NUM cana-380 102 14 2 2 NUM cana-380 102 15 βˆ’ βˆ’ PROPN cana-380 102 16 2πœ”1𝛼𝑑1 2πœ”1𝛼𝑑1 NUM cana-380 102 17 ) ) PUNCT cana-380 102 18 ] ] PUNCT cana-380 103 1 βˆ’ βˆ’ PROPN cana-380 103 2 { { PUNCT cana-380 103 3 πœ”1π›Όπœƒ4+(βˆ’πœ”1π›½βˆ’2πœ”2𝛼)πœƒ+3πœ”2𝛽 πœ”1π›Όπœƒ4+(βˆ’πœ”1π›½βˆ’2πœ”2𝛼)πœƒ+3πœ”2𝛽 PUNCT cana-380 103 4 πœƒ4 πœƒ4 PROPN cana-380 103 5 } } PUNCT cana-380 103 6 βˆ’ βˆ’ PROPN cana-380 103 7 𝐢𝑆 𝐢𝑆 NOUN cana-380 104 1 [ [ X cana-380 104 2 ( ( PUNCT cana-380 104 3 πœ”1+πœ”2𝑇 πœ”1+πœ”2𝑇 X cana-380 104 4 πœ‡2 πœ‡2 VERB cana-380 104 5 βˆ’ βˆ’ PROPN cana-380 104 6 2πœ”2 2πœ”2 NUM cana-380 104 7 πœ‡3 πœ‡3 NOUN cana-380 104 8 ) ) PUNCT cana-380 104 9 βˆ’ βˆ’ PROPN cana-380 105 1 ( ( PUNCT cana-380 105 2 πœ”1+πœ”2𝑑1 πœ”1+πœ”2𝑑1 PROPN cana-380 105 3 πœ‡2 πœ‡2 PROPN cana-380 105 4 βˆ’ βˆ’ PROPN cana-380 105 5 2πœ”2 2πœ”2 NUM cana-380 105 6 πœ‡3 πœ‡3 NOUN cana-380 105 7 ) ) PUNCT cana-380 106 1 + + CCONJ cana-380 106 2 ( ( PUNCT cana-380 106 3 𝑇 𝑇 PROPN cana-380 106 4 βˆ’ βˆ’ PROPN cana-380 106 5 𝑑1 𝑑1 NOUN cana-380 106 6 ) ) PUNCT cana-380 106 7 ( ( PUNCT cana-380 106 8 πœ”1+πœ”2𝑑1 πœ”1+πœ”2𝑑1 PROPN cana-380 106 9 πœ‡2 πœ‡2 PROPN cana-380 106 10 βˆ’ βˆ’ PROPN cana-380 106 11 πœ”2 πœ”2 PROPN cana-380 106 12 πœ‡3 πœ‡3 PROPN cana-380 106 13 ) ) PUNCT cana-380 106 14 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 π‘’βˆ’πœ‡(π‘‡βˆ’π‘‘1 PROPN cana-380 106 15 ) ) PUNCT cana-380 106 16 ] ] PUNCT cana-380 107 1 + + CCONJ cana-380 107 2 π‘žπ›Ύβˆ’1 π‘žπ›Ύβˆ’1 NOUN cana-380 107 3 + + CCONJ cana-380 107 4 𝐢𝐷 𝐢𝐷 PROPN cana-380 107 5 [ [ X cana-380 107 6 ( ( PUNCT cana-380 107 7 πœ”1+πœ”2𝑑1 πœ”1+πœ”2𝑑1 PROPN cana-380 107 8 πœƒ πœƒ NOUN cana-380 107 9 βˆ’ βˆ’ NOUN cana-380 107 10 πœ”2 πœ”2 ADJ cana-380 107 11 πœƒ2 πœƒ2 NOUN cana-380 107 12 ) ) PUNCT cana-380 107 13 π‘’πœƒπ‘‘1 π‘’πœƒπ‘‘1 PROPN cana-380 107 14 βˆ’ βˆ’ PROPN cana-380 107 15 ( ( PUNCT cana-380 107 16 πœ”1 πœ”1 ADJ cana-380 107 17 πœƒ πœƒ PRON cana-380 107 18 βˆ’ βˆ’ NOUN cana-380 107 19 πœ”2 πœ”2 ADJ cana-380 107 20 πœƒ2 πœƒ2 PROPN cana-380 107 21 ) ) PUNCT cana-380 107 22 βˆ’ βˆ’ PROPN cana-380 107 23 ( ( PUNCT cana-380 107 24 πœ”1𝑑1 πœ”1𝑑1 PUNCT cana-380 107 25 + + CCONJ cana-380 107 26 πœ”2𝑑1 πœ”2𝑑1 X cana-380 107 27 2 2 NUM cana-380 107 28 2 2 NUM cana-380 107 29 ) ) PUNCT cana-380 107 30 ] ] PUNCT cana-380 108 1 βˆ’ βˆ’ PROPN cana-380 108 2 𝛿𝐢𝐷 𝛿𝐢𝐷 NOUN cana-380 108 3 [ [ X cana-380 108 4 ( ( PUNCT cana-380 108 5 πœ”1+πœ”2𝑑1 πœ”1+πœ”2𝑑1 PROPN cana-380 108 6 πœƒ πœƒ NOUN cana-380 108 7 βˆ’ βˆ’ NOUN cana-380 108 8 πœ”2 πœ”2 ADJ cana-380 108 9 πœƒ2 πœƒ2 NOUN cana-380 108 10 ) ) PUNCT cana-380 108 11 π‘’πœƒπ‘‘1 π‘’πœƒπ‘‘1 PROPN cana-380 108 12 βˆ’ βˆ’ PROPN cana-380 109 1 ( ( PUNCT cana-380 109 2 πœ”1 πœ”1 ADJ cana-380 109 3 πœƒ πœƒ PRON cana-380 109 4 βˆ’ βˆ’ NOUN cana-380 109 5 πœ”2 πœ”2 ADJ cana-380 109 6 πœƒ2 πœƒ2 PROPN cana-380 109 7 ) ) PUNCT cana-380 109 8 βˆ’ βˆ’ PROPN cana-380 109 9 ( ( PUNCT cana-380 109 10 πœ”1𝑑1 πœ”1𝑑1 PUNCT cana-380 109 11 + + CCONJ cana-380 109 12 πœ”2𝑑1 πœ”2𝑑1 X cana-380 109 13 2 2 NUM cana-380 109 14 2 2 NUM cana-380 109 15 ) ) PUNCT cana-380 109 16 ] ] PUNCT cana-380 109 17 ] ] X cana-380 109 18 ( ( PUNCT cana-380 109 19 11 11 NUM cana-380 109 20 ) ) PUNCT cana-380 109 21 the the DET cana-380 109 22 model model NOUN cana-380 109 23 's 's PART cana-380 109 24 objective objective NOUN cana-380 109 25 is be AUX cana-380 109 26 to to PART cana-380 109 27 locate locate VERB cana-380 109 28 the the DET cana-380 109 29 best good ADJ cana-380 109 30 values value NOUN cana-380 109 31 of of ADP cana-380 109 32 𝑑1 𝑑1 NOUN cana-380 109 33 and and CCONJ cana-380 109 34 𝑇 𝑇 PROPN cana-380 109 35 to to PART cana-380 109 36 decrease decrease VERB cana-380 109 37 the the DET cana-380 109 38 mean mean ADJ cana-380 109 39 total total ADJ cana-380 109 40 expenditure expenditure NOUN cana-380 109 41 per per ADP cana-380 109 42 unit unit NOUN cana-380 109 43 time time NOUN cana-380 109 44 𝑇𝐢. 𝑇𝐢. PUNCT cana-380 109 45 for for ADP cana-380 109 46 the the DET cana-380 109 47 optimal optimal ADJ cana-380 109 48 value value NOUN cana-380 109 49 , , PUNCT cana-380 109 50 we we PRON cana-380 109 51 have have VERB cana-380 109 52 to to PART cana-380 109 53 get get VERB cana-380 109 54 a a DET cana-380 109 55 partial partial ADJ cana-380 109 56 derivative derivative NOUN cana-380 109 57 of of ADP cana-380 109 58 𝑑1 𝑑1 NOUN cana-380 109 59 and and CCONJ cana-380 109 60 𝑇 𝑇 PROPN cana-380 109 61 and and CCONJ cana-380 109 62 equating equate VERB cana-380 109 63 to to ADP cana-380 109 64 zero zero NUM cana-380 109 65 . . PUNCT cana-380 110 1 πœ•(𝑇𝐢 πœ•(𝑇𝐢 X cana-380 110 2 ) ) PUNCT cana-380 110 3 πœ•π‘‡ πœ•π‘‡ X cana-380 111 1 = = PUNCT cana-380 111 2 βˆ’ βˆ’ PROPN cana-380 111 3 1 1 NUM cana-380 111 4 𝑇2 𝑇2 NOUN cana-380 111 5 [ [ X cana-380 111 6 { { PUNCT cana-380 111 7 1 1 NUM cana-380 111 8 2 2 NUM cana-380 111 9 1 1 NUM cana-380 111 10 πœƒ4 πœƒ4 NOUN cana-380 111 11 { { PUNCT cana-380 111 12 ( ( PUNCT cana-380 111 13 πœƒ2(𝛽(2πœ”2𝑑1 πœƒ2(𝛽(2πœ”2𝑑1 X cana-380 111 14 2 2 NUM cana-380 111 15 + + NOUN cana-380 111 16 2πœ”1𝑑1 2πœ”1𝑑1 NUM cana-380 111 17 ) ) PUNCT cana-380 111 18 + + CCONJ cana-380 111 19 𝛼(2πœ”2𝑑1 𝛼(2πœ”2𝑑1 PROPN cana-380 111 20 + + NUM cana-380 111 21 2πœ”1 2πœ”1 NUM cana-380 111 22 ) ) PUNCT cana-380 111 23 ) ) PUNCT cana-380 112 1 + + CCONJ cana-380 112 2 πœƒ(𝛽(βˆ’6πœ”2𝑑1 πœƒ(𝛽(βˆ’6πœ”2𝑑1 ADJ cana-380 112 3 βˆ’ βˆ’ NOUN cana-380 112 4 2πœ”1 2πœ”1 NUM cana-380 112 5 ) ) PUNCT cana-380 112 6 βˆ’ βˆ’ NOUN cana-380 112 7 4πœ”2𝛼 4πœ”2𝛼 NOUN cana-380 112 8 ) ) PUNCT cana-380 113 1 + + CCONJ cana-380 114 1 6πœ”2𝛽)(βˆ’π‘‘1πœƒ 6πœ”2𝛽)(βˆ’π‘‘1πœƒ NUM cana-380 114 2 + + CCONJ cana-380 114 3 1 1 NUM cana-380 114 4 ) ) PUNCT cana-380 114 5 + + NUM cana-380 114 6 πœƒ2(πœ”2𝛽𝑑1 πœƒ2(πœ”2𝛽𝑑1 NOUN cana-380 114 7 2 2 NUM cana-380 114 8 + + NUM cana-380 114 9 2π›Όπœ”2𝑑1 2π›Όπœ”2𝑑1 NUM cana-380 114 10 ) ) PUNCT cana-380 114 11 + + NUM cana-380 114 12 πœƒ3(βˆ’πœ”1𝛽𝑑1 πœƒ3(βˆ’πœ”1𝛽𝑑1 NUM cana-380 114 13 2 2 NUM cana-380 114 14 βˆ’ βˆ’ NUM cana-380 114 15 2πœ”1𝛼𝑑1 2πœ”1𝛼𝑑1 NUM cana-380 114 16 ) ) PUNCT cana-380 114 17 } } PUNCT cana-380 114 18 βˆ’ βˆ’ ADP cana-380 114 19 πœ”1π›Όπœƒ4+(βˆ’πœ”1π›½βˆ’2π›Όπœ”2)πœƒ+3πœ”2𝛽 πœ”1π›Όπœƒ4+(βˆ’πœ”1π›½βˆ’2π›Όπœ”2)πœƒ+3πœ”2𝛽 INTJ cana-380 114 20 πœƒ4 πœƒ4 PROPN cana-380 114 21 } } PUNCT cana-380 114 22 + + CCONJ cana-380 114 23 𝐢𝑆 𝐢𝑆 PROPN cana-380 114 24 ( ( PUNCT cana-380 114 25 πœ”2𝑇+πœ”1 πœ”2𝑇+πœ”1 ADJ cana-380 114 26 πœ‡2 πœ‡2 NOUN cana-380 114 27 βˆ’ βˆ’ PROPN cana-380 114 28 2πœ”2 2πœ”2 NUM cana-380 114 29 πœ‡3 πœ‡3 NOUN cana-380 114 30 ) ) PUNCT cana-380 115 1 βˆ’ βˆ’ ADP cana-380 115 2 πœ”2𝑑+πœ”1 πœ”2𝑑+πœ”1 PROPN cana-380 115 3 πœ‡2 πœ‡2 NOUN cana-380 115 4 + + CCONJ cana-380 115 5 2πœ”2 2πœ”2 NUM cana-380 115 6 πœ‡3 πœ‡3 NOUN cana-380 115 7 + + CCONJ cana-380 115 8 ( ( PUNCT cana-380 115 9 𝑇 𝑇 PROPN cana-380 115 10 βˆ’ βˆ’ PROPN cana-380 115 11 𝑑1 𝑑1 NOUN cana-380 115 12 ) ) PUNCT cana-380 115 13 ( ( PUNCT cana-380 115 14 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 115 15 πœ‡2 πœ‡2 NOUN cana-380 115 16 βˆ’ βˆ’ PROPN cana-380 115 17 πœ”2 πœ”2 PROPN cana-380 115 18 πœ‡3 πœ‡3 NOUN cana-380 115 19 ) ) PUNCT cana-380 115 20 { { PUNCT cana-380 115 21 1 1 NUM cana-380 115 22 βˆ’ βˆ’ PROPN cana-380 115 23 πœ‡(𝑇 πœ‡(𝑇 NOUN cana-380 115 24 βˆ’ βˆ’ PROPN cana-380 115 25 𝑑1 𝑑1 NOUN cana-380 115 26 ) ) PUNCT cana-380 115 27 } } PUNCT cana-380 116 1 + + CCONJ cana-380 116 2 π‘žπ›Ύβˆ’1 π‘žπ›Ύβˆ’1 NOUN cana-380 116 3 + + CCONJ cana-380 116 4 𝐢𝐷 𝐢𝐷 PROPN cana-380 116 5 { { PUNCT cana-380 116 6 ( ( PUNCT cana-380 116 7 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 116 8 πœƒ πœƒ NOUN cana-380 116 9 βˆ’ βˆ’ NOUN cana-380 116 10 πœ”2 πœ”2 PROPN cana-380 116 11 πœƒ2 πœƒ2 PROPN cana-380 116 12 ) ) PUNCT cana-380 116 13 ( ( PUNCT cana-380 116 14 βˆ’π‘‘1πœƒ βˆ’π‘‘1πœƒ NUM cana-380 116 15 + + CCONJ cana-380 116 16 1 1 NUM cana-380 116 17 ) ) PUNCT cana-380 116 18 βˆ’ βˆ’ NOUN cana-380 117 1 πœ”1 πœ”1 ADJ cana-380 117 2 πœƒ πœƒ X cana-380 117 3 + + CCONJ cana-380 117 4 πœ”2 πœ”2 ADV cana-380 117 5 πœƒ2 πœƒ2 PRON cana-380 117 6 βˆ’ βˆ’ PROPN cana-380 117 7 πœ”1𝑑1 πœ”1𝑑1 PUNCT cana-380 117 8 βˆ’ βˆ’ PROPN cana-380 117 9 1 1 NUM cana-380 117 10 2 2 NUM cana-380 117 11 πœ”2𝑑1 πœ”2𝑑1 SYM cana-380 117 12 2 2 NUM cana-380 117 13 } } PUNCT cana-380 117 14 βˆ’ βˆ’ PROPN cana-380 117 15 𝛿𝐢𝐷 𝛿𝐢𝐷 NOUN cana-380 117 16 { { PUNCT cana-380 117 17 ( ( PUNCT cana-380 117 18 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 117 19 πœƒ πœƒ NOUN cana-380 117 20 βˆ’ βˆ’ NOUN cana-380 117 21 πœ”2 πœ”2 ADJ cana-380 117 22 πœƒ2 πœƒ2 PROPN cana-380 117 23 ) ) PUNCT cana-380 117 24 ( ( PUNCT cana-380 117 25 βˆ’π‘‘1πœƒ βˆ’π‘‘1πœƒ NUM cana-380 117 26 + + CCONJ cana-380 117 27 1 1 NUM cana-380 117 28 ) ) PUNCT cana-380 117 29 βˆ’ βˆ’ NOUN cana-380 117 30 πœ”1 πœ”1 ADJ cana-380 117 31 πœƒ πœƒ X cana-380 117 32 + + CCONJ cana-380 117 33 πœ”2 πœ”2 ADV cana-380 117 34 πœƒ2 πœƒ2 PRON cana-380 117 35 βˆ’ βˆ’ PROPN cana-380 117 36 πœ”1𝑑1 πœ”1𝑑1 PUNCT cana-380 117 37 βˆ’ βˆ’ PROPN cana-380 117 38 1 1 NUM cana-380 117 39 2 2 NUM cana-380 117 40 πœ”2𝑑1 πœ”2𝑑1 SYM cana-380 117 41 2 2 NUM cana-380 117 42 } } PUNCT cana-380 117 43 + + CCONJ cana-380 117 44 1 1 NUM cana-380 117 45 𝑇 𝑇 NOUN cana-380 117 46 { { PUNCT cana-380 117 47 πΆπ‘†πœ”2 πΆπ‘†πœ”2 PROPN cana-380 117 48 πœ‡2 πœ‡2 NOUN cana-380 117 49 + + CCONJ cana-380 117 50 ( ( PUNCT cana-380 117 51 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 117 52 πœ‡2 πœ‡2 NOUN cana-380 117 53 βˆ’ βˆ’ PROPN cana-380 117 54 πœ”2 πœ”2 PROPN cana-380 117 55 πœ‡3 πœ‡3 NOUN cana-380 117 56 ) ) PUNCT cana-380 117 57 { { PUNCT cana-380 117 58 1 1 NUM cana-380 117 59 βˆ’ βˆ’ PROPN cana-380 117 60 πœ‡(𝑇 πœ‡(𝑇 NOUN cana-380 117 61 βˆ’ βˆ’ PROPN cana-380 117 62 𝑑1 𝑑1 NOUN cana-380 117 63 ) ) PUNCT cana-380 117 64 } } PUNCT cana-380 117 65 βˆ’ βˆ’ PROPN cana-380 117 66 ( ( PUNCT cana-380 117 67 𝑇 𝑇 PROPN cana-380 117 68 βˆ’ βˆ’ PROPN cana-380 117 69 𝑑1 𝑑1 NOUN cana-380 117 70 ) ) PUNCT cana-380 117 71 + + CCONJ cana-380 117 72 ( ( PUNCT cana-380 117 73 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 117 74 πœ‡2 πœ‡2 NOUN cana-380 117 75 βˆ’ βˆ’ PROPN cana-380 117 76 πœ”2 πœ”2 PROPN cana-380 117 77 πœ‡3 πœ‡3 NOUN cana-380 117 78 ) ) PUNCT cana-380 117 79 πœ‡ πœ‡ ADP cana-380 117 80 } } PUNCT cana-380 117 81 ] ] PUNCT cana-380 117 82 ( ( PUNCT cana-380 117 83 12 12 NUM cana-380 117 84 ) ) PUNCT cana-380 117 85 communications communication NOUN cana-380 117 86 on on ADP cana-380 117 87 applied apply VERB cana-380 117 88 nonlinear nonlinear ADJ cana-380 117 89 analysis analysis NOUN cana-380 117 90 issn issn NOUN cana-380 117 91 : : PUNCT cana-380 117 92 1074 1074 NUM cana-380 117 93 - - PUNCT cana-380 117 94 133x 133x NUM cana-380 117 95 vol vol NOUN cana-380 117 96 31 31 NUM cana-380 117 97 no no NOUN cana-380 117 98 . . NOUN cana-380 117 99 1 1 NUM cana-380 117 100 ( ( PUNCT cana-380 117 101 2024 2024 NUM cana-380 117 102 ) ) PUNCT cana-380 117 103 182 182 NUM cana-380 117 104 https://internationalpubls.com https://internationalpubls.com X cana-380 117 105 πœ•(𝑇𝐢 πœ•(𝑇𝐢 NOUN cana-380 117 106 ) ) PUNCT cana-380 117 107 πœ•π‘‘1 πœ•π‘‘1 NOUN cana-380 118 1 = = PUNCT cana-380 118 2 1 1 NUM cana-380 118 3 𝑇 𝑇 PROPN cana-380 118 4 [ [ PUNCT cana-380 118 5 1 1 NUM cana-380 118 6 2 2 NUM cana-380 118 7 1 1 NUM cana-380 118 8 πœƒ4 πœƒ4 NOUN cana-380 118 9 { { PUNCT cana-380 118 10 ( ( PUNCT cana-380 118 11 πœƒ2(𝛽4πœ”2 πœƒ2(𝛽4πœ”2 PROPN cana-380 118 12 + + NOUN cana-380 118 13 2π›½πœ”1 2π›½πœ”1 NUM cana-380 118 14 ) ) PUNCT cana-380 118 15 + + X cana-380 118 16 2πœ”2𝛼 2πœ”2𝛼 NUM cana-380 118 17 ) ) PUNCT cana-380 118 18 βˆ’ βˆ’ PROPN cana-380 119 1 6πœƒπœ”2𝛽 6πœƒπœ”2𝛽 NUM cana-380 119 2 } } PUNCT cana-380 119 3 βˆ’ βˆ’ PROPN cana-380 119 4 ( ( PUNCT cana-380 119 5 βˆ’π‘‘1πœƒ βˆ’π‘‘1πœƒ NUM cana-380 120 1 + + NUM cana-380 120 2 1 1 NUM cana-380 120 3 ) ) PUNCT cana-380 120 4 βˆ’ βˆ’ PROPN cana-380 120 5 ( ( PUNCT cana-380 120 6 πœƒ2(𝛽(2πœ”2𝑑1 πœƒ2(𝛽(2πœ”2𝑑1 PROPN cana-380 120 7 2 2 NUM cana-380 120 8 + + NOUN cana-380 120 9 2πœ”1𝑑1 2πœ”1𝑑1 NUM cana-380 120 10 ) ) PUNCT cana-380 120 11 + + CCONJ cana-380 120 12 𝛼(2πœ”2𝑑1 𝛼(2πœ”2𝑑1 PROPN cana-380 120 13 + + NUM cana-380 120 14 2πœ”1 2πœ”1 NUM cana-380 120 15 ) ) PUNCT cana-380 120 16 ) ) PUNCT cana-380 121 1 + + CCONJ cana-380 121 2 πœƒ(𝛽(βˆ’6πœ”2𝑑1 πœƒ(𝛽(βˆ’6πœ”2𝑑1 ADJ cana-380 121 3 βˆ’ βˆ’ NOUN cana-380 121 4 2πœ”1 2πœ”1 NUM cana-380 121 5 ) ) PUNCT cana-380 121 6 βˆ’ βˆ’ PROPN cana-380 121 7 4πœ”1𝛼 4πœ”1𝛼 NOUN cana-380 121 8 ) ) PUNCT cana-380 122 1 + + NUM cana-380 122 2 6πœ”2𝛽)πœƒ 6πœ”2𝛽)πœƒ NUM cana-380 122 3 + + CCONJ cana-380 122 4 πœƒ2(2πœ”2𝛽𝑑1 πœƒ2(2πœ”2𝛽𝑑1 NOUN cana-380 122 5 + + CCONJ cana-380 122 6 2π›Όπœ”2 2π›Όπœ”2 NUM cana-380 122 7 ) ) PUNCT cana-380 123 1 + + CCONJ cana-380 123 2 πœƒ3(βˆ’2πœ”1𝛽𝑑1 πœƒ3(βˆ’2πœ”1𝛽𝑑1 NUM cana-380 123 3 βˆ’ βˆ’ NUM cana-380 123 4 2πœ”1𝛼 2πœ”1𝛼 NOUN cana-380 123 5 ) ) PUNCT cana-380 123 6 βˆ’ βˆ’ PROPN cana-380 124 1 πœ”2 πœ”2 PROPN cana-380 124 2 πœ‡2 πœ‡2 PROPN cana-380 124 3 βˆ’ βˆ’ PROPN cana-380 124 4 ( ( PUNCT cana-380 124 5 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 124 6 πœ‡2 πœ‡2 NOUN cana-380 124 7 βˆ’ βˆ’ PROPN cana-380 124 8 πœ”2 πœ”2 PROPN cana-380 124 9 πœ‡3 πœ‡3 NOUN cana-380 124 10 ) ) PUNCT cana-380 124 11 ( ( PUNCT cana-380 124 12 1 1 NUM cana-380 124 13 βˆ’ βˆ’ PROPN cana-380 124 14 πœ‡(𝑇 πœ‡(𝑇 NOUN cana-380 124 15 βˆ’ βˆ’ PROPN cana-380 124 16 𝑑1 𝑑1 NOUN cana-380 124 17 ) ) PUNCT cana-380 124 18 ) ) PUNCT cana-380 125 1 + + CCONJ cana-380 125 2 ( ( PUNCT cana-380 125 3 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 125 4 πœ‡2 πœ‡2 NOUN cana-380 125 5 βˆ’ βˆ’ PROPN cana-380 125 6 πœ”2 πœ”2 PROPN cana-380 125 7 πœ‡3 πœ‡3 NOUN cana-380 125 8 ) ) PUNCT cana-380 126 1 πœ‡ πœ‡ ADP cana-380 126 2 + + X cana-380 126 3 𝐢𝐷 𝐢𝐷 X cana-380 126 4 ( ( PUNCT cana-380 126 5 ( ( PUNCT cana-380 126 6 πœ”2(βˆ’π‘‘1πœƒ+1 πœ”2(βˆ’π‘‘1πœƒ+1 PROPN cana-380 126 7 ) ) PUNCT cana-380 126 8 πœƒ πœƒ NOUN cana-380 126 9 βˆ’ βˆ’ PROPN cana-380 126 10 ( ( PUNCT cana-380 126 11 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 126 12 πœƒ πœƒ NUM cana-380 126 13 βˆ’ βˆ’ NOUN cana-380 126 14 πœ”2 πœ”2 PROPN cana-380 126 15 πœƒ2 πœƒ2 PROPN cana-380 126 16 ) ) PUNCT cana-380 126 17 πœƒ πœƒ NOUN cana-380 126 18 ) ) PUNCT cana-380 126 19 βˆ’ βˆ’ NOUN cana-380 126 20 πœ”1 πœ”1 ADJ cana-380 126 21 βˆ’ βˆ’ NOUN cana-380 126 22 πœ”2𝑑1 πœ”2𝑑1 NOUN cana-380 126 23 ) ) PUNCT cana-380 126 24 βˆ’ βˆ’ PROPN cana-380 126 25 𝛿𝐢𝐷 𝛿𝐢𝐷 NOUN cana-380 126 26 ( ( PUNCT cana-380 126 27 ( ( PUNCT cana-380 126 28 πœ”2(βˆ’π‘‘1πœƒ+1 πœ”2(βˆ’π‘‘1πœƒ+1 PROPN cana-380 126 29 ) ) PUNCT cana-380 126 30 πœƒ πœƒ NOUN cana-380 126 31 βˆ’ βˆ’ PROPN cana-380 126 32 ( ( PUNCT cana-380 126 33 πœ”2𝑑1+πœ”1 πœ”2𝑑1+πœ”1 X cana-380 126 34 πœƒ πœƒ NUM cana-380 126 35 βˆ’ βˆ’ NOUN cana-380 126 36 πœ”2 πœ”2 PROPN cana-380 126 37 πœƒ2 πœƒ2 PROPN cana-380 126 38 ) ) PUNCT cana-380 126 39 πœƒ πœƒ NOUN cana-380 126 40 ) ) PUNCT cana-380 126 41 βˆ’ βˆ’ NOUN cana-380 126 42 πœ”1 πœ”1 ADJ cana-380 126 43 βˆ’ βˆ’ NOUN cana-380 126 44 πœ”2𝑑1 πœ”2𝑑1 X cana-380 126 45 ) ) PUNCT cana-380 126 46 ] ] X cana-380 126 47 ( ( PUNCT cana-380 126 48 13 13 NUM cana-380 126 49 ) ) PUNCT cana-380 126 50 we we PRON cana-380 126 51 get get VERB cana-380 126 52 the the DET cana-380 126 53 optimal optimal ADJ cana-380 126 54 value value NOUN cana-380 126 55 of of ADP cana-380 126 56 𝑑1 𝑑1 NOUN cana-380 126 57 and and CCONJ cana-380 126 58 𝑇 𝑇 PROPN cana-380 126 59 by by ADP cana-380 126 60 solving solve VERB cana-380 126 61 the the DET cana-380 126 62 equation equation NOUN cana-380 126 63 ( ( PUNCT cana-380 126 64 12 12 NUM cana-380 126 65 ) ) PUNCT cana-380 126 66 and and CCONJ cana-380 126 67 ( ( PUNCT cana-380 126 68 13 13 NUM cana-380 126 69 ) ) PUNCT cana-380 126 70 by by ADP cana-380 126 71 using use VERB cana-380 126 72 maple18 maple18 NOUN cana-380 126 73 . . PUNCT cana-380 127 1 4 4 X cana-380 127 2 . . X cana-380 127 3 numerical numerical PROPN cana-380 127 4 example example NOUN cana-380 127 5 a a DET cana-380 127 6 hypothetical hypothetical ADJ cana-380 127 7 system system NOUN cana-380 127 8 with with ADP cana-380 127 9 the the DET cana-380 127 10 following follow VERB cana-380 127 11 values value NOUN cana-380 127 12 of of ADP cana-380 127 13 multiple multiple ADJ cana-380 127 14 considerations consideration NOUN cana-380 127 15 have have AUX cana-380 127 16 been be AUX cana-380 127 17 investigated investigate VERB cana-380 127 18 πœ”1 πœ”1 ADJ cana-380 127 19 = = SYM cana-380 127 20 4 4 NUM cana-380 127 21 , , PUNCT cana-380 127 22 πœ”2 πœ”2 NOUN cana-380 127 23 = = NOUN cana-380 127 24 8 8 NUM cana-380 127 25 , , PUNCT cana-380 127 26 𝐢𝑆 𝐢𝑆 PROPN cana-380 127 27 = = SYM cana-380 127 28 10 10 NUM cana-380 127 29 , , PUNCT cana-380 127 30 π‘ž π‘ž X cana-380 127 31 = = PROPN cana-380 127 32 7 7 NUM cana-380 127 33 , , PUNCT cana-380 127 34 𝛾 𝛾 NOUN cana-380 127 35 = = SYM cana-380 127 36 3 3 NUM cana-380 127 37 , , PUNCT cana-380 127 38 𝐢𝐷 𝐢𝐷 PROPN cana-380 127 39 = = SYM cana-380 127 40 3 3 NUM cana-380 127 41 , , PUNCT cana-380 127 42 πœƒ πœƒ NOUN cana-380 127 43 = = SYM cana-380 127 44 0.9 0.9 NUM cana-380 127 45 , , PUNCT cana-380 127 46 𝛿 𝛿 PRON cana-380 127 47 = = SYM cana-380 127 48 110 110 NUM cana-380 127 49 , , PUNCT cana-380 127 50 πœ‡ πœ‡ ADP cana-380 127 51 = = NOUN cana-380 127 52 0.1 0.1 NUM cana-380 127 53 , , PUNCT cana-380 127 54 𝛼 𝛼 NOUN cana-380 127 55 = = SYM cana-380 127 56 10 10 NUM cana-380 127 57 , , PUNCT cana-380 127 58 𝛽 𝛽 NOUN cana-380 127 59 = = SYM cana-380 127 60 25 25 NUM cana-380 127 61 we we PRON cana-380 127 62 utilised utilise VERB cana-380 127 63 maple maple NOUN cana-380 127 64 18 18 NUM cana-380 127 65 to to PART cana-380 127 66 solve solve VERB cana-380 127 67 the the DET cana-380 127 68 problem problem NOUN cana-380 127 69 at at ADP cana-380 127 70 hand hand NOUN cana-380 127 71 the the DET cana-380 127 72 optimum optimum ADJ cana-380 127 73 rarity rarity NOUN cana-380 127 74 value value NOUN cana-380 127 75 , , PUNCT cana-380 127 76 the the DET cana-380 127 77 optimal optimal ADJ cana-380 127 78 duration duration NOUN cana-380 127 79 of of ADP cana-380 127 80 the the DET cana-380 127 81 ordering ordering NOUN cana-380 127 82 cycle cycle NOUN cana-380 127 83 is be AUX cana-380 127 84 𝑇 𝑇 PROPN cana-380 127 85 = = SYM cana-380 127 86 32.48365353 32.48365353 NUM cana-380 127 87 unit unit NOUN cana-380 127 88 time time NOUN cana-380 127 89 and and CCONJ cana-380 127 90 𝑑1 𝑑1 NOUN cana-380 127 91 = = SYM cana-380 127 92 32.48365353per 32.48365353per NUM cana-380 127 93 unit unit NOUN cana-380 127 94 time time NOUN cana-380 127 95 . . PUNCT cana-380 128 1 the the DET cana-380 128 2 total total ADJ cana-380 128 3 inventory inventory NOUN cana-380 128 4 cost cost NOUN cana-380 128 5 is be AUX cana-380 128 6 𝑇𝐢 𝑇𝐢 ADJ cana-380 128 7 = = SYM cana-380 128 8 8994.779218 8994.779218 NOUN cana-380 128 9 . . PUNCT cana-380 129 1 fig fig NOUN cana-380 129 2 . . PUNCT cana-380 130 1 2 2 NUM cana-380 130 2 total total NOUN cana-380 130 3 inventory inventory NOUN cana-380 130 4 cost cost NOUN cana-380 130 5 tc tc NOUN cana-380 130 6 vs. vs. ADP cana-380 130 7 time time NOUN cana-380 130 8 5 5 NUM cana-380 130 9 . . PUNCT cana-380 130 10 sensitive sensitive ADJ cana-380 130 11 analysis analysis NOUN cana-380 130 12 to to PART cana-380 130 13 investigate investigate VERB cana-380 130 14 the the DET cana-380 130 15 impact impact NOUN cana-380 130 16 of of ADP cana-380 130 17 under under ADP cana-380 130 18 and and CCONJ cana-380 130 19 overestimating overestimate VERB cana-380 130 20 demand demand NOUN cana-380 130 21 , , PUNCT cana-380 130 22 deterioration deterioration NOUN cana-380 130 23 , , PUNCT cana-380 130 24 shortage shortage NOUN cana-380 130 25 cost cost NOUN cana-380 130 26 , , PUNCT cana-380 130 27 ordering order VERB cana-380 130 28 cost cost NOUN cana-380 130 29 , , PUNCT cana-380 130 30 and and CCONJ cana-380 130 31 holding hold VERB cana-380 130 32 cost cost NOUN cana-380 130 33 variable variable NOUN cana-380 130 34 on on ADP cana-380 130 35 maximising maximise VERB cana-380 130 36 system system NOUN cana-380 130 37 profit profit NOUN cana-380 130 38 , , PUNCT cana-380 130 39 sensitivity sensitivity NOUN cana-380 130 40 analysis analysis NOUN cana-380 130 41 was be AUX cana-380 130 42 conducted conduct VERB cana-380 130 43 on on ADP cana-380 130 44 the the DET cana-380 130 45 previously previously ADV cana-380 130 46 described describe VERB cana-380 130 47 numerical numerical ADJ cana-380 130 48 example example NOUN cana-380 130 49 . . PUNCT cana-380 131 1 to to PART cana-380 131 2 conduct conduct VERB cana-380 131 3 this this DET cana-380 131 4 analysis analysis NOUN cana-380 131 5 , , PUNCT cana-380 131 6 we we PRON cana-380 131 7 varied vary VERB cana-380 131 8 the the DET cana-380 131 9 value value NOUN cana-380 131 10 of of ADP cana-380 131 11 a a DET cana-380 131 12 single single ADJ cana-380 131 13 parameter parameter NOUN cana-380 131 14 ( ( PUNCT cana-380 131 15 from from ADP cana-380 131 16 -20 -20 NUM cana-380 131 17 % % NOUN cana-380 131 18 to to PART cana-380 131 19 +20 +20 NUM cana-380 131 20 % % NOUN cana-380 131 21 ) ) PUNCT cana-380 131 22 while while SCONJ cana-380 131 23 keeping keep VERB cana-380 131 24 all all DET cana-380 131 25 others other NOUN cana-380 131 26 constant constant ADJ cana-380 131 27 . . PUNCT cana-380 132 1 you you PRON cana-380 132 2 can can AUX cana-380 132 3 see see VERB cana-380 132 4 the the DET cana-380 132 5 outcomes outcome NOUN cana-380 132 6 of of ADP cana-380 132 7 these these DET cana-380 132 8 studies study NOUN cana-380 132 9 in in ADP cana-380 132 10 table table NOUN cana-380 132 11 1 1 NUM cana-380 132 12 . . PUNCT cana-380 132 13 communications communication NOUN cana-380 132 14 on on ADP cana-380 132 15 applied apply VERB cana-380 132 16 nonlinear nonlinear ADJ cana-380 132 17 analysis analysis NOUN cana-380 132 18 issn issn NOUN cana-380 132 19 : : PUNCT cana-380 132 20 1074 1074 NUM cana-380 132 21 - - PUNCT cana-380 132 22 133x 133x NUM cana-380 132 23 vol vol NOUN cana-380 132 24 31 31 NUM cana-380 132 25 no no NOUN cana-380 132 26 . . NOUN cana-380 132 27 1 1 NUM cana-380 132 28 ( ( PUNCT cana-380 132 29 2024 2024 NUM cana-380 132 30 ) ) PUNCT cana-380 132 31 183 183 NUM cana-380 132 32 https://internationalpubls.com https://internationalpubls.com X cana-380 132 33 table table NOUN cana-380 132 34 1 1 NUM cana-380 132 35 sensitive sensitive ADJ cana-380 132 36 analysis analysis NOUN cana-380 132 37 concerning concern VERB cana-380 132 38 different different ADJ cana-380 132 39 parameters parameter NOUN cana-380 132 40 parameter parameter NOUN cana-380 132 41 % % NOUN cana-380 132 42 change change NOUN cana-380 132 43 change change NOUN cana-380 132 44 in in ADP cana-380 132 45 t t PROPN cana-380 132 46 t1 t1 NOUN cana-380 132 47 q q PROPN cana-380 132 48 tc tc PROPN cana-380 132 49 𝑀1 𝑀1 VERB cana-380 132 50 20 20 NUM cana-380 132 51 32.44435934 32.44435934 NUM cana-380 132 52 8.860404894 8.860404894 NUM cana-380 132 53 1195.347733 1195.347733 NUM cana-380 132 54 9604.449743 9604.449743 NOUN cana-380 132 55 10 10 NUM cana-380 132 56 32.46402837 32.46402837 NUM cana-380 132 57 8.911875947 8.911875947 NUM cana-380 132 58 1189.898073 1189.898073 NUM cana-380 132 59 9597.337511 9597.337511 NOUN cana-380 132 60 -10 -10 SYM cana-380 132 61 32.5032319 32.5032319 NUM cana-380 133 1 9.014936609 9.014936609 NUM cana-380 133 2 1179.003918 1179.003918 NUM cana-380 133 3 9582.785599 9582.785599 NUM cana-380 133 4 -20 -20 NUM cana-380 133 5 32.52276059 32.52276059 NUM cana-380 133 6 9.066524693 9.066524693 NUM cana-380 133 7 1173.55884 1173.55884 NUM cana-380 133 8 9575.351379 9575.351379 PROPN cana-380 133 9 𝑀2 𝑀2 NOUN cana-380 133 10 20 20 NUM cana-380 133 11 32.51635628 32.51635628 NUM cana-380 133 12 9.049409871 9.049409871 NUM cana-380 133 13 1410.469628 1410.469628 NUM cana-380 133 14 11493.10771 11493.10771 NUM cana-380 133 15 10 10 NUM cana-380 133 16 32.50150881 32.50150881 NUM cana-380 133 17 9.010295229 9.010295229 NUM cana-380 133 18 1297.459474 1297.459474 NOUN cana-380 133 19 10541.65116 10541.65116 NUM cana-380 133 20 -10 -10 SYM cana-380 133 21 32.46177675 32.46177675 NUM cana-380 133 22 8.906098139 8.906098139 NUM cana-380 133 23 1071.442485 1071.442485 NUM cana-380 133 24 8638.47087 8638.47087 NOUN cana-380 133 25 -20 -20 NUM cana-380 133 26 32.43435353 32.43435353 NUM cana-380 133 27 8.83455679 8.83455679 NUM cana-380 133 28 958.4372594 958.4372594 NUM cana-380 133 29 7686.673133 7686.673133 NUM cana-380 133 30 𝐢𝑆 𝐢𝑆 ADP cana-380 133 31 20 20 NUM cana-380 133 32 -7.18351398 -7.18351398 NOUN cana-380 133 33 8.386866499 8.386866499 NUM cana-380 133 34 -1703.510229 -1703.510229 NOUN cana-380 133 35 5936.38726 5936.38726 NUM cana-380 133 36 10 10 NUM cana-380 133 37 32.67056652 32.67056652 NUM cana-380 133 38 9.125484922 9.125484922 NUM cana-380 133 39 1217.91362 1217.91362 NUM cana-380 133 40 9911.266027 9911.266027 NUM cana-380 133 41 -10 -10 NUM cana-380 133 42 32.28341066 32.28341066 NUM cana-380 133 43 8.799451309 8.799451309 NUM cana-380 133 44 1150.266525 1150.266525 NOUN cana-380 133 45 9271.826164 9271.826164 NOUN cana-380 133 46 -20 -20 NUM cana-380 133 47 32.06914071 32.06914071 NUM cana-380 133 48 8.633266262 8.633266262 NUM cana-380 133 49 1115.325694 1115.325694 NUM cana-380 133 50 8956.639099 8956.639099 NUM cana-380 133 51 q q NOUN cana-380 133 52 20 20 NUM cana-380 133 53 32.48338612 32.48338612 NUM cana-380 133 54 8.963161565 8.963161565 NUM cana-380 133 55 1184.403494 1184.403494 NUM cana-380 133 56 9590.778939 9590.778939 NUM cana-380 133 57 10 10 NUM cana-380 133 58 32.48352591 32.48352591 NUM cana-380 133 59 8.963279287 8.963279287 NUM cana-380 133 60 1184.427926 1184.427926 NUM cana-380 133 61 9590.431993 9590.431993 NUM cana-380 133 62 -10 -10 SYM cana-380 133 63 32.48376899 32.48376899 NUM cana-380 133 64 8.96348402 8.96348402 NUM cana-380 133 65 1184.470414 1184.470414 NUM cana-380 133 66 9589.828614 9589.828614 NUM cana-380 133 67 -20 -20 NUM cana-380 133 68 32.4838723 32.4838723 NUM cana-380 133 69 8.963571031 8.963571031 NUM cana-380 133 70 1184.488472 1184.488472 NUM cana-380 133 71 9589.572181 9589.572181 NUM cana-380 133 72 𝐢𝐷 𝐢𝐷 VERB cana-380 133 73 20 20 NUM cana-380 133 74 35.81636369 35.81636369 NUM cana-380 133 75 8.602033267 8.602033267 NUM cana-380 133 76 1384.613584 1384.613584 NUM cana-380 133 77 11191.63675 11191.63675 NOUN cana-380 133 78 10 10 NUM cana-380 133 79 34.25891999 34.25891999 NUM cana-380 133 80 8.759876309 8.759876309 NUM cana-380 133 81 1292.017818 1292.017818 NUM cana-380 133 82 10427.49246 10427.49246 NUM cana-380 133 83 -10 -10 PUNCT cana-380 133 84 30.33682651 30.33682651 NUM cana-380 134 1 9.247697539 9.247697539 NUM cana-380 135 1 1050.485579 1050.485579 NUM cana-380 135 2 8649.492292 8649.492292 NUM cana-380 135 3 -20 -20 NUM cana-380 135 4 27.29715106 27.29715106 NUM cana-380 136 1 9.729613477 9.729613477 NUM cana-380 136 2 850.1471854 850.1471854 NUM cana-380 136 3 7425.210406 7425.210406 NUM cana-380 136 4 πœ‡ πœ‡ ADP cana-380 136 5 20 20 NUM cana-380 136 6 -13.00795588 -13.00795588 SYM cana-380 136 7 5.889472258 5.889472258 NUM cana-380 136 8 -1345.473025 -1345.473025 NOUN cana-380 136 9 -422.23059 -422.23059 PROPN cana-380 136 10 10 10 NUM cana-380 136 11 32.24998362 32.24998362 NUM cana-380 136 12 7.911044345 7.911044345 NUM cana-380 136 13 1159.991768 1159.991768 NUM cana-380 136 14 8568.936419 8568.936419 NUM cana-380 136 15 -10 -10 PUNCT cana-380 136 16 32.42011627 32.42011627 NUM cana-380 136 17 10.36323689 10.36323689 NUM cana-380 136 18 1159.381322 1159.381322 NUM cana-380 136 19 10603.69929 10603.69929 NUM cana-380 136 20 -20 -20 NUM cana-380 136 21 22.38175361 22.38175361 NUM cana-380 136 22 14.217159 14.217159 NUM cana-380 136 23 44.4843059 44.4843059 NUM cana-380 136 24 11651.00788 11651.00788 NUM cana-380 136 25 𝛿 𝛿 ADJ cana-380 136 26 20 20 NUM cana-380 136 27 35.84340917 35.84340917 NUM cana-380 136 28 8.599448461 8.599448461 NUM cana-380 136 29 1386.209366 1386.209366 NUM cana-380 136 30 11205.09329 11205.09329 NUM cana-380 136 31 10 10 NUM cana-380 136 32 34.27405401 34.27405401 NUM cana-380 136 33 8.75825374 8.75825374 NUM cana-380 136 34 1292.9248 1292.9248 NUM cana-380 136 35 10434.8029 10434.8029 NUM cana-380 136 36 -10 -10 PUNCT cana-380 136 37 30.31444565 30.31444565 NUM cana-380 136 38 9.250899012 9.250899012 NUM cana-380 136 39 1049.061371 1049.061371 NUM cana-380 136 40 8640.231256 8640.231256 NUM cana-380 136 41 -20 -20 NUM cana-380 136 42 16.27301748 16.27301748 NUM cana-380 136 43 11.63030261 11.63030261 NUM cana-380 136 44 -74.9144711 -74.9144711 SYM cana-380 136 45 8121.780064 8121.780064 NOUN cana-380 136 46 πœƒ πœƒ NUM cana-380 136 47 20 20 NUM cana-380 136 48 33.90269066 33.90269066 NUM cana-380 136 49 8.855904645 8.855904645 NUM cana-380 136 50 1251.776572 1251.776572 NUM cana-380 136 51 10065.92668 10065.92668 NUM cana-380 136 52 10 10 NUM cana-380 136 53 -10.22258989 -10.22258989 SYM cana-380 136 54 7.315248156 7.315248156 NUM cana-380 136 55 -1691.350087 -1691.350087 NUM cana-380 136 56 121.66668 121.66668 NUM cana-380 136 57 -10 -10 SYM cana-380 136 58 31.56554 31.56554 NUM cana-380 136 59 9.035790259 9.035790259 NUM cana-380 136 60 1140.777255 1140.777255 NUM cana-380 136 61 9301.996899 9301.996899 NOUN cana-380 136 62 -20 -20 NUM cana-380 136 63 30.45273246 30.45273246 NUM cana-380 136 64 9.127406793 9.127406793 NUM cana-380 136 65 1087.892922 1087.892922 NUM cana-380 136 66 8973.232869 8973.232869 NUM cana-380 136 67 𝛾 𝛾 PROPN cana-380 136 68 20 20 NUM cana-380 136 69 32.48230768 32.48230768 NUM cana-380 136 70 8.962253483 8.962253483 NUM cana-380 136 71 1184.215025 1184.215025 NUM cana-380 136 72 9593.455147 9593.455147 NUM cana-380 136 73 10 10 NUM cana-380 136 74 32.4831717 32.4831717 NUM cana-380 136 75 8.962980991 8.962980991 NUM cana-380 136 76 1184.366017 1184.366017 NUM cana-380 136 77 9591.311112 9591.311112 NUM cana-380 136 78 communications communication NOUN cana-380 136 79 on on ADP cana-380 136 80 applied apply VERB cana-380 136 81 nonlinear nonlinear ADJ cana-380 136 82 analysis analysis NOUN cana-380 136 83 issn issn NOUN cana-380 136 84 : : PUNCT cana-380 136 85 1074 1074 NUM cana-380 136 86 - - PUNCT cana-380 136 87 133x 133x NUM cana-380 136 88 vol vol NOUN cana-380 136 89 31 31 NUM cana-380 136 90 no no NOUN cana-380 136 91 . . NOUN cana-380 136 92 1 1 NUM cana-380 136 93 ( ( PUNCT cana-380 136 94 2024 2024 NUM cana-380 136 95 ) ) PUNCT cana-380 136 96 184 184 NUM cana-380 136 97 https://internationalpubls.com https://internationalpubls.com X cana-380 136 98 -10 -10 PUNCT cana-380 136 99 32.48392225 32.48392225 NUM cana-380 136 100 8.963613108 8.963613108 NUM cana-380 136 101 1184.497204 1184.497204 NUM cana-380 136 102 9589.44817 9589.44817 NUM cana-380 136 103 -20 -20 NUM cana-380 136 104 32.48407213 32.48407213 NUM cana-380 137 1 8.963739355 8.963739355 NUM cana-380 137 2 1184.523404 1184.523404 NUM cana-380 138 1 9589.076098 9589.076098 NUM cana-380 138 2 𝛼 𝛼 PROPN cana-380 138 3 20 20 NUM cana-380 138 4 32.40692585 32.40692585 NUM cana-380 138 5 8.970135186 8.970135186 NUM cana-380 138 6 1179.431191 1179.431191 NOUN cana-380 139 1 9563.041069 9563.041069 NUM cana-380 139 2 10 10 NUM cana-380 139 3 32.44535279 32.44535279 NUM cana-380 139 4 8.966750509 8.966750509 NUM cana-380 139 5 1181.945297 1181.945297 NUM cana-380 139 6 9576.592845 9576.592845 NUM cana-380 139 7 -10 -10 PUNCT cana-380 139 8 32.52182941 32.52182941 NUM cana-380 139 9 8.96004373 8.96004373 NUM cana-380 139 10 1186.946098 1186.946098 NUM cana-380 140 1 9603.608408 9603.608408 NUM cana-380 140 2 -20 -20 NUM cana-380 140 3 32.55988174 32.55988174 NUM cana-380 140 4 8.956721143 8.956721143 NUM cana-380 140 5 1189.432992 1189.432992 NUM cana-380 140 6 9617.072611 9617.072611 NOUN cana-380 140 7 𝛽 𝛽 NOUN cana-380 140 8 20 20 NUM cana-380 140 9 29.83616174 29.83616174 NUM cana-380 140 10 9.121449156 9.121449156 NUM cana-380 140 11 999.2641367 999.2641367 NUM cana-380 140 12 8951.810835 8951.810835 NUM cana-380 140 13 10 10 NUM cana-380 140 14 31.24618305 31.24618305 NUM cana-380 141 1 9.034264799 9.034264799 NUM cana-380 141 2 1098.401849 1098.401849 NUM cana-380 141 3 9282.591388 9282.591388 SYM cana-380 141 4 -10 -10 SYM cana-380 141 5 33.59965309 33.59965309 NUM cana-380 141 6 8.903679015 8.903679015 NUM cana-380 141 7 1261.381806 1261.381806 NUM cana-380 141 8 9879.219623 9879.219623 NUM cana-380 141 9 -20 -20 NUM cana-380 141 10 -11.17740669 -11.17740669 PUNCT cana-380 141 11 7.293205014 7.293205014 NUM cana-380 141 12 -1734.118399 -1734.118399 NUM cana-380 141 13 -287.172516 -287.172516 NUM cana-380 141 14 β€’ β€’ NOUN cana-380 141 15 with with ADP cana-380 141 16 an an DET cana-380 141 17 increase increase NOUN cana-380 141 18 or or CCONJ cana-380 141 19 decrease decrease NOUN cana-380 141 20 in in ADP cana-380 141 21 πœ”1π‘Žπ‘›π‘‘ πœ”1π‘Žπ‘›π‘‘ VERB cana-380 141 22 πœ”2 πœ”2 PROPN cana-380 141 23 , , PUNCT cana-380 141 24 𝑇𝐢 𝑇𝐢 ADJ cana-380 141 25 increases increase NOUN cana-380 141 26 or or CCONJ cana-380 141 27 decreases decrease NOUN cana-380 141 28 , , PUNCT cana-380 141 29 respectively respectively ADV cana-380 141 30 , , PUNCT cana-380 141 31 and and CCONJ cana-380 141 32 𝑄 𝑄 PRON cana-380 141 33 varies vary VERB cana-380 141 34 . . PUNCT cana-380 142 1 β€’ β€’ NUM cana-380 142 2 in in ADP cana-380 142 3 𝐢𝑆 𝐢𝑆 PROPN cana-380 142 4 ( ( PUNCT cana-380 142 5 shortage shortage NOUN cana-380 142 6 cost cost NOUN cana-380 142 7 ) ) PUNCT cana-380 142 8 and and CCONJ cana-380 142 9 πœ‡ πœ‡ ADP cana-380 142 10 are be AUX cana-380 142 11 small small ADJ cana-380 142 12 increases increase NOUN cana-380 142 13 then then ADV cana-380 142 14 𝑇𝐢 𝑇𝐢 ADJ cana-380 142 15 increase increase NOUN cana-380 142 16 but but CCONJ cana-380 142 17 after after ADP cana-380 142 18 more more ADJ cana-380 142 19 increase increase NOUN cana-380 142 20 it it PRON cana-380 142 21 will will AUX cana-380 142 22 be be AUX cana-380 142 23 decreases decrease NOUN cana-380 142 24 and and CCONJ cana-380 142 25 if if SCONJ cana-380 142 26 𝐢𝑆 𝐢𝑆 PROPN cana-380 142 27 decreases decrease VERB cana-380 142 28 then then ADV cana-380 142 29 𝑇𝐢 𝑇𝐢 ADJ cana-380 142 30 decreases decrease VERB cana-380 142 31 . . PUNCT cana-380 143 1 β€’ β€’ INTJ cana-380 143 2 if if SCONJ cana-380 143 3 π‘ž π‘ž X cana-380 143 4 ( ( PUNCT cana-380 143 5 ordering order VERB cana-380 143 6 variable variable NOUN cana-380 143 7 ) ) PUNCT cana-380 143 8 increases increase NOUN cana-380 143 9 or or CCONJ cana-380 143 10 decreases decrease NOUN cana-380 143 11 , , PUNCT cana-380 143 12 𝑇𝐢 𝑇𝐢 ADJ cana-380 143 13 not not PART cana-380 143 14 much much ADV cana-380 143 15 very very ADV cana-380 143 16 . . PUNCT cana-380 144 1 β€’ β€’ NOUN cana-380 144 2 if if SCONJ cana-380 144 3 holding hold VERB cana-380 144 4 parameters parameter NOUN cana-380 144 5 𝛼 𝛼 VERB cana-380 144 6 and and CCONJ cana-380 144 7 𝛽 𝛽 NOUN cana-380 144 8 are be AUX cana-380 144 9 increase increase VERB cana-380 144 10 𝑇𝐢 𝑇𝐢 ADJ cana-380 144 11 decreases decrease NOUN cana-380 144 12 and and CCONJ cana-380 144 13 if if SCONJ cana-380 144 14 holding hold VERB cana-380 144 15 parameter parameter NOUN cana-380 144 16 decreases decrease VERB cana-380 144 17 then then ADV cana-380 144 18 𝑇𝐢 𝑇𝐢 ADJ cana-380 144 19 increases increase NOUN cana-380 144 20 but but CCONJ cana-380 144 21 𝛽 𝛽 NOUN cana-380 144 22 is be AUX cana-380 144 23 sensitive sensitive ADJ cana-380 144 24 and and CCONJ cana-380 144 25 𝑄 𝑄 PRON cana-380 144 26 changes change NOUN cana-380 144 27 . . PUNCT cana-380 145 1 β€’ β€’ ADV cana-380 145 2 if if SCONJ cana-380 145 3 Ξ³ Ξ³ NOUN cana-380 145 4 increases increase NOUN cana-380 145 5 , , PUNCT cana-380 145 6 𝑇𝐢 𝑇𝐢 ADJ cana-380 145 7 increases increase NOUN cana-380 145 8 , , PUNCT cana-380 145 9 but but CCONJ cana-380 145 10 when when SCONJ cana-380 145 11 Ξ³ Ξ³ PROPN cana-380 145 12 decreases decrease VERB cana-380 145 13 then then ADV cana-380 145 14 𝑇𝐢 𝑇𝐢 VERB cana-380 145 15 not not PART cana-380 145 16 changed change VERB cana-380 145 17 and and CCONJ cana-380 145 18 q q ADJ cana-380 145 19 not not PART cana-380 145 20 very very ADV cana-380 145 21 . . PUNCT cana-380 146 1 β€’ β€’ NUM cana-380 146 2 in in ADP cana-380 146 3 the the DET cana-380 146 4 small small ADJ cana-380 146 5 increment increment NOUN cana-380 146 6 of of ADP cana-380 146 7 πœƒ πœƒ NOUN cana-380 146 8 , , PUNCT cana-380 146 9 𝑇𝐢 𝑇𝐢 ADJ cana-380 146 10 and and CCONJ cana-380 146 11 𝑄 𝑄 PRON cana-380 146 12 decreases decrease VERB cana-380 146 13 ( ( PUNCT cana-380 146 14 10 10 NUM cana-380 146 15 % % NOUN cana-380 146 16 ) ) PUNCT cana-380 146 17 and and CCONJ cana-380 146 18 after after ADP cana-380 146 19 that that PRON cana-380 146 20 with with ADP cana-380 146 21 πœƒ. πœƒ. NOUN cana-380 146 22 tc tc PROPN cana-380 146 23 and and CCONJ cana-380 146 24 q q NOUN cana-380 146 25 increases increase NOUN cana-380 146 26 and and CCONJ cana-380 146 27 if if SCONJ cana-380 146 28 πœƒ πœƒ PRON cana-380 146 29 is be AUX cana-380 146 30 decreases decrease NOUN cana-380 146 31 both both PRON cana-380 146 32 are be AUX cana-380 146 33 increases increase NOUN cana-380 146 34 β€’ β€’ ADP cana-380 146 35 𝑇𝐢 𝑇𝐢 ADJ cana-380 146 36 is be AUX cana-380 146 37 increase increase NOUN cana-380 146 38 and and CCONJ cana-380 146 39 decreases decrease NOUN cana-380 146 40 when when SCONJ cana-380 146 41 𝛿 𝛿 ADJ cana-380 146 42 and and CCONJ cana-380 146 43 𝐢𝑑 𝐢𝑑 PROPN cana-380 146 44 increases increase NOUN cana-380 146 45 and and CCONJ cana-380 146 46 decrease decrease VERB cana-380 146 47 respectively respectively ADV cana-380 146 48 . . PUNCT cana-380 147 1 6 6 NUM cana-380 147 2 . . X cana-380 147 3 conclusions conclusion NOUN cana-380 147 4 in in ADP cana-380 147 5 this this DET cana-380 147 6 study study NOUN cana-380 147 7 , , PUNCT cana-380 147 8 it it PRON cana-380 147 9 is be AUX cana-380 147 10 hypothesized hypothesize VERB cana-380 147 11 that that SCONJ cana-380 147 12 the the DET cana-380 147 13 demand demand NOUN cana-380 147 14 rate rate NOUN cana-380 147 15 would would AUX cana-380 147 16 be be AUX cana-380 147 17 time time NOUN cana-380 147 18 sensitive sensitive ADJ cana-380 147 19 and and CCONJ cana-380 147 20 that that SCONJ cana-380 147 21 the the DET cana-380 147 22 rate rate NOUN cana-380 147 23 of of ADP cana-380 147 24 degradation degradation NOUN cana-380 147 25 will will AUX cana-380 147 26 be be AUX cana-380 147 27 proportional proportional ADJ cana-380 147 28 to to ADP cana-380 147 29 time time NOUN cana-380 147 30 ; ; PUNCT cana-380 147 31 hence hence ADV cana-380 147 32 , , PUNCT cana-380 147 33 an an DET cana-380 147 34 inventory inventory NOUN cana-380 147 35 representation representation NOUN cana-380 147 36 of of ADP cana-380 147 37 things thing NOUN cana-380 147 38 experiencing experience VERB cana-380 147 39 depreciation depreciation NOUN cana-380 147 40 is be AUX cana-380 147 41 established establish VERB cana-380 147 42 . . PUNCT cana-380 148 1 the the DET cana-380 148 2 issue issue NOUN cana-380 148 3 is be AUX cana-380 148 4 remedied remedied ADJ cana-380 148 5 when when SCONJ cana-380 148 6 shortages shortage NOUN cana-380 148 7 are be AUX cana-380 148 8 tolerable tolerable ADJ cana-380 148 9 and and CCONJ cana-380 148 10 partial partial ADJ cana-380 148 11 backorders backorder NOUN cana-380 148 12 are be AUX cana-380 148 13 placed place VERB cana-380 148 14 . . PUNCT cana-380 149 1 the the DET cana-380 149 2 costs cost NOUN cana-380 149 3 of of ADP cana-380 149 4 keeping keep VERB cana-380 149 5 and and CCONJ cana-380 149 6 ordering ordering NOUN cana-380 149 7 vary vary NOUN cana-380 149 8 . . PUNCT cana-380 150 1 the the DET cana-380 150 2 salvage salvage NOUN cana-380 150 3 value value NOUN cana-380 150 4 is be AUX cana-380 150 5 assigned assign VERB cana-380 150 6 to to ADP cana-380 150 7 items item NOUN cana-380 150 8 in in ADP cana-380 150 9 the the DET cana-380 150 10 system system NOUN cana-380 150 11 that that PRON cana-380 150 12 have have AUX cana-380 150 13 degraded degrade VERB cana-380 150 14 . . PUNCT cana-380 151 1 the the DET cana-380 151 2 sensitivity sensitivity NOUN cana-380 151 3 of of ADP cana-380 151 4 the the DET cana-380 151 5 models model NOUN cana-380 151 6 is be AUX cana-380 151 7 discussed discuss VERB cana-380 151 8 using use VERB cana-380 151 9 a a DET cana-380 151 10 numerical numerical ADJ cana-380 151 11 example example NOUN cana-380 151 12 . . PUNCT cana-380 152 1 7 7 X cana-380 152 2 . . X cana-380 152 3 application application NOUN cana-380 152 4 the the DET cana-380 152 5 suggested suggest VERB cana-380 152 6 deterministic deterministic ADJ cana-380 152 7 inventory inventory NOUN cana-380 152 8 model model NOUN cana-380 152 9 takes take VERB cana-380 152 10 into into ADP cana-380 152 11 consideration consideration NOUN cana-380 152 12 dynamic dynamic ADJ cana-380 152 13 demand demand NOUN cana-380 152 14 and and CCONJ cana-380 152 15 stock stock NOUN cana-380 152 16 , , PUNCT cana-380 152 17 partial partial ADJ cana-380 152 18 supply supply NOUN cana-380 152 19 backlogs backlog NOUN cana-380 152 20 , , PUNCT cana-380 152 21 and and CCONJ cana-380 152 22 the the DET cana-380 152 23 expiration expiration NOUN cana-380 152 24 of of ADP cana-380 152 25 perishable perishable ADJ cana-380 152 26 commodities commodity NOUN cana-380 152 27 . . PUNCT cana-380 153 1 this this DET cana-380 153 2 strategy strategy NOUN cana-380 153 3 can can AUX cana-380 153 4 be be AUX cana-380 153 5 used use VERB cana-380 153 6 to to PART cana-380 153 7 reduce reduce VERB cana-380 153 8 overall overall ADJ cana-380 153 9 inventory inventory NOUN cana-380 153 10 costs cost NOUN cana-380 153 11 for for ADP cana-380 153 12 companies company NOUN cana-380 153 13 in in ADP cana-380 153 14 the the DET cana-380 153 15 chemical chemical NOUN cana-380 153 16 industry industry NOUN cana-380 153 17 , , PUNCT cana-380 153 18 where where SCONJ cana-380 153 19 supply supply NOUN cana-380 153 20 and and CCONJ cana-380 153 21 demand demand NOUN cana-380 153 22 are be AUX cana-380 153 23 tightly tightly ADV cana-380 153 24 tied tie VERB cana-380 153 25 and and CCONJ cana-380 153 26 some some DET cana-380 153 27 shortages shortage NOUN cana-380 153 28 have have AUX cana-380 153 29 been be AUX cana-380 153 30 postponed postpone VERB cana-380 153 31 . . PUNCT cana-380 154 1 the the DET cana-380 154 2 model model NOUN cana-380 154 3 employed employ VERB cana-380 154 4 in in ADP cana-380 154 5 this this DET cana-380 154 6 study study NOUN cana-380 154 7 includes include VERB cana-380 154 8 a a DET cana-380 154 9 general general ADJ cana-380 154 10 architecture architecture NOUN cana-380 154 11 that that PRON cana-380 154 12 allows allow VERB cana-380 154 13 variable variable ADJ cana-380 154 14 setup setup NOUN cana-380 154 15 costs cost NOUN cana-380 154 16 to to PART cana-380 154 17 be be AUX cana-380 154 18 accounted account VERB cana-380 154 19 for for ADP cana-380 154 20 while while SCONJ cana-380 154 21 keeping keep VERB cana-380 154 22 stock stock NOUN cana-380 154 23 levels level NOUN cana-380 154 24 constant constant ADJ cana-380 154 25 . . PUNCT cana-380 155 1 the the DET cana-380 155 2 cost cost NOUN cana-380 155 3 function function NOUN cana-380 155 4 's 's PART cana-380 155 5 convexity convexity NOUN cana-380 155 6 condition condition NOUN cana-380 155 7 ensures ensure VERB cana-380 155 8 the the DET cana-380 155 9 existence existence NOUN cana-380 155 10 of of ADP cana-380 155 11 a a DET cana-380 155 12 unique unique ADJ cana-380 155 13 minimum minimum NOUN cana-380 155 14 . . PUNCT cana-380 156 1 inventory inventory NOUN cana-380 156 2 management management NOUN cana-380 156 3 is be AUX cana-380 156 4 useful useful ADJ cana-380 156 5 for for ADP cana-380 156 6 non non ADJ cana-380 156 7 - - ADJ cana-380 156 8 perishable perishable ADJ cana-380 156 9 commodities commodity NOUN cana-380 156 10 such such ADJ cana-380 156 11 as as ADP cana-380 156 12 food food NOUN cana-380 156 13 , , PUNCT cana-380 156 14 gadgets gadget NOUN cana-380 156 15 , , PUNCT cana-380 156 16 and and CCONJ cana-380 156 17 apparel apparel NOUN cana-380 156 18 accessories accessory NOUN cana-380 156 19 . . PUNCT cana-380 157 1 the the DET cana-380 157 2 demand demand NOUN cana-380 157 3 function function NOUN cana-380 157 4 can can AUX cana-380 157 5 be be AUX cana-380 157 6 extended extend VERB cana-380 157 7 to to PART cana-380 157 8 include include VERB cana-380 157 9 stochastically stochastically ADV cana-380 157 10 shifting shift VERB cana-380 157 11 demand demand NOUN cana-380 157 12 patterns pattern NOUN cana-380 157 13 or or CCONJ cana-380 157 14 stock stock NOUN cana-380 157 15 - - PUNCT cana-380 157 16 dependent dependent ADJ cana-380 157 17 demand demand NOUN cana-380 157 18 rates rate NOUN cana-380 157 19 . . PUNCT cana-380 158 1 communications communication NOUN cana-380 158 2 on on ADP cana-380 158 3 applied apply VERB cana-380 158 4 nonlinear nonlinear ADJ cana-380 158 5 analysis analysis NOUN cana-380 158 6 issn issn NOUN cana-380 158 7 : : PUNCT cana-380 158 8 1074 1074 NUM cana-380 158 9 - - PUNCT cana-380 158 10 133x 133x NUM cana-380 158 11 vol vol NOUN cana-380 158 12 31 31 NUM cana-380 158 13 no no NOUN cana-380 158 14 . . NOUN cana-380 158 15 1 1 NUM cana-380 158 16 ( ( PUNCT cana-380 158 17 2024 2024 NUM cana-380 158 18 ) ) PUNCT cana-380 158 19 185 185 NUM cana-380 158 20 https://internationalpubls.com https://internationalpubls.com X cana-380 158 21 8 8 NUM cana-380 158 22 . . PUNCT cana-380 159 1 future future ADJ cana-380 159 2 scope scope NOUN cana-380 159 3 the the DET cana-380 159 4 proposed propose VERB cana-380 159 5 model model NOUN cana-380 159 6 can can AUX cana-380 159 7 be be AUX cana-380 159 8 developed develop VERB cana-380 159 9 to to PART cana-380 159 10 accommodate accommodate VERB cana-380 159 11 more more ADJ cana-380 159 12 types type NOUN cana-380 159 13 of of ADP cana-380 159 14 demand demand NOUN cana-380 159 15 , , PUNCT cana-380 159 16 such such ADJ cana-380 159 17 as as ADP cana-380 159 18 uncertain uncertain ADJ cana-380 159 19 demand demand NOUN cana-380 159 20 , , PUNCT cana-380 159 21 stock stock NOUN cana-380 159 22 - - PUNCT cana-380 159 23 dependent dependent ADJ cana-380 159 24 demand demand NOUN cana-380 159 25 , , PUNCT cana-380 159 26 probabilistic probabilistic ADJ cana-380 159 27 demand demand NOUN cana-380 159 28 , , PUNCT cana-380 159 29 and and CCONJ cana-380 159 30 many many ADJ cana-380 159 31 others other NOUN cana-380 159 32 . . PUNCT cana-380 160 1 furthermore furthermore ADV cana-380 160 2 , , PUNCT cana-380 160 3 in in ADP cana-380 160 4 order order NOUN cana-380 160 5 to to PART cana-380 160 6 facilitate facilitate VERB cana-380 160 7 additional additional ADJ cana-380 160 8 study study NOUN cana-380 160 9 , , PUNCT cana-380 160 10 the the DET cana-380 160 11 model model NOUN cana-380 160 12 can can AUX cana-380 160 13 be be AUX cana-380 160 14 developed develop VERB cana-380 160 15 to to PART cana-380 160 16 include include VERB cana-380 160 17 more more ADV cana-380 160 18 realistic realistic ADJ cana-380 160 19 components component NOUN cana-380 160 20 such such ADJ cana-380 160 21 as as ADP cana-380 160 22 quantity quantity NOUN cana-380 160 23 count count NOUN cana-380 160 24 , , PUNCT cana-380 160 25 two two NUM cana-380 160 26 - - PUNCT cana-380 160 27 level level NOUN cana-380 160 28 trade trade NOUN cana-380 160 29 credit credit NOUN cana-380 160 30 policy policy NOUN cana-380 160 31 , , PUNCT cana-380 160 32 multi multi NOUN cana-380 160 33 - - NOUN cana-380 160 34 item item NOUN cana-380 160 35 with with ADP cana-380 160 36 constraint constraint NOUN cana-380 160 37 , , PUNCT cana-380 160 38 and and CCONJ cana-380 160 39 so so ADV cana-380 160 40 on on ADV cana-380 160 41 . . PUNCT cana-380 161 1 this this PRON cana-380 161 2 can can AUX cana-380 161 3 be be AUX cana-380 161 4 done do VERB cana-380 161 5 in in ADP cana-380 161 6 order order NOUN cana-380 161 7 to to PART cana-380 161 8 improve improve VERB cana-380 161 9 the the DET cana-380 161 10 model model NOUN cana-380 161 11 's 's PART cana-380 161 12 accuracy accuracy NOUN cana-380 161 13 . . PUNCT cana-380 162 1 furthermore furthermore ADV cana-380 162 2 , , PUNCT cana-380 162 3 the the DET cana-380 162 4 current current ADJ cana-380 162 5 scope scope NOUN cana-380 162 6 of of ADP cana-380 162 7 this this DET cana-380 162 8 approach approach NOUN cana-380 162 9 can can AUX cana-380 162 10 be be AUX cana-380 162 11 expanded expand VERB cana-380 162 12 to to PART cana-380 162 13 include include VERB cana-380 162 14 less less ADV cana-380 162 15 precise precise ADJ cana-380 162 16 settings setting NOUN cana-380 162 17 such such ADJ cana-380 162 18 as as ADP cana-380 162 19 fuzzy fuzzy ADJ cana-380 162 20 , , PUNCT cana-380 162 21 rough rough ADJ cana-380 162 22 , , PUNCT cana-380 162 23 random random ADJ cana-380 162 24 , , PUNCT cana-380 162 25 fuzzy fuzzy ADJ cana-380 162 26 - - PUNCT cana-380 162 27 random random ADJ cana-380 162 28 , , PUNCT cana-380 162 29 bifuzzy bifuzzy NOUN cana-380 162 30 , , PUNCT cana-380 162 31 type2 type2 PROPN cana-380 162 32 fuzzy fuzzy ADJ cana-380 162 33 , , PUNCT cana-380 162 34 and and CCONJ cana-380 162 35 so so ADV cana-380 162 36 on on ADV cana-380 162 37 . . PUNCT cana-380 163 1 references reference NOUN cana-380 163 2 [ [ X cana-380 163 3 1 1 NUM cana-380 163 4 ] ] X cana-380 163 5 ghare ghare PROPN cana-380 163 6 , , PUNCT cana-380 163 7 p.m. p.m. NOUN cana-380 163 8 , , PUNCT cana-380 163 9 and and CCONJ cana-380 163 10 schrader schrader PROPN cana-380 163 11 , , PUNCT cana-380 163 12 g.h g.h PROPN cana-380 163 13 . . PROPN cana-380 163 14 : : PUNCT cana-380 163 15 a a DET cana-380 163 16 model model NOUN cana-380 163 17 for for ADP cana-380 163 18 exponentially exponentially ADV cana-380 163 19 decaying decay VERB cana-380 163 20 inventory inventory NOUN cana-380 163 21 system system NOUN cana-380 163 22 . . PUNCT cana-380 164 1 international international ADJ cana-380 164 2 journal journal PROPN cana-380 164 3 of of ADP cana-380 164 4 production production NOUN cana-380 164 5 research research NOUN cana-380 164 6 , , PUNCT cana-380 164 7 21 21 NUM cana-380 164 8 , , PUNCT cana-380 164 9 449 449 NUM cana-380 164 10 - - SYM cana-380 164 11 460 460 NUM cana-380 164 12 ( ( PUNCT cana-380 164 13 1963 1963 NUM cana-380 164 14 ) ) PUNCT cana-380 165 1 [ [ X cana-380 165 2 2 2 NUM cana-380 165 3 ] ] PUNCT cana-380 165 4 aggarwal aggarwal NOUN cana-380 165 5 , , PUNCT cana-380 165 6 s.p s.p PROPN cana-380 165 7 . . PROPN cana-380 165 8 : : PUNCT cana-380 165 9 a a DET cana-380 165 10 note note NOUN cana-380 165 11 on on ADP cana-380 165 12 an an DET cana-380 165 13 order order NOUN cana-380 165 14 - - PUNCT cana-380 165 15 level level NOUN cana-380 165 16 model model NOUN cana-380 165 17 for for ADP cana-380 165 18 a a DET cana-380 165 19 system system NOUN cana-380 165 20 with with ADP cana-380 165 21 constant constant ADJ cana-380 165 22 rate rate NOUN cana-380 165 23 of of ADP cana-380 165 24 deterioration deterioration NOUN cana-380 165 25 . . PUNCT cana-380 166 1 opsearch opsearch PROPN cana-380 166 2 , , PUNCT cana-380 166 3 15 15 NUM cana-380 166 4 , , PUNCT cana-380 166 5 184 184 NUM cana-380 166 6 - - SYM cana-380 166 7 187 187 NUM cana-380 166 8 ( ( PUNCT cana-380 166 9 1978 1978 NUM cana-380 166 10 ) ) PUNCT cana-380 167 1 [ [ X cana-380 167 2 3 3 NUM cana-380 167 3 ] ] X cana-380 167 4 shah shah NOUN cana-380 167 5 , , PUNCT cana-380 167 6 y.k y.k PROPN cana-380 167 7 . . PROPN cana-380 167 8 , , PUNCT cana-380 167 9 and and CCONJ cana-380 167 10 jaiswal jaiswal PROPN cana-380 167 11 , , PUNCT cana-380 167 12 m.c m.c PROPN cana-380 167 13 . . PROPN cana-380 167 14 : : PUNCT cana-380 167 15 an an DET cana-380 167 16 order order NOUN cana-380 167 17 - - PUNCT cana-380 167 18 level level NOUN cana-380 167 19 inventory inventory NOUN cana-380 167 20 model model NOUN cana-380 167 21 for for ADP cana-380 167 22 a a DET cana-380 167 23 system system NOUN cana-380 167 24 with with ADP cana-380 167 25 constant constant ADJ cana-380 167 26 rate rate NOUN cana-380 167 27 of of ADP cana-380 167 28 deterioration deterioration NOUN cana-380 167 29 . . PUNCT cana-380 168 1 opsearch opsearch PROPN cana-380 168 2 , , PUNCT cana-380 168 3 14 14 NUM cana-380 168 4 , , PUNCT cana-380 168 5 174 174 NUM cana-380 168 6 - - SYM cana-380 168 7 184 184 NUM cana-380 168 8 ( ( PUNCT cana-380 168 9 1977 1977 NUM cana-380 168 10 ) ) PUNCT cana-380 169 1 [ [ X cana-380 169 2 4 4 NUM cana-380 169 3 ] ] X cana-380 169 4 goyal goyal PROPN cana-380 169 5 s. s. PROPN cana-380 169 6 k. k. PROPN cana-380 169 7 and and CCONJ cana-380 169 8 giri giri PROPN cana-380 169 9 b. b. PROPN cana-380 169 10 c. c. PROPN cana-380 169 11 : : PUNCT cana-380 169 12 recent recent ADJ cana-380 169 13 trends trend NOUN cana-380 169 14 in in ADP cana-380 169 15 modeling modeling NOUN cana-380 169 16 of of ADP cana-380 169 17 deteriorating deteriorate VERB cana-380 169 18 inventory inventory NOUN cana-380 169 19 . . PUNCT cana-380 170 1 european european ADJ cana-380 170 2 journal journal PROPN cana-380 170 3 of of ADP cana-380 170 4 operational operational ADJ cana-380 170 5 research research NOUN cana-380 170 6 , , PUNCT cana-380 170 7 134(1 134(1 NUM cana-380 170 8 ) ) PUNCT cana-380 170 9 , , PUNCT cana-380 170 10 1 1 NUM cana-380 170 11 - - SYM cana-380 170 12 16 16 NUM cana-380 170 13 ( ( PUNCT cana-380 170 14 2001 2001 NUM cana-380 170 15 ) ) PUNCT cana-380 171 1 [ [ X cana-380 171 2 5 5 X cana-380 171 3 ] ] PUNCT cana-380 171 4 alamri alamri ADJ cana-380 171 5 a. a. NOUN cana-380 171 6 a. a. NOUN cana-380 171 7 , , PUNCT cana-380 171 8 and and CCONJ cana-380 171 9 balkhi balkhi PROPN cana-380 171 10 z. z. PROPN cana-380 171 11 t. t. PROPN cana-380 171 12 : : PUNCT cana-380 171 13 the the DET cana-380 171 14 effects effect NOUN cana-380 171 15 of of ADP cana-380 171 16 learning learn VERB cana-380 171 17 and and CCONJ cana-380 171 18 forgetting forget VERB cana-380 171 19 on on ADP cana-380 171 20 the the DET cana-380 171 21 optimal optimal ADJ cana-380 171 22 production production NOUN cana-380 171 23 lot lot NOUN cana-380 171 24 size size NOUN cana-380 171 25 for for ADP cana-380 171 26 deteriorating deteriorate VERB cana-380 171 27 items item NOUN cana-380 171 28 with with ADP cana-380 171 29 time time NOUN cana-380 171 30 varying vary VERB cana-380 171 31 demand demand NOUN cana-380 171 32 and and CCONJ cana-380 171 33 deterioration deterioration NOUN cana-380 171 34 rates rate NOUN cana-380 171 35 . . PUNCT cana-380 172 1 international international ADJ cana-380 172 2 journal journal PROPN cana-380 172 3 of of ADP cana-380 172 4 production production NOUN cana-380 172 5 economics economic NOUN cana-380 172 6 , , PUNCT cana-380 172 7 vol vol NOUN cana-380 172 8 . . PUNCT cana-380 172 9 107 107 NUM cana-380 172 10 , , PUNCT cana-380 172 11 pp pp ADV cana-380 172 12 . . PUNCT cana-380 173 1 125 125 NUM cana-380 173 2 - - SYM cana-380 173 3 138 138 NUM cana-380 173 4 ( ( PUNCT cana-380 173 5 2007 2007 NUM cana-380 173 6 ) ) PUNCT cana-380 174 1 [ [ X cana-380 174 2 6 6 NUM cana-380 174 3 ] ] X cana-380 174 4 dye dye PROPN cana-380 174 5 , , PUNCT cana-380 174 6 c. c. PROPN cana-380 174 7 y. y. PROPN cana-380 174 8 , , PUNCT cana-380 174 9 hsieh hsieh PROPN cana-380 174 10 , , PUNCT cana-380 174 11 t. t. PROPN cana-380 174 12 p. p. PROPN cana-380 174 13 , , PUNCT cana-380 174 14 & & CCONJ cana-380 174 15 ouyang ouyang PROPN cana-380 174 16 , , PUNCT cana-380 174 17 l. l. PROPN cana-380 174 18 y. y. PROPN cana-380 174 19 : : PUNCT cana-380 174 20 determining determine VERB cana-380 174 21 optimal optimal ADJ cana-380 174 22 selling selling NOUN cana-380 174 23 price price NOUN cana-380 174 24 and and CCONJ cana-380 174 25 lot lot NOUN cana-380 174 26 size size NOUN cana-380 174 27 with with ADP cana-380 174 28 a a DET cana-380 174 29 varying vary VERB cana-380 174 30 rate rate NOUN cana-380 174 31 of of ADP cana-380 174 32 deterioration deterioration NOUN cana-380 174 33 and and CCONJ cana-380 174 34 exponential exponential ADJ cana-380 174 35 partial partial ADJ cana-380 174 36 backlogging backlogging NOUN cana-380 174 37 . . PUNCT cana-380 175 1 european european ADJ cana-380 175 2 journal journal PROPN cana-380 175 3 of of ADP cana-380 175 4 operational operational ADJ cana-380 175 5 research research NOUN cana-380 175 6 , , PUNCT cana-380 175 7 181(2 181(2 NUM cana-380 175 8 ) ) PUNCT cana-380 175 9 , , PUNCT cana-380 175 10 668 668 NUM cana-380 175 11 - - SYM cana-380 175 12 678 678 NUM cana-380 175 13 ( ( PUNCT cana-380 175 14 2007 2007 NUM cana-380 175 15 ) ) PUNCT cana-380 176 1 [ [ X cana-380 176 2 7 7 X cana-380 176 3 ] ] X cana-380 176 4 mishra mishra PROPN cana-380 176 5 v. v. PROPN cana-380 176 6 k. k. PROPN cana-380 176 7 : : PUNCT cana-380 176 8 inventory inventory NOUN cana-380 176 9 model model NOUN cana-380 176 10 for for ADP cana-380 176 11 time time NOUN cana-380 176 12 dependent dependent ADJ cana-380 176 13 holding holding NOUN cana-380 176 14 cost cost NOUN cana-380 176 15 and and CCONJ cana-380 176 16 deterioration deterioration NOUN cana-380 176 17 with with ADP cana-380 176 18 salvage salvage NOUN cana-380 176 19 value value NOUN cana-380 176 20 and and CCONJ cana-380 176 21 shortages shortage NOUN cana-380 176 22 . . PUNCT cana-380 177 1 the the DET cana-380 177 2 journal journal NOUN cana-380 177 3 of of ADP cana-380 177 4 mathematics mathematic NOUN cana-380 177 5 and and CCONJ cana-380 177 6 computer computer NOUN cana-380 177 7 science science NOUN cana-380 177 8 , , PUNCT cana-380 177 9 4(1 4(1 NOUN cana-380 177 10 ) ) PUNCT cana-380 177 11 , , PUNCT cana-380 177 12 37 37 NUM cana-380 177 13 - - SYM cana-380 177 14 47 47 NUM cana-380 177 15 ( ( PUNCT cana-380 177 16 2012 2012 NUM cana-380 177 17 ) ) PUNCT cana-380 178 1 [ [ X cana-380 178 2 8 8 NUM cana-380 178 3 ] ] X cana-380 178 4 mishra mishra PROPN cana-380 178 5 , , PUNCT cana-380 178 6 v. v. PROPN cana-380 178 7 k. k. PROPN cana-380 178 8 , , PUNCT cana-380 178 9 singh singh PROPN cana-380 178 10 , , PUNCT cana-380 178 11 l. l. PROPN cana-380 178 12 s. s. PROPN cana-380 178 13 , , PUNCT cana-380 178 14 & & CCONJ cana-380 178 15 kumar kumar PROPN cana-380 178 16 , , PUNCT cana-380 178 17 r. r. PROPN cana-380 178 18 : : PUNCT cana-380 178 19 an an DET cana-380 178 20 inventory inventory NOUN cana-380 178 21 model model NOUN cana-380 178 22 for for ADP cana-380 178 23 deteriorating deteriorate VERB cana-380 178 24 items item NOUN cana-380 178 25 with with ADP cana-380 178 26 timedependent timedependent NOUN cana-380 178 27 demand demand NOUN cana-380 178 28 and and CCONJ cana-380 178 29 time time NOUN cana-380 178 30 - - PUNCT cana-380 178 31 varying vary VERB cana-380 178 32 holding hold VERB cana-380 178 33 cost cost NOUN cana-380 178 34 under under ADP cana-380 178 35 partial partial ADJ cana-380 178 36 backlogging backlogging NOUN cana-380 178 37 . . PUNCT cana-380 179 1 journal journal PROPN cana-380 179 2 of of ADP cana-380 179 3 industrial industrial ADJ cana-380 179 4 engineering engineering PROPN cana-380 179 5 international international ADJ cana-380 179 6 , , PUNCT cana-380 179 7 9 9 NUM cana-380 179 8 , , PUNCT cana-380 179 9 1 1 NUM cana-380 179 10 - - SYM cana-380 179 11 5 5 NUM cana-380 179 12 ( ( PUNCT cana-380 179 13 2013 2013 NUM cana-380 179 14 ) ) PUNCT cana-380 180 1 [ [ X cana-380 180 2 9 9 NUM cana-380 180 3 ] ] SYM cana-380 180 4 mohan mohan PROPN cana-380 180 5 , , PUNCT cana-380 180 6 r. r. PROPN cana-380 180 7 : : PUNCT cana-380 180 8 quadratic quadratic ADJ cana-380 180 9 demand demand NOUN cana-380 180 10 , , PUNCT cana-380 180 11 variable variable ADJ cana-380 180 12 holding holding NOUN cana-380 180 13 cost cost NOUN cana-380 180 14 with with ADP cana-380 180 15 time time NOUN cana-380 180 16 dependent dependent ADJ cana-380 180 17 deterioration deterioration NOUN cana-380 180 18 without without ADP cana-380 180 19 shortages shortage NOUN cana-380 180 20 and and CCONJ cana-380 180 21 salvage salvage NOUN cana-380 180 22 value value NOUN cana-380 180 23 . . PUNCT cana-380 181 1 iosr iosr PROPN cana-380 181 2 j. j. PROPN cana-380 181 3 math.(iosr math.(iosr PROPN cana-380 181 4 - - PROPN cana-380 181 5 jm jm NOUN cana-380 181 6 ) ) PUNCT cana-380 181 7 , , PUNCT cana-380 181 8 13(2 13(2 PROPN cana-380 181 9 ) ) PUNCT cana-380 181 10 , , PUNCT cana-380 181 11 59 59 NUM cana-380 181 12 - - SYM cana-380 181 13 66 66 NUM cana-380 181 14 ( ( PUNCT cana-380 181 15 2017 2017 NUM cana-380 181 16 ) ) PUNCT cana-380 182 1 [ [ X cana-380 182 2 10 10 NUM cana-380 182 3 ] ] X cana-380 182 4 priya priya PROPN cana-380 182 5 , , PUNCT cana-380 182 6 r. r. PROPN cana-380 182 7 k. k. PROPN cana-380 182 8 , , PUNCT cana-380 182 9 & & CCONJ cana-380 182 10 senbagam senbagam PROPN cana-380 182 11 , , PUNCT cana-380 182 12 k. k. PROPN cana-380 182 13 : : PUNCT cana-380 182 14 eoq eoq VERB cana-380 182 15 inventory inventory NOUN cana-380 182 16 model model NOUN cana-380 182 17 for for ADP cana-380 182 18 time time NOUN cana-380 182 19 dependent dependent ADJ cana-380 182 20 deteriorating deteriorate VERB cana-380 182 21 products product NOUN cana-380 182 22 with with ADP cana-380 182 23 quadratic quadratic ADJ cana-380 182 24 time time NOUN cana-380 182 25 varying vary VERB cana-380 182 26 demand demand NOUN cana-380 182 27 variable variable ADJ cana-380 182 28 deterioration deterioration NOUN cana-380 182 29 and and CCONJ cana-380 182 30 partialbacklogging partialbacklogging NOUN cana-380 182 31 . . PUNCT cana-380 183 1 arpn arpn VERB cana-380 183 2 j. j. PROPN cana-380 183 3 eng eng PROPN cana-380 183 4 . . PROPN cana-380 183 5 appl appl PROPN cana-380 183 6 . . PUNCT cana-380 184 1 sci sci PROPN cana-380 184 2 . . PROPN cana-380 184 3 , , PUNCT cana-380 184 4 13(7 13(7 NUM cana-380 184 5 ) ) PUNCT cana-380 184 6 , , PUNCT cana-380 184 7 2674 2674 NUM cana-380 184 8 - - SYM cana-380 184 9 2678 2678 NUM cana-380 184 10 ( ( PUNCT cana-380 184 11 2018 2018 NUM cana-380 184 12 ) ) PUNCT cana-380 185 1 [ [ X cana-380 185 2 11 11 NUM cana-380 185 3 ] ] PUNCT cana-380 185 4 pervin pervin NOUN cana-380 185 5 , , PUNCT cana-380 185 6 m. m. NOUN cana-380 185 7 , , PUNCT cana-380 185 8 roy roy PROPN cana-380 185 9 , , PUNCT cana-380 185 10 s. s. PROPN cana-380 185 11 k. k. PROPN cana-380 185 12 , , PUNCT cana-380 185 13 & & CCONJ cana-380 185 14 weber weber PROPN cana-380 185 15 , , PUNCT cana-380 185 16 g. g. PROPN cana-380 185 17 w. w. PROPN cana-380 185 18 : : PUNCT cana-380 185 19 analysis analysis NOUN cana-380 185 20 of of ADP cana-380 185 21 inventory inventory NOUN cana-380 185 22 control control NOUN cana-380 185 23 model model NOUN cana-380 185 24 with with ADP cana-380 185 25 shortage shortage NOUN cana-380 185 26 under under ADP cana-380 185 27 time time NOUN cana-380 185 28 - - PUNCT cana-380 185 29 dependent dependent ADJ cana-380 185 30 demand demand NOUN cana-380 185 31 and and CCONJ cana-380 185 32 time time NOUN cana-380 185 33 - - PUNCT cana-380 185 34 varying vary VERB cana-380 185 35 holding hold VERB cana-380 185 36 cost cost NOUN cana-380 185 37 including include VERB cana-380 185 38 stochastic stochastic ADJ cana-380 185 39 deterioration deterioration NOUN cana-380 185 40 . . PUNCT cana-380 186 1 annals annal NOUN cana-380 186 2 of of ADP cana-380 186 3 operations operation NOUN cana-380 186 4 research research NOUN cana-380 186 5 , , PUNCT cana-380 186 6 260 260 NUM cana-380 186 7 , , PUNCT cana-380 186 8 437 437 NUM cana-380 186 9 - - SYM cana-380 186 10 460 460 NUM cana-380 186 11 ( ( PUNCT cana-380 186 12 2018 2018 NUM cana-380 186 13 ) ) PUNCT cana-380 187 1 [ [ X cana-380 187 2 12 12 NUM cana-380 187 3 ] ] X cana-380 187 4 singh singh PROPN cana-380 187 5 , , PUNCT cana-380 187 6 r. r. PROPN cana-380 187 7 , , PUNCT cana-380 187 8 & & CCONJ cana-380 187 9 mishra mishra PROPN cana-380 187 10 , , PUNCT cana-380 187 11 v. v. PROPN cana-380 187 12 k. k. PROPN cana-380 187 13 : : PUNCT cana-380 187 14 an an DET cana-380 187 15 inventory inventory NOUN cana-380 187 16 model model NOUN cana-380 187 17 for for ADP cana-380 187 18 non non ADJ cana-380 187 19 - - ADJ cana-380 187 20 instantaneous instantaneous ADJ cana-380 187 21 deteriorating deteriorate VERB cana-380 187 22 items item NOUN cana-380 187 23 with with ADP cana-380 187 24 substitution substitution NOUN cana-380 187 25 and and CCONJ cana-380 187 26 carbon carbon NOUN cana-380 187 27 emission emission NOUN cana-380 187 28 under under ADP cana-380 187 29 triangular triangular NOUN cana-380 187 30 type type NOUN cana-380 187 31 demand demand NOUN cana-380 187 32 . . PUNCT cana-380 188 1 international international ADJ cana-380 188 2 journal journal PROPN cana-380 188 3 of of ADP cana-380 188 4 applied applied ADJ cana-380 188 5 and and CCONJ cana-380 188 6 computational computational ADJ cana-380 188 7 mathematics mathematic NOUN cana-380 188 8 , , PUNCT cana-380 188 9 7(4 7(4 NUM cana-380 188 10 ) ) PUNCT cana-380 188 11 , , PUNCT cana-380 188 12 127 127 NUM cana-380 188 13 ( ( PUNCT cana-380 188 14 2021 2021 NUM cana-380 188 15 ) ) PUNCT cana-380 188 16 communications communication NOUN cana-380 188 17 on on ADP cana-380 188 18 applied apply VERB cana-380 188 19 nonlinear nonlinear ADJ cana-380 188 20 analysis analysis NOUN cana-380 188 21 issn issn NOUN cana-380 188 22 : : PUNCT cana-380 188 23 1074 1074 NUM cana-380 188 24 - - PUNCT cana-380 188 25 133x 133x NUM cana-380 188 26 vol vol NOUN cana-380 188 27 31 31 NUM cana-380 188 28 no no NOUN cana-380 188 29 . . NOUN cana-380 188 30 1 1 NUM cana-380 188 31 ( ( PUNCT cana-380 188 32 2024 2024 NUM cana-380 188 33 ) ) PUNCT cana-380 188 34 186 186 NUM cana-380 188 35 https://internationalpubls.com https://internationalpubls.com X cana-380 189 1 [ [ X cana-380 189 2 13 13 NUM cana-380 189 3 ] ] X cana-380 189 4 fatma fatma PROPN cana-380 189 5 , , PUNCT cana-380 189 6 s. s. PROPN cana-380 189 7 , , PUNCT cana-380 189 8 mishra mishra PROPN cana-380 189 9 , , PUNCT cana-380 189 10 v. v. PROPN cana-380 189 11 k. k. PROPN cana-380 189 12 , , PUNCT cana-380 189 13 & & CCONJ cana-380 189 14 singh singh PROPN cana-380 189 15 , , PUNCT cana-380 189 16 r. r. PROPN cana-380 189 17 : : PUNCT cana-380 189 18 inventory inventory NOUN cana-380 189 19 model model NOUN cana-380 189 20 for for ADP cana-380 189 21 instantaneous instantaneous ADJ cana-380 189 22 deteriorating deteriorate VERB cana-380 189 23 items item NOUN cana-380 189 24 with with ADP cana-380 189 25 time time NOUN cana-380 189 26 sensitive sensitive ADJ cana-380 189 27 demand demand NOUN cana-380 189 28 for for ADP cana-380 189 29 post post NOUN cana-380 189 30 covid-19 covid-19 PROPN cana-380 189 31 recovery recovery NOUN cana-380 189 32 . . PUNCT cana-380 190 1 yugoslav yugoslav ADJ cana-380 190 2 journal journal PROPN cana-380 190 3 of of ADP cana-380 190 4 operations operation NOUN cana-380 190 5 research research NOUN cana-380 190 6 , , PUNCT cana-380 190 7 ( ( PUNCT cana-380 190 8 2023 2023 NUM cana-380 190 9 ) ) PUNCT