id sid tid token lemma pos cana-772 1 1 communications communication NOUN cana-772 1 2 on on ADP cana-772 1 3 applied apply VERB cana-772 1 4 nonlinear nonlinear ADJ cana-772 1 5 analysis analysis NOUN cana-772 1 6 issn issn NOUN cana-772 1 7 : : PUNCT cana-772 1 8 1074 1074 NUM cana-772 1 9 - - PUNCT cana-772 1 10 133x 133x NUM cana-772 1 11 vol vol NOUN cana-772 1 12 31 31 NUM cana-772 1 13 no no NOUN cana-772 1 14 . . PUNCT cana-772 2 1 3s 3s NUM cana-772 2 2 ( ( PUNCT cana-772 2 3 2024 2024 NUM cana-772 2 4 ) ) PUNCT cana-772 2 5 325 325 NUM cana-772 2 6 https://internationalpubls.com https://internationalpubls.com X cana-772 2 7 determination determination NOUN cana-772 2 8 of of ADP cana-772 2 9 continuous continuous ADJ cana-772 2 10 deterioration deterioration NOUN cana-772 2 11 level level NOUN cana-772 2 12 due due ADP cana-772 2 13 to to ADP cana-772 2 14 changing change VERB cana-772 2 15 demand demand NOUN cana-772 2 16 rates rate NOUN cana-772 2 17 in in ADP cana-772 2 18 inventory inventory NOUN cana-772 2 19 1quazzafi 1quazzafi NUM cana-772 2 20 rabbani rabbani NOUN cana-772 2 21 , , PUNCT cana-772 2 22 2nilesh 2nilesh NUM cana-772 2 23 kumar kumar PROPN cana-772 2 24 , , PUNCT cana-772 2 25 3nurul 3nurul PROPN cana-772 2 26 azeez azeez NOUN cana-772 2 27 khan khan PROPN cana-772 2 28 1,2department 1,2department NUM cana-772 2 29 of of ADP cana-772 2 30 mathematics mathematics PROPN cana-772 2 31 & & CCONJ cana-772 2 32 statistics statistic NOUN cana-772 2 33 , , PUNCT cana-772 2 34 integral integral ADJ cana-772 2 35 university university NOUN cana-772 2 36 , , PUNCT cana-772 2 37 lucknow lucknow PROPN cana-772 2 38 , , PUNCT cana-772 2 39 india india PROPN cana-772 2 40 . . PUNCT cana-772 3 1 1nileshkrr@student.iul.ac.in 1nileshkrr@student.iul.ac.in NUM cana-772 3 2 2quazzafi@iul.ac.in 2quazzafi@iul.ac.in NUM cana-772 3 3 3department 3department NUM cana-772 3 4 of of ADP cana-772 3 5 mathematics mathematic NOUN cana-772 3 6 , , PUNCT cana-772 3 7 dav dav NOUN cana-772 3 8 pg pg PROPN cana-772 3 9 college college PROPN cana-772 3 10 , , PUNCT cana-772 3 11 azamgarh azamgarh PROPN cana-772 3 12 , , PUNCT cana-772 3 13 india india PROPN cana-772 3 14 nurulkhan1890@gmail.com nurulkhan1890@gmail.com PROPN cana-772 4 1 corresponding correspond VERB cana-772 4 2 author author NOUN cana-772 4 3 : : PUNCT cana-772 4 4 nilesh nilesh PROPN cana-772 4 5 kumar kumar PROPN cana-772 4 6 article article PROPN cana-772 4 7 history history NOUN cana-772 4 8 : : PUNCT cana-772 4 9 received receive VERB cana-772 4 10 : : PUNCT cana-772 4 11 08 08 NUM cana-772 4 12 - - PUNCT cana-772 4 13 04 04 NUM cana-772 4 14 - - PUNCT cana-772 4 15 2024 2024 NUM cana-772 4 16 revised revise VERB cana-772 4 17 : : PUNCT cana-772 4 18 20 20 NUM cana-772 4 19 - - SYM cana-772 4 20 05 05 NUM cana-772 4 21 - - PUNCT cana-772 4 22 2024 2024 NUM cana-772 4 23 accepted accept VERB cana-772 4 24 : : PUNCT cana-772 4 25 15 15 NUM cana-772 4 26 - - SYM cana-772 4 27 06 06 NUM cana-772 4 28 - - PUNCT cana-772 4 29 2024 2024 NUM cana-772 4 30 abstract abstract NOUN cana-772 4 31 : : PUNCT cana-772 4 32 a a DET cana-772 4 33 significant significant ADJ cana-772 4 34 portion portion NOUN cana-772 4 35 of of ADP cana-772 4 36 the the DET cana-772 4 37 retail retail ADJ cana-772 4 38 sector sector NOUN cana-772 4 39 deals deal NOUN cana-772 4 40 with with ADP cana-772 4 41 products product NOUN cana-772 4 42 whose whose DET cana-772 4 43 freshness freshness NOUN cana-772 4 44 deteriorates deteriorate VERB cana-772 4 45 with with ADP cana-772 4 46 time time NOUN cana-772 4 47 and and CCONJ cana-772 4 48 lowers lower VERB cana-772 4 49 demand demand NOUN cana-772 4 50 at at ADP cana-772 4 51 the the DET cana-772 4 52 same same ADJ cana-772 4 53 price price NOUN cana-772 4 54 . . PUNCT cana-772 5 1 later later ADV cana-772 5 2 , , PUNCT cana-772 5 3 when when SCONJ cana-772 5 4 it it PRON cana-772 5 5 is be AUX cana-772 5 6 normal normal ADJ cana-772 5 7 to to PART cana-772 5 8 offer offer VERB cana-772 5 9 a a DET cana-772 5 10 discount discount NOUN cana-772 5 11 to to PART cana-772 5 12 stimulate stimulate VERB cana-772 5 13 sales sale NOUN cana-772 5 14 , , PUNCT cana-772 5 15 the the DET cana-772 5 16 item item NOUN cana-772 5 17 may may AUX cana-772 5 18 start start VERB cana-772 5 19 to to PART cana-772 5 20 deteriorate deteriorate VERB cana-772 5 21 . . PUNCT cana-772 6 1 if if SCONJ cana-772 6 2 chosen choose VERB cana-772 6 3 wisely wisely ADV cana-772 6 4 , , PUNCT cana-772 6 5 inventory inventory NOUN cana-772 6 6 management management NOUN cana-772 6 7 could could AUX cana-772 6 8 have have VERB cana-772 6 9 numerous numerous ADJ cana-772 6 10 advantages advantage NOUN cana-772 6 11 for for ADP cana-772 6 12 the the DET cana-772 6 13 retailer retailer NOUN cana-772 6 14 . . PUNCT cana-772 7 1 the the DET cana-772 7 2 demand demand NOUN cana-772 7 3 rates rate NOUN cana-772 7 4 are be AUX cana-772 7 5 changing change VERB cana-772 7 6 with with ADP cana-772 7 7 and and CCONJ cana-772 7 8 without without ADP cana-772 7 9 shortages shortage NOUN cana-772 7 10 of of ADP cana-772 7 11 the the DET cana-772 7 12 products product NOUN cana-772 7 13 . . PUNCT cana-772 8 1 this this PRON cana-772 8 2 served serve VERB cana-772 8 3 as as ADP cana-772 8 4 an an DET cana-772 8 5 inspiration inspiration NOUN cana-772 8 6 for for ADP cana-772 8 7 creating create VERB cana-772 8 8 and and CCONJ cana-772 8 9 analysing analyse VERB cana-772 8 10 an an DET cana-772 8 11 inventory inventory NOUN cana-772 8 12 model model NOUN cana-772 8 13 in in ADP cana-772 8 14 which which PRON cana-772 8 15 the the DET cana-772 8 16 demand demand NOUN cana-772 8 17 for for ADP cana-772 8 18 a a DET cana-772 8 19 degrading degrade VERB cana-772 8 20 product product NOUN cana-772 8 21 is be AUX cana-772 8 22 first first ADV cana-772 8 23 driven drive VERB cana-772 8 24 solely solely ADV cana-772 8 25 by by ADP cana-772 8 26 its its PRON cana-772 8 27 selling selling NOUN cana-772 8 28 price price NOUN cana-772 8 29 and and CCONJ cana-772 8 30 then then ADV cana-772 8 31 by by ADP cana-772 8 32 its its PRON cana-772 8 33 level level NOUN cana-772 8 34 of of ADP cana-772 8 35 freshness freshness NOUN cana-772 8 36 . . PUNCT cana-772 9 1 for for ADP cana-772 9 2 an an DET cana-772 9 3 inventory inventory NOUN cana-772 9 4 model model NOUN cana-772 9 5 with with ADP cana-772 9 6 lost lose VERB cana-772 9 7 sales sale NOUN cana-772 9 8 shortage shortage NOUN cana-772 9 9 , , PUNCT cana-772 9 10 researchers researcher NOUN cana-772 9 11 consider consider VERB cana-772 9 12 general general ADJ cana-772 9 13 deterioration deterioration NOUN cana-772 9 14 distribution distribution NOUN cana-772 9 15 and and CCONJ cana-772 9 16 general general ADJ cana-772 9 17 demand demand NOUN cana-772 9 18 function function NOUN cana-772 9 19 . . PUNCT cana-772 10 1 it it PRON cana-772 10 2 is be AUX cana-772 10 3 demonstrated demonstrate VERB cana-772 10 4 that that SCONJ cana-772 10 5 net net ADJ cana-772 10 6 profit profit NOUN cana-772 10 7 is be AUX cana-772 10 8 a a DET cana-772 10 9 conditionally conditionally ADV cana-772 10 10 concave concave VERB cana-772 10 11 function function NOUN cana-772 10 12 of of ADP cana-772 10 13 discount discount NOUN cana-772 10 14 and and CCONJ cana-772 10 15 a a DET cana-772 10 16 concave concave ADJ cana-772 10 17 function function NOUN cana-772 10 18 of of ADP cana-772 10 19 the the DET cana-772 10 20 period period NOUN cana-772 10 21 with with ADP cana-772 10 22 positive positive ADJ cana-772 10 23 inventory inventory NOUN cana-772 10 24 . . PUNCT cana-772 11 1 significant significant ADJ cana-772 11 2 management management NOUN cana-772 11 3 insights insight NOUN cana-772 11 4 gained gain VERB cana-772 11 5 from from ADP cana-772 11 6 sensitivity sensitivity NOUN cana-772 11 7 analysis analysis NOUN cana-772 11 8 indicate indicate VERB cana-772 11 9 that that SCONJ cana-772 11 10 certain certain ADJ cana-772 11 11 policies policy NOUN cana-772 11 12 run run VERB cana-772 11 13 opposed opposed ADJ cana-772 11 14 to to ADP cana-772 11 15 those those PRON cana-772 11 16 that that PRON cana-772 11 17 merchants merchant NOUN cana-772 11 18 often often ADV cana-772 11 19 implement implement VERB cana-772 11 20 , , PUNCT cana-772 11 21 while while SCONJ cana-772 11 22 others other NOUN cana-772 11 23 align align VERB cana-772 11 24 with with ADP cana-772 11 25 popular popular ADJ cana-772 11 26 practices practice NOUN cana-772 11 27 . . PUNCT cana-772 12 1 in in ADP cana-772 12 2 this this DET cana-772 12 3 study study NOUN cana-772 12 4 , , PUNCT cana-772 12 5 a a DET cana-772 12 6 brief brief ADJ cana-772 12 7 introduction introduction NOUN cana-772 12 8 will will AUX cana-772 12 9 be be AUX cana-772 12 10 provided provide VERB cana-772 12 11 where where SCONJ cana-772 12 12 the the DET cana-772 12 13 guidelines guideline NOUN cana-772 12 14 will will AUX cana-772 12 15 be be AUX cana-772 12 16 applied apply VERB cana-772 12 17 to to PART cana-772 12 18 manage manage VERB cana-772 12 19 inventory inventory NOUN cana-772 12 20 and and CCONJ cana-772 12 21 keep keep VERB cana-772 12 22 up up ADP cana-772 12 23 the the DET cana-772 12 24 quality quality NOUN cana-772 12 25 of of ADP cana-772 12 26 the the DET cana-772 12 27 products product NOUN cana-772 12 28 so so SCONJ cana-772 12 29 that that SCONJ cana-772 12 30 the the DET cana-772 12 31 demand demand NOUN cana-772 12 32 rate rate NOUN cana-772 12 33 is be AUX cana-772 12 34 satisfied satisfied ADJ cana-772 12 35 . . PUNCT cana-772 13 1 the the DET cana-772 13 2 research research NOUN cana-772 13 3 will will AUX cana-772 13 4 focus focus VERB cana-772 13 5 on on ADP cana-772 13 6 the the DET cana-772 13 7 problems problem NOUN cana-772 13 8 of of ADP cana-772 13 9 the the DET cana-772 13 10 deterioration deterioration NOUN cana-772 13 11 of of ADP cana-772 13 12 inventory inventory NOUN cana-772 13 13 with with ADP cana-772 13 14 and and CCONJ cana-772 13 15 without without ADP cana-772 13 16 shortages shortage NOUN cana-772 13 17 and and CCONJ cana-772 13 18 different different ADJ cana-772 13 19 demand demand NOUN cana-772 13 20 rates rate NOUN cana-772 13 21 . . PUNCT cana-772 14 1 the the DET cana-772 14 2 chosen choose VERB cana-772 14 3 methodology methodology NOUN cana-772 14 4 will will AUX cana-772 14 5 be be AUX cana-772 14 6 a a DET cana-772 14 7 mixed mixed ADJ cana-772 14 8 approach approach NOUN cana-772 14 9 with with ADP cana-772 14 10 primary primary ADJ cana-772 14 11 qualitative qualitative NOUN cana-772 14 12 and and CCONJ cana-772 14 13 secondary secondary ADJ cana-772 14 14 qualitative qualitative ADJ cana-772 14 15 data datum NOUN cana-772 14 16 analysis analysis NOUN cana-772 14 17 . . PUNCT cana-772 15 1 the the DET cana-772 15 2 research research NOUN cana-772 15 3 finds find VERB cana-772 15 4 out out ADP cana-772 15 5 that that PRON cana-772 15 6 meeting meeting NOUN cana-772 15 7 customer customer NOUN cana-772 15 8 demand demand NOUN cana-772 15 9 and and CCONJ cana-772 15 10 maintaining maintain VERB cana-772 15 11 product product NOUN cana-772 15 12 stock stock NOUN cana-772 15 13 is be AUX cana-772 15 14 possible possible ADJ cana-772 15 15 by by ADP cana-772 15 16 applying apply VERB cana-772 15 17 a a DET cana-772 15 18 quick quick ADJ cana-772 15 19 functioning function VERB cana-772 15 20 inventory inventory NOUN cana-772 15 21 control control NOUN cana-772 15 22 system system NOUN cana-772 15 23 . . PUNCT cana-772 16 1 the the DET cana-772 16 2 research research NOUN cana-772 16 3 has have AUX cana-772 16 4 also also ADV cana-772 16 5 given give VERB cana-772 16 6 recommendations recommendation NOUN cana-772 16 7 on on ADP cana-772 16 8 maximising maximise VERB cana-772 16 9 the the DET cana-772 16 10 profit profit NOUN cana-772 16 11 function function NOUN cana-772 16 12 and and CCONJ cana-772 16 13 control control NOUN cana-772 16 14 inventories inventory NOUN cana-772 16 15 while while SCONJ cana-772 16 16 keeping keep VERB cana-772 16 17 them they PRON cana-772 16 18 at at ADP cana-772 16 19 optimum optimum ADJ cana-772 16 20 level level NOUN cana-772 16 21 . . PUNCT cana-772 17 1 keywords keyword NOUN cana-772 17 2 : : PUNCT cana-772 17 3 inventory inventory NOUN cana-772 17 4 model model NOUN cana-772 17 5 , , PUNCT cana-772 17 6 dependent dependent ADJ cana-772 17 7 demand demand NOUN cana-772 17 8 , , PUNCT cana-772 17 9 deteriorating deteriorate VERB cana-772 17 10 conditions condition NOUN cana-772 17 11 , , PUNCT cana-772 17 12 shortage shortage NOUN cana-772 17 13 levels level NOUN cana-772 17 14 . . PUNCT cana-772 18 1 1 1 X cana-772 18 2 . . X cana-772 18 3 introduction introduction NOUN cana-772 18 4 inventory inventory NOUN cana-772 18 5 theory theory NOUN cana-772 18 6 seeks seek VERB cana-772 18 7 to to PART cana-772 18 8 provide provide VERB cana-772 18 9 guidelines guideline NOUN cana-772 18 10 that that SCONJ cana-772 18 11 managers manager NOUN cana-772 18 12 can can AUX cana-772 18 13 apply apply VERB cana-772 18 14 to to PART cana-772 18 15 reduce reduce VERB cana-772 18 16 the the DET cana-772 18 17 expenses expense NOUN cana-772 18 18 related relate VERB cana-772 18 19 to to ADP cana-772 18 20 keeping keep VERB cana-772 18 21 inventory inventory NOUN cana-772 18 22 levels level NOUN cana-772 18 23 high high ADJ cana-772 18 24 and and CCONJ cana-772 18 25 satisfying satisfy VERB cana-772 18 26 consumer consumer NOUN cana-772 18 27 demand demand NOUN cana-772 18 28 . . PUNCT cana-772 19 1 the the DET cana-772 19 2 " " PUNCT cana-772 19 3 inventory inventory NOUN cana-772 19 4 management management NOUN cana-772 19 5 system system NOUN cana-772 19 6 " " PUNCT cana-772 19 7 was be AUX cana-772 19 8 created create VERB cana-772 19 9 to to PART cana-772 19 10 replace replace VERB cana-772 19 11 the the DET cana-772 19 12 manual manual ADJ cana-772 19 13 system system NOUN cana-772 19 14 that that PRON cana-772 19 15 was be AUX cana-772 19 16 in in ADP cana-772 19 17 use use NOUN cana-772 19 18 at at ADP cana-772 19 19 the the DET cana-772 19 20 time time NOUN cana-772 19 21 and and CCONJ cana-772 19 22 solve solve VERB cana-772 19 23 its its PRON cana-772 19 24 issues issue NOUN cana-772 19 25 . . PUNCT cana-772 20 1 this this DET cana-772 20 2 software software NOUN cana-772 20 3 is be AUX cana-772 20 4 intended intend VERB cana-772 20 5 to to PART cana-772 20 6 remove remove VERB cana-772 20 7 , , PUNCT cana-772 20 8 or or CCONJ cana-772 20 9 at at ADP cana-772 20 10 least least ADJ cana-772 20 11 lessen lessen VERB cana-772 20 12 , , PUNCT cana-772 20 13 the the DET cana-772 20 14 difficulties difficulty NOUN cana-772 20 15 this this DET cana-772 20 16 current current ADJ cana-772 20 17 system system NOUN cana-772 20 18 presents present NOUN cana-772 20 19 . . PUNCT cana-772 21 1 additionally additionally ADV cana-772 21 2 , , PUNCT cana-772 21 3 this this DET cana-772 21 4 system system NOUN cana-772 21 5 is be AUX cana-772 21 6 tailored tailor VERB cana-772 21 7 to to ADP cana-772 21 8 the the DET cana-772 21 9 specific specific ADJ cana-772 21 10 requirements requirement NOUN cana-772 21 11 of of ADP cana-772 21 12 the the DET cana-772 21 13 business business NOUN cana-772 21 14 to to PART cana-772 21 15 ensure ensure VERB cana-772 21 16 efficient efficient ADJ cana-772 21 17 and and CCONJ cana-772 21 18 successful successful ADJ cana-772 21 19 operation operation NOUN cana-772 21 20 . . PUNCT cana-772 22 1 communications communication NOUN cana-772 22 2 on on ADP cana-772 22 3 applied apply VERB cana-772 22 4 nonlinear nonlinear ADJ cana-772 22 5 analysis analysis NOUN cana-772 22 6 issn issn NOUN cana-772 22 7 : : PUNCT cana-772 22 8 1074 1074 NUM cana-772 22 9 - - PUNCT cana-772 22 10 133x 133x NUM cana-772 22 11 vol vol NOUN cana-772 22 12 31 31 NUM cana-772 22 13 no no NOUN cana-772 22 14 . . PUNCT cana-772 23 1 3s 3s NUM cana-772 23 2 ( ( PUNCT cana-772 23 3 2024 2024 NUM cana-772 23 4 ) ) PUNCT cana-772 23 5 326 326 NUM cana-772 23 6 https://internationalpubls.com https://internationalpubls.com X cana-772 24 1 in in ADP cana-772 24 2 addition addition NOUN cana-772 24 3 to to ADP cana-772 24 4 reducing reduce VERB cana-772 24 5 errors error NOUN cana-772 24 6 as as ADV cana-772 24 7 much much ADV cana-772 24 8 as as ADP cana-772 24 9 possible possible ADJ cana-772 24 10 during during ADP cana-772 24 11 data datum NOUN cana-772 24 12 entry entry NOUN cana-772 24 13 , , PUNCT cana-772 24 14 the the DET cana-772 24 15 application application NOUN cana-772 24 16 also also ADV cana-772 24 17 displays display VERB cana-772 24 18 error error NOUN cana-772 24 19 messages message NOUN cana-772 24 20 when when SCONJ cana-772 24 21 incorrect incorrect ADJ cana-772 24 22 data datum NOUN cana-772 24 23 is be AUX cana-772 24 24 entered enter VERB cana-772 24 25 . . PUNCT cana-772 25 1 to to PART cana-772 25 2 operate operate VERB cana-772 25 3 this this DET cana-772 25 4 system system NOUN cana-772 25 5 , , PUNCT cana-772 25 6 a a DET cana-772 25 7 user user NOUN cana-772 25 8 is be AUX cana-772 25 9 not not PART cana-772 25 10 required require VERB cana-772 25 11 to to PART cana-772 25 12 possess possess VERB cana-772 25 13 any any DET cana-772 25 14 formal formal ADJ cana-772 25 15 knowledge knowledge NOUN cana-772 25 16 . . PUNCT cana-772 26 1 this this PRON cana-772 26 2 alone alone ADV cana-772 26 3 demonstrates demonstrate VERB cana-772 26 4 that that SCONJ cana-772 26 5 it it PRON cana-772 26 6 is be AUX cana-772 26 7 user user NOUN cana-772 26 8 - - PUNCT cana-772 26 9 friendly friendly ADJ cana-772 26 10 . . PUNCT cana-772 27 1 as as SCONJ cana-772 27 2 previously previously ADV cana-772 27 3 mentioned mention VERB cana-772 27 4 , , PUNCT cana-772 27 5 an an DET cana-772 27 6 inventory inventory NOUN cana-772 27 7 management management NOUN cana-772 27 8 system system NOUN cana-772 27 9 can can AUX cana-772 27 10 result result VERB cana-772 27 11 in in ADP cana-772 27 12 a a DET cana-772 27 13 secure secure ADJ cana-772 27 14 , , PUNCT cana-772 27 15 dependable dependable ADJ cana-772 27 16 , , PUNCT cana-772 27 17 quick quick ADJ cana-772 27 18 , , PUNCT cana-772 27 19 and and CCONJ cana-772 27 20 error error NOUN cana-772 27 21 - - PUNCT cana-772 27 22 free free ADJ cana-772 27 23 management management NOUN cana-772 27 24 system system NOUN cana-772 27 25 . . PUNCT cana-772 28 1 instead instead ADV cana-772 28 2 of of ADP cana-772 28 3 focusing focus VERB cana-772 28 4 on on ADP cana-772 28 5 the the DET cana-772 28 6 recordkeeping recordkeeping NOUN cana-772 28 7 , , PUNCT cana-772 28 8 it it PRON cana-772 28 9 can can AUX cana-772 28 10 help help VERB cana-772 28 11 the the DET cana-772 28 12 user user NOUN cana-772 28 13 focus focus VERB cana-772 28 14 on on ADP cana-772 28 15 other other ADJ cana-772 28 16 things thing NOUN cana-772 28 17 . . PUNCT cana-772 29 1 as as ADP cana-772 29 2 a a DET cana-772 29 3 result result NOUN cana-772 29 4 , , PUNCT cana-772 29 5 it it PRON cana-772 29 6 will will AUX cana-772 29 7 aid aid VERB cana-772 29 8 the the DET cana-772 29 9 organisation organisation NOUN cana-772 29 10 in in ADP cana-772 29 11 making make VERB cana-772 29 12 better well ADJ cana-772 29 13 use use NOUN cana-772 29 14 of of ADP cana-772 29 15 its its PRON cana-772 29 16 resources resource NOUN cana-772 29 17 . . PUNCT cana-772 30 1 all all DET cana-772 30 2 organisations organisation NOUN cana-772 30 3 , , PUNCT cana-772 30 4 regardless regardless ADV cana-772 30 5 of of ADP cana-772 30 6 size size NOUN cana-772 30 7 , , PUNCT cana-772 30 8 face face VERB cana-772 30 9 obstacles obstacle NOUN cana-772 30 10 in in ADP cana-772 30 11 handling handle VERB cana-772 30 12 inventory inventory NOUN cana-772 30 13 , , PUNCT cana-772 30 14 stock stock NOUN cana-772 30 15 , , PUNCT cana-772 30 16 sales sale NOUN cana-772 30 17 , , PUNCT cana-772 30 18 product product NOUN cana-772 30 19 , , PUNCT cana-772 30 20 category category NOUN cana-772 30 21 , , PUNCT cana-772 30 22 and and CCONJ cana-772 30 23 customer customer NOUN cana-772 30 24 data datum NOUN cana-772 30 25 . . PUNCT cana-772 31 1 by by ADP cana-772 31 2 creating create VERB cana-772 31 3 unique unique ADJ cana-772 31 4 personnel personnel NOUN cana-772 31 5 management management NOUN cana-772 31 6 systems system NOUN cana-772 31 7 that that PRON cana-772 31 8 are be AUX cana-772 31 9 tailored tailor VERB cana-772 31 10 to to ADP cana-772 31 11 managerial managerial ADJ cana-772 31 12 demands demand NOUN cana-772 31 13 because because SCONJ cana-772 31 14 every every DET cana-772 31 15 inventory inventory NOUN cana-772 31 16 management management NOUN cana-772 31 17 system system NOUN cana-772 31 18 has have VERB cana-772 31 19 various various ADJ cana-772 31 20 stock stock NOUN cana-772 31 21 needs need NOUN cana-772 31 22 . . PUNCT cana-772 32 1 this this PRON cana-772 32 2 is be AUX cana-772 32 3 intended intend VERB cana-772 32 4 to to PART cana-772 32 5 help help VERB cana-772 32 6 with with ADP cana-772 32 7 strategic strategic ADJ cana-772 32 8 planning planning NOUN cana-772 32 9 and and CCONJ cana-772 32 10 will will AUX cana-772 32 11 guarantee guarantee VERB cana-772 32 12 that that SCONJ cana-772 32 13 the the DET cana-772 32 14 company company NOUN cana-772 32 15 has have VERB cana-772 32 16 the the DET cana-772 32 17 appropriate appropriate ADJ cana-772 32 18 amount amount NOUN cana-772 32 19 of of ADP cana-772 32 20 data datum NOUN cana-772 32 21 and and CCONJ cana-772 32 22 specifics specific NOUN cana-772 32 23 in in ADP cana-772 32 24 place place NOUN cana-772 32 25 to to PART cana-772 32 26 support support VERB cana-772 32 27 long long ADJ cana-772 32 28 - - PUNCT cana-772 32 29 term term NOUN cana-772 32 30 objectives objective NOUN cana-772 32 31 . . PUNCT cana-772 33 1 additionally additionally ADV cana-772 33 2 , , PUNCT cana-772 33 3 the the DET cana-772 33 4 solutions solution NOUN cana-772 33 5 have have VERB cana-772 33 6 remote remote ADJ cana-772 33 7 access access NOUN cana-772 33 8 capabilities capability NOUN cana-772 33 9 that that PRON cana-772 33 10 lets let VERB cana-772 33 11 a a DET cana-772 33 12 company company NOUN cana-772 33 13 manage manage VERB cana-772 33 14 staff staff NOUN cana-772 33 15 from from ADP cana-772 33 16 anywhere anywhere ADV cana-772 33 17 at at ADP cana-772 33 18 any any DET cana-772 33 19 time time NOUN cana-772 33 20 , , PUNCT cana-772 33 21 perfect perfect ADJ cana-772 33 22 for for ADP cana-772 33 23 busy busy ADJ cana-772 33 24 executives executive NOUN cana-772 33 25 who who PRON cana-772 33 26 are be AUX cana-772 33 27 constantly constantly ADV cana-772 33 28 on on ADP cana-772 33 29 the the DET cana-772 33 30 road road NOUN cana-772 33 31 . . PUNCT cana-772 34 1 in in ADP cana-772 34 2 the the DET cana-772 34 3 end end NOUN cana-772 34 4 , , PUNCT cana-772 34 5 these these DET cana-772 34 6 technologies technology NOUN cana-772 34 7 will will AUX cana-772 34 8 enable enable VERB cana-772 34 9 a a DET cana-772 34 10 person person NOUN cana-772 34 11 to to PART cana-772 34 12 handle handle VERB cana-772 34 13 resources resource NOUN cana-772 34 14 more more ADV cana-772 34 15 effectively effectively ADV cana-772 34 16 [ [ X cana-772 34 17 6 6 NUM cana-772 34 18 ] ] PUNCT cana-772 34 19 . . PUNCT cana-772 35 1 men man NOUN cana-772 35 2 , , PUNCT cana-772 35 3 machinery machinery NOUN cana-772 35 4 , , PUNCT cana-772 35 5 materials material NOUN cana-772 35 6 , , PUNCT cana-772 35 7 money money NOUN cana-772 35 8 , , PUNCT cana-772 35 9 and and CCONJ cana-772 35 10 other other ADJ cana-772 35 11 resources resource NOUN cana-772 35 12 that that PRON cana-772 35 13 are be AUX cana-772 35 14 usable usable ADJ cana-772 35 15 inventory inventory NOUN cana-772 35 16 . . PUNCT cana-772 36 1 the the DET cana-772 36 2 inventory inventory NOUN cana-772 36 3 is be AUX cana-772 36 4 frequently frequently ADV cana-772 36 5 referred refer VERB cana-772 36 6 to to ADP cana-772 36 7 as as ADP cana-772 36 8 " " PUNCT cana-772 36 9 stock stock NOUN cana-772 36 10 " " PUNCT cana-772 36 11 when when SCONJ cana-772 36 12 material material ADJ cana-772 36 13 resources resource NOUN cana-772 36 14 are be AUX cana-772 36 15 involved involve VERB cana-772 36 16 . . PUNCT cana-772 37 1 if if SCONJ cana-772 37 2 resources resource NOUN cana-772 37 3 are be AUX cana-772 37 4 controlled control VERB cana-772 37 5 or or CCONJ cana-772 37 6 if if SCONJ cana-772 37 7 there there PRON cana-772 37 8 is be VERB cana-772 37 9 at at ADV cana-772 37 10 least least ADJ cana-772 37 11 one one NUM cana-772 37 12 expense expense NOUN cana-772 37 13 that that PRON cana-772 37 14 goes go VERB cana-772 37 15 down down ADP cana-772 37 16 as as ADP cana-772 37 17 inventory inventory NOUN cana-772 37 18 rises rise NOUN cana-772 37 19 , , PUNCT cana-772 37 20 then then ADV cana-772 37 21 there there PRON cana-772 37 22 is be VERB cana-772 37 23 an an DET cana-772 37 24 inventory inventory NOUN cana-772 37 25 problem problem NOUN cana-772 37 26 . . PUNCT cana-772 38 1 the the DET cana-772 38 2 goal goal NOUN cana-772 38 3 is be AUX cana-772 38 4 to to PART cana-772 38 5 reduce reduce VERB cana-772 38 6 the the DET cana-772 38 7 overall overall ADJ cana-772 38 8 cost cost NOUN cana-772 38 9 , , PUNCT cana-772 38 10 whether whether SCONJ cana-772 38 11 it it PRON cana-772 38 12 be be AUX cana-772 38 13 anticipated anticipate VERB cana-772 38 14 or or CCONJ cana-772 38 15 real real ADJ cana-772 38 16 . . PUNCT cana-772 39 1 but but CCONJ cana-772 39 2 when when SCONJ cana-772 39 3 inventory inventory NOUN cana-772 39 4 influences influence VERB cana-772 39 5 demand demand NOUN cana-772 39 6 , , PUNCT cana-772 39 7 the the DET cana-772 39 8 goal goal NOUN cana-772 39 9 might might AUX cana-772 39 10 also also ADV cana-772 39 11 be be AUX cana-772 39 12 to to PART cana-772 39 13 maximise maximise VERB cana-772 39 14 profit profit NOUN cana-772 39 15 . . PUNCT cana-772 40 1 using use VERB cana-772 40 2 the the DET cana-772 40 3 model model NOUN cana-772 40 4 helps help VERB cana-772 40 5 the the DET cana-772 40 6 supplier supplier NOUN cana-772 40 7 at at ADP cana-772 40 8 every every DET cana-772 40 9 stage stage NOUN cana-772 40 10 by by ADP cana-772 40 11 lowering lower VERB cana-772 40 12 the the DET cana-772 40 13 order order NOUN cana-772 40 14 amount amount NOUN cana-772 40 15 and and CCONJ cana-772 40 16 reducing reduce VERB cana-772 40 17 production production NOUN cana-772 40 18 loss loss NOUN cana-772 40 19 from from ADP cana-772 40 20 deterioration deterioration NOUN cana-772 40 21 . . PUNCT cana-772 41 1 in in ADP cana-772 41 2 addition addition NOUN cana-772 41 3 , , PUNCT cana-772 41 4 by by ADP cana-772 41 5 selecting select VERB cana-772 41 6 the the DET cana-772 41 7 following following ADJ cana-772 41 8 variables variable NOUN cana-772 41 9 , , PUNCT cana-772 41 10 the the DET cana-772 41 11 practitioner practitioner NOUN cana-772 41 12 must must AUX cana-772 41 13 determine determine VERB cana-772 41 14 not not PART cana-772 41 15 only only ADV cana-772 41 16 the the DET cana-772 41 17 conventional conventional ADJ cana-772 41 18 order order NOUN cana-772 41 19 quantity quantity NOUN cana-772 41 20 decision decision NOUN cana-772 41 21 but but CCONJ cana-772 41 22 also also ADV cana-772 41 23 the the DET cana-772 41 24 quality quality NOUN cana-772 41 25 control control NOUN cana-772 41 26 deterioration deterioration NOUN cana-772 41 27 rate rate NOUN cana-772 41 28 . . PUNCT cana-772 42 1 1 1 X cana-772 42 2 ) ) PUNCT cana-772 42 3 the the DET cana-772 42 4 commodities commodity NOUN cana-772 42 5 ' ' PART cana-772 42 6 diminishing diminishing NOUN cana-772 42 7 value value NOUN cana-772 42 8 2 2 NUM cana-772 42 9 ) ) PUNCT cana-772 42 10 cutting cut VERB cana-772 42 11 expenses expense NOUN cana-772 42 12 while while SCONJ cana-772 42 13 preserving preserve VERB cana-772 42 14 3 3 NUM cana-772 42 15 ) ) PUNCT cana-772 42 16 demand demand NOUN cana-772 42 17 sensitivity sensitivity NOUN cana-772 42 18 to to ADP cana-772 42 19 quality quality NOUN cana-772 42 20 . . PUNCT cana-772 43 1 2 2 X cana-772 43 2 . . X cana-772 43 3 notations notation NOUN cana-772 43 4 for for ADP cana-772 43 5 mathematical mathematical ADJ cana-772 43 6 model model NOUN cana-772 43 7 the the DET cana-772 43 8 following follow VERB cana-772 43 9 are be AUX cana-772 43 10 the the DET cana-772 43 11 notions notion NOUN cana-772 43 12 involved involve VERB cana-772 43 13 in in ADP cana-772 43 14 the the DET cana-772 43 15 study study NOUN cana-772 43 16 : : PUNCT cana-772 43 17 𝐼(𝑑 𝐼(𝑑 NUM cana-772 43 18 ) ) PUNCT cana-772 43 19 = = SYM cana-772 44 1 πΌπ‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦π‘™π‘’π‘Žπ‘£π‘™π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ πΌπ‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦π‘™π‘’π‘Žπ‘£π‘™π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ PROPN cana-772 44 2 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 44 3 ) ) PUNCT cana-772 44 4 = = SYM cana-772 45 1 π·π‘’π‘šπ‘Žπ‘›π‘‘π‘Ÿπ‘Žπ‘‘π‘’π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ π·π‘’π‘šπ‘Žπ‘›π‘‘π‘Ÿπ‘Žπ‘‘π‘’π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ NOUN cana-772 45 2 𝑅(𝑑 𝑅(𝑑 NOUN cana-772 45 3 ) ) PUNCT cana-772 45 4 = = SYM cana-772 46 1 π‘…π‘’π‘π‘™π‘’π‘›π‘–π‘ β„Žπ‘šπ‘’π‘›π‘‘π‘Ÿπ‘Žπ‘‘π‘’π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ π‘…π‘’π‘π‘™π‘’π‘›π‘–π‘ β„Žπ‘šπ‘’π‘›π‘‘π‘Ÿπ‘Žπ‘‘π‘’π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ PROPN cana-772 46 2 β„Ž(𝑑 β„Ž(𝑑 PROPN cana-772 46 3 ) ) PUNCT cana-772 47 1 = = PUNCT cana-772 47 2 π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Ÿπ‘Žπ‘‘π‘’π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Ÿπ‘Žπ‘‘π‘’π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ PROPN cana-772 47 3 𝐢(𝑑 𝐢(𝑑 NUM cana-772 47 4 ) ) PUNCT cana-772 47 5 = = SYM cana-772 47 6 π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘™π‘’π‘£π‘’π‘™π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘™π‘’π‘£π‘’π‘™π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ PROPN cana-772 47 7 𝑆(𝑑 𝑆(𝑑 NUM cana-772 47 8 ) ) PUNCT cana-772 47 9 = = SYM cana-772 47 10 π‘†β„Žπ‘œπ‘Ÿπ‘‘π‘Žπ‘”π‘’π‘™π‘’π‘£π‘’π‘™π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ π‘†β„Žπ‘œπ‘Ÿπ‘‘π‘Žπ‘”π‘’π‘™π‘’π‘£π‘’π‘™π‘Žπ‘‘π‘‘π‘–π‘šπ‘’π‘‘ PROPN cana-772 47 11 𝐻 𝐻 PROPN cana-772 47 12 = = SYM cana-772 47 13 π»π‘œπ‘™π‘‘π‘–π‘›π‘”π‘π‘œπ‘ π‘‘π‘π‘’π‘Ÿπ‘’π‘›π‘–π‘‘π‘œπ‘“π‘–π‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦π‘π‘’π‘Ÿπ‘‘π‘–π‘šπ‘’π‘π‘’π‘Ÿπ‘–π‘œπ‘‘ π»π‘œπ‘™π‘‘π‘–π‘›π‘”π‘π‘œπ‘ π‘‘π‘π‘’π‘Ÿπ‘’π‘›π‘–π‘‘π‘œπ‘“π‘–π‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦π‘π‘’π‘Ÿπ‘‘π‘–π‘šπ‘’π‘π‘’π‘Ÿπ‘–π‘œπ‘‘ PROPN cana-772 47 14 𝐢 𝐢 PROPN cana-772 47 15 = = PROPN cana-772 47 16 π‘†β„Žπ‘œπ‘Ÿπ‘‘π‘Žπ‘”π‘’π‘π‘œπ‘ π‘‘π‘π‘’π‘Ÿπ‘’π‘›π‘–π‘‘π‘œπ‘“π‘’π‘›π‘ π‘Žπ‘‘π‘–π‘ π‘“π‘–π‘’π‘‘π‘‘π‘’π‘šπ‘Žπ‘›π‘‘ π‘†β„Žπ‘œπ‘Ÿπ‘‘π‘Žπ‘”π‘’π‘π‘œπ‘ π‘‘π‘π‘’π‘Ÿπ‘’π‘›π‘–π‘‘π‘œπ‘“π‘’π‘›π‘ π‘Žπ‘‘π‘–π‘ π‘“π‘–π‘’π‘‘π‘‘π‘’π‘šπ‘Žπ‘›π‘‘ PROPN cana-772 47 17 communications communication NOUN cana-772 47 18 on on ADP cana-772 47 19 applied apply VERB cana-772 47 20 nonlinear nonlinear ADJ cana-772 47 21 analysis analysis NOUN cana-772 47 22 issn issn NOUN cana-772 47 23 : : PUNCT cana-772 47 24 1074 1074 NUM cana-772 47 25 - - PUNCT cana-772 47 26 133x 133x NUM cana-772 47 27 vol vol NOUN cana-772 47 28 31 31 NUM cana-772 47 29 no no NOUN cana-772 47 30 . . PUNCT cana-772 48 1 3s 3s NUM cana-772 48 2 ( ( PUNCT cana-772 48 3 2024 2024 NUM cana-772 48 4 ) ) PUNCT cana-772 48 5 327 327 NUM cana-772 48 6 https://internationalpubls.com https://internationalpubls.com X cana-772 48 7 β„Ž β„Ž X cana-772 48 8 = = SYM cana-772 48 9 π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘π‘œπ‘ π‘‘π‘π‘’π‘Ÿπ‘’π‘›π‘–π‘‘π‘œπ‘“π‘–π‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦π‘π‘’π‘Ÿπ‘‘π‘–π‘šπ‘’π‘π‘’π‘Ÿπ‘–π‘œπ‘‘ π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘π‘œπ‘ π‘‘π‘π‘’π‘Ÿπ‘’π‘›π‘–π‘‘π‘œπ‘“π‘–π‘›π‘£π‘’π‘›π‘‘π‘œπ‘Ÿπ‘¦π‘π‘’π‘Ÿπ‘‘π‘–π‘šπ‘’π‘π‘’π‘Ÿπ‘–π‘œπ‘‘ PROPN cana-772 48 10 𝐼0 𝐼0 ADJ cana-772 48 11 = = PUNCT cana-772 48 12 πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™πΌπ‘›π‘£π‘’π‘›π‘‘π‘’π‘Ÿπ‘¦π‘™π‘’π‘£π‘’π‘™ πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™πΌπ‘›π‘£π‘’π‘›π‘‘π‘’π‘Ÿπ‘¦π‘™π‘’π‘£π‘’π‘™ PROPN cana-772 48 13 𝐢0 𝐢0 NOUN cana-772 48 14 = = PUNCT cana-772 48 15 πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘™π‘’π‘£π‘’π‘™ πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™π·π‘’π‘‘π‘’π‘Ÿπ‘–π‘œπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘™π‘’π‘£π‘’π‘™ PROPN cana-772 48 16 𝑆0 𝑆0 NOUN cana-772 49 1 = = PUNCT cana-772 49 2 πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™π‘†β„Žπ‘œπ‘Ÿπ‘‘π‘Žπ‘”π‘’π‘™π‘’π‘£π‘’π‘™ πΌπ‘›π‘–π‘‘π‘–π‘Žπ‘™π‘†β„Žπ‘œπ‘Ÿπ‘‘π‘Žπ‘”π‘’π‘™π‘’π‘£π‘’π‘™ PROPN cana-772 49 3 assumptions assumption VERB cana-772 49 4 1 1 NUM cana-772 49 5 . . PUNCT cana-772 49 6 continuous continuous ADJ cana-772 49 7 inventory inventory NOUN cana-772 49 8 level level NOUN cana-772 49 9 𝑑𝐼 𝑑𝐼 ADJ cana-772 49 10 𝑑𝑑 𝑑𝑑 ADP cana-772 49 11 = = PUNCT cana-772 49 12 𝑅(𝑑 𝑅(𝑑 NOUN cana-772 49 13 ) ) PUNCT cana-772 49 14 βˆ’ βˆ’ PROPN cana-772 49 15 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 49 16 ) ) PUNCT cana-772 49 17 βˆ’ βˆ’ NOUN cana-772 49 18 β„Ž(𝑑)𝐼(𝑑)(2.1 β„Ž(𝑑)𝐼(𝑑)(2.1 NOUN cana-772 49 19 ) ) PUNCT cana-772 49 20 in in ADP cana-772 49 21 the the DET cana-772 49 22 equation equation NOUN cana-772 49 23 ( ( PUNCT cana-772 49 24 2.1 2.1 NUM cana-772 49 25 ) ) PUNCT cana-772 49 26 𝑅(𝑑 𝑅(𝑑 NOUN cana-772 49 27 ) ) PUNCT cana-772 49 28 is be AUX cana-772 49 29 the the DET cana-772 49 30 replenishment replenishment NOUN cana-772 49 31 rate rate NOUN cana-772 49 32 , , PUNCT cana-772 49 33 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 49 34 ) ) PUNCT cana-772 49 35 is be AUX cana-772 49 36 the the DET cana-772 49 37 demand demand NOUN cana-772 49 38 rate rate NOUN cana-772 49 39 , , PUNCT cana-772 49 40 𝐼(𝑑 𝐼(𝑑 NUM cana-772 49 41 ) ) PUNCT cana-772 49 42 is be AUX cana-772 49 43 the the DET cana-772 49 44 inventory inventory NOUN cana-772 49 45 level level NOUN cana-772 49 46 . . PUNCT cana-772 50 1 for for ADP cana-772 50 2 dairy dairy NOUN cana-772 50 3 products product NOUN cana-772 50 4 β„Ž(𝑑 β„Ž(𝑑 PROPN cana-772 50 5 ) ) PUNCT cana-772 50 6 is be AUX cana-772 50 7 rate rate NOUN cana-772 50 8 of of ADP cana-772 50 9 spoilage spoilage NOUN cana-772 50 10 or or CCONJ cana-772 50 11 deterioration deterioration NOUN cana-772 50 12 . . PUNCT cana-772 51 1 the the DET cana-772 51 2 above above ADJ cana-772 51 3 equation equation NOUN cana-772 51 4 represents represent VERB cana-772 51 5 continuous continuous ADJ cana-772 51 6 change change NOUN cana-772 51 7 in in ADP cana-772 51 8 inventory inventory NOUN cana-772 51 9 level level NOUN cana-772 51 10 over over ADP cana-772 51 11 the the DET cana-772 51 12 time time NOUN cana-772 51 13 . . PUNCT cana-772 52 1 2 2 X cana-772 52 2 . . X cana-772 52 3 continuous continuous ADJ cana-772 52 4 deterioration deterioration NOUN cana-772 52 5 level level NOUN cana-772 52 6 𝑑𝐢 𝑑𝐢 VERB cana-772 52 7 𝑑𝑑 𝑑𝑑 ADP cana-772 52 8 = = PUNCT cana-772 52 9 ( ( PUNCT cana-772 52 10 1 1 NUM cana-772 52 11 βˆ’ βˆ’ NOUN cana-772 52 12 𝑃(𝑑 𝑃(𝑑 NUM cana-772 52 13 ) ) PUNCT cana-772 52 14 ) ) PUNCT cana-772 52 15 . . PUNCT cana-772 53 1 β„Ž(𝑑 β„Ž(𝑑 PROPN cana-772 53 2 ) ) PUNCT cana-772 53 3 . . PUNCT cana-772 54 1 𝐼(𝑑)(2.2 𝐼(𝑑)(2.2 NOUN cana-772 54 2 ) ) PUNCT cana-772 54 3 in in ADP cana-772 54 4 equation equation NOUN cana-772 54 5 ( ( PUNCT cana-772 54 6 2.2 2.2 NUM cana-772 54 7 ) ) PUNCT cana-772 54 8 β„Ž(𝑑 β„Ž(𝑑 PROPN cana-772 54 9 ) ) PUNCT cana-772 54 10 is be AUX cana-772 54 11 the the DET cana-772 54 12 deterioration deterioration NOUN cana-772 54 13 time time NOUN cana-772 54 14 , , PUNCT cana-772 54 15 𝐼(𝑑 𝐼(𝑑 PRON cana-772 54 16 ) ) PUNCT cana-772 54 17 is be AUX cana-772 54 18 the the DET cana-772 54 19 inventory inventory NOUN cana-772 54 20 level level NOUN cana-772 54 21 , , PUNCT cana-772 54 22 𝑃(𝑑 𝑃(𝑑 NUM cana-772 54 23 ) ) PUNCT cana-772 54 24 is be AUX cana-772 54 25 the the DET cana-772 54 26 preservative preservative ADJ cana-772 54 27 factor factor NOUN cana-772 54 28 . . PUNCT cana-772 55 1 this this DET cana-772 55 2 equation equation NOUN cana-772 55 3 accounts account VERB cana-772 55 4 for for ADP cana-772 55 5 the the DET cana-772 55 6 effects effect NOUN cana-772 55 7 of of ADP cana-772 55 8 a a DET cana-772 55 9 preservative preservative ADJ cana-772 55 10 factor factor NOUN cana-772 55 11 𝑃(𝑑 𝑃(𝑑 ADV cana-772 55 12 ) ) PUNCT cana-772 55 13 on on ADP cana-772 55 14 reducing reduce VERB cana-772 55 15 the the DET cana-772 55 16 deterioration deterioration NOUN cana-772 55 17 rate rate NOUN cana-772 55 18 β„Ž(𝑑 β„Ž(𝑑 PROPN cana-772 55 19 ) ) PUNCT cana-772 55 20 of of ADP cana-772 55 21 dairy dairy NOUN cana-772 55 22 products product NOUN cana-772 55 23 . . PUNCT cana-772 56 1 3 3 X cana-772 56 2 . . X cana-772 56 3 shortage shortage NOUN cana-772 56 4 level level NOUN cana-772 56 5 𝑆(𝑑 𝑆(𝑑 NOUN cana-772 56 6 ) ) PUNCT cana-772 56 7 = = PUNCT cana-772 56 8 π‘šπ‘Žπ‘₯(0 π‘šπ‘Žπ‘₯(0 NOUN cana-772 56 9 , , PUNCT cana-772 56 10 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 56 11 ) ) PUNCT cana-772 56 12 βˆ’ βˆ’ PROPN cana-772 56 13 𝐼(𝑑))(2.3 𝐼(𝑑))(2.3 PROPN cana-772 56 14 ) ) PUNCT cana-772 56 15 in in ADP cana-772 56 16 equation equation NOUN cana-772 56 17 ( ( PUNCT cana-772 56 18 2.3 2.3 NUM cana-772 56 19 ) ) PUNCT cana-772 56 20 𝐼(𝑑 𝐼(𝑑 NUM cana-772 56 21 ) ) PUNCT cana-772 56 22 is be AUX cana-772 56 23 the the DET cana-772 56 24 inventory inventory NOUN cana-772 56 25 level level NOUN cana-772 56 26 and and CCONJ cana-772 56 27 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 56 28 ) ) PUNCT cana-772 56 29 is be AUX cana-772 56 30 the the DET cana-772 56 31 deterioration deterioration NOUN cana-772 56 32 time time NOUN cana-772 56 33 . . PUNCT cana-772 57 1 this this DET cana-772 57 2 equation equation NOUN cana-772 57 3 shows show VERB cana-772 57 4 the the DET cana-772 57 5 shortage shortage NOUN cana-772 57 6 level level NOUN cana-772 57 7 at at ADP cana-772 57 8 time time NOUN cana-772 57 9 t. t. NOUN cana-772 57 10 the the DET cana-772 57 11 above above ADJ cana-772 57 12 equations equation NOUN cana-772 57 13 ( ( PUNCT cana-772 57 14 1 1 NUM cana-772 57 15 ) ) PUNCT cana-772 57 16 , , PUNCT cana-772 57 17 ( ( PUNCT cana-772 57 18 2 2 X cana-772 57 19 ) ) PUNCT cana-772 57 20 and and CCONJ cana-772 57 21 ( ( PUNCT cana-772 57 22 3 3 X cana-772 57 23 ) ) PUNCT cana-772 57 24 helps help VERB cana-772 57 25 firms firm NOUN cana-772 57 26 understand understand VERB cana-772 57 27 the the DET cana-772 57 28 gap gap NOUN cana-772 57 29 between between ADP cana-772 57 30 demand demand NOUN cana-772 57 31 and and CCONJ cana-772 57 32 available available ADJ cana-772 57 33 supply supply NOUN cana-772 57 34 , , PUNCT cana-772 57 35 guiding guide VERB cana-772 57 36 decisions decision NOUN cana-772 57 37 on on ADP cana-772 57 38 inventory inventory NOUN cana-772 57 39 replenishment replenishment NOUN cana-772 57 40 and and CCONJ cana-772 57 41 management management NOUN cana-772 57 42 . . PUNCT cana-772 58 1 these these DET cana-772 58 2 equations equation NOUN cana-772 58 3 provide provide VERB cana-772 58 4 a a DET cana-772 58 5 mathematical mathematical ADJ cana-772 58 6 framework framework NOUN cana-772 58 7 for for ADP cana-772 58 8 analysing analyse VERB cana-772 58 9 the the DET cana-772 58 10 effects effect NOUN cana-772 58 11 of of ADP cana-772 58 12 deterioration deterioration NOUN cana-772 58 13 on on ADP cana-772 58 14 dairy dairy NOUN cana-772 58 15 product product NOUN cana-772 58 16 inventory inventory NOUN cana-772 58 17 , , PUNCT cana-772 58 18 exploring explore VERB cana-772 58 19 preservation preservation NOUN cana-772 58 20 strategies strategy NOUN cana-772 58 21 , , PUNCT cana-772 58 22 and and CCONJ cana-772 58 23 ensuring ensure VERB cana-772 58 24 the the DET cana-772 58 25 availability availability NOUN cana-772 58 26 of of ADP cana-772 58 27 products product NOUN cana-772 58 28 to to PART cana-772 58 29 meet meet VERB cana-772 58 30 demand demand NOUN cana-772 58 31 . . PUNCT cana-772 59 1 by by ADP cana-772 59 2 incorporating incorporate VERB cana-772 59 3 these these DET cana-772 59 4 equations equation NOUN cana-772 59 5 into into ADP cana-772 59 6 inventory inventory NOUN cana-772 59 7 management management NOUN cana-772 59 8 models model NOUN cana-772 59 9 , , PUNCT cana-772 59 10 firms firm NOUN cana-772 59 11 can can AUX cana-772 59 12 optimize optimize VERB cana-772 59 13 their their PRON cana-772 59 14 strategies strategy NOUN cana-772 59 15 to to PART cana-772 59 16 minimize minimize VERB cana-772 59 17 losses loss NOUN cana-772 59 18 due due ADJ cana-772 59 19 to to ADP cana-772 59 20 deterioration deterioration NOUN cana-772 59 21 , , PUNCT cana-772 59 22 maximize maximize VERB cana-772 59 23 product product NOUN cana-772 59 24 quality quality NOUN cana-772 59 25 , , PUNCT cana-772 59 26 and and CCONJ cana-772 59 27 meet meet VERB cana-772 59 28 customer customer NOUN cana-772 59 29 demand demand NOUN cana-772 59 30 effectively effectively ADV cana-772 59 31 . . PUNCT cana-772 60 1 communications communication NOUN cana-772 60 2 on on ADP cana-772 60 3 applied apply VERB cana-772 60 4 nonlinear nonlinear ADJ cana-772 60 5 analysis analysis NOUN cana-772 60 6 issn issn NOUN cana-772 60 7 : : PUNCT cana-772 60 8 1074 1074 NUM cana-772 60 9 - - PUNCT cana-772 60 10 133x 133x NUM cana-772 60 11 vol vol NOUN cana-772 60 12 31 31 NUM cana-772 60 13 no no NOUN cana-772 60 14 . . PUNCT cana-772 61 1 3s 3s NUM cana-772 61 2 ( ( PUNCT cana-772 61 3 2024 2024 NUM cana-772 61 4 ) ) PUNCT cana-772 61 5 328 328 NUM cana-772 61 6 https://internationalpubls.com https://internationalpubls.com X cana-772 61 7 figure figure NOUN cana-772 61 8 1 1 NUM cana-772 61 9 3 3 NUM cana-772 61 10 . . PUNCT cana-772 61 11 model model NOUN cana-772 61 12 formulation formulation NOUN cana-772 61 13 and and CCONJ cana-772 61 14 solution solution NOUN cana-772 61 15 mathematical mathematical ADJ cana-772 61 16 modelling modelling NOUN cana-772 61 17 provides provide VERB cana-772 61 18 a a DET cana-772 61 19 powerful powerful ADJ cana-772 61 20 tool tool NOUN cana-772 61 21 to to PART cana-772 61 22 analyse analyse VERB cana-772 61 23 and and CCONJ cana-772 61 24 optimize optimize VERB cana-772 61 25 inventory inventory NOUN cana-772 61 26 management management NOUN cana-772 61 27 strategies strategy NOUN cana-772 61 28 . . PUNCT cana-772 62 1 the the DET cana-772 62 2 model model NOUN cana-772 62 3 formulation formulation NOUN cana-772 62 4 involves involve VERB cana-772 62 5 expressing express VERB cana-772 62 6 the the DET cana-772 62 7 relationships relationship NOUN cana-772 62 8 between between ADP cana-772 62 9 inventory inventory NOUN cana-772 62 10 levels level NOUN cana-772 62 11 , , PUNCT cana-772 62 12 replenishment replenishment NOUN cana-772 62 13 rates rate NOUN cana-772 62 14 , , PUNCT cana-772 62 15 demand demand NOUN cana-772 62 16 rates rate NOUN cana-772 62 17 , , PUNCT cana-772 62 18 and and CCONJ cana-772 62 19 deterioration deterioration NOUN cana-772 62 20 rates rate NOUN cana-772 62 21 through through ADP cana-772 62 22 differential differential ADJ cana-772 62 23 equations equation NOUN cana-772 62 24 . . PUNCT cana-772 63 1 these these DET cana-772 63 2 equations equation NOUN cana-772 63 3 capture capture VERB cana-772 63 4 the the DET cana-772 63 5 dynamic dynamic ADJ cana-772 63 6 behavior behavior NOUN cana-772 63 7 of of ADP cana-772 63 8 the the DET cana-772 63 9 inventory inventory NOUN cana-772 63 10 system system NOUN cana-772 63 11 over over ADP cana-772 63 12 time time NOUN cana-772 63 13 . . PUNCT cana-772 64 1 the the DET cana-772 64 2 provided provide VERB cana-772 64 3 set set NOUN cana-772 64 4 of of ADP cana-772 64 5 equations equation NOUN cana-772 64 6 represents represent VERB cana-772 64 7 the the DET cana-772 64 8 change change NOUN cana-772 64 9 in in ADP cana-772 64 10 inventory inventory NOUN cana-772 64 11 level level NOUN cana-772 64 12 𝐼𝑑 𝐼𝑑 ADV cana-772 64 13 over over ADP cana-772 64 14 time time NOUN cana-772 64 15 interval interval NOUN cana-772 64 16 [ [ X cana-772 64 17 0 0 NUM cana-772 64 18 , , PUNCT cana-772 64 19 𝑇 𝑇 PROPN cana-772 64 20 ] ] PUNCT cana-772 64 21 for for ADP cana-772 64 22 different different ADJ cana-772 64 23 intervals interval NOUN cana-772 64 24 , , PUNCT cana-772 64 25 each each PRON cana-772 64 26 characterized characterize VERB cana-772 64 27 by by ADP cana-772 64 28 different different ADJ cana-772 64 29 rates rate NOUN cana-772 64 30 of of ADP cana-772 64 31 replenishment replenishment NOUN cana-772 64 32 and and CCONJ cana-772 64 33 demand demand NOUN cana-772 64 34 . . PUNCT cana-772 65 1 let let VERB cana-772 65 2 's us PRON cana-772 65 3 break break VERB cana-772 65 4 down down ADP cana-772 65 5 these these DET cana-772 65 6 equations equation NOUN cana-772 65 7 and and CCONJ cana-772 65 8 their their PRON cana-772 65 9 intervals interval NOUN cana-772 65 10 𝑑𝐼𝑑 𝑑𝐼𝑑 NOUN cana-772 65 11 𝑑𝑑 𝑑𝑑 ADP cana-772 65 12 = = PUNCT cana-772 65 13 { { PUNCT cana-772 65 14 πœƒπΌπ‘‘ πœƒπΌπ‘‘ X cana-772 65 15 βˆ’ βˆ’ PROPN cana-772 65 16 𝑝1 𝑝1 NOUN cana-772 65 17 βˆ’ βˆ’ PROPN cana-772 65 18 π‘Ž π‘Ž NOUN cana-772 65 19 , , PUNCT cana-772 65 20 0 0 NUM cana-772 65 21 ≀ ≀ NUM cana-772 66 1 𝑑 𝑑 PROPN cana-772 66 2 ≀ ≀ NUM cana-772 66 3 𝑑1 𝑑1 NOUN cana-772 66 4 πœƒπΌπ‘‘ πœƒπΌπ‘‘ NOUN cana-772 66 5 βˆ’ βˆ’ PROPN cana-772 66 6 𝑝2 𝑝2 NOUN cana-772 66 7 βˆ’ βˆ’ PROPN cana-772 66 8 π‘Ž π‘Ž NOUN cana-772 66 9 , , PUNCT cana-772 66 10 𝑑1 𝑑1 ADJ cana-772 66 11 ≀ ≀ NUM cana-772 66 12 𝑑 𝑑 PROPN cana-772 66 13 ≀ ≀ NOUN cana-772 66 14 𝑑2 𝑑2 ADJ cana-772 66 15 πœƒπΌπ‘‘ πœƒπΌπ‘‘ PUNCT cana-772 66 16 βˆ’ βˆ’ PROPN cana-772 66 17 π‘Ž π‘Ž NOUN cana-772 66 18 , , PUNCT cana-772 66 19 𝑑2 𝑑2 ADJ cana-772 66 20 ≀ ≀ NUM cana-772 66 21 𝑑 𝑑 PROPN cana-772 66 22 ≀ ≀ PROPN cana-772 66 23 𝑑3 𝑑3 PROPN cana-772 66 24 βˆ’ βˆ’ PROPN cana-772 66 25 π‘Ž π‘Ž PROPN cana-772 66 26 , , PUNCT cana-772 66 27 𝑑3 𝑑3 PROPN cana-772 66 28 ≀ ≀ NUM cana-772 66 29 𝑑 𝑑 PROPN cana-772 66 30 ≀ ≀ ADJ cana-772 66 31 𝑑4 𝑑4 PROPN cana-772 66 32 𝑝2 𝑝2 NOUN cana-772 66 33 βˆ’ βˆ’ PROPN cana-772 66 34 π‘Ž π‘Ž PROPN cana-772 66 35 , , PUNCT cana-772 66 36 𝑑4 𝑑4 PROPN cana-772 66 37 ≀ ≀ NUM cana-772 66 38 𝑑 𝑑 PROPN cana-772 66 39 ≀ ≀ ADJ cana-772 66 40 𝑇 𝑇 PROPN cana-772 66 41 ( ( PUNCT cana-772 66 42 3.1 3.1 NUM cana-772 66 43 ) ) PUNCT cana-772 66 44 the the DET cana-772 66 45 boundary boundary ADJ cana-772 66 46 conditions condition NOUN cana-772 66 47 here here ADV cana-772 66 48 is be AUX cana-772 66 49 𝐼(0 𝐼(0 NOUN cana-772 66 50 ) ) PUNCT cana-772 66 51 = = SYM cana-772 66 52 𝐼0continuity 𝐼0continuity NOUN cana-772 66 53 of of ADP cana-772 66 54 inventory inventory NOUN cana-772 66 55 level level NOUN cana-772 66 56 at at ADP cana-772 66 57 𝑑1 𝑑1 NOUN cana-772 66 58 , , PUNCT cana-772 66 59 𝑑2 𝑑2 PROPN cana-772 66 60 , , PUNCT cana-772 66 61 𝑑3 𝑑3 PROPN cana-772 66 62 ∧ ∧ PROPN cana-772 66 63 𝑑4𝑖𝑠 𝑑4𝑖𝑠 PUNCT cana-772 66 64 𝐼 𝐼 ADP cana-772 66 65 these these DET cana-772 66 66 conditions condition NOUN cana-772 66 67 ensure ensure VERB cana-772 66 68 that that SCONJ cana-772 66 69 the the DET cana-772 66 70 inventory inventory NOUN cana-772 66 71 level level NOUN cana-772 66 72 remains remain VERB cana-772 66 73 continuous continuous ADJ cana-772 66 74 at at ADP cana-772 66 75 the the DET cana-772 66 76 boundaries boundary NOUN cana-772 66 77 of of ADP cana-772 66 78 each each DET cana-772 66 79 time time NOUN cana-772 66 80 interval interval NOUN cana-772 66 81 . . PUNCT cana-772 67 1 the the DET cana-772 67 2 solutions solution NOUN cana-772 67 3 for for ADP cana-772 67 4 the the DET cana-772 67 5 equation equation NOUN cana-772 67 6 ( ( PUNCT cana-772 67 7 3.1 3.1 NUM cana-772 67 8 ) ) PUNCT cana-772 67 9 are be AUX cana-772 67 10 as as SCONJ cana-772 67 11 follows follow VERB cana-772 67 12 : : PUNCT cana-772 67 13 𝐼𝑑 𝐼𝑑 ADP cana-772 67 14 = = PUNCT cana-772 67 15 πœƒ πœƒ PROPN cana-772 67 16 πœƒ πœƒ NOUN cana-772 67 17 βˆ’ βˆ’ PROPN cana-772 67 18 𝑝1 𝑝1 NOUN cana-772 67 19 ( ( PUNCT cana-772 67 20 𝐼0 𝐼0 PROPN cana-772 67 21 βˆ’ βˆ’ PROPN cana-772 67 22 ( ( PUNCT cana-772 67 23 𝑝1 𝑝1 NOUN cana-772 67 24 + + NOUN cana-772 67 25 π‘Ž)π‘’βˆ’πœƒπ‘‘ π‘Ž)π‘’βˆ’πœƒπ‘‘ NOUN cana-772 67 26 ) ) PUNCT cana-772 68 1 + + CCONJ cana-772 68 2 ( ( PUNCT cana-772 68 3 𝑝1 𝑝1 NOUN cana-772 68 4 + + PROPN cana-772 68 5 π‘Ž)π‘’βˆ’πœƒπ‘‘ π‘Ž)π‘’βˆ’πœƒπ‘‘ PROPN cana-772 68 6 , , PUNCT cana-772 68 7 0 0 NUM cana-772 68 8 ≀ ≀ NUM cana-772 68 9 𝑑 𝑑 PROPN cana-772 68 10 ≀ ≀ ADJ cana-772 68 11 𝑑1 𝑑1 NOUN cana-772 68 12 ( ( PUNCT cana-772 68 13 3.3 3.3 NUM cana-772 68 14 ) ) PUNCT cana-772 68 15 πΆπ‘’πœƒ(π‘‘βˆ’π‘‘1 πΆπ‘’πœƒ(π‘‘βˆ’π‘‘1 ADP cana-772 68 16 ) ) PUNCT cana-772 68 17 + + NUM cana-772 68 18 𝑝2 𝑝2 NOUN cana-772 68 19 + + CCONJ cana-772 68 20 π‘Ž π‘Ž PROPN cana-772 68 21 πœƒ πœƒ NOUN cana-772 68 22 , , PUNCT cana-772 68 23 𝑑1 𝑑1 ADJ cana-772 68 24 ≀ ≀ NUM cana-772 68 25 𝑑 𝑑 PROPN cana-772 68 26 ≀ ≀ NOUN cana-772 68 27 𝑑2 𝑑2 NOUN cana-772 68 28 ( ( PUNCT cana-772 68 29 3.4 3.4 NUM cana-772 68 30 ) ) PUNCT cana-772 68 31 π·π‘’πœƒ(π‘‘βˆ’π‘‘2 π·π‘’πœƒ(π‘‘βˆ’π‘‘2 NOUN cana-772 68 32 ) ) PUNCT cana-772 68 33 + + CCONJ cana-772 68 34 π‘Ž π‘Ž X cana-772 68 35 πœƒ πœƒ NOUN cana-772 68 36 , , PUNCT cana-772 68 37 𝑑2 𝑑2 ADJ cana-772 68 38 ≀ ≀ NUM cana-772 68 39 𝑑 𝑑 PROPN cana-772 68 40 ≀ ≀ PROPN cana-772 68 41 𝑑3 𝑑3 PROPN cana-772 68 42 ( ( PUNCT cana-772 68 43 3.5 3.5 NUM cana-772 68 44 ) ) PUNCT cana-772 68 45 βˆ’π‘Žπ‘‘ βˆ’π‘Žπ‘‘ NOUN cana-772 68 46 + + CCONJ cana-772 68 47 𝐸 𝐸 PROPN cana-772 68 48 , , PUNCT cana-772 68 49 𝑑3 𝑑3 PROPN cana-772 68 50 ≀ ≀ NUM cana-772 68 51 𝑑 𝑑 PROPN cana-772 68 52 ≀ ≀ ADJ cana-772 68 53 𝑑4 𝑑4 NOUN cana-772 68 54 ( ( PUNCT cana-772 68 55 3.6 3.6 NUM cana-772 68 56 ) ) PUNCT cana-772 68 57 𝑝2 𝑝2 NOUN cana-772 68 58 βˆ’ βˆ’ NOUN cana-772 68 59 π‘Ž π‘Ž NOUN cana-772 68 60 πœƒ πœƒ X cana-772 68 61 ( ( PUNCT cana-772 68 62 1 1 NUM cana-772 68 63 βˆ’ βˆ’ PROPN cana-772 68 64 π‘’βˆ’πœƒ(π‘‘βˆ’π‘‘4 π‘’βˆ’πœƒ(π‘‘βˆ’π‘‘4 NOUN cana-772 68 65 ) ) PUNCT cana-772 68 66 ) ) PUNCT cana-772 69 1 + + CCONJ cana-772 69 2 𝐹 𝐹 PROPN cana-772 69 3 ( ( PUNCT cana-772 69 4 3.7 3.7 NUM cana-772 69 5 ) ) PUNCT cana-772 69 6 in in ADP cana-772 69 7 the the DET cana-772 69 8 above above ADJ cana-772 69 9 equations equation NOUN cana-772 69 10 ( ( PUNCT cana-772 69 11 3.4 3.4 NUM cana-772 69 12 ) ) PUNCT cana-772 69 13 , , PUNCT cana-772 69 14 ( ( PUNCT cana-772 69 15 3.5 3.5 NUM cana-772 69 16 ) ) PUNCT cana-772 69 17 , , PUNCT cana-772 69 18 ( ( PUNCT cana-772 69 19 3.6 3.6 NUM cana-772 69 20 ) ) PUNCT cana-772 69 21 , , PUNCT cana-772 69 22 ( ( PUNCT cana-772 69 23 3.7 3.7 NUM cana-772 69 24 ) ) PUNCT cana-772 69 25 c c NOUN cana-772 69 26 , , PUNCT cana-772 69 27 d d NOUN cana-772 69 28 , , PUNCT cana-772 69 29 e e NOUN cana-772 69 30 , , PUNCT cana-772 69 31 f f PROPN cana-772 69 32 are be AUX cana-772 69 33 the the DET cana-772 69 34 constants constant NOUN cana-772 69 35 determined determine VERB cana-772 69 36 by by ADP cana-772 69 37 the the DET cana-772 69 38 continuity continuity NOUN cana-772 69 39 conditions condition NOUN cana-772 69 40 . . PUNCT cana-772 70 1 communications communication NOUN cana-772 70 2 on on ADP cana-772 70 3 applied apply VERB cana-772 70 4 nonlinear nonlinear ADJ cana-772 70 5 analysis analysis NOUN cana-772 70 6 issn issn NOUN cana-772 70 7 : : PUNCT cana-772 70 8 1074 1074 NUM cana-772 70 9 - - PUNCT cana-772 70 10 133x 133x NUM cana-772 70 11 vol vol NOUN cana-772 70 12 31 31 NUM cana-772 70 13 no no NOUN cana-772 70 14 . . PUNCT cana-772 71 1 3s 3s NUM cana-772 71 2 ( ( PUNCT cana-772 71 3 2024 2024 NUM cana-772 71 4 ) ) PUNCT cana-772 71 5 329 329 NUM cana-772 71 6 https://internationalpubls.com https://internationalpubls.com X cana-772 71 7 the the DET cana-772 71 8 solutions solution NOUN cana-772 71 9 for for ADP cana-772 71 10 the the DET cana-772 71 11 inventory inventory NOUN cana-772 71 12 level level NOUN cana-772 71 13 equations equation NOUN cana-772 71 14 ( ( PUNCT cana-772 71 15 3.3 3.3 NUM cana-772 71 16 ) ) PUNCT cana-772 71 17 to to ADP cana-772 71 18 ( ( PUNCT cana-772 71 19 3.7 3.7 NUM cana-772 71 20 ) ) PUNCT cana-772 71 21 offer offer VERB cana-772 71 22 insights insight NOUN cana-772 71 23 into into ADP cana-772 71 24 the the DET cana-772 71 25 effects effect NOUN cana-772 71 26 of of ADP cana-772 71 27 deterioration deterioration NOUN cana-772 71 28 on on ADP cana-772 71 29 inventory inventory NOUN cana-772 71 30 dynamics dynamic NOUN cana-772 71 31 . . PUNCT cana-772 72 1 by by ADP cana-772 72 2 introducing introduce VERB cana-772 72 3 preservation preservation NOUN cana-772 72 4 factors factor NOUN cana-772 72 5 𝑃(𝑑 𝑃(𝑑 NUM cana-772 72 6 ) ) PUNCT cana-772 72 7 into into ADP cana-772 72 8 the the DET cana-772 72 9 deterioration deterioration NOUN cana-772 72 10 term term NOUN cana-772 72 11 of of ADP cana-772 72 12 the the DET cana-772 72 13 differential differential ADJ cana-772 72 14 equation equation NOUN cana-772 72 15 , , PUNCT cana-772 72 16 we we PRON cana-772 72 17 can can AUX cana-772 72 18 modify modify VERB cana-772 72 19 the the DET cana-772 72 20 deterioration deterioration NOUN cana-772 72 21 rate rate NOUN cana-772 72 22 and and CCONJ cana-772 72 23 observe observe VERB cana-772 72 24 how how SCONJ cana-772 72 25 it it PRON cana-772 72 26 affects affect VERB cana-772 72 27 the the DET cana-772 72 28 inventory inventory NOUN cana-772 72 29 over over ADP cana-772 72 30 time time NOUN cana-772 72 31 . . PUNCT cana-772 73 1 this this PRON cana-772 73 2 allows allow VERB cana-772 73 3 us we PRON cana-772 73 4 to to PART cana-772 73 5 analyse analyse VERB cana-772 73 6 how how SCONJ cana-772 73 7 different different ADJ cana-772 73 8 preservation preservation NOUN cana-772 73 9 methods method NOUN cana-772 73 10 can can AUX cana-772 73 11 help help VERB cana-772 73 12 mitigate mitigate VERB cana-772 73 13 the the DET cana-772 73 14 impact impact NOUN cana-772 73 15 of of ADP cana-772 73 16 deterioration deterioration NOUN cana-772 73 17 . . PUNCT cana-772 74 1 𝑑𝐼𝑑 𝑑𝐼𝑑 NOUN cana-772 74 2 𝑑𝑑 𝑑𝑑 ADP cana-772 74 3 = = NOUN cana-772 74 4 𝑃(𝑑 𝑃(𝑑 NUM cana-772 74 5 ) ) PUNCT cana-772 74 6 . . PUNCT cana-772 75 1 ( ( PUNCT cana-772 75 2 πœƒπΌπ‘‘ πœƒπΌπ‘‘ X cana-772 75 3 βˆ’ βˆ’ PROPN cana-772 75 4 𝑝1 𝑝1 NOUN cana-772 75 5 βˆ’ βˆ’ PROPN cana-772 75 6 π‘Ž π‘Ž NOUN cana-772 75 7 ) ) PUNCT cana-772 75 8 ( ( PUNCT cana-772 75 9 3.8 3.8 NUM cana-772 75 10 ) ) PUNCT cana-772 75 11 the the DET cana-772 75 12 boundary boundary ADJ cana-772 75 13 condition condition NOUN cana-772 75 14 here here ADV cana-772 75 15 is be AUX cana-772 75 16 𝐼(0 𝐼(0 NOUN cana-772 75 17 ) ) PUNCT cana-772 75 18 = = SYM cana-772 75 19 𝐼0 𝐼0 ADJ cana-772 75 20 here here ADV cana-772 75 21 𝐼0 𝐼0 PROPN cana-772 76 1 = = SYM cana-772 76 2 𝐢1 𝐢1 NOUN cana-772 76 3 separating separate VERB cana-772 76 4 the the DET cana-772 76 5 variable variable ADJ cana-772 76 6 𝑑𝐼 𝑑𝐼 NOUN cana-772 76 7 πœƒπΌπ‘‘ πœƒπΌπ‘‘ PRON cana-772 76 8 βˆ’ βˆ’ PROPN cana-772 76 9 𝑝1βˆ’π‘Ž 𝑝1βˆ’π‘Ž PROPN cana-772 76 10 = = PUNCT cana-772 76 11 𝑃(𝑑)𝑑𝑑 𝑃(𝑑)𝑑𝑑 NOUN cana-772 76 12 ( ( PUNCT cana-772 76 13 3.9 3.9 NUM cana-772 76 14 ) ) PUNCT cana-772 76 15 ∫ ∫ PROPN cana-772 76 16 ⬚ ⬚ PROPN cana-772 76 17 ⬚ ⬚ PROPN cana-772 76 18 ⬚ ⬚ PROPN cana-772 76 19 𝑑𝐼 𝑑𝐼 ADJ cana-772 76 20 πœƒπΌπ‘‘ πœƒπΌπ‘‘ PRON cana-772 76 21 βˆ’ βˆ’ PROPN cana-772 76 22 𝑝1 𝑝1 NOUN cana-772 76 23 βˆ’ βˆ’ PROPN cana-772 76 24 π‘Ž π‘Ž PROPN cana-772 76 25 = = SYM cana-772 76 26 ∫ ∫ PROPN cana-772 76 27 ⬚ ⬚ PROPN cana-772 76 28 ⬚ ⬚ PROPN cana-772 76 29 ⬚ ⬚ PROPN cana-772 76 30 𝑃(𝑑)𝑑𝑑 𝑃(𝑑)𝑑𝑑 NOUN cana-772 76 31 ( ( PUNCT cana-772 76 32 3.10 3.10 NUM cana-772 76 33 ) ) PUNCT cana-772 76 34 here here ADV cana-772 76 35 𝑒 𝑒 X cana-772 76 36 = = SYM cana-772 76 37 πœƒπΌπ‘‘ πœƒπΌπ‘‘ PUNCT cana-772 76 38 βˆ’ βˆ’ PROPN cana-772 76 39 𝑝1βˆ’π‘Ž 𝑝1βˆ’π‘Ž PROPN cana-772 76 40 then then ADV cana-772 76 41 𝑑𝑒 𝑑𝑒 PROPN cana-772 77 1 = = SYM cana-772 77 2 πœƒπ‘‘πΌ πœƒπ‘‘πΌ PROPN cana-772 77 3 then then ADV cana-772 77 4 , , PUNCT cana-772 77 5 ∫ ∫ PROPN cana-772 77 6 ⬚ ⬚ PROPN cana-772 77 7 ⬚ ⬚ PROPN cana-772 77 8 ⬚ ⬚ PROPN cana-772 77 9 1 1 NUM cana-772 77 10 𝑒 𝑒 NOUN cana-772 77 11 𝑑𝑒 𝑑𝑒 NOUN cana-772 77 12 = = SYM cana-772 77 13 πœƒ πœƒ PROPN cana-772 77 14 ∫ ∫ PROPN cana-772 77 15 ⬚ ⬚ PROPN cana-772 77 16 ⬚ ⬚ PROPN cana-772 77 17 ⬚ ⬚ PROPN cana-772 77 18 𝑑𝑑 𝑑𝑑 ADP cana-772 77 19 ( ( PUNCT cana-772 77 20 3.11 3.11 NUM cana-772 77 21 ) ) PUNCT cana-772 77 22 𝑙𝑛|𝑒| 𝑙𝑛|𝑒| NOUN cana-772 78 1 = = PUNCT cana-772 78 2 πœƒπ‘‘ πœƒπ‘‘ PROPN cana-772 78 3 + + CCONJ cana-772 78 4 𝐢1 𝐢1 NUM cana-772 78 5 ( ( PUNCT cana-772 78 6 3.12 3.12 NUM cana-772 78 7 ) ) PUNCT cana-772 78 8 𝐢1 𝐢1 PROPN cana-772 78 9 is be AUX cana-772 78 10 the the DET cana-772 78 11 constant constant ADJ cana-772 78 12 of of ADP cana-772 78 13 integration integration NOUN cana-772 78 14 providing provide VERB cana-772 78 15 exponentials exponential NOUN cana-772 78 16 on on ADP cana-772 78 17 both both CCONJ cana-772 78 18 the the DET cana-772 78 19 side side NOUN cana-772 78 20 on on ADP cana-772 78 21 equation equation NOUN cana-772 78 22 ( ( PUNCT cana-772 78 23 3.12 3.12 NUM cana-772 78 24 ) ) PUNCT cana-772 79 1 |𝑒| |𝑒| NOUN cana-772 79 2 = = SYM cana-772 79 3 π‘’πœƒπ‘‘+𝐢1 π‘’πœƒπ‘‘+𝐢1 PROPN cana-772 79 4 ( ( PUNCT cana-772 79 5 3.13 3.13 NUM cana-772 79 6 ) ) PUNCT cana-772 79 7 removing remove VERB cana-772 79 8 absolute absolute ADJ cana-772 79 9 value value NOUN cana-772 79 10 from from ADP cana-772 79 11 the the DET cana-772 79 12 equation equation NOUN cana-772 79 13 ( ( PUNCT cana-772 79 14 3.13 3.13 NUM cana-772 79 15 ) ) PUNCT cana-772 79 16 𝑒 𝑒 PROPN cana-772 79 17 = = SYM cana-772 79 18 Β±π‘’πœƒπ‘‘+𝐢1 Β±π‘’πœƒπ‘‘+𝐢1 PROPN cana-772 79 19 ( ( PUNCT cana-772 79 20 3.14 3.14 NUM cana-772 79 21 ) ) PUNCT cana-772 79 22 denoting denote VERB cana-772 79 23 𝐢2 𝐢2 ADV cana-772 80 1 = = PUNCT cana-772 80 2 ±𝑒𝐢1 ±𝑒𝐢1 PROPN cana-772 80 3 so so SCONJ cana-772 80 4 the the DET cana-772 80 5 equation equation NOUN cana-772 80 6 ( ( PUNCT cana-772 80 7 3.14 3.14 NUM cana-772 80 8 ) ) PUNCT cana-772 80 9 becomes become VERB cana-772 80 10 , , PUNCT cana-772 80 11 πœƒπΌ πœƒπΌ ADJ cana-772 80 12 βˆ’ βˆ’ NOUN cana-772 81 1 𝑝1 𝑝1 NOUN cana-772 82 1 βˆ’ βˆ’ NOUN cana-772 82 2 π‘Ž π‘Ž NOUN cana-772 82 3 = = SYM cana-772 82 4 𝐢2π‘’πœƒπ‘‘ 𝐢2π‘’πœƒπ‘‘ PROPN cana-772 82 5 ( ( PUNCT cana-772 82 6 3.15 3.15 NUM cana-772 82 7 ) ) PUNCT cana-772 82 8 rearranging rearrange VERB cana-772 82 9 equation equation NOUN cana-772 82 10 ( ( PUNCT cana-772 82 11 3.12 3.12 NUM cana-772 82 12 ) ) PUNCT cana-772 82 13 in in ADP cana-772 82 14 order order NOUN cana-772 82 15 to to PART cana-772 82 16 solve solve VERB cana-772 82 17 𝐼 𝐼 ADP cana-772 82 18 𝐼 𝐼 PROPN cana-772 82 19 = = PUNCT cana-772 82 20 𝐢2π‘’πœƒπ‘‘ 𝐢2π‘’πœƒπ‘‘ PROPN cana-772 82 21 + + CCONJ cana-772 82 22 𝑝1 𝑝1 NOUN cana-772 82 23 + + CCONJ cana-772 82 24 π‘Ž π‘Ž PROPN cana-772 82 25 πœƒ πœƒ NOUN cana-772 82 26 ( ( PUNCT cana-772 82 27 3.16 3.16 NUM cana-772 82 28 ) ) PUNCT cana-772 82 29 this this PRON cana-772 82 30 the the DET cana-772 82 31 general general ADJ cana-772 82 32 equation equation NOUN cana-772 82 33 ( ( PUNCT cana-772 82 34 3.16 3.16 NUM cana-772 82 35 ) ) PUNCT cana-772 82 36 for for ADP cana-772 82 37 i(t i(t NOUN cana-772 82 38 ) ) PUNCT cana-772 82 39 . . PUNCT cana-772 83 1 to to PART cana-772 83 2 find find VERB cana-772 83 3 specific specific ADJ cana-772 83 4 solution solution NOUN cana-772 83 5 , , PUNCT cana-772 83 6 we we PRON cana-772 83 7 consider consider VERB cana-772 83 8 initial initial ADJ cana-772 83 9 condition condition NOUN cana-772 83 10 𝐼(0 𝐼(0 NOUN cana-772 83 11 ) ) PUNCT cana-772 83 12 = = SYM cana-772 84 1 𝐼0 𝐼0 PROPN cana-772 84 2 applying apply VERB cana-772 84 3 initial initial ADJ cana-772 84 4 conditions condition NOUN cana-772 84 5 with with ADP cana-772 84 6 𝑑 𝑑 PROPN cana-772 84 7 = = SYM cana-772 84 8 0 0 NUM cana-772 84 9 and and CCONJ cana-772 84 10 𝐼 𝐼 PROPN cana-772 84 11 = = PUNCT cana-772 84 12 𝐼0 𝐼0 ADJ cana-772 84 13 in in ADP cana-772 84 14 the the DET cana-772 84 15 general general ADJ cana-772 84 16 equation equation NOUN cana-772 84 17 ( ( PUNCT cana-772 84 18 3.16 3.16 NUM cana-772 84 19 ) ) PUNCT cana-772 84 20 𝐼0 𝐼0 NOUN cana-772 84 21 = = SYM cana-772 84 22 𝐢2π‘’πœƒπ‘‘ 𝐢2π‘’πœƒπ‘‘ PROPN cana-772 84 23 + + CCONJ cana-772 84 24 𝑝1 𝑝1 NOUN cana-772 84 25 + + CCONJ cana-772 84 26 π‘Ž π‘Ž PROPN cana-772 84 27 πœƒ πœƒ NOUN cana-772 84 28 ( ( PUNCT cana-772 84 29 3.17 3.17 NUM cana-772 84 30 ) ) PUNCT cana-772 84 31 solving solve VERB cana-772 84 32 equation equation NOUN cana-772 84 33 ( ( PUNCT cana-772 84 34 3.17 3.17 NUM cana-772 84 35 ) ) PUNCT cana-772 84 36 for for ADP cana-772 84 37 𝐢2 𝐢2 PROPN cana-772 84 38 communications communication NOUN cana-772 84 39 on on ADP cana-772 84 40 applied apply VERB cana-772 84 41 nonlinear nonlinear ADJ cana-772 84 42 analysis analysis NOUN cana-772 84 43 issn issn NOUN cana-772 84 44 : : PUNCT cana-772 84 45 1074 1074 NUM cana-772 84 46 - - PUNCT cana-772 84 47 133x 133x NUM cana-772 84 48 vol vol NOUN cana-772 84 49 31 31 NUM cana-772 84 50 no no NOUN cana-772 84 51 . . PUNCT cana-772 85 1 3s 3s NUM cana-772 85 2 ( ( PUNCT cana-772 85 3 2024 2024 NUM cana-772 85 4 ) ) PUNCT cana-772 85 5 330 330 NUM cana-772 85 6 https://internationalpubls.com https://internationalpubls.com X cana-772 85 7 𝐢2 𝐢2 PROPN cana-772 85 8 = = SYM cana-772 85 9 πœƒπΌ0 πœƒπΌ0 PROPN cana-772 85 10 βˆ’ βˆ’ PROPN cana-772 85 11 𝑝1 𝑝1 NOUN cana-772 85 12 βˆ’ βˆ’ PROPN cana-772 85 13 π‘Ž π‘Ž X cana-772 85 14 ( ( PUNCT cana-772 85 15 3.18 3.18 NUM cana-772 85 16 ) ) PUNCT cana-772 85 17 substituting substitute VERB cana-772 85 18 the the DET cana-772 85 19 value value NOUN cana-772 85 20 of of ADP cana-772 85 21 𝐢2 𝐢2 INTJ cana-772 85 22 in in ADP cana-772 85 23 general general ADJ cana-772 85 24 equation equation NOUN cana-772 85 25 ( ( PUNCT cana-772 85 26 3.16 3.16 NUM cana-772 85 27 ) ) PUNCT cana-772 85 28 𝐼(𝑑 𝐼(𝑑 NUM cana-772 85 29 ) ) PUNCT cana-772 85 30 = = SYM cana-772 85 31 ( ( PUNCT cana-772 85 32 πœƒπΌ0 πœƒπΌ0 PROPN cana-772 85 33 βˆ’ βˆ’ PROPN cana-772 85 34 𝑝1 𝑝1 NOUN cana-772 85 35 βˆ’ βˆ’ PROPN cana-772 85 36 π‘Ž)π‘’πœƒπ‘‘ π‘Ž)π‘’πœƒπ‘‘ NOUN cana-772 85 37 + + CCONJ cana-772 85 38 𝑝1 𝑝1 NOUN cana-772 85 39 + + CCONJ cana-772 85 40 π‘Ž π‘Ž PROPN cana-772 85 41 πœƒ πœƒ NOUN cana-772 85 42 ( ( PUNCT cana-772 85 43 3.19 3.19 NUM cana-772 85 44 ) ) PUNCT cana-772 85 45 now now ADV cana-772 85 46 solving solve VERB cana-772 85 47 this this DET cana-772 85 48 equation equation NOUN cana-772 85 49 ( ( PUNCT cana-772 85 50 3.19 3.19 NUM cana-772 85 51 ) ) PUNCT cana-772 85 52 𝑃(𝑑 𝑃(𝑑 NUM cana-772 85 53 ) ) PUNCT cana-772 85 54 = = NOUN cana-772 85 55 𝑃0 𝑃0 NOUN cana-772 85 56 for for ADP cana-772 85 57 simplicity simplicity NOUN cana-772 85 58 , , PUNCT cana-772 85 59 assuming assume VERB cana-772 85 60 its its PRON cana-772 85 61 constant constant ADJ cana-772 85 62 over over ADP cana-772 85 63 each each DET cana-772 85 64 time time NOUN cana-772 85 65 interval interval NOUN cana-772 85 66 . . PUNCT cana-772 86 1 πœƒ πœƒ X cana-772 86 2 , , PUNCT cana-772 86 3 𝑝1 𝑝1 NOUN cana-772 86 4 , , PUNCT cana-772 86 5 π‘Ž π‘Ž PROPN cana-772 86 6 , , PUNCT cana-772 86 7 𝐼0 𝐼0 ADJ cana-772 86 8 are be AUX cana-772 86 9 the the DET cana-772 86 10 given give VERB cana-772 86 11 constants constant NOUN cana-772 86 12 . . PUNCT cana-772 87 1 substituting substitute VERB cana-772 87 2 the the DET cana-772 87 3 values value NOUN cana-772 87 4 in in ADP cana-772 87 5 equation equation NOUN cana-772 87 6 ( ( PUNCT cana-772 87 7 3.19 3.19 NUM cana-772 87 8 ) ) PUNCT cana-772 87 9 for for ADP cana-772 87 10 different different ADJ cana-772 87 11 time time NOUN cana-772 87 12 intervals interval NOUN cana-772 87 13 . . PUNCT cana-772 88 1 for for ADP cana-772 88 2 0 0 NUM cana-772 88 3 ≀ ≀ NUM cana-772 88 4 𝑑 𝑑 PROPN cana-772 88 5 ≀ ≀ ADJ cana-772 88 6 𝑑1 𝑑1 NOUN cana-772 88 7 𝐼(𝑇 𝐼(𝑇 NOUN cana-772 88 8 ) ) PUNCT cana-772 88 9 = = SYM cana-772 88 10 ( ( PUNCT cana-772 88 11 πœƒπΌ0 πœƒπΌ0 PROPN cana-772 88 12 βˆ’ βˆ’ PROPN cana-772 88 13 𝑝1 𝑝1 NOUN cana-772 88 14 βˆ’ βˆ’ PROPN cana-772 88 15 π‘Ž)π‘’πœƒπ‘‡ π‘Ž)π‘’πœƒπ‘‡ X cana-772 89 1 + + CCONJ cana-772 89 2 𝑝1 𝑝1 NOUN cana-772 89 3 + + CCONJ cana-772 89 4 π‘Ž π‘Ž PROPN cana-772 89 5 πœƒ πœƒ NOUN cana-772 89 6 ( ( PUNCT cana-772 89 7 3.20 3.20 NUM cana-772 89 8 ) ) PUNCT cana-772 89 9 for for ADP cana-772 89 10 𝑑1 𝑑1 NOUN cana-772 89 11 ≀ ≀ NUM cana-772 90 1 𝑑 𝑑 PROPN cana-772 90 2 ≀ ≀ ADJ cana-772 90 3 𝑑2 𝑑2 ADJ cana-772 90 4 𝐼(𝑇 𝐼(𝑇 NOUN cana-772 90 5 ) ) PUNCT cana-772 90 6 = = SYM cana-772 90 7 ( ( PUNCT cana-772 90 8 πœƒπΌ(𝑑1 πœƒπΌ(𝑑1 PROPN cana-772 90 9 ) ) PUNCT cana-772 91 1 βˆ’ βˆ’ PROPN cana-772 91 2 𝑝1 𝑝1 NOUN cana-772 91 3 βˆ’ βˆ’ PROPN cana-772 91 4 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘1 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘1 NUM cana-772 91 5 ) ) PUNCT cana-772 92 1 + + CCONJ cana-772 92 2 𝑝1 𝑝1 NOUN cana-772 92 3 + + CCONJ cana-772 92 4 π‘Ž π‘Ž PROPN cana-772 92 5 πœƒ πœƒ NOUN cana-772 92 6 ( ( PUNCT cana-772 92 7 3.21 3.21 NUM cana-772 92 8 ) ) PUNCT cana-772 92 9 for for ADP cana-772 92 10 𝑑2 𝑑2 ADJ cana-772 92 11 ≀ ≀ NUM cana-772 92 12 𝑑 𝑑 PROPN cana-772 92 13 ≀ ≀ PROPN cana-772 92 14 𝑑3 𝑑3 NOUN cana-772 92 15 𝐼(𝑇 𝐼(𝑇 NOUN cana-772 92 16 ) ) PUNCT cana-772 92 17 = = SYM cana-772 92 18 ( ( PUNCT cana-772 92 19 πœƒπΌ(𝑑2 πœƒπΌ(𝑑2 PROPN cana-772 92 20 ) ) PUNCT cana-772 93 1 βˆ’ βˆ’ PROPN cana-772 93 2 𝑝1 𝑝1 NOUN cana-772 93 3 βˆ’ βˆ’ NOUN cana-772 93 4 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘2 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘2 NOUN cana-772 93 5 ) ) PUNCT cana-772 94 1 + + CCONJ cana-772 94 2 𝑝1 𝑝1 NOUN cana-772 94 3 + + CCONJ cana-772 94 4 π‘Ž π‘Ž PROPN cana-772 94 5 πœƒ πœƒ NOUN cana-772 94 6 ( ( PUNCT cana-772 94 7 3.22 3.22 NUM cana-772 94 8 ) ) PUNCT cana-772 94 9 for for ADP cana-772 94 10 𝑑3 𝑑3 PROPN cana-772 94 11 ≀ ≀ NUM cana-772 95 1 𝑑 𝑑 PROPN cana-772 95 2 ≀ ≀ ADJ cana-772 95 3 𝑑4 𝑑4 NOUN cana-772 95 4 𝐼(𝑇 𝐼(𝑇 NOUN cana-772 95 5 ) ) PUNCT cana-772 95 6 = = SYM cana-772 95 7 ( ( PUNCT cana-772 95 8 πœƒπΌ(𝑑3 πœƒπΌ(𝑑3 NOUN cana-772 95 9 ) ) PUNCT cana-772 95 10 βˆ’ βˆ’ PROPN cana-772 95 11 𝑝1 𝑝1 NOUN cana-772 95 12 βˆ’ βˆ’ PROPN cana-772 95 13 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘3 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘3 PROPN cana-772 95 14 ) ) PUNCT cana-772 96 1 + + CCONJ cana-772 96 2 𝑝1 𝑝1 NOUN cana-772 96 3 + + CCONJ cana-772 96 4 π‘Ž π‘Ž PROPN cana-772 96 5 πœƒ πœƒ NOUN cana-772 96 6 ( ( PUNCT cana-772 96 7 3.23 3.23 NUM cana-772 96 8 ) ) PUNCT cana-772 96 9 for for ADP cana-772 96 10 𝑑4 𝑑4 NOUN cana-772 96 11 ≀ ≀ NUM cana-772 96 12 𝑑 𝑑 PROPN cana-772 96 13 ≀ ≀ ADJ cana-772 96 14 𝑇 𝑇 PROPN cana-772 96 15 𝐼(𝑇 𝐼(𝑇 NOUN cana-772 96 16 ) ) PUNCT cana-772 96 17 = = SYM cana-772 96 18 ( ( PUNCT cana-772 96 19 πœƒπΌ(𝑑4 πœƒπΌ(𝑑4 PROPN cana-772 96 20 ) ) PUNCT cana-772 96 21 βˆ’ βˆ’ PROPN cana-772 96 22 𝑝1 𝑝1 NOUN cana-772 96 23 βˆ’ βˆ’ PROPN cana-772 96 24 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘4 π‘Ž)π‘’πœƒ(π‘‡βˆ’π‘‘4 PROPN cana-772 96 25 ) ) PUNCT cana-772 96 26 + + CCONJ cana-772 96 27 𝑝1 𝑝1 NOUN cana-772 96 28 + + CCONJ cana-772 96 29 π‘Ž π‘Ž PROPN cana-772 96 30 πœƒ πœƒ NOUN cana-772 96 31 ( ( PUNCT cana-772 96 32 3.24 3.24 NUM cana-772 96 33 ) ) PUNCT cana-772 96 34 the the DET cana-772 96 35 equation equation NOUN cana-772 96 36 ( ( PUNCT cana-772 96 37 3.21 3.21 NUM cana-772 96 38 ) ) PUNCT cana-772 96 39 , , PUNCT cana-772 96 40 ( ( PUNCT cana-772 96 41 3.22 3.22 NUM cana-772 96 42 ) ) PUNCT cana-772 96 43 , , PUNCT cana-772 96 44 ( ( PUNCT cana-772 96 45 3.23 3.23 NUM cana-772 96 46 ) ) PUNCT cana-772 96 47 and and CCONJ cana-772 96 48 ( ( PUNCT cana-772 96 49 3.24 3.24 NUM cana-772 96 50 ) ) PUNCT cana-772 96 51 provides provide VERB cana-772 96 52 the the DET cana-772 96 53 value value NOUN cana-772 96 54 of of ADP cana-772 96 55 i(t i(t NOUN cana-772 96 56 ) ) PUNCT cana-772 96 57 for for ADP cana-772 96 58 different different ADJ cana-772 96 59 time time NOUN cana-772 96 60 intervals interval NOUN cana-772 96 61 . . PUNCT cana-772 97 1 this this DET cana-772 97 2 equation equation NOUN cana-772 97 3 solved solve VERB cana-772 97 4 based base VERB cana-772 97 5 on on ADP cana-772 97 6 initial initial ADJ cana-772 97 7 conditions condition NOUN cana-772 97 8 and and CCONJ cana-772 97 9 given give VERB cana-772 97 10 parameters parameter NOUN cana-772 97 11 . . PUNCT cana-772 98 1 shortage shortage NOUN cana-772 98 2 level level NOUN cana-772 98 3 equation equation NOUN cana-772 98 4 𝑆(𝑑 𝑆(𝑑 NOUN cana-772 98 5 ) ) PUNCT cana-772 98 6 = = PUNCT cana-772 99 1 π‘šπ‘Žπ‘₯(0 π‘šπ‘Žπ‘₯(0 NOUN cana-772 99 2 , , PUNCT cana-772 99 3 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 99 4 ) ) PUNCT cana-772 99 5 βˆ’ βˆ’ PROPN cana-772 99 6 𝐼(𝑑 𝐼(𝑑 NUM cana-772 99 7 ) ) PUNCT cana-772 99 8 ) ) PUNCT cana-772 100 1 here here ADV cana-772 100 2 , , PUNCT cana-772 100 3 considering consider VERB cana-772 100 4 the the DET cana-772 100 5 cases case NOUN cana-772 100 6 where where SCONJ cana-772 100 7 demand demand NOUN cana-772 100 8 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 100 9 ) ) PUNCT cana-772 100 10 exceeds exceed VERB cana-772 100 11 inventory inventory NOUN cana-772 100 12 level level NOUN cana-772 100 13 𝐼(𝑑 𝐼(𝑑 PROPN cana-772 100 14 ) ) PUNCT cana-772 100 15 and and CCONJ cana-772 100 16 where where SCONJ cana-772 100 17 inventory inventory NOUN cana-772 100 18 level level NOUN cana-772 100 19 is be AUX cana-772 100 20 sufficient sufficient ADJ cana-772 100 21 to to PART cana-772 100 22 meet meet VERB cana-772 100 23 demand demand NOUN cana-772 100 24 . . PUNCT cana-772 101 1 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 101 2 ) ) PUNCT cana-772 101 3 ≀ ≀ NOUN cana-772 102 1 𝐼(𝑑 𝐼(𝑑 NUM cana-772 102 2 ) ) PUNCT cana-772 102 3 there there PRON cana-772 102 4 is be VERB cana-772 102 5 no no DET cana-772 102 6 shortage shortage NOUN cana-772 102 7 , , PUNCT cana-772 102 8 so so ADV cana-772 102 9 𝑆(𝑑 𝑆(𝑑 ADJ cana-772 102 10 ) ) PUNCT cana-772 102 11 = = SYM cana-772 102 12 0 0 NUM cana-772 102 13 ( ( PUNCT cana-772 102 14 3.25 3.25 NUM cana-772 102 15 ) ) PUNCT cana-772 102 16 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 102 17 ) ) PUNCT cana-772 102 18 > > X cana-772 102 19 𝐼(𝑑 𝐼(𝑑 NUM cana-772 102 20 ) ) PUNCT cana-772 102 21 in in ADP cana-772 102 22 this this DET cana-772 102 23 case case NOUN cana-772 102 24 , , PUNCT cana-772 102 25 the the DET cana-772 102 26 shortage shortage NOUN cana-772 102 27 is be AUX cana-772 102 28 equal equal ADJ cana-772 102 29 to to ADP cana-772 102 30 the the DET cana-772 102 31 difference difference NOUN cana-772 102 32 between between ADP cana-772 102 33 demand demand NOUN cana-772 102 34 and and CCONJ cana-772 102 35 inventory inventory NOUN cana-772 102 36 level level NOUN cana-772 102 37 so so ADV cana-772 102 38 , , PUNCT cana-772 102 39 communications communication NOUN cana-772 102 40 on on ADP cana-772 102 41 applied apply VERB cana-772 102 42 nonlinear nonlinear ADJ cana-772 102 43 analysis analysis NOUN cana-772 102 44 issn issn NOUN cana-772 102 45 : : PUNCT cana-772 102 46 1074 1074 NUM cana-772 102 47 - - PUNCT cana-772 102 48 133x 133x NUM cana-772 102 49 vol vol NOUN cana-772 102 50 31 31 NUM cana-772 102 51 no no NOUN cana-772 102 52 . . PUNCT cana-772 103 1 3s 3s NUM cana-772 103 2 ( ( PUNCT cana-772 103 3 2024 2024 NUM cana-772 103 4 ) ) PUNCT cana-772 103 5 331 331 NUM cana-772 103 6 https://internationalpubls.com https://internationalpubls.com X cana-772 103 7 𝑆(𝑑 𝑆(𝑑 ADJ cana-772 103 8 ) ) PUNCT cana-772 103 9 = = SYM cana-772 103 10 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 103 11 ) ) PUNCT cana-772 103 12 βˆ’ βˆ’ PROPN cana-772 103 13 𝐼(𝑑 𝐼(𝑑 NUM cana-772 103 14 ) ) PUNCT cana-772 103 15 ( ( PUNCT cana-772 103 16 3.26 3.26 NUM cana-772 103 17 ) ) PUNCT cana-772 103 18 hence hence ADV cana-772 103 19 , , PUNCT cana-772 103 20 from from ADP cana-772 103 21 equation equation NOUN cana-772 103 22 ( ( PUNCT cana-772 103 23 3.25 3.25 NUM cana-772 103 24 ) ) PUNCT cana-772 103 25 and and CCONJ cana-772 103 26 ( ( PUNCT cana-772 103 27 3.26 3.26 NUM cana-772 103 28 ) ) PUNCT cana-772 103 29 the the DET cana-772 103 30 solution solution NOUN cana-772 103 31 for for ADP cana-772 103 32 the the DET cana-772 103 33 shortage shortage NOUN cana-772 103 34 level level NOUN cana-772 103 35 equation equation NOUN cana-772 103 36 is be AUX cana-772 103 37 written write VERB cana-772 103 38 as as ADP cana-772 103 39 : : PUNCT cana-772 103 40 𝑆(𝑑 𝑆(𝑑 ADJ cana-772 103 41 ) ) PUNCT cana-772 103 42 = = PRON cana-772 103 43 { { PUNCT cana-772 103 44 0𝑖𝑓𝐷(𝑑 0𝑖𝑓𝐷(𝑑 PROPN cana-772 103 45 ) ) PUNCT cana-772 103 46 ≀ ≀ NOUN cana-772 103 47 𝐼(𝑑 𝐼(𝑑 NUM cana-772 103 48 ) ) PUNCT cana-772 103 49 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 103 50 ) ) PUNCT cana-772 103 51 βˆ’ βˆ’ PROPN cana-772 103 52 𝐼(𝑑)𝑖𝑓𝐷(𝑑 𝐼(𝑑)𝑖𝑓𝐷(𝑑 PROPN cana-772 103 53 ) ) PUNCT cana-772 103 54 > > X cana-772 104 1 𝐼(𝑑 𝐼(𝑑 NUM cana-772 104 2 ) ) PUNCT cana-772 104 3 ( ( PUNCT cana-772 104 4 3.27 3.27 NUM cana-772 104 5 ) ) PUNCT cana-772 104 6 this this DET cana-772 104 7 equation equation NOUN cana-772 104 8 ( ( PUNCT cana-772 104 9 3.27 3.27 NUM cana-772 104 10 ) ) PUNCT cana-772 104 11 represents represent VERB cana-772 104 12 the the DET cana-772 104 13 shortage shortage NOUN cana-772 104 14 level level NOUN cana-772 104 15 at at ADP cana-772 104 16 time time NOUN cana-772 104 17 𝑑 𝑑 PROPN cana-772 104 18 based base VERB cana-772 104 19 on on ADP cana-772 104 20 the the DET cana-772 104 21 comparison comparison NOUN cana-772 104 22 between between ADP cana-772 104 23 demand demand NOUN cana-772 104 24 and and CCONJ cana-772 104 25 inventory inventory NOUN cana-772 104 26 level level NOUN cana-772 104 27 . . PUNCT cana-772 105 1 if if SCONJ cana-772 105 2 demand demand NOUN cana-772 105 3 exceeds exceed VERB cana-772 105 4 inventory inventory NOUN cana-772 105 5 , , PUNCT cana-772 105 6 the the DET cana-772 105 7 shortage shortage NOUN cana-772 105 8 is be AUX cana-772 105 9 the the DET cana-772 105 10 difference difference NOUN cana-772 105 11 between between ADP cana-772 105 12 demand demand NOUN cana-772 105 13 and and CCONJ cana-772 105 14 inventory inventory NOUN cana-772 105 15 . . PUNCT cana-772 106 1 otherwise otherwise ADV cana-772 106 2 , , PUNCT cana-772 106 3 there there PRON cana-772 106 4 is be VERB cana-772 106 5 no no DET cana-772 106 6 shortage shortage NOUN cana-772 106 7 . . PUNCT cana-772 107 1 4 4 X cana-772 107 2 . . X cana-772 107 3 numerical numerical ADJ cana-772 107 4 examples example NOUN cana-772 107 5 example example VERB cana-772 107 6 4.1 4.1 NUM cana-772 107 7 : : PUNCT cana-772 107 8 let let VERB cana-772 107 9 ’s ’s PRON cana-772 107 10 use use VERB cana-772 107 11 some some DET cana-772 107 12 arbitrary arbitrary ADJ cana-772 107 13 values value NOUN cana-772 107 14 for for ADP cana-772 107 15 the the DET cana-772 107 16 parameters parameter NOUN cana-772 107 17 and and CCONJ cana-772 107 18 functions function NOUN cana-772 107 19 involved involve VERB cana-772 107 20 replenishment replenishment NOUN cana-772 107 21 rate rate NOUN cana-772 107 22 r(t r(t NOUN cana-772 107 23 ) ) PUNCT cana-772 107 24 is be AUX cana-772 107 25 100 100 NUM cana-772 107 26 units unit NOUN cana-772 107 27 per per ADP cana-772 107 28 day day NOUN cana-772 107 29 , , PUNCT cana-772 107 30 deman deman NOUN cana-772 107 31 rate rate NOUN cana-772 107 32 d(t d(t PROPN cana-772 107 33 ) ) PUNCT cana-772 107 34 is be AUX cana-772 107 35 80 80 NUM cana-772 107 36 + + NUM cana-772 107 37 10 10 NUM cana-772 107 38 t t NOUN cana-772 107 39 units unit NOUN cana-772 107 40 per per ADP cana-772 107 41 day day NOUN cana-772 107 42 , , PUNCT cana-772 107 43 deterioration deterioration NOUN cana-772 107 44 rate rate NOUN cana-772 107 45 h(t h(t PROPN cana-772 107 46 ) ) PUNCT cana-772 107 47 is be AUX cana-772 107 48 0.1 0.1 NUM cana-772 107 49 units unit NOUN cana-772 107 50 per per ADP cana-772 107 51 day day NOUN cana-772 107 52 , , PUNCT cana-772 108 1 initial initial ADJ cana-772 108 2 inventory inventory NOUN cana-772 108 3 level level NOUN cana-772 108 4 i i PRON cana-772 108 5 ( ( PUNCT cana-772 108 6 0 0 NUM cana-772 108 7 ) ) PUNCT cana-772 108 8 is be AUX cana-772 108 9 500 500 NUM cana-772 108 10 units unit NOUN cana-772 108 11 . . PUNCT cana-772 109 1 solutions solution NOUN cana-772 109 2 𝑑𝐼 𝑑𝐼 ADJ cana-772 109 3 𝑑𝑑 𝑑𝑑 ADP cana-772 109 4 = = PUNCT cana-772 109 5 𝑅(𝑑 𝑅(𝑑 NOUN cana-772 109 6 ) ) PUNCT cana-772 109 7 βˆ’ βˆ’ PROPN cana-772 109 8 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 109 9 ) ) PUNCT cana-772 109 10 βˆ’ βˆ’ PROPN cana-772 109 11 β„Ž(𝑑)𝐼(𝑑 β„Ž(𝑑)𝐼(𝑑 PROPN cana-772 109 12 ) ) PUNCT cana-772 110 1 𝑑𝐼 𝑑𝐼 ADP cana-772 110 2 𝑑𝑑 𝑑𝑑 ADP cana-772 110 3 = = SYM cana-772 110 4 100 100 NUM cana-772 110 5 – – PUNCT cana-772 110 6 ( ( PUNCT cana-772 110 7 80 80 NUM cana-772 110 8 + + NOUN cana-772 110 9 10.1 10.1 NUM cana-772 110 10 ) ) PUNCT cana-772 110 11 – – PUNCT cana-772 110 12 ( ( PUNCT cana-772 110 13 0.1 0.1 NUM cana-772 110 14 ) ) PUNCT cana-772 110 15 ( ( PUNCT cana-772 110 16 500 500 NUM cana-772 110 17 ) ) PUNCT cana-772 110 18 𝑑𝐼 𝑑𝐼 ADJ cana-772 110 19 𝑑𝑑 𝑑𝑑 ADP cana-772 110 20 = = SYM cana-772 110 21 100 100 NUM cana-772 110 22 – – SYM cana-772 110 23 90 90 NUM cana-772 110 24 – – SYM cana-772 110 25 50 50 NUM cana-772 110 26 𝑑𝐼 𝑑𝐼 NOUN cana-772 110 27 𝑑𝑑 𝑑𝑑 ADP cana-772 110 28 = = NOUN cana-772 110 29 -40 -40 PROPN cana-772 110 30 now now ADV cana-772 110 31 , , PUNCT cana-772 110 32 integrating integrate VERB cana-772 110 33 both both DET cana-772 110 34 the the DET cana-772 110 35 side side NOUN cana-772 110 36 with with ADP cana-772 110 37 respect respect NOUN cana-772 110 38 to to ADP cana-772 110 39 t t PROPN cana-772 110 40 : : PUNCT cana-772 110 41 ∫ ∫ PROPN cana-772 111 1 ⬚ ⬚ PROPN cana-772 111 2 ⬚ ⬚ PROPN cana-772 111 3 ⬚ ⬚ PROPN cana-772 111 4 𝑑𝐼 𝑑𝐼 NOUN cana-772 111 5 = = SYM cana-772 111 6 ∫ ∫ PROPN cana-772 111 7 ⬚ ⬚ PROPN cana-772 111 8 ⬚ ⬚ PROPN cana-772 111 9 ⬚ ⬚ PROPN cana-772 111 10 ( ( PUNCT cana-772 111 11 βˆ’40)𝑑𝑑 βˆ’40)𝑑𝑑 NOUN cana-772 111 12 𝐼(𝑑 𝐼(𝑑 PROPN cana-772 111 13 ) ) PUNCT cana-772 111 14 = = SYM cana-772 112 1 βˆ’40𝑑 βˆ’40𝑑 PROPN cana-772 113 1 + + CCONJ cana-772 113 2 𝐢 𝐢 PROPN cana-772 113 3 applying apply VERB cana-772 113 4 the the DET cana-772 113 5 initial initial ADJ cana-772 113 6 condition condition NOUN cana-772 113 7 𝐼(0 𝐼(0 NOUN cana-772 113 8 ) ) PUNCT cana-772 113 9 = = SYM cana-772 114 1 500 500 NUM cana-772 114 2 500 500 NUM cana-772 114 3 = = NUM cana-772 114 4 βˆ’40 βˆ’40 NOUN cana-772 114 5 βˆ— βˆ— NOUN cana-772 114 6 0 0 NUM cana-772 115 1 + + CCONJ cana-772 115 2 𝐢 𝐢 PROPN cana-772 115 3 c c NOUN cana-772 115 4 = = SYM cana-772 115 5 500 500 NUM cana-772 115 6 hence hence ADV cana-772 115 7 , , PUNCT cana-772 115 8 the the DET cana-772 115 9 solution solution NOUN cana-772 115 10 i(t i(t NOUN cana-772 115 11 ) ) PUNCT cana-772 115 12 is be AUX cana-772 115 13 : : PUNCT cana-772 115 14 𝐼(𝑑 𝐼(𝑑 NUM cana-772 115 15 ) ) PUNCT cana-772 115 16 = = PUNCT cana-772 115 17 βˆ’40𝑑 βˆ’40𝑑 PROPN cana-772 116 1 + + NUM cana-772 116 2 500 500 NUM cana-772 116 3 example example NOUN cana-772 116 4 4.2 4.2 NUM cana-772 116 5 : : PUNCT cana-772 116 6 let let VERB cana-772 116 7 ’s ’s PRON cana-772 116 8 assume assume VERB cana-772 116 9 preservative preservative ADJ cana-772 116 10 factor factor NOUN cana-772 116 11 p(t p(t NOUN cana-772 116 12 ) ) PUNCT cana-772 116 13 is be AUX cana-772 116 14 0.3 0.3 NUM cana-772 116 15 and and CCONJ cana-772 116 16 initial initial ADJ cana-772 116 17 deterioration deterioration NOUN cana-772 116 18 level level NOUN cana-772 116 19 c(0 c(0 NOUN cana-772 116 20 ) ) PUNCT cana-772 116 21 is be AUX cana-772 116 22 50 50 NUM cana-772 116 23 units unit NOUN cana-772 116 24 solutions solution NOUN cana-772 116 25 𝑑𝐢 𝑑𝐢 NOUN cana-772 116 26 𝑑𝑑 𝑑𝑑 ADP cana-772 116 27 = = PUNCT cana-772 116 28 ( ( PUNCT cana-772 116 29 1 1 NUM cana-772 116 30 βˆ’ βˆ’ NOUN cana-772 116 31 𝑃(𝑑 𝑃(𝑑 NUM cana-772 116 32 ) ) PUNCT cana-772 116 33 ) ) PUNCT cana-772 116 34 . . PUNCT cana-772 117 1 β„Ž(𝑑 β„Ž(𝑑 PROPN cana-772 117 2 ) ) PUNCT cana-772 117 3 . . PUNCT cana-772 118 1 𝐼(𝑑 𝐼(𝑑 X cana-772 118 2 ) ) PUNCT cana-772 118 3 𝑑𝐢 𝑑𝐢 NOUN cana-772 118 4 𝑑𝑑 𝑑𝑑 ADP cana-772 118 5 = = SYM cana-772 118 6 ( ( PUNCT cana-772 118 7 1 1 NUM cana-772 118 8 βˆ’ βˆ’ NOUN cana-772 118 9 0.3 0.3 NUM cana-772 118 10 ) ) PUNCT cana-772 118 11 βˆ— βˆ— NOUN cana-772 118 12 0.1 0.1 NUM cana-772 118 13 βˆ— βˆ— NOUN cana-772 118 14 ( ( PUNCT cana-772 118 15 βˆ’40𝑑 βˆ’40𝑑 X cana-772 119 1 + + CCONJ cana-772 119 2 500 500 NUM cana-772 119 3 ) ) PUNCT cana-772 119 4 𝑑𝐢 𝑑𝐢 NOUN cana-772 119 5 𝑑𝑑 𝑑𝑑 ADP cana-772 119 6 = = SYM cana-772 119 7 0.07 0.07 NUM cana-772 119 8 βˆ— βˆ— NOUN cana-772 119 9 ( ( PUNCT cana-772 119 10 βˆ’40𝑑 βˆ’40𝑑 X cana-772 120 1 + + CCONJ cana-772 120 2 500 500 NUM cana-772 120 3 ) ) PUNCT cana-772 120 4 communications communication NOUN cana-772 120 5 on on ADP cana-772 120 6 applied apply VERB cana-772 120 7 nonlinear nonlinear ADJ cana-772 120 8 analysis analysis NOUN cana-772 120 9 issn issn NOUN cana-772 120 10 : : PUNCT cana-772 120 11 1074 1074 NUM cana-772 120 12 - - PUNCT cana-772 120 13 133x 133x NUM cana-772 120 14 vol vol NOUN cana-772 120 15 31 31 NUM cana-772 120 16 no no NOUN cana-772 120 17 . . PUNCT cana-772 121 1 3s 3s NUM cana-772 121 2 ( ( PUNCT cana-772 121 3 2024 2024 NUM cana-772 121 4 ) ) PUNCT cana-772 121 5 332 332 NUM cana-772 121 6 https://internationalpubls.com https://internationalpubls.com X cana-772 121 7 𝑑𝐢 𝑑𝐢 NOUN cana-772 121 8 𝑑𝑑 𝑑𝑑 ADP cana-772 121 9 = = PUNCT cana-772 121 10 βˆ’2.8𝑑 βˆ’2.8𝑑 NOUN cana-772 121 11 + + CCONJ cana-772 121 12 35 35 NUM cana-772 121 13 now now ADV cana-772 121 14 , , PUNCT cana-772 121 15 integrating integrate VERB cana-772 121 16 both both DET cana-772 121 17 sides side NOUN cana-772 121 18 with with ADP cana-772 121 19 respect respect NOUN cana-772 121 20 to to ADP cana-772 121 21 t t PROPN cana-772 121 22 : : PUNCT cana-772 121 23 ∫ ∫ PROPN cana-772 121 24 ⬚ ⬚ PROPN cana-772 121 25 ⬚ ⬚ PROPN cana-772 121 26 ⬚ ⬚ PROPN cana-772 121 27 𝑑𝐢 𝑑𝐢 PROPN cana-772 121 28 = = SYM cana-772 121 29 ∫ ∫ PROPN cana-772 121 30 ⬚ ⬚ PROPN cana-772 121 31 ⬚ ⬚ PROPN cana-772 121 32 ⬚ ⬚ PROPN cana-772 121 33 ( ( PUNCT cana-772 121 34 βˆ’2.8𝑑 βˆ’2.8𝑑 NOUN cana-772 121 35 + + CCONJ cana-772 121 36 35)𝑑𝑑 35)𝑑𝑑 NUM cana-772 121 37 𝐢(𝑑 𝐢(𝑑 NOUN cana-772 121 38 ) ) PUNCT cana-772 121 39 = = NOUN cana-772 121 40 βˆ’1.4𝑑2 βˆ’1.4𝑑2 PUNCT cana-772 122 1 + + CCONJ cana-772 122 2 3.5𝑑 3.5𝑑 NUM cana-772 122 3 + + SYM cana-772 122 4 𝐷 𝐷 NOUN cana-772 122 5 applying apply VERB cana-772 122 6 the the DET cana-772 122 7 initial initial ADJ cana-772 122 8 solution solution NOUN cana-772 122 9 c(0 c(0 NOUN cana-772 122 10 ) ) PUNCT cana-772 122 11 is be AUX cana-772 122 12 50 50 NUM cana-772 122 13 50 50 NUM cana-772 122 14 = = NOUN cana-772 122 15 βˆ’1.402 βˆ’1.402 NOUN cana-772 122 16 + + CCONJ cana-772 122 17 35 35 NUM cana-772 122 18 βˆ— βˆ— NOUN cana-772 122 19 0 0 NUM cana-772 123 1 + + CCONJ cana-772 123 2 𝐷 𝐷 PROPN cana-772 123 3 d d NOUN cana-772 123 4 = = NOUN cana-772 123 5 50 50 NUM cana-772 123 6 the the DET cana-772 123 7 solution solution NOUN cana-772 123 8 for for ADP cana-772 123 9 c(t c(t PROPN cana-772 123 10 ) ) PUNCT cana-772 123 11 is be AUX cana-772 123 12 𝐢(𝑑 𝐢(𝑑 ADJ cana-772 123 13 ) ) PUNCT cana-772 123 14 = = NOUN cana-772 124 1 βˆ’1.4𝑑2 βˆ’1.4𝑑2 PUNCT cana-772 125 1 + + CCONJ cana-772 125 2 3.5𝑑 3.5𝑑 NUM cana-772 125 3 + + SYM cana-772 125 4 50 50 NUM cana-772 125 5 example example NOUN cana-772 125 6 4.3 4.3 NUM cana-772 125 7 solutions solution NOUN cana-772 125 8 for for ADP cana-772 125 9 shortage shortage NOUN cana-772 125 10 level level NOUN cana-772 125 11 equation equation NOUN cana-772 125 12 𝑆(𝑑 𝑆(𝑑 NOUN cana-772 125 13 ) ) PUNCT cana-772 125 14 = = PUNCT cana-772 125 15 π‘šπ‘Žπ‘₯(0 π‘šπ‘Žπ‘₯(0 NOUN cana-772 125 16 , , PUNCT cana-772 125 17 𝐷(𝑑 𝐷(𝑑 NOUN cana-772 125 18 ) ) PUNCT cana-772 125 19 βˆ’ βˆ’ PROPN cana-772 125 20 𝐼(𝑑 𝐼(𝑑 NUM cana-772 125 21 ) ) PUNCT cana-772 125 22 ) ) PUNCT cana-772 126 1 substituting substitute VERB cana-772 126 2 the the DET cana-772 126 3 values value NOUN cana-772 126 4 of of ADP cana-772 126 5 d(t d(t PROPN cana-772 126 6 ) ) PUNCT cana-772 126 7 and and CCONJ cana-772 126 8 i(t i(t NOUN cana-772 126 9 ) ) PUNCT cana-772 126 10 𝑆(𝑑 𝑆(𝑑 NUM cana-772 126 11 ) ) PUNCT cana-772 126 12 = = SYM cana-772 126 13 π‘šπ‘Žπ‘₯ π‘šπ‘Žπ‘₯ X cana-772 126 14 ( ( PUNCT cana-772 126 15 0 0 NUM cana-772 126 16 , , PUNCT cana-772 126 17 ( ( PUNCT cana-772 126 18 80 80 NUM cana-772 126 19 + + NOUN cana-772 126 20 10𝑑 10𝑑 NOUN cana-772 126 21 ) ) PUNCT cana-772 126 22 βˆ’ βˆ’ PROPN cana-772 127 1 ( ( PUNCT cana-772 127 2 βˆ’40𝑑 βˆ’40𝑑 ADP cana-772 127 3 + + CCONJ cana-772 127 4 500 500 NUM cana-772 127 5 ) ) PUNCT cana-772 127 6 ) ) PUNCT cana-772 127 7 s(t s(t PROPN cana-772 127 8 ) ) PUNCT cana-772 128 1 = = SYM cana-772 128 2 max max X cana-772 128 3 ( ( PUNCT cana-772 128 4 0 0 NUM cana-772 128 5 , , PUNCT cana-772 128 6 80 80 NUM cana-772 128 7 + + SYM cana-772 128 8 10 10 NUM cana-772 128 9 t t NOUN cana-772 128 10 + + CCONJ cana-772 128 11 40 40 NUM cana-772 128 12 t t NOUN cana-772 128 13 -500 -500 NUM cana-772 128 14 ) ) PUNCT cana-772 128 15 s(t s(t PROPN cana-772 128 16 ) ) PUNCT cana-772 129 1 = = SYM cana-772 129 2 max max PROPN cana-772 129 3 ( ( PUNCT cana-772 129 4 0,50 0,50 X cana-772 129 5 t t PROPN cana-772 129 6 – – PUNCT cana-772 129 7 420 420 NUM cana-772 129 8 ) ) PUNCT cana-772 129 9 since since SCONJ cana-772 129 10 s(t s(t PROPN cana-772 129 11 ) ) PUNCT cana-772 129 12 can can AUX cana-772 129 13 not not PART cana-772 129 14 negative negative VERB cana-772 129 15 , , PUNCT cana-772 129 16 the the DET cana-772 129 17 expression expression NOUN cana-772 129 18 inside inside ADP cana-772 129 19 the the DET cana-772 129 20 max max PROPN cana-772 129 21 function function NOUN cana-772 129 22 must must AUX cana-772 129 23 be be AUX cana-772 129 24 greater great ADJ cana-772 129 25 than than ADP cana-772 129 26 or or CCONJ cana-772 129 27 equal equal ADJ cana-772 129 28 to to ADP cana-772 129 29 zero zero NUM cana-772 129 30 : : PUNCT cana-772 129 31 solving solve VERB cana-772 129 32 for for ADP cana-772 129 33 t t PROPN cana-772 129 34 50𝑑 50𝑑 NUM cana-772 129 35 β‰₯ β‰₯ VERB cana-772 129 36 420 420 NUM cana-772 129 37 𝑑 𝑑 PROPN cana-772 129 38 β‰₯ β‰₯ NOUN cana-772 129 39 420 420 NUM cana-772 129 40 50 50 NUM cana-772 129 41 𝑑 𝑑 NOUN cana-772 129 42 β‰₯ β‰₯ NOUN cana-772 129 43 8.4 8.4 NUM cana-772 129 44 the the DET cana-772 129 45 shortage shortage NOUN cana-772 129 46 level level NOUN cana-772 129 47 s(t s(t PROPN cana-772 129 48 ) ) PUNCT cana-772 129 49 will will AUX cana-772 129 50 be be AUX cana-772 129 51 zero zero NUM cana-772 129 52 for for ADP cana-772 129 53 𝑑 𝑑 NOUN cana-772 129 54 < < X cana-772 129 55 8.4days 8.4days NUM cana-772 129 56 and and CCONJ cana-772 129 57 it it PRON cana-772 129 58 will will AUX cana-772 129 59 be be AUX cana-772 129 60 positive positive ADJ cana-772 129 61 for for ADP cana-772 129 62 𝑑 𝑑 PROPN cana-772 129 63 β‰₯ β‰₯ NOUN cana-772 129 64 8.4 8.4 NUM cana-772 129 65 days day NOUN cana-772 129 66 . . PUNCT cana-772 130 1 sensitivity sensitivity NOUN cana-772 130 2 analysis analysis NOUN cana-772 130 3 of of ADP cana-772 130 4 example example NOUN cana-772 130 5 4.1 4.1 NUM cana-772 130 6 changing change VERB cana-772 130 7 parameters parameter NOUN cana-772 130 8 change(t change(t ADJ cana-772 130 9 ) ) PUNCT cana-772 130 10 change change NOUN cana-772 130 11 in in ADP cana-772 130 12 percentage percentage NOUN cana-772 130 13 Ξ΄% Ξ΄% ADJ cana-772 130 14 in in ADP cana-772 130 15 r(t r(t NOUN cana-772 130 16 ) ) PUNCT cana-772 130 17 Ξ΄% Ξ΄% ADJ cana-772 130 18 in in ADP cana-772 130 19 d(t d(t PROPN cana-772 130 20 ) ) PUNCT cana-772 130 21 Ξ΄% Ξ΄% ADJ cana-772 130 22 in in ADP cana-772 130 23 c(t c(t PROPN cana-772 130 24 ) ) PUNCT cana-772 130 25 i(t i(t PROPN cana-772 130 26 ) ) PUNCT cana-772 130 27 t= t= NOUN cana-772 131 1 0 0 NUM cana-772 131 2 500 500 NUM cana-772 131 3 550 550 NUM cana-772 131 4 10 10 NUM cana-772 131 5 % % NOUN cana-772 131 6 t=1 t=1 PROPN cana-772 131 7 510 510 NUM cana-772 131 8 560 560 NUM cana-772 131 9 9.80 9.80 NUM cana-772 131 10 % % NOUN cana-772 131 11 t=2 t=2 PROPN cana-772 131 12 520 520 NUM cana-772 131 13 570 570 NUM cana-772 131 14 9.60 9.60 NUM cana-772 131 15 % % NOUN cana-772 131 16 t=3 t=3 NOUN cana-772 131 17 530 530 NUM cana-772 131 18 580 580 NUM cana-772 131 19 9.40 9.40 NUM cana-772 131 20 % % NOUN cana-772 131 21 communications communication NOUN cana-772 131 22 on on ADP cana-772 131 23 applied apply VERB cana-772 131 24 nonlinear nonlinear ADJ cana-772 131 25 analysis analysis NOUN cana-772 131 26 issn issn NOUN cana-772 131 27 : : PUNCT cana-772 131 28 1074 1074 NUM cana-772 131 29 - - PUNCT cana-772 131 30 133x 133x NUM cana-772 131 31 vol vol NOUN cana-772 131 32 31 31 NUM cana-772 131 33 no no NOUN cana-772 131 34 . . PUNCT cana-772 132 1 3s 3s NUM cana-772 132 2 ( ( PUNCT cana-772 132 3 2024 2024 NUM cana-772 132 4 ) ) PUNCT cana-772 132 5 333 333 NUM cana-772 132 6 https://internationalpubls.com https://internationalpubls.com X cana-772 132 7 r(t r(t NOUN cana-772 132 8 ) ) PUNCT cana-772 132 9 t=0 t=0 PROPN cana-772 132 10 100 100 NUM cana-772 132 11 120 120 NUM cana-772 132 12 20 20 NUM cana-772 132 13 % % NOUN cana-772 132 14 t=1 t=1 NOUN cana-772 132 15 100 100 NUM cana-772 132 16 120 120 NUM cana-772 132 17 20 20 NUM cana-772 132 18 % % NOUN cana-772 132 19 t=2 t=2 PROPN cana-772 132 20 100 100 NUM cana-772 132 21 120 120 NUM cana-772 132 22 20 20 NUM cana-772 132 23 % % NOUN cana-772 132 24 t=3 t=3 PROPN cana-772 132 25 100 100 NUM cana-772 132 26 120 120 NUM cana-772 132 27 20 20 NUM cana-772 132 28 % % NOUN cana-772 132 29 d(t d(t PROPN cana-772 132 30 ) ) PUNCT cana-772 132 31 t=0 t=0 PROPN cana-772 132 32 80 80 NUM cana-772 132 33 90 90 NUM cana-772 132 34 13 13 NUM cana-772 132 35 % % NOUN cana-772 132 36 t=1 t=1 PROPN cana-772 132 37 90 90 NUM cana-772 132 38 100 100 NUM cana-772 132 39 11.10 11.10 NUM cana-772 132 40 % % NOUN cana-772 132 41 t=2 t=2 PROPN cana-772 132 42 100 100 NUM cana-772 132 43 110 110 NUM cana-772 132 44 10 10 NUM cana-772 132 45 % % NOUN cana-772 132 46 t=3 t=3 ADP cana-772 132 47 110 110 NUM cana-772 132 48 120 120 NUM cana-772 132 49 9 9 NUM cana-772 132 50 % % NOUN cana-772 132 51 h(t h(t NUM cana-772 132 52 ) ) PUNCT cana-772 132 53 t=0 t=0 PROPN cana-772 132 54 0.1 0.1 NUM cana-772 132 55 0.12 0.12 NUM cana-772 132 56 20 20 NUM cana-772 132 57 % % NOUN cana-772 132 58 t=1 t=1 PROPN cana-772 132 59 0.1 0.1 NUM cana-772 132 60 0.12 0.12 NUM cana-772 132 61 20 20 NUM cana-772 132 62 % % NOUN cana-772 132 63 t=2 t=2 PROPN cana-772 132 64 0.1 0.1 NUM cana-772 132 65 0.12 0.12 NUM cana-772 132 66 20 20 NUM cana-772 132 67 % % NOUN cana-772 132 68 t=3 t=3 PROPN cana-772 132 69 0.1 0.1 NUM cana-772 132 70 0.12 0.12 NUM cana-772 132 71 20 20 NUM cana-772 132 72 % % NOUN cana-772 132 73 sensitivity sensitivity NOUN cana-772 132 74 analysis analysis NOUN cana-772 132 75 of of ADP cana-772 132 76 example example NOUN cana-772 132 77 4.2 4.2 NUM cana-772 132 78 changing change VERB cana-772 132 79 parameters parameter NOUN cana-772 132 80 change(t change(t ADJ cana-772 132 81 ) ) PUNCT cana-772 132 82 change change NOUN cana-772 132 83 in in ADP cana-772 132 84 percentage percentage NOUN cana-772 132 85 equation equation NOUN cana-772 132 86 c(t c(t PROPN cana-772 132 87 ) ) PUNCT cana-772 132 88 Ξ΄% Ξ΄% ADJ cana-772 132 89 in in ADP cana-772 132 90 c(t c(t PROPN cana-772 132 91 ) ) PUNCT cana-772 132 92 p(t p(t NOUN cana-772 132 93 ) ) PUNCT cana-772 132 94 0.2 0.2 NUM cana-772 132 95 40 40 NUM cana-772 133 1 + + SYM cana-772 133 2 40 40 NUM cana-772 133 3 t t NOUN cana-772 133 4 0 0 NUM cana-772 133 5 0.3 0.3 NUM cana-772 133 6 50 50 NUM cana-772 134 1 + + NUM cana-772 134 2 35 35 NUM cana-772 134 3 t t NOUN cana-772 134 4 25 25 NUM cana-772 134 5 % % NOUN cana-772 134 6 0.4 0.4 NUM cana-772 134 7 60 60 NUM cana-772 134 8 + + SYM cana-772 134 9 30 30 NUM cana-772 134 10 t t NOUN cana-772 134 11 50 50 NUM cana-772 134 12 % % NOUN cana-772 134 13 0.5 0.5 NUM cana-772 134 14 70 70 NUM cana-772 134 15 + + SYM cana-772 134 16 25 25 NUM cana-772 134 17 t t NOUN cana-772 134 18 75 75 NUM cana-772 134 19 % % NOUN cana-772 134 20 sensitivity sensitivity NOUN cana-772 134 21 analysis analysis NOUN cana-772 134 22 of of ADP cana-772 134 23 example example NOUN cana-772 134 24 4.3 4.3 NUM cana-772 134 25 changing change VERB cana-772 134 26 parameters parameter NOUN cana-772 134 27 change change VERB cana-772 134 28 change change NOUN cana-772 134 29 in in ADP cana-772 134 30 percentage percentage NOUN cana-772 134 31 d(t d(t PROPN cana-772 134 32 ) ) PUNCT cana-772 134 33 i(t i(t PROPN cana-772 134 34 ) ) PUNCT cana-772 134 35 Ξ΄% Ξ΄% ADJ cana-772 134 36 in in ADP cana-772 134 37 s(t s(t PROPN cana-772 134 38 ) ) PUNCT cana-772 134 39 d(t d(t PROPN cana-772 134 40 ) ) PUNCT cana-772 134 41 t=0 t=0 PROPN cana-772 134 42 80 80 NUM cana-772 134 43 90 90 NUM cana-772 134 44 12.50 12.50 NUM cana-772 134 45 % % NOUN cana-772 134 46 t=1 t=1 PROPN cana-772 134 47 90 90 NUM cana-772 134 48 100 100 NUM cana-772 134 49 11 11 NUM cana-772 134 50 % % NOUN cana-772 134 51 t=2 t=2 PROPN cana-772 134 52 100 100 NUM cana-772 134 53 110 110 NUM cana-772 134 54 10 10 NUM cana-772 134 55 % % NOUN cana-772 134 56 t=3 t=3 ADP cana-772 134 57 110 110 NUM cana-772 134 58 120 120 NUM cana-772 134 59 9 9 NUM cana-772 134 60 % % NOUN cana-772 134 61 i(t i(t NOUN cana-772 134 62 ) ) PUNCT cana-772 134 63 t=0 t=0 PROPN cana-772 135 1 500 500 NUM cana-772 135 2 550 550 NUM cana-772 135 3 10 10 NUM cana-772 135 4 % % NOUN cana-772 135 5 t=1 t=1 ADP cana-772 135 6 460 460 NUM cana-772 135 7 510 510 NUM cana-772 135 8 10.87 10.87 NUM cana-772 135 9 % % NOUN cana-772 135 10 t=2 t=2 PROPN cana-772 135 11 420 420 NUM cana-772 135 12 470 470 NUM cana-772 135 13 11.90 11.90 NUM cana-772 135 14 % % NOUN cana-772 135 15 t=3 t=3 PROPN cana-772 135 16 380 380 NUM cana-772 135 17 430 430 NUM cana-772 135 18 13.16 13.16 NUM cana-772 135 19 % % NOUN cana-772 135 20 5 5 NUM cana-772 135 21 . . PUNCT cana-772 135 22 conclusion conclusion NOUN cana-772 135 23 the the DET cana-772 135 24 research research NOUN cana-772 135 25 findings finding NOUN cana-772 135 26 emphasise emphasise VERB cana-772 135 27 the the DET cana-772 135 28 significance significance NOUN cana-772 135 29 of of ADP cana-772 135 30 efficient efficient ADJ cana-772 135 31 inventory inventory NOUN cana-772 135 32 management management NOUN cana-772 135 33 in in ADP cana-772 135 34 retail retail ADJ cana-772 135 35 operations operation NOUN cana-772 135 36 , , PUNCT cana-772 135 37 specifically specifically ADV cana-772 135 38 in in ADP cana-772 135 39 the the DET cana-772 135 40 management management NOUN cana-772 135 41 of of ADP cana-772 135 42 deteriorating deteriorate VERB cana-772 135 43 inventory inventory NOUN cana-772 135 44 items item NOUN cana-772 135 45 . . PUNCT cana-772 136 1 the the DET cana-772 136 2 study study NOUN cana-772 136 3 's 's PART cana-772 136 4 key key ADJ cana-772 136 5 findings finding NOUN cana-772 136 6 are be AUX cana-772 136 7 as as SCONJ cana-772 136 8 follows follow VERB cana-772 136 9 : : PUNCT cana-772 136 10 effective effective ADJ cana-772 136 11 inventory inventory NOUN cana-772 136 12 management management NOUN cana-772 136 13 systems system NOUN cana-772 136 14 are be AUX cana-772 136 15 essential essential ADJ cana-772 136 16 for for ADP cana-772 136 17 meeting meet VERB cana-772 136 18 customer customer NOUN cana-772 136 19 demand demand NOUN cana-772 136 20 , , PUNCT cana-772 136 21 ensuring ensure VERB cana-772 136 22 product product NOUN cana-772 136 23 availability availability NOUN cana-772 136 24 , , PUNCT cana-772 136 25 and and CCONJ cana-772 136 26 optimising optimise VERB cana-772 136 27 profitability profitability NOUN cana-772 136 28 . . PUNCT cana-772 137 1 the the DET cana-772 137 2 study study NOUN cana-772 137 3 highlights highlight VERB cana-772 137 4 the the DET cana-772 137 5 necessity necessity NOUN cana-772 137 6 of of ADP cana-772 137 7 efficient efficient ADJ cana-772 137 8 inventory inventory NOUN cana-772 137 9 control control NOUN cana-772 137 10 systems system NOUN cana-772 137 11 to to PART cana-772 137 12 ensure ensure VERB cana-772 137 13 seamless seamless ADJ cana-772 137 14 operations operation NOUN cana-772 137 15 and and CCONJ cana-772 137 16 reduce reduce VERB cana-772 137 17 disruptions disruption NOUN cana-772 137 18 . . PUNCT cana-772 138 1 preservation preservation NOUN cana-772 138 2 technology technology NOUN cana-772 138 3 is be AUX cana-772 138 4 crucial crucial ADJ cana-772 138 5 in in ADP cana-772 138 6 reducing reduce VERB cana-772 138 7 the the DET cana-772 138 8 impact impact NOUN cana-772 138 9 of of ADP cana-772 138 10 deterioration deterioration NOUN cana-772 138 11 on on ADP cana-772 138 12 inventory inventory NOUN cana-772 138 13 items item NOUN cana-772 138 14 , , PUNCT cana-772 138 15 particularly particularly ADV cana-772 138 16 perishable perishable ADJ cana-772 138 17 communications communication NOUN cana-772 138 18 on on ADP cana-772 138 19 applied apply VERB cana-772 138 20 nonlinear nonlinear ADJ cana-772 138 21 analysis analysis NOUN cana-772 138 22 issn issn NOUN cana-772 138 23 : : PUNCT cana-772 138 24 1074 1074 NUM cana-772 138 25 - - PUNCT cana-772 138 26 133x 133x NUM cana-772 138 27 vol vol NOUN cana-772 138 28 31 31 NUM cana-772 138 29 no no NOUN cana-772 138 30 . . PUNCT cana-772 139 1 3s 3s NUM cana-772 139 2 ( ( PUNCT cana-772 139 3 2024 2024 NUM cana-772 139 4 ) ) PUNCT cana-772 139 5 334 334 NUM cana-772 139 6 https://internationalpubls.com https://internationalpubls.com X cana-772 139 7 goods good NOUN cana-772 139 8 such such ADJ cana-772 139 9 as as ADP cana-772 139 10 dairy dairy NOUN cana-772 139 11 products product NOUN cana-772 139 12 . . PUNCT cana-772 140 1 allocating allocate VERB cana-772 140 2 resources resource NOUN cana-772 140 3 towards towards ADP cana-772 140 4 preservation preservation NOUN cana-772 140 5 technology technology NOUN cana-772 140 6 can can AUX cana-772 140 7 effectively effectively ADV cana-772 140 8 mitigate mitigate VERB cana-772 140 9 financial financial ADJ cana-772 140 10 losses loss NOUN cana-772 140 11 , , PUNCT cana-772 140 12 elevate elevate VERB cana-772 140 13 the the DET cana-772 140 14 standard standard NOUN cana-772 140 15 of of ADP cana-772 140 16 service service NOUN cana-772 140 17 , , PUNCT cana-772 140 18 and and CCONJ cana-772 140 19 bolster bolster VERB cana-772 140 20 competitiveness competitiveness NOUN cana-772 140 21 within within ADP cana-772 140 22 the the DET cana-772 140 23 retail retail ADJ cana-772 140 24 industry industry NOUN cana-772 140 25 . . PUNCT cana-772 141 1 this this DET cana-772 141 2 study study NOUN cana-772 141 3 investigates investigate VERB cana-772 141 4 the the DET cana-772 141 5 intricacies intricacy NOUN cana-772 141 6 of of ADP cana-772 141 7 inventory inventory NOUN cana-772 141 8 systems system NOUN cana-772 141 9 , , PUNCT cana-772 141 10 encompassing encompass VERB cana-772 141 11 diverse diverse ADJ cana-772 141 12 categories category NOUN cana-772 141 13 of of ADP cana-772 141 14 inventory inventory NOUN cana-772 141 15 items item NOUN cana-772 141 16 and and CCONJ cana-772 141 17 the the DET cana-772 141 18 challenges challenge NOUN cana-772 141 19 associated associate VERB cana-772 141 20 with with ADP cana-772 141 21 their their PRON cana-772 141 22 management management NOUN cana-772 141 23 . . PUNCT cana-772 142 1 challenges challenge NOUN cana-772 142 2 arising arise VERB cana-772 142 3 from from ADP cana-772 142 4 supply supply NOUN cana-772 142 5 shortages shortage NOUN cana-772 142 6 , , PUNCT cana-772 142 7 improper improper ADJ cana-772 142 8 management management NOUN cana-772 142 9 , , PUNCT cana-772 142 10 and and CCONJ cana-772 142 11 deterioration deterioration NOUN cana-772 142 12 necessitate necessitate ADJ cana-772 142 13 the the DET cana-772 142 14 implementation implementation NOUN cana-772 142 15 of of ADP cana-772 142 16 effective effective ADJ cana-772 142 17 inventory inventory NOUN cana-772 142 18 control control NOUN cana-772 142 19 strategies strategy NOUN cana-772 142 20 . . PUNCT cana-772 143 1 ethical ethical ADJ cana-772 143 2 considerations consideration NOUN cana-772 143 3 are be AUX cana-772 143 4 fundamental fundamental ADJ cana-772 143 5 to to PART cana-772 143 6 research research VERB cana-772 143 7 on on ADP cana-772 143 8 inventory inventory NOUN cana-772 143 9 management management NOUN cana-772 143 10 , , PUNCT cana-772 143 11 encompassing encompass VERB cana-772 143 12 the the DET cana-772 143 13 reduction reduction NOUN cana-772 143 14 of of ADP cana-772 143 15 environmental environmental ADJ cana-772 143 16 impact impact NOUN cana-772 143 17 , , PUNCT cana-772 143 18 the the DET cana-772 143 19 promotion promotion NOUN cana-772 143 20 of of ADP cana-772 143 21 social social ADJ cana-772 143 22 responsibility responsibility NOUN cana-772 143 23 , , PUNCT cana-772 143 24 the the DET cana-772 143 25 guarantee guarantee NOUN cana-772 143 26 of of ADP cana-772 143 27 data datum NOUN cana-772 143 28 privacy privacy NOUN cana-772 143 29 and and CCONJ cana-772 143 30 security security NOUN cana-772 143 31 , , PUNCT cana-772 143 32 and and CCONJ cana-772 143 33 the the DET cana-772 143 34 preservation preservation NOUN cana-772 143 35 of of ADP cana-772 143 36 transparency transparency NOUN cana-772 143 37 and and CCONJ cana-772 143 38 consumer consumer NOUN cana-772 143 39 information information NOUN cana-772 143 40 . . PUNCT cana-772 144 1 in in ADP cana-772 144 2 summary summary NOUN cana-772 144 3 , , PUNCT cana-772 144 4 the the DET cana-772 144 5 study study NOUN cana-772 144 6 highlights highlight VERB cana-772 144 7 the the DET cana-772 144 8 crucial crucial ADJ cana-772 144 9 significance significance NOUN cana-772 144 10 of of ADP cana-772 144 11 efficient efficient ADJ cana-772 144 12 inventory inventory NOUN cana-772 144 13 management management NOUN cana-772 144 14 strategies strategy NOUN cana-772 144 15 , , PUNCT cana-772 144 16 preservation preservation NOUN cana-772 144 17 technology technology NOUN cana-772 144 18 , , PUNCT cana-772 144 19 and and CCONJ cana-772 144 20 ethical ethical ADJ cana-772 144 21 considerations consideration NOUN cana-772 144 22 in in ADP cana-772 144 23 retail retail ADJ cana-772 144 24 operations operation NOUN cana-772 144 25 . . PUNCT cana-772 145 1 through through ADP cana-772 145 2 the the DET cana-772 145 3 utilisation utilisation NOUN cana-772 145 4 of of ADP cana-772 145 5 mathematical mathematical ADJ cana-772 145 6 modelling modelling NOUN cana-772 145 7 and and CCONJ cana-772 145 8 analytical analytical ADJ cana-772 145 9 techniques technique NOUN cana-772 145 10 , , PUNCT cana-772 145 11 businesses business NOUN cana-772 145 12 can can AUX cana-772 145 13 enhance enhance VERB cana-772 145 14 inventory inventory NOUN cana-772 145 15 management management NOUN cana-772 145 16 practices practice NOUN cana-772 145 17 , , PUNCT cana-772 145 18 reduce reduce VERB cana-772 145 19 expenses expense NOUN cana-772 145 20 , , PUNCT cana-772 145 21 and and CCONJ cana-772 145 22 effectively effectively ADV cana-772 145 23 meet meet VERB cana-772 145 24 market market NOUN cana-772 145 25 demands demand NOUN cana-772 145 26 while while SCONJ cana-772 145 27 maintaining maintain VERB cana-772 145 28 the the DET cana-772 145 29 quality quality NOUN cana-772 145 30 of of ADP cana-772 145 31 perishable perishable ADJ cana-772 145 32 goods good NOUN cana-772 145 33 . . PUNCT cana-772 146 1 the the DET cana-772 146 2 study study NOUN cana-772 146 3 's 's PART cana-772 146 4 mathematical mathematical ADJ cana-772 146 5 modelling modelling NOUN cana-772 146 6 provides provide VERB cana-772 146 7 valuable valuable ADJ cana-772 146 8 insights insight NOUN cana-772 146 9 into into ADP cana-772 146 10 strategies strategy NOUN cana-772 146 11 for for ADP cana-772 146 12 managing manage VERB cana-772 146 13 inventory inventory NOUN cana-772 146 14 , , PUNCT cana-772 146 15 especially especially ADV cana-772 146 16 when when SCONJ cana-772 146 17 dealing deal VERB cana-772 146 18 with with ADP cana-772 146 19 deteriorating deteriorate VERB cana-772 146 20 inventory inventory NOUN cana-772 146 21 items item NOUN cana-772 146 22 . . PUNCT cana-772 147 1 the the DET cana-772 147 2 study study NOUN cana-772 147 3 showcases showcase VERB cana-772 147 4 the the DET cana-772 147 5 dynamic dynamic ADJ cana-772 147 6 nature nature NOUN cana-772 147 7 of of ADP cana-772 147 8 inventory inventory NOUN cana-772 147 9 systems system NOUN cana-772 147 10 and and CCONJ cana-772 147 11 the the DET cana-772 147 12 influence influence NOUN cana-772 147 13 of of ADP cana-772 147 14 factors factor NOUN cana-772 147 15 like like ADP cana-772 147 16 demand demand NOUN cana-772 147 17 rates rate NOUN cana-772 147 18 , , PUNCT cana-772 147 19 replenishment replenishment NOUN cana-772 147 20 rates rate NOUN cana-772 147 21 , , PUNCT cana-772 147 22 and and CCONJ cana-772 147 23 deterioration deterioration NOUN cana-772 147 24 rates rate NOUN cana-772 147 25 on on ADP cana-772 147 26 inventory inventory NOUN cana-772 147 27 levels level NOUN cana-772 147 28 through through ADP cana-772 147 29 the the DET cana-772 147 30 formulation formulation NOUN cana-772 147 31 and and CCONJ cana-772 147 32 analysis analysis NOUN cana-772 147 33 of of ADP cana-772 147 34 differential differential ADJ cana-772 147 35 equations equation NOUN cana-772 147 36 and and CCONJ cana-772 147 37 their their PRON cana-772 147 38 solutions solution NOUN cana-772 147 39 [ [ X cana-772 147 40 14 14 NUM cana-772 147 41 ] ] PUNCT cana-772 147 42 . . PUNCT cana-772 148 1 the the DET cana-772 148 2 mathematical mathematical ADJ cana-772 148 3 modelling modelling NOUN cana-772 148 4 yielded yield VERB cana-772 148 5 several several ADJ cana-772 148 6 significant significant ADJ cana-772 148 7 findings finding NOUN cana-772 148 8 : : PUNCT cana-772 148 9 the the DET cana-772 148 10 study study NOUN cana-772 148 11 formulates formulate VERB cana-772 148 12 differential differential ADJ cana-772 148 13 equations equation NOUN cana-772 148 14 to to PART cana-772 148 15 model model VERB cana-772 148 16 the the DET cana-772 148 17 temporal temporal ADJ cana-772 148 18 evolution evolution NOUN cana-772 148 19 of of ADP cana-772 148 20 inventory inventory NOUN cana-772 148 21 levels level NOUN cana-772 148 22 , , PUNCT cana-772 148 23 considering consider VERB cana-772 148 24 variables variable NOUN cana-772 148 25 such such ADJ cana-772 148 26 as as ADP cana-772 148 27 replenishment replenishment NOUN cana-772 148 28 rates rate NOUN cana-772 148 29 , , PUNCT cana-772 148 30 demand demand NOUN cana-772 148 31 rates rate NOUN cana-772 148 32 , , PUNCT cana-772 148 33 and and CCONJ cana-772 148 34 deterioration deterioration NOUN cana-772 148 35 rates rate NOUN cana-772 148 36 . . PUNCT cana-772 149 1 these these DET cana-772 149 2 equations equation NOUN cana-772 149 3 offer offer VERB cana-772 149 4 a a DET cana-772 149 5 mathematical mathematical ADJ cana-772 149 6 framework framework NOUN cana-772 149 7 for for ADP cana-772 149 8 examining examine VERB cana-772 149 9 inventory inventory NOUN cana-772 149 10 dynamics dynamic NOUN cana-772 149 11 and and CCONJ cana-772 149 12 optimising optimise VERB cana-772 149 13 inventory inventory NOUN cana-772 149 14 management management NOUN cana-772 149 15 strategies strategy NOUN cana-772 149 16 . . PUNCT cana-772 150 1 by by ADP cana-772 150 2 integrating integrate VERB cana-772 150 3 and and CCONJ cana-772 150 4 solving solve VERB cana-772 150 5 differential differential ADJ cana-772 150 6 equations equation NOUN cana-772 150 7 , , PUNCT cana-772 150 8 this this DET cana-772 150 9 study study NOUN cana-772 150 10 obtains obtain VERB cana-772 150 11 solutions solution NOUN cana-772 150 12 for for ADP cana-772 150 13 inventory inventory NOUN cana-772 150 14 levels level NOUN cana-772 150 15 , , PUNCT cana-772 150 16 deterioration deterioration NOUN cana-772 150 17 levels level NOUN cana-772 150 18 , , PUNCT cana-772 150 19 and and CCONJ cana-772 150 20 shortage shortage NOUN cana-772 150 21 levels level NOUN cana-772 150 22 at at ADP cana-772 150 23 various various ADJ cana-772 150 24 time time NOUN cana-772 150 25 intervals interval NOUN cana-772 150 26 . . PUNCT cana-772 151 1 these these DET cana-772 151 2 solutions solution NOUN cana-772 151 3 provide provide VERB cana-772 151 4 valuable valuable ADJ cana-772 151 5 understanding understanding NOUN cana-772 151 6 of of ADP cana-772 151 7 inventory inventory NOUN cana-772 151 8 system system NOUN cana-772 151 9 dynamics dynamic NOUN cana-772 151 10 and and CCONJ cana-772 151 11 the the DET cana-772 151 12 impact impact NOUN cana-772 151 13 of of ADP cana-772 151 14 deterioration deterioration NOUN cana-772 151 15 on on ADP cana-772 151 16 inventory inventory NOUN cana-772 151 17 levels level NOUN cana-772 151 18 over over ADP cana-772 151 19 a a DET cana-772 151 20 period period NOUN cana-772 151 21 . . PUNCT cana-772 152 1 the the DET cana-772 152 2 study study NOUN cana-772 152 3 performs perform VERB cana-772 152 4 a a DET cana-772 152 5 sensitivity sensitivity NOUN cana-772 152 6 analysis analysis NOUN cana-772 152 7 to to PART cana-772 152 8 investigate investigate VERB cana-772 152 9 the the DET cana-772 152 10 influence influence NOUN cana-772 152 11 of of ADP cana-772 152 12 altering alter VERB cana-772 152 13 parameters parameter NOUN cana-772 152 14 , , PUNCT cana-772 152 15 such such ADJ cana-772 152 16 as as ADP cana-772 152 17 demand demand NOUN cana-772 152 18 rates rate NOUN cana-772 152 19 , , PUNCT cana-772 152 20 preservation preservation NOUN cana-772 152 21 factors factor NOUN cana-772 152 22 , , PUNCT cana-772 152 23 and and CCONJ cana-772 152 24 initial initial ADJ cana-772 152 25 inventory inventory NOUN cana-772 152 26 levels level NOUN cana-772 152 27 , , PUNCT cana-772 152 28 on on ADP cana-772 152 29 the the DET cana-772 152 30 dynamics dynamic NOUN cana-772 152 31 of of ADP cana-772 152 32 inventory inventory NOUN cana-772 152 33 . . PUNCT cana-772 153 1 this this DET cana-772 153 2 analysis analysis NOUN cana-772 153 3 facilitates facilitate VERB cana-772 153 4 the the DET cana-772 153 5 identification identification NOUN cana-772 153 6 of of ADP cana-772 153 7 crucial crucial ADJ cana-772 153 8 factors factor NOUN cana-772 153 9 that that PRON cana-772 153 10 influence influence VERB cana-772 153 11 decisions decision NOUN cana-772 153 12 regarding regard VERB cana-772 153 13 inventory inventory NOUN cana-772 153 14 management management NOUN cana-772 153 15 and and CCONJ cana-772 153 16 enables enable VERB cana-772 153 17 the the DET cana-772 153 18 optimisation optimisation NOUN cana-772 153 19 of of ADP cana-772 153 20 strategies strategy NOUN cana-772 153 21 for for ADP cana-772 153 22 controlling control VERB cana-772 153 23 inventory inventory NOUN cana-772 153 24 . . PUNCT cana-772 154 1 numerical numerical ADJ cana-772 154 2 examples example NOUN cana-772 154 3 exemplify exemplify VERB cana-772 154 4 the the DET cana-772 154 5 utilisation utilisation NOUN cana-772 154 6 of of ADP cana-772 154 7 mathematical mathematical ADJ cana-772 154 8 models model NOUN cana-772 154 9 in in ADP cana-772 154 10 practical practical ADJ cana-772 154 11 situations situation NOUN cana-772 154 12 , , PUNCT cana-772 154 13 showcasing showcase VERB cana-772 154 14 how how SCONJ cana-772 154 15 these these DET cana-772 154 16 models model NOUN cana-772 154 17 can can AUX cana-772 154 18 be be AUX cana-772 154 19 employed employ VERB cana-772 154 20 to to PART cana-772 154 21 scrutinise scrutinise VERB cana-772 154 22 inventory inventory NOUN cana-772 154 23 systems system NOUN cana-772 154 24 , , PUNCT cana-772 154 25 forecast forecast VERB cana-772 154 26 inventory inventory NOUN cana-772 154 27 levels level NOUN cana-772 154 28 , , PUNCT cana-772 154 29 and and CCONJ cana-772 154 30 enhance enhance VERB cana-772 154 31 inventory inventory NOUN cana-772 154 32 management management NOUN cana-772 154 33 practices practice NOUN cana-772 154 34 . . PUNCT cana-772 155 1 in in ADP cana-772 155 2 summary summary NOUN cana-772 155 3 , , PUNCT cana-772 155 4 the the DET cana-772 155 5 mathematical mathematical ADJ cana-772 155 6 modelling modelling NOUN cana-772 155 7 presented present VERB cana-772 155 8 in in ADP cana-772 155 9 the the DET cana-772 155 10 study study NOUN cana-772 155 11 offers offer VERB cana-772 155 12 a a DET cana-772 155 13 rigorous rigorous ADJ cana-772 155 14 analytical analytical ADJ cana-772 155 15 framework framework NOUN cana-772 155 16 for for ADP cana-772 155 17 comprehending comprehend VERB cana-772 155 18 and and CCONJ cana-772 155 19 enhancing enhance VERB cana-772 155 20 inventory inventory NOUN cana-772 155 21 management management NOUN cana-772 155 22 strategies strategy NOUN cana-772 155 23 when when SCONJ cana-772 155 24 dealing deal VERB cana-772 155 25 with with ADP cana-772 155 26 deteriorating deteriorate VERB cana-772 155 27 inventory inventory NOUN cana-772 155 28 items item NOUN cana-772 155 29 . . PUNCT cana-772 156 1 acknowledgement acknowledgement NOUN cana-772 156 2 authors author NOUN cana-772 156 3 are be AUX cana-772 156 4 thankful thankful ADJ cana-772 156 5 to to ADP cana-772 156 6 integral integral ADJ cana-772 156 7 university university NOUN cana-772 156 8 , , PUNCT cana-772 156 9 lucknow lucknow NOUN cana-772 156 10 for for ADP cana-772 156 11 providing provide VERB cana-772 156 12 mcn mcn PROPN cana-772 156 13 : : PUNCT cana-772 156 14 iu iu ADP cana-772 156 15 / / SYM cana-772 156 16 r&d/2024mcn0002639 r&d/2024mcn0002639 NOUN cana-772 156 17 for for ADP cana-772 156 18 this this DET cana-772 156 19 research research NOUN cana-772 156 20 article article NOUN cana-772 156 21 . . PUNCT cana-772 157 1 references reference NOUN cana-772 157 2 [ [ X cana-772 157 3 1 1 NUM cana-772 157 4 ] ] X cana-772 157 5 murty murty PROPN cana-772 157 6 rama rama PROPN cana-772 157 7 , , PUNCT cana-772 157 8 p.(2005 p.(2005 PROPN cana-772 157 9 ) ) PUNCT cana-772 157 10 : : PUNCT cana-772 157 11 operations operation NOUN cana-772 157 12 research research NOUN cana-772 157 13 , , PUNCT cana-772 157 14 new new ADJ cana-772 157 15 age age NOUN cana-772 157 16 india india PROPN cana-772 157 17 publications publication NOUN cana-772 157 18 , , PUNCT cana-772 157 19 new new ADJ cana-772 157 20 delhi delhi PROPN cana-772 157 21 , , PUNCT cana-772 157 22 [ [ X cana-772 157 23 2 2 NUM cana-772 157 24 ] ] X cana-772 157 25 taha taha PROPN cana-772 157 26 , , PUNCT cana-772 157 27 h.a h.a PROPN cana-772 157 28 . . PROPN cana-772 157 29 ( ( PUNCT cana-772 157 30 2007 2007 NUM cana-772 157 31 ): ): PUNCT cana-772 157 32 operations operation NOUN cana-772 157 33 research research NOUN cana-772 157 34 - - PUNCT cana-772 157 35 an an DET cana-772 157 36 introduction introduction NOUN cana-772 157 37 , , PUNCT cana-772 157 38 pearson pearson PROPN cana-772 157 39 education education PROPN cana-772 157 40 , , PUNCT cana-772 157 41 usa usa PROPN cana-772 157 42 . . PUNCT cana-772 158 1 [ [ X cana-772 158 2 3 3 X cana-772 158 3 ] ] X cana-772 158 4 c.k c.k PROPN cana-772 158 5 jaggi jaggi PROPN cana-772 158 6 , , PUNCT cana-772 158 7 k.k k.k PROPN cana-772 158 8 . . PROPN cana-772 158 9 aggarwal aggarwal PROPN cana-772 158 10 and and CCONJ cana-772 158 11 s.k.goel s.k.goel PROPN cana-772 158 12 ( ( PUNCT cana-772 158 13 2007 2007 NUM cana-772 158 14 ): ): PUNCT cana-772 158 15 optimal optimal ADJ cana-772 158 16 order order NOUN cana-772 158 17 policy policy NOUN cana-772 158 18 for for ADP cana-772 158 19 deteriorating deteriorate VERB cana-772 158 20 items item NOUN cana-772 158 21 with with ADP cana-772 158 22 in in ADP cana-772 158 23 flat flat ADJ cana-772 158 24 ion ion NOUN cana-772 158 25 induced induce VERB cana-772 158 26 demand demand NOUN cana-772 158 27 , , PUNCT cana-772 158 28 international international ADJ cana-772 158 29 journal journal NOUN cana-772 158 30 of of ADP cana-772 158 31 production production NOUN cana-772 158 32 economics,103(2 economics,103(2 PROPN cana-772 158 33 ) ) PUNCT cana-772 158 34 , , PUNCT cana-772 159 1 p p PROPN cana-772 159 2 p. p. NOUN cana-772 159 3 707 707 NUM cana-772 159 4 - - SYM cana-772 159 5 714 714 NUM cana-772 159 6 . . PUNCT cana-772 160 1 [ [ X cana-772 160 2 4 4 NUM cana-772 160 3 ] ] X cana-772 160 4 srinivasan srinivasan NOUN cana-772 160 5 , , PUNCT cana-772 160 6 g. g. PROPN cana-772 160 7 ( ( PUNCT cana-772 160 8 2010 2010 NUM cana-772 160 9 ): ): PUNCT cana-772 160 10 operations operation NOUN cana-772 160 11 research research NOUN cana-772 160 12 : : PUNCT cana-772 160 13 principles principle NOUN cana-772 160 14 and and CCONJ cana-772 160 15 applications application NOUN cana-772 160 16 . . PUNCT cana-772 161 1 phi phi NOUN cana-772 161 2 publication publication NOUN cana-772 161 3 , , PUNCT cana-772 161 4 new new ADJ cana-772 161 5 delhi delhi PROPN cana-772 161 6 , , PUNCT cana-772 161 7 india india PROPN cana-772 161 8 . . PUNCT cana-772 162 1 communications communication NOUN cana-772 162 2 on on ADP cana-772 162 3 applied apply VERB cana-772 162 4 nonlinear nonlinear ADJ cana-772 162 5 analysis analysis NOUN cana-772 162 6 issn issn NOUN cana-772 162 7 : : PUNCT cana-772 162 8 1074 1074 NUM cana-772 162 9 - - PUNCT cana-772 162 10 133x 133x NUM cana-772 162 11 vol vol NOUN cana-772 162 12 31 31 NUM cana-772 162 13 no no NOUN cana-772 162 14 . . PUNCT cana-772 163 1 3s 3s NUM cana-772 163 2 ( ( PUNCT cana-772 163 3 2024 2024 NUM cana-772 163 4 ) ) PUNCT cana-772 163 5 335 335 NUM cana-772 163 6 https://internationalpubls.com https://internationalpubls.com X cana-772 164 1 [ [ X cana-772 164 2 5 5 NUM cana-772 164 3 ] ] X cana-772 164 4 mandal mandal PROPN cana-772 164 5 , , PUNCT cana-772 164 6 b. b. PROPN cana-772 164 7 ( ( PUNCT cana-772 164 8 2010 2010 NUM cana-772 164 9 ): ): PUNCT cana-772 164 10 an an DET cana-772 164 11 eoq eoq NOUN cana-772 164 12 inventory inventory NOUN cana-772 164 13 model model NOUN cana-772 164 14 for for ADP cana-772 164 15 weibull weibull PROPN cana-772 164 16 distributed distribute VERB cana-772 164 17 deteriorating deteriorate VERB cana-772 164 18 under under ADP cana-772 164 19 ramp ramp NOUN cana-772 164 20 type type NOUN cana-772 164 21 demand demand NOUN cana-772 164 22 and and CCONJ cana-772 164 23 shortages shortage NOUN cana-772 164 24 , , PUNCT cana-772 164 25 opsearch opsearch NOUN cana-772 164 26 , , PUNCT cana-772 164 27 42(2 42(2 PROPN cana-772 164 28 ) ) PUNCT cana-772 164 29 , , PUNCT cana-772 164 30 158 158 NUM cana-772 164 31 – – SYM cana-772 164 32 165 165 NUM cana-772 164 33 . . PUNCT cana-772 165 1 [ [ X cana-772 165 2 6 6 NUM cana-772 165 3 ] ] SYM cana-772 165 4 amutha amutha NOUN cana-772 165 5 , , PUNCT cana-772 165 6 r. r. PROPN cana-772 165 7 and and CCONJ cana-772 165 8 chandrasekaran chandrasekaran VERB cana-772 165 9 , , PUNCT cana-772 165 10 e. e. PROPN cana-772 165 11 ( ( PUNCT cana-772 165 12 2013 2013 NUM cana-772 165 13 ): ): PUNCT cana-772 165 14 an an DET cana-772 165 15 eoq eoq NOUN cana-772 165 16 model model NOUN cana-772 165 17 for for ADP cana-772 165 18 deteriorating deteriorate VERB cana-772 165 19 items item NOUN cana-772 165 20 with with ADP cana-772 165 21 quadratic quadratic ADJ cana-772 165 22 demand demand NOUN cana-772 165 23 and and CCONJ cana-772 165 24 time time NOUN cana-772 165 25 dependent dependent ADJ cana-772 165 26 holding holding NOUN cana-772 165 27 cost cost NOUN cana-772 165 28 , , PUNCT cana-772 165 29 international international ADJ cana-772 165 30 journal journal NOUN cana-772 165 31 of of ADP cana-772 165 32 emerging emerge VERB cana-772 165 33 science science NOUN cana-772 165 34 and and CCONJ cana-772 165 35 engineering engineering NOUN cana-772 165 36 , , PUNCT cana-772 165 37 1(5 1(5 NUM cana-772 165 38 ) ) PUNCT cana-772 165 39 , , PUNCT cana-772 165 40 5 5 NUM cana-772 165 41 – – SYM cana-772 165 42 6 6 NUM cana-772 165 43 . . PUNCT cana-772 166 1 [ [ X cana-772 166 2 7 7 NUM cana-772 166 3 ] ] X cana-772 166 4 chaudhry chaudhry PROPN cana-772 166 5 , , PUNCT cana-772 166 6 r.r r.r PROPN cana-772 166 7 . . PROPN cana-772 166 8 and and CCONJ cana-772 166 9 sharma sharma PROPN cana-772 166 10 , , PUNCT cana-772 166 11 v. v. PROPN cana-772 166 12 ( ( PUNCT cana-772 166 13 2013 2013 NUM cana-772 166 14 ): ): PUNCT cana-772 166 15 an an DET cana-772 166 16 inventory inventory NOUN cana-772 166 17 model model NOUN cana-772 166 18 for for ADP cana-772 166 19 deteriorating deteriorate VERB cana-772 166 20 items item NOUN cana-772 166 21 with with ADP cana-772 166 22 weibull weibull PROPN cana-772 166 23 deterioration deterioration NOUN cana-772 166 24 with with ADP cana-772 166 25 time time NOUN cana-772 166 26 dependent dependent ADJ cana-772 166 27 demand demand NOUN cana-772 166 28 and and CCONJ cana-772 166 29 shortages shortage NOUN cana-772 166 30 , , PUNCT cana-772 166 31 research research NOUN cana-772 166 32 journal journal NOUN cana-772 166 33 of of ADP cana-772 166 34 management management NOUN cana-772 166 35 sciences science NOUN cana-772 166 36 . . PUNCT cana-772 167 1 vol.2 vol.2 PROPN cana-772 167 2 , , PUNCT cana-772 167 3 no.3 no.3 VERB cana-772 167 4 , , PUNCT cana-772 167 5 pp.1 pp.1 NOUN cana-772 167 6 - - PUNCT cana-772 167 7 4 4 NUM cana-772 167 8 . . PUNCT cana-772 168 1 [ [ X cana-772 168 2 8 8 NUM cana-772 168 3 ] ] X cana-772 168 4 karmakar karmakar PROPN cana-772 168 5 , , PUNCT cana-772 168 6 b. b. PROPN cana-772 168 7 and and CCONJ cana-772 168 8 choudhuri choudhuri PROPN cana-772 168 9 , , PUNCT cana-772 168 10 k.d k.d PROPN cana-772 168 11 . . PROPN cana-772 168 12 ( ( PUNCT cana-772 168 13 2013 2013 NUM cana-772 168 14 ): ): PUNCT cana-772 168 15 inventory inventory NOUN cana-772 168 16 models model NOUN cana-772 168 17 with with ADP cana-772 168 18 ramp ramp NOUN cana-772 168 19 type type NOUN cana-772 168 20 demand demand NOUN cana-772 168 21 for for ADP cana-772 168 22 deteriorating deteriorate VERB cana-772 168 23 items item NOUN cana-772 168 24 with with ADP cana-772 168 25 partial partial ADJ cana-772 168 26 backlogging backlogging NOUN cana-772 168 27 and and CCONJ cana-772 168 28 time time NOUN cana-772 168 29 varying vary VERB cana-772 168 30 holding hold VERB cana-772 168 31 cost cost NOUN cana-772 168 32 , , PUNCT cana-772 168 33 yugoslav yugoslav ADJ cana-772 168 34 journal journal PROPN cana-772 168 35 of of ADP cana-772 168 36 operation operation NOUN cana-772 168 37 research research NOUN cana-772 168 38 , , PUNCT cana-772 168 39 23(2 23(2 NOUN cana-772 168 40 ) ) PUNCT cana-772 168 41 , , PUNCT cana-772 168 42 pp.1 pp.1 NOUN cana-772 168 43 - - PUNCT cana-772 168 44 17 17 NUM cana-772 168 45 . . PUNCT cana-772 169 1 [ [ X cana-772 169 2 9 9 NUM cana-772 169 3 ] ] X cana-772 169 4 koumanakos koumanakos NOUN cana-772 169 5 , , PUNCT cana-772 169 6 d.p d.p PROPN cana-772 169 7 . . PROPN cana-772 169 8 , , PUNCT cana-772 169 9 ( ( PUNCT cana-772 169 10 2008 2008 NUM cana-772 169 11 ): ): PUNCT cana-772 169 12 the the DET cana-772 169 13 effect effect NOUN cana-772 169 14 of of ADP cana-772 169 15 inventory inventory NOUN cana-772 169 16 management management NOUN cana-772 169 17 on on ADP cana-772 169 18 firm firm ADJ cana-772 169 19 performance performance NOUN cana-772 169 20 . . PUNCT cana-772 170 1 international international ADJ cana-772 170 2 journal journal PROPN cana-772 170 3 of of ADP cana-772 170 4 productivity productivity NOUN cana-772 170 5 and and CCONJ cana-772 170 6 performance performance NOUN cana-772 170 7 management management NOUN cana-772 170 8 , , PUNCT cana-772 170 9 57(5 57(5 NOUN cana-772 170 10 ) ) PUNCT cana-772 170 11 , , PUNCT cana-772 170 12 pp.355 pp.355 PROPN cana-772 170 13 - - PUNCT cana-772 170 14 369 369 NUM cana-772 170 15 . . PUNCT cana-772 171 1 [ [ X cana-772 171 2 10 10 NUM cana-772 171 3 ] ] X cana-772 171 4 goΕ‚aΕ› goΕ‚aΕ› NOUN cana-772 171 5 , , PUNCT cana-772 171 6 z. z. PROPN cana-772 171 7 , , PUNCT cana-772 171 8 ( ( PUNCT cana-772 171 9 2020 2020 NUM cana-772 171 10 ): ): PUNCT cana-772 171 11 effect effect NOUN cana-772 171 12 of of ADP cana-772 171 13 inventory inventory NOUN cana-772 171 14 management management NOUN cana-772 171 15 on on ADP cana-772 171 16 profitability profitability NOUN cana-772 171 17 : : PUNCT cana-772 171 18 evidence evidence NOUN cana-772 171 19 from from ADP cana-772 171 20 the the DET cana-772 171 21 polish polish ADJ cana-772 171 22 food food NOUN cana-772 171 23 industry industry NOUN cana-772 171 24 : : PUNCT cana-772 171 25 case case NOUN cana-772 171 26 study study NOUN cana-772 171 27 . . PUNCT cana-772 172 1 [ [ X cana-772 172 2 11 11 NUM cana-772 172 3 ] ] PUNCT cana-772 172 4 gebisa gebisa NOUN cana-772 172 5 , , PUNCT cana-772 172 6 d. d. PROPN cana-772 172 7 , , PUNCT cana-772 172 8 ( ( PUNCT cana-772 172 9 2023 2023 NUM cana-772 172 10 ): ): PUNCT cana-772 172 11 the the DET cana-772 172 12 impact impact NOUN cana-772 172 13 of of ADP cana-772 172 14 information information NOUN cana-772 172 15 sharing sharing NOUN cana-772 172 16 and and CCONJ cana-772 172 17 inventory inventory NOUN cana-772 172 18 management management NOUN cana-772 172 19 practices practice NOUN cana-772 172 20 on on ADP cana-772 172 21 firms firm NOUN cana-772 172 22 ' ' PART cana-772 172 23 performance performance NOUN cana-772 172 24 in in ADP cana-772 172 25 supply supply NOUN cana-772 172 26 chain chain NOUN cana-772 172 27 practices practice NOUN cana-772 172 28 . . PUNCT cana-772 173 1 gadjah gadjah PROPN cana-772 173 2 mada mada PROPN cana-772 173 3 international international PROPN cana-772 173 4 journal journal PROPN cana-772 173 5 of of ADP cana-772 173 6 business business NOUN cana-772 173 7 , , PUNCT cana-772 173 8 25(2 25(2 NUM cana-772 173 9 ) ) PUNCT cana-772 173 10 , , PUNCT cana-772 173 11 pp.199 pp.199 NOUN cana-772 173 12 - - PUNCT cana-772 173 13 225 225 NUM cana-772 173 14 . . PUNCT cana-772 174 1 [ [ X cana-772 174 2 12 12 NUM cana-772 174 3 ] ] X cana-772 174 4 shokouhifar shokouhifar NOUN cana-772 174 5 , , PUNCT cana-772 174 6 m. m. NOUN cana-772 174 7 , , PUNCT cana-772 174 8 sabbaghi sabbaghi PROPN cana-772 174 9 , , PUNCT cana-772 174 10 m.m m.m PROPN cana-772 174 11 . . PROPN cana-772 174 12 and and CCONJ cana-772 174 13 pilevari pilevari NOUN cana-772 174 14 , , PUNCT cana-772 174 15 n. n. NOUN cana-772 174 16 , , PUNCT cana-772 174 17 ( ( PUNCT cana-772 174 18 2021 2021 NUM cana-772 174 19 ) ) PUNCT cana-772 174 20 . . PUNCT cana-772 175 1 inventory inventory NOUN cana-772 175 2 management management NOUN cana-772 175 3 in in ADP cana-772 175 4 blood blood NOUN cana-772 175 5 supply supply NOUN cana-772 175 6 chain chain NOUN cana-772 175 7 considering consider VERB cana-772 175 8 fuzzy fuzzy ADJ cana-772 175 9 supply supply NOUN cana-772 175 10 / / SYM cana-772 175 11 demand demand NOUN cana-772 175 12 uncertainties uncertainty NOUN cana-772 175 13 and and CCONJ cana-772 175 14 lateral lateral ADJ cana-772 175 15 transshipment transshipment NOUN cana-772 175 16 . . PUNCT cana-772 176 1 transfusion transfusion NOUN cana-772 176 2 and and CCONJ cana-772 176 3 apheresis apheresis NOUN cana-772 176 4 science science NOUN cana-772 176 5 , , PUNCT cana-772 176 6 60(3 60(3 NOUN cana-772 176 7 ) ) PUNCT cana-772 176 8 , , PUNCT cana-772 176 9 p.103103 p.103103 NOUN cana-772 176 10 . . PUNCT cana-772 177 1 [ [ X cana-772 177 2 13 13 NUM cana-772 177 3 ] ] SYM cana-772 177 4 minner minner NOUN cana-772 177 5 , , PUNCT cana-772 177 6 s. s. PROPN cana-772 177 7 and and CCONJ cana-772 177 8 sachs sachs PROPN cana-772 177 9 , , PUNCT cana-772 177 10 a.l a.l PROPN cana-772 177 11 . . PROPN cana-772 177 12 , , PUNCT cana-772 177 13 ( ( PUNCT cana-772 177 14 2023 2023 NUM cana-772 177 15 ): ): PUNCT cana-772 177 16 retail retail ADJ cana-772 177 17 inventory inventory NOUN cana-772 177 18 systems system NOUN cana-772 177 19 . . PUNCT cana-772 178 1 research research NOUN cana-772 178 2 handbook handbook NOUN cana-772 178 3 on on ADP cana-772 178 4 inventory inventory NOUN cana-772 178 5 management management NOUN cana-772 178 6 , , PUNCT cana-772 178 7 p.476 p.476 NOUN cana-772 178 8 . . PUNCT cana-772 179 1 [ [ X cana-772 179 2 14 14 NUM cana-772 179 3 ] ] PUNCT cana-772 179 4 utami utami NOUN cana-772 179 5 , , PUNCT cana-772 179 6 n.p n.p PROPN cana-772 179 7 . . PROPN cana-772 179 8 , , PUNCT cana-772 179 9 bahit bahit ADJ cana-772 179 10 , , PUNCT cana-772 179 11 m. m. NOUN cana-772 179 12 and and CCONJ cana-772 179 13 cahyani cahyani NOUN cana-772 179 14 , , PUNCT cana-772 179 15 t.r t.r PROPN cana-772 179 16 . . PROPN cana-772 179 17 , , PUNCT cana-772 179 18 ( ( PUNCT cana-772 179 19 2023 2023 NUM cana-772 179 20 ): ): PUNCT cana-772 179 21 september september PROPN cana-772 179 22 . . PUNCT cana-772 180 1 implementation implementation NOUN cana-772 180 2 of of ADP cana-772 180 3 a a DET cana-772 180 4 web web NOUN cana-772 180 5 - - PUNCT cana-772 180 6 based base VERB cana-772 180 7 accounting accounting NOUN cana-772 180 8 information information NOUN cana-772 180 9 system system NOUN cana-772 180 10 for for ADP cana-772 180 11 management management NOUN cana-772 180 12 of of ADP cana-772 180 13 consumable consumable ADJ cana-772 180 14 goods good NOUN cana-772 180 15 inventory inventory NOUN cana-772 180 16 case case NOUN cana-772 180 17 study study NOUN cana-772 180 18 : : PUNCT cana-772 180 19 banjarbaru banjarbaru PROPN cana-772 180 20 city city PROPN cana-772 180 21 regional regional PROPN cana-772 180 22 revenue revenue NOUN cana-772 180 23 service service NOUN cana-772 180 24 unit unit NOUN cana-772 180 25 . . PUNCT cana-772 181 1 in in ADP cana-772 181 2 the the DET cana-772 181 3 international international ADJ cana-772 181 4 conference conference NOUN cana-772 181 5 on on ADP cana-772 181 6 education education NOUN cana-772 181 7 , , PUNCT cana-772 181 8 social social ADJ cana-772 181 9 sciences science NOUN cana-772 181 10 and and CCONJ cana-772 181 11 technology technology NOUN cana-772 181 12 ( ( PUNCT cana-772 181 13 icesst icesst NOUN cana-772 181 14 ) ) PUNCT cana-772 181 15 ( ( PUNCT cana-772 181 16 vol vol NOUN cana-772 181 17 . . NOUN cana-772 181 18 2 2 NUM cana-772 181 19 , , PUNCT cana-772 181 20 no no INTJ cana-772 181 21 . . NOUN cana-772 181 22 2 2 NUM cana-772 181 23 , , PUNCT cana-772 181 24 pp pp ADJ cana-772 181 25 . . PUNCT cana-772 181 26 170 170 NUM cana-772 181 27 - - SYM cana-772 181 28 181 181 NUM cana-772 181 29 ) ) PUNCT cana-772 181 30 . . PUNCT cana-772 182 1 [ [ X cana-772 182 2 15 15 NUM cana-772 182 3 ] ] X cana-772 182 4 kumar kumar PROPN cana-772 182 5 , , PUNCT cana-772 182 6 n. n. NOUN cana-772 182 7 , , PUNCT cana-772 182 8 rabbani rabbani PROPN cana-772 182 9 , , PUNCT cana-772 182 10 q. q. PROPN cana-772 182 11 and and CCONJ cana-772 182 12 khan khan PROPN cana-772 182 13 , , PUNCT cana-772 182 14 n.a n.a PROPN cana-772 182 15 . . PROPN cana-772 182 16 ( ( PUNCT cana-772 182 17 2024 2024 NUM cana-772 182 18 ): ): PUNCT cana-772 182 19 an an DET cana-772 182 20 evaluation evaluation NOUN cana-772 182 21 of of ADP cana-772 182 22 the the DET cana-772 182 23 potential potential NOUN cana-772 182 24 for for ADP cana-772 182 25 disruption disruption NOUN cana-772 182 26 to to ADP cana-772 182 27 the the DET cana-772 182 28 entire entire ADJ cana-772 182 29 inventory inventory NOUN cana-772 182 30 management management NOUN cana-772 182 31 function function NOUN cana-772 182 32 schedule schedule NOUN cana-772 182 33 , , PUNCT cana-772 182 34 educational educational ADJ cana-772 182 35 administration administration NOUN cana-772 182 36 : : PUNCT cana-772 182 37 theory theory NOUN cana-772 182 38 and and CCONJ cana-772 182 39 practice practice NOUN cana-772 182 40 , , PUNCT cana-772 182 41 30(4),8061 30(4),8061 NUM cana-772 182 42 - - SYM cana-772 182 43 8066 8066 NUM cana-772 182 44 . . PUNCT cana-772 183 1 doi doi NOUN cana-772 183 2 : : PUNCT cana-772 183 3 10.53555 10.53555 NUM cana-772 183 4 / / SYM cana-772 183 5 kuey.v30i4.1942 kuey.v30i4.1942 NOUN cana-772 183 6 . . PUNCT