Optimal Buyer-Seller Inventory Models in Supply Chain

Transcription

1 Inernaonal Conference on Educaon echnology and Informaon Sysem (ICEIS 03 Opmal Buyer-Seller Invenory Models n Supply Chan Gaobo L Shandong Women s Unversy, Jnan, 50300,Chna emal: lgaobo_979@63.com Keywords: Invenory; Deeroraon merchandse; Jon cos; Quany dscoun Absrac. In hs sudy, we focus mprovemen nvenory models on wo member s smple buyer-seller sysem n supply chan. An nvenory model s developed for a me-varyng demand deerorang nvenory o deermne he opmal order nerval and dscoun prce so ha he jon oal cos s mnmzed durng a fne plannng horzon. Inroducon he ncreasng of globalzaon of markes and compeon pressure, forces companes o develop he parnershp of supply chan o respond quckly o cusomer requremen. Supply chan managemen s he use of he effecve negraon of supplers, manufacures, dsrbuors, dsrbuon and nvenory and so on, so ha goods can be n he rgh quany and be sen o he rgh place a he rgh me, makng he sysem(sysem-wdecos o a mnmum and meeng he requred servce level a he same me. In he supply chan, nvenory of goods s he man operang acvy and he source of prof. In order o mee he operang acvy s needs and gve he goods o he cusomer on me, boh buyers are approprae o hold goods. However, wh operang acvy for boh buyers, as well as he sorage and managemen of goods, he relevan nvenory cos s brough for boh buyers. he plannng and managemen performance of he nvenory are val o he survval and developmen of he company. Boh buyers n supply chan are commed o make he relevan nvenory cos o a mnmum and he prof o he hghes. In order o make nvenory model agree wh he curren of he operang acvy,negraed nvenory model consderng mulple facors gradually ncreases, whch makes he dervaon of he model more complex, so ha par of leraure dscussng he model consruced by he nvenory problem only derves approxmae soluon of he nvenory model. ha shows here s room for mprovemen of sorage of he nvenory problem. herefore, hs research based on hese facors and Gao yushu s(996 hypohess, uses dfferen mahemacal derved sysems and consrucs opmal buyer-seller nvenory model of supply chan, o explore he moderae smplfcaon and possbles of mprovemen of he relevan nvenory model and derve he opmal decson-makng soluon of he nvenory model. Sudy on he heores of he nvenory model. Sudy on he heores of he buyer-seller nvenory model Douglas(996 pu forward a lo of radonal nvenory models focused on he decson of buyer s opmal order number, and such models may gnore he wo chances: Frsly, he nvesmen of maeral handlng equpmen or daa exchange echnology, for example, elecronc nformaon exchange sysem, can reduce he cos whou changng he orderng sraegy. Secondly, he company can fnd he opmal jon order number for boh buyers and decde how o allocae he savng value hrough he pares consulaon. Lal and Saeln(994 proposed he response model for he seller of he buyer s prcng plans, o encourage he buyer o order even greaer number of movemens per me and make boh buyers relevan nvenory cos mnmum. Nahan(994 pu forward he opmal quany dscoun prce for he seller of he buyer s order level,o make he seller oban he maxmum prof and no ncrease he seller s cos of he nvenory model. In he 03. he auhors - Publshed by Alans Press 76

2 random condon, Banerjee(996 processed he analyss model conrolled by he sngle good nvenory for he developmen of he sngle seller and he mul-buyer and used he EDI o make he coordnaon n hs model become more easy. In he real ndusry,lu Yuchang(999 nvesgaed he decson-makng model of he nvenory of he prce n supplers and realers and he order quany when he buyer s demand s nfluenced by he prce. Mos of hem jus conras he opmal model and develop he model of calculus n he buy s opnon, and no analyze how o develop he bes quoaon archecure of he seller o nfluence he buyer s purchasng sraegy. o nvesgae he nvenory for he seller, he buyer, or boh buyers s o make he seller and he buyer s relevan nvenory cos and boh buyers jon cos mnmum. However, f only he buyer or he seller profs, he sysem wll no las long. Many sudes have shown ha, boh buyers can reduce he jon cos and ncrease he prof n he coordnaon and cooperaon mode. So hs research s manly o explore he opmal buyer-seller nvenory model..sudy on he relevan heores of he deeroraon nvenory model Ghare and Scrader(973 consdered he problem of he deeroraon merchandse nvenory n her developmen nvenory model. Msra(975 proposed he nvenory model whose replenshmen rae s fne, and he deeroraon of he merchandse obeys he exponenal dsrbuon and Webb dsrbuon wh wo parameers. In accordance wh he buyer and he seller n sngle, Gao Yushu(996 explored he opmal nvenory model n he fxed ndex loss when he seller s replenshmen rae s fne and nfne, and he buyer s demand changes over me and s lner. Consderng he demand s fxed and he ndex loss s fxed, Wu Meyng(999pu he concep of he small bach ransporaon no he nvenory o oban he opmal jon cos of he mul-buyer and he sngle seller. In he lgh of he pershable goods, Han Jahong(00bul up he mul-sage order sraegy n perod of valdy o solve he problem of sngle sage order n perod of valdy of he radonal nvenory model. 3.Sudy on he heores of he quany dscoun nvenory model In he commercal acves, he buyer should consder how much he order quany s, when s me o replensh he nvenory and how much o mnmze he oal relevan cos. Bu he seller always res o provde he quany dscoun o nfluence he buyer s order behavor and encourage he buyer o order more, lookng for reducng he seup cos and he ransacon cos. Susan and Zhmn(995 denfed hree man areas of research: he frs s o explore he nvenory model n he pon of he buyer s opmal order quany,or he buyer obans he quany dscoun of he seller because of a large order. he second s o explore he nvenory model n he pon of he seller, and o acheve he purpose of he lowes ransacon cos hrough quany dscoun or dfference n prce. he hrd s o explore he jon nvenory model n he pon of boh buyers and o mprove ransacon effcency akng no he neress of boh buyers. Ln Xuy(997used he equlbrum heory o explore he opmal sysem order quany,order prce and delvery mes for boh buyers under he dfferen subordnae relaonshp,and o esablsh a prce dscoun model n mulple dsrbuon envronmen o analyze he sensvy of he changes of he demand, he budge of he buyer, he order cos, he shorage percenage, he dsrbuon cos and he holng cos. 4.Sudy on he heores of he prof sharng Facors of esrangemen beween buyers and sellers are: nconssency, crcal ncden, conflc and perceved dfferences. here are many poenal sources of conflc beween buyers and sellers, ncludng: prce, qualy, delvery, delayed paymen, fnancal penales for non-performance, order cancellaons and nellecual propery. Bu all of he procuremen professonals are very clear mos me should be spen on he problem abou he purchase prce. he coordnaon and cooperaon of boh buyer s advanageous o reduce he conflc. How o dsrbue he co-creaon prof of 77

3 coordnaon and cooperaon s a key facor o make boh buyers susan cooperaon or ncrease conflc. herefore, he problem of dsrbuon of profs n he opmal buyer-seller nvenory model s also valued by researchers. Consrucon of he nvenory model.research he framework Accordng o he heory above, a lo of researches mprove he ransacon effcency o make he buyer-seller relevan nvenory cos mnmum. Sudy he heores of he deeroraon nvenory s o explore he opmal nvenory model under dfferen crcumsances of he loss. Sudy he heores of he quany dscoun s o seek o derve he opmal prce and replenshmen sraegy n varous quany dscoun model o mnmze he buyer-seller relevan nvenory cos. Sudy on he heores of he prof sharng s o consruc he model of prof sharng as he addonal prof sharng sysem for boh buyers consderng he wegh facors or usng dfferen negoaon model afer obanng he mnmum jon cos. We fnd n he sudy ha Gao Yushu(996explored he opmal nvenory model of he deeroraon merchandse when he buyer s demand changes over me. In order o make he buyer-seller jon cos mnmum, he used ral and error mehod o deermne he opmal order cycle and he opmal approxmae soluon o he dscoun prce. hs sudy based on he assumpon by Gao YUshu(996 uses dfferen analycal mehods o derve he opmal order cycle and he opmal soluon o he dscoun prce o mnmze he buyer-seller jon cos. Accordng o o he dscusson above consdered, we pu forward he research framework, as shown on fg.. he quany dscoun Appropraon of prof he defnon of he buyer-seller nvenory model he dervaon of he consrucon of he buyer-seller nvenory model he opmal buyer-seller nvenory model Consderng deeroraon he Fg.. he research framework of he hess Fg.. he model ha he demand changes wh me, relaonshp beween nvenory levels and me.he basc assumpon of he nvenory he symbols used n he nvenory are as follows: H :Plannng perod;m : he order number n he plannng perod; P :he orgnal prce of he goods; p :he dscoun prce of he goods n he cycle,,,..., m ; : he deeroraon rae of he goods; r :he nvenory rao n un me of he buyer s per un; K :he order processng cos of he seller; S :he seup cos of he seller; A : he order processng cos of he buyer; BS :he savng value of he buyer n per un me; SS : he savng value of he seller n per un me; α ;he dsrbuon proporon of he savng value n buyer-seller sysem; I :he oal capacy of he nvenory n he cycle; :Any order cycle,,,..., m ; :he me pon,,..., m ( of he nvenory depleon n any cycle, +,,,... m, 0; H 0 m m. 0 0; m H ;,,,... m ; +,,,... m D :he demand rae, a funcon of me, D( a+ b, 0 H;a 78

4 andb are consans, 0, a+ b 0 demand decreases wh me. ( p ( p a ; When b 0,he demand ncreases wh me; When b 0 B, : he cos of he buyer n he cycle,,,..., m. S, : he cos of he seller n he cycle,,,..., m. J ( p, : he jon cos of boh buyers n he cycle,,,..., m Q ( : he nvenory cos n any me n he cycle.., he o solve he nvenory model hs chaper wll derve he opmal nvenory model and use he analyss mehod o oban he soluon o he opmal buyer-seller nvenory model. Accordng o he hypohess, when he demand ncreases lnearly wh me, relaonshp beween nvenory levels and me s as shown n fg.. If Q ( denoes he cycle, he nvenory level a any me, and. he nvenorylevel can be expressed by he followng equaon: d d ( + Q ( + ( a + b 0 Q,Namely, b a b Q ( + e. c and pu no( Q, le Fg. shows ha, ( 0 + ( So, ( Q e a b b e a Le,he nal nvenory levelq n he cycle s gven by: Q ( a + b b + b e a + b Q ( e (3 he oal nvenory I ( n he cycle s gven by: I a + b b b a b ( Q ( d e e d + Because Q ( 0,, m I When and,so (4s gven by:,... + a + b b b a b ( e e + d, (for he sake of convenence, here oban he nvenory n he frs cycle: I a + b 3 b ( e a + he buyer s demand n he cycle s: D ( a + b d a + b a b b b ( (4 (5 and pu 0 no(5,you can 0 (6 (7 79

5 Le, he relevan cos for boh buyers n he frs cycle per un me can be gven by: he relevan cos for he buyer n he frs cycle per un me can be gven by: B ( p, A p Q p ri + + (8 he relevan cos for he seller n he frs cycle per un me can be gven by: ( p S + K ( P p S, Q + (9 he relevan jon cos for boh buyers n he frs cycle per un me can be gven by: J ( p, A + S + K PQ p ri + + (0 he mnmum cos proves o be exsed (he suaon ha he buyer and he seller s no uned: Le B ( P, B (, mnmze he relevan cos for he buyer n he frs cycle per un me, he ' necessary condon s: B ( 0. Pu I Q, p P, no(8,, A a b b a b a b b a b b B( + P e Pr 3 ( e ( '' ' Seek he dervave and second dervave of (, b ( e 0 B ( 0 B ( A ' a ncreasng funcon.also, B ( 0 0, B ( lm ( B( + So '' '' exss, such ha B ( 0, when ( 0, ; B ( 0 he graph of funcon B '' ( s shown as fg.3. B '' (, when. B ( s 0 O. '' Fg.3. he graph of funcon B ( Fg.4.he graph of funcon B ( I s known ha ' B ( 0, also B ' ( 0, ( 0,, B ( decreases; ( B ( ncreases. he graph of funcon B ( s shown as fg.4. B ' 0,, So, he mnmum cos B ( proves o be exsed n, namely he mnmum cos s B (. he mnmum buyer-seller jon cos J ( can be proved o be exsed n n a smlar J. Here s no proof. way, namely he mnmum cos s ( 80

6 Sudy on he opmal nvenory model Based on he analyss of he dervaon of he model, he relevan cos for boh buyers may change as follows: When he seller doesn provde he quany dscoun n he frs cycle, he buyer has o seek he opmal order cycle o mnmze he relevan cos per un me. he relevan cos for boh buyers s respecvely: B ( P, ( he relevan cos n he smalles un of me of he buyer n he order cycle S P, ( ( he relevan cos n he smalles un of me of he seller n he order cycle he mnmum jon cos for boh buyers s obaned n he order cycle. he relevan cos for boh buyers s respecvely: B ( p, ( he relevan cos per un me of he buyer n he order cycle S ( p, ( he relevan cos per un me of he buyer n he order cycle, so f he seller doesn provde he quany dscoun n he suaon ha he buyer and he seller une, namely p P,he relevan cos of he buyer per un me s: B ( P, B ( P, >,whch means he relevan cos ncreases n he suaon ha he buyer unes and he nenon of he buyer s nfluenced. If he seller provdes he quany dscoun o encourage he buyer n he suaon ha he buyer and he seller une, he relevan cos of he seller per un S me s: ( p (, S P, >, whch means he relevan cos ncreases n he suaon ha he seller provdes quany dscoun and he jon nenon of he seller s also nfluenced. Based on he analyss above, n order o make he buyer and he seller une and mnmze he jon cos for boh buyers, we mus seek he bes dscoun prce p ha replaces p and he opmal order cycle ha replaces,meeng he condon ha B ( p, B ( P, and S ( p (, S P, Concluson. p and are proved o be exsed,and hs paper wll no demonsrae n deal. hrough he analyss of nvenory model va he dervaon, under he suaon ha he buyer and he seller une, and accordng o he model hs research provdes, we ge he opmal order cycle and he opmal quany dscoun o acheve he wn-wn goal of mnmzng he jon cos and savng he relevan cos for boh buyers. References [].Gao Yushu, he buyer-seller nvenory model of he deeroraon merchandse wh me-varyng demand, ndusral engneerng, 996. [].Mnes, Creang World Class Supplers[M], Pman Publshng,Landon,994,(0. [3].Wang Yngyun, Supply chan managemen he mehod of modelng and daa mnng[m],bejng: snghua Unversy press,005,(5. [4].Lu Juqang,he enerprse logscs ousourcng and research of parner selecon[j],journal of managemen scence,006. 8