A Generalized Order-Up-To Policy and Altruistic Behavior in a Three-level Supply Chain

Transcription

1 A Geeralzed rder-up-to Polcy ad Alrusc Behavor a Three-level Supply Cha Takamch Hosoda ad Sephe M. sey Cardff Busess School UK Absrac: Assumg a sochasc exeral marke demad hs research sudes he beef of he order coordao a serally lked hree-level supply cha. Each player s cos s represeed by he fe horzo sadard devao of he ed of perod e sock levels. To represe he acvy of a player a supply cha he geeralzed order-up-o polcy proposed by Hosoda ad sey 006a s exploed. I s show ha o mmze he oal supply cha cos he aude of he frs level player o cos creases s esseal. Ths ype of order coordao s called alrusc behavor here ad ca produce a large cos reduco more ha 0% o he overall supply cha. A coordao model whch may be more applcable praccal segs s also roduced wh hs beef. Keywords: order-up-o polcy alrusc behavor order coordao Iroduco A order coordao polcy based o he rder-up-to UT polcy ha mmzes he oal veory coss for a hree-level supply cha wll be examed. or a sgle level of a supply cha assa 955 roduced a orderg polcy wh a Work I Progress WIP feedback loop ad showed ha hs orderg polcy mmzes he varace of he ed of perod e sock levels. I addo assa showed ha he mmzed varace of he ed-perod e veory level s decal o he varace of he error he forecas of demad over he lead-me plus revew perod. I hs research assa's orderg polcy s called as he radoal UT polcy. rom assa's semal corbuo s obvous ha a sgle level supply cha case he radoal UT polcy s a opmal polcy for mmzg he varace of he ed of perod e sock levels over me. I a mul-level supply cha scearo however mgh be reasoable o assume ha a sequece of radoal UT polces may o be opmal aymore as here s o guaraee ha a successo of local mmzaos wll resul a global opmum as show Hosoda ad sey 006a. Sce he radoal UT polcy does o provde I should be oed ha several researchers adop a alerave expresso for he UT polcy ha explos a me varyg UT arge see ee e al. 000 for example however he dyamcs gve by hese wo exposos s decal as show Hosoda ad sey 006b.

2 much freedom o mapulae he dyamcs of he orderg process Hosoda ad sey 006a have vesgaed a wo-level supply cha usg he radoal UT polcy modfed o clude a proporoal coroller. Ths brgs more flexbly o aler he dyamcs of he orderg process ad shows ha a sequece of radoal UT polces s o loger opmal. They also show ha o ejoy he cos savg he aude of he frs level player o cos creases s a esseal facor. They call hs aude alrusc behavor. I hs chaper he model show Hosoda ad sey 006a wll be exeded o a hree-level supply cha model ad he beef of he alrusc behavor ad roles of he frs ad he secod level players a hree-level supply cha wll be aalyzed. I addo as a bechmark for performace comparsos a sequece of hree radoal UT polces supply cha model show Hosoda ad sey 006b wll be used. eraure revew As a ype of supply cha coordao formao sharg has bee suded by may researchers. However couer-uvely o all resuls suppor he beef of formao sharg. Graves 999 sudes a wo-level supply cha wh he UT polcy ermed adapve base-sock polcy hs paper a o-saoary demad process IMA process wh Mmum Mea Square Error MMSE forecasg. Graves fds ha sharg demad formao brgs o beef o he upsream player f he upsream players kow he coeffces of he cusomer demad process. Km ad Rya 00 aalyse he value of demad formao sharg usg he model wh a ukow demad process ad a expoeal smoohg forecas. They coclude ha sharg demad daa ca sgfcaly reduce he coss upper-sream players of he supply cha. However he beef s lmed whe he upper-sream player has a large amou of hsorcal order daa as by explog hs daa he upper-sream player ca mprove s forecas accuracy. Assumg a kow demad process ad he MMSE forecas Raghuaha 00 repors smlar resuls ha he se of order hsory daa coas all he ecessary formao o allow he upper-sream player o reduce hs coss. Assumg a AR demad process ee e al. 000 develop a wo-level supply cha model ad vesgae he beef of demad formao sharg. Uder her assumpo ha he maufacurer uses oly he laes observed demad formao s forecas hey coclude ha he maufacurer ca oba veory ad coss reducos wh formao sharg. Hosoda e al. Readers are ecouraged o vs our web se hp:// o see how he alrusc behavor brgs he beefs o a supply cha. or he deals of a MMSE forecasg see Box e al. 994.

3 008 vesgae he beef of sharg he marke demad formao usg a se of daa obaed from a real real supply cha. I s show ha here s a beef of formao sharg ad a source of such beef s he error erms whch are orgally hdde he marke demad process ad dffcul o exrac whou shared marke demad formao. I addo o formao sharg some researchers have aalysed operaoal coordao of supply chas such as edor Maaged Iveory MI. Ths feld of research has araced abuda aeo sce he lae 990s. sey ad Towll 00a develop a wo-level MI supply cha model ad compare he measured bullwhp wh a radoal serally lked supply cha. They repor ha he MI scheme ca subsaally reduce he bullwhp. I her MI scheme formao abou he frs-level sock level he goods ras he secod-level sock level ad he reorder po s used o deerme he arge veory level. Usg her MI model sey ad Towll 00b vesgae each of he poeal sources of he bullwhp proposed by ee e al They show ha wo of he four causes; he raog game ad order bachg ca be compleely elmaed by he adopo of MI scheme a supply cha ad oher wo causes also ca be reduced sgfcaly. Avv ad edergrue 998 sudy he beefs of a MI scheme usg a wo-echelo supply cha model cossg of a sgle suppler ad J realers. They sudy hree scearos: a radoal deceralsed sysem a MI sysem ad a sysem wh full formao sharg bewee players. Uder he MI program he mg ad magude of he repleshme shpmes o he realers are decded by he suppler o he bass of he full formao gve by all realers. A comparso was made ad hey coclude ha he MI program where formao o veory levels s also shared has much more poeal ad ca reduce coss by 4.7% o average. The beefs of MI agas he full formao sharg scearo become larger whe capacy s gh sce MI scheme eables he suppler o crease s ulzao rae. Usg a serally lked wo-level supply cha wh a AR marke demad Hosoda ad sey 006a vesgae he mpac of alrusc behavor o he overall supply cha cos. To realze alrusc behavor a he frs level hey roduced a radoal UT polcy wh a sgle proporoal coroller he sysem feedback loop. Ths proporoal coroller eables us o mapulae he order placed by he realer o acheve lower oal supply cha cos. The sum of he sadard devaos of e sock levels a each level was used as a objecve fuco o be mmsed. I s suggesed ha alrusc behavor by he frs level player mgaes he bullwhp effec ad hs lower bullwhp s he source of he beef a he secod level. Also he cos beef a he secod level s large eough o compesae he loss a he frs level. I s show ha o average more ha 0% cos reduco ca be acheved.

4 Some researchers assume ha he secod level player ca modfy he frs level player s order paer by offerg ceves ad fd ha he frs level player should be alrusc o acheve lower oal coss. I hs wolevel supply cha model Gavre 006 assumes ha he suppler ca aler he paer of orders placed by he realer by offerg flucuag prces. As he resul of hs ceve he realer s orderg paer s o opmum for self aymore ad hus he realer s cos wll crease. However he beef a he suppler s suffce eough o compesae he crease a he realer. The overall supply cha performace ca be mproved by 5% o average wh he ad of formao sharg. uo 007 cosders a coordao scheme a wo-level supply cha cossg of a vedor ad a buyer. The vedor asks he buyer o chage s order quay o acheve lower se up orderg ad veory holdg coss of he vedor. To covce he buyer a cred perod ceve s offered by he vedor. I s show ha he beef o he vedor s always greaer ha he loss of he buyer so ha hs cooperao scheme ca brg he beefs o overall supply cha. rom hese wo papers mgh be reasoable o coclude ha he ype of ceves for he frs level player affecs he oal amou of savg coss. her ceves o ecourage he frs level player o cur cos crease clude quay flexbly Tsay 999 quay dscous Weg 995 ad reveue sharg Gaoccaro ad Poradolfo 004. The leraure revew suggess some useful sghs o our problem. rs sharg marke demad formao may brg beefs o a supply cha bu he amou of such beef s o clear. I our model herefore o egae he beef comg from sharg he marke demad formao s assumed ha up-o-dae marke demad formao s shared ad commo kowledge he supply cha. Ths assumpo eables us o focus o he beefs oly from he alrusc behavor. Secodly mgh be beer o assume a ceralzed supply cha model o quafy he beef of he alrusc behavor. I he case of a deceralzed supply cha ceves ad/or a way of redsrbuo of he geeraed beefs may sgfcaly affec he behavor of each player a supply cha. The ceralzed supply cha assumpo allows us o gore such ssues. Therefore we wll assume ha he supply cha here are o ceve coflcs all ecessary formao s shared ad all players wll cooperae o mmze he oal cos. The model A serally lked hree-level supply cha sysem s aalyzed. All hree players explo a perodc revew sysem ad he repleshme lead-me s cosa ad kow. The orderg polcy used here s he UT polcy. The UT level s adjused each me perod accordg o he laes updaed demad forecas ad he shared formao. The kowledge

5 abou he marke demad process capured by he frs level player s shared wh all oher players whou delay. I s assumed ha he rue marke demad process s correcly capured. The cos parameers ad he orderg polces he supply cha are commo kowledge.. Sequece of eves ad coss The sequece of eves ay perod a ay level s as follows: he order placed earler s receved ad he demad s fulflled a he begg of he perod he e sock level s revewed ad orderg decso s made a he ed of he perod. We wll ow descrbe he hree-level supply cha model where each level uses he UT polcy wh he MMSE forecasg scheme. We assume a perodc revew polcy bu do o assume a specfc legh of he revew perod. All of he resuls here are cosse whaever revew perod s adoped day week moh ec.. We wll use he subscrp = o represe he level of he supply cha. I s assumed ha he coss he supply cha are drecly proporoal o he sadard devao of he e sock level a each level as Hosoda ad sey 006a. Therefore he objecve fuco used hs research ca be wre as J. where represes he sable varace of he e sock level a h level of he supply cha.. Marke demad e us assume he demad paer faced by he realer s a AR process. The AR demad process assumpo s commo whe auocorrelao exss amog he demad process. May researchers employ hs assumpo see Hosoda e al. 008 for example. The formulao of AR process s gve by d where s he observed marke demad a me perod d s he cosa erm s he auoregressve coeffce < ad s a..d. whe ose process wh a mea of zero ad a varace of. The sable varace of s /. ealed dscussos abou a AR model ca be see Box e al. 997.

6 . rderg polcy The radoal UT polcy for he player a level he supply cha ca be descrbed as follows assa 955 S S ˆ where WIP safey sock s he order rae a me S s he UT level a me ad WIP s he sum of orders ha are already placed bu o ye receved a me ad ca be expressed as WIP. s he ed of perod e sock level a me ad ˆ s he codoal esmae of he oal demad from he level player over me perods whch s he lead-me plus revew perod. or = ˆ s deoed as ˆ. To realze our geeralzed UT polcy le us beg by modfyg he radoal UT polcy. S WIP ˆ WIP safey sock ~ ˆ WIP safey sock ~ ˆ WIP safey sock ~ IP WIP safey sock. ~ where s E he codoal esmae of he demad ~ me perod made a. Therefore ˆ ˆ. Whe = ~ s ~ E ad deoed as. IP s a esred Iveory Poso a me ad IP = ˆ = E. Noe ha IP = 0 f =. Icorporag a proporoal coroller o Eq.. yelds he orderg polcy he geeralzed UT polcy. ~ IP WIP safey sock where 0 < < as show Hosoda ad sey 006a. bvously f = he polcy s decal o he radoal UT polcy. I wha follows for smplcy we wll se d = 0 ad safey sock = 0 whou loss of geeraly

7 sce hese values are me vara values ad do o affec he value of J. 4 Scearos Three dffere scearos wll be cosdered here. Scearo s he hree-level radoal UT polcy supply cha ha was vesgaed Hosoda ad sey 006b. Scearo wll form he basele scearo for he oher scearos o be compared agas. Scearo s he geeralzed UT polcy supply cha case where he frs ad he secod level players explo he geeralzed UT polcy ad he hrd level player adops he radoal UT polcy. Scearo s a specal case of Scearo ; here o oly he hrd level player bu also he frs level player adops he radoal UT polcy o mmze s ow varace of he e sock. ly he mddle level player s cocered wh mmzg he objecve fuco by ug s proporoal coroller. Scearo s expeced o brg eough beef so ha hs scearo mgh be a more accepable sraegy for a real supply cha where usually he u cos of he e sock a he frs level real sore for example s he mos expesve. If Scearo s successful he varace of e sock level a he frs level player amely he real sore s mmzed due o he radoal UT polcy ad a he same me he complee supply cha ca also ejoy a cos reduco geeraed by he alrusc behavor of he secod level player. 4. Scearo : The radoal UT polcy supply cha I wha follows wll be used o show he varace of e sock level a radoal UT polcy supply cha. As show Hosoda ad sey 006b he expressos of he varaces of e sock level a each level a serally lked hree-level supply cha model are expressed as; 4.. Therefore he objecve fuco for Scearo JS becomes

8 . S J 4. Scearo : The geeralzed UT polcy supply cha Scearo assumes ha he geeralzed UT polcy s used he hreelevel supply cha. To mmze he objecve fuco Eq.. from he Prcple of pmaly Bellma 957 he hghes level player mus use he polcy whch mmzes hs ow varace of he e sock level as show Hosoda ad sey 006a. Thus he hrd level player should use he radoal UT polcy. As he resul oly he frs wo players he supply cha employ he geeralzed UT polcy. 4.. The orderg process ad MMSE forecass To oba a MMSE forecas kowledge of he srucure of he order process s requred. I he case of Scearo he process of ad he volume of orders placed by he frs ad he secod players respecvely ca be descrbed as where ad. Hosoda 005 provdes deals. Eq. 4. ad Eq. 4. yeld expressos for he MMSE forecass of over me perods ˆ where = ad.

9 ˆ E. ˆ E Hosoda 005 provdes deals. Noe ha f a sequece of he radoal UT polces are used he supply cha ha s he ˆ = ad ˆ. 4.. The objecve fuco rom here he expresso wll be used for he varace of e sock levels of he geeralzed UT polcy a he h level. As show he appedx ad Hosoda 005 he e sock levels a he frs ad he secod levels follow ARMA processes where = ad respecvely. By explog hs propery we ca have he followg:

10 where = =. ealed seps o oba Eq. 4.4 ad Eq. 4.5 are show he appedx. Sce he hrd level player adops he radoal UT polcy o corbue o he mmzao of he objecve fuco he forecas error over he lead-me plus revew perod ca be used as a alerave. E ˆ r r / / 4.6. eals of he dervao of Eq. 4.6 are show Hosoda 005. I should be oed ha Eq. 4.6 cao be used whe ad/or whe 0 because of a sgulary he deomaor. However soluos do exs a he sgulary ad hey are also show Hosoda 005. I hs seco Eq. 4.6 wll be used he aalyss. The objecve fuco for he hree-level geeralzed supply cha model s J S

11 4.7. / / r r 4. Scearo : The geeralzed UT polcy supply cha whe I Scearo a specal case of scearo where wll be cosdered. I hs scearo oly he secod player employs he geeralzed UT polcy he supply cha order o mapulae he dyamcs of he supply cha. I Scearo from Eq. 4. he orderg process ca be expressed as. rom Eq. 4.5 by seg he varace of he e sock level a he secod Scearo ca be expressed as

12 . 4.8 The varace of he e sock level a he hrd level Scearo ca be wre as r r r r 4.9. eals are show Hosoda 005. By usg Eq. 4. Eq. 4.8 ad Eq. 4.9 S J he objecve fuco for Scearo ca be descrbed as J S

13 . 4.0 ue o he raher uweldy expressos of he objecve fucos furher aalycal vesgaos are dffcul o prese. Thus umercal vesgaos wll be exploed. 5 Numercal vesgaos I hs seco he hree scearos wh wo lead-me segs = = = ad = = = wll be vesgaed umercally. = s assumed. By usg Eq. 4.7 ad Eq. 4.0 he values of S J have bee ploed g. 5. ad he values of S J g wh he resrco ha 0 < < ad 0 < < whe = ad 0.7 for boh lead-me segs. rom hese fgures ca be see ha S J ad S J have a uque mmum value for he gve values of ad. The opmum values of he proporoal corollers ad o mmze he objecve fucos S J ad S J respecvely are obaed by usg he cyldrcal algebrac decomposo algorhm Colls e al. 00. S J ad S J wll be used o represe he mmzed values of S J ad S J respecvely.

14 5. Beef of Scearo Tables show he resuls of Scearo ad Tables hghlgh he resuls for Scearo. rom Tables he followg sghs ca be obaed. S J S J for all values of ad all lead-me segs. Ths meas ha he geeralzed UT polcy supply cha always ouperforms he radoal UT polcy supply cha. Boh ad ever have u value. The value of = s affeced by boh he value of ad he lead-me segs. S J S J s acheved by alrusc behavor he frs level player by accepg a greaer level of e sock o acheve a predeermed cusomer servce level. Tha s accepg. I almos all parameer segs he secod level player ejoys he beef ha s. The oly excepo he pos of he soluo space we have chose s he case whe = = = ad = 0.9.

15 gure 5.: The values of J S

16 gure 5.: The values of J S whe = = = gure 5.: The values of J S whe = = =

17 Table 5.: alues of J S : = = = Table 5.: alues of J S : = = =

18 Table 5.: alues of J S : = = = Table 5.4: alues of J S : = = =

19 g. 5.4 shows J S a measure of he beef of alrusc behavor descrbed as J S J S / J S. The average values of he J S are 6.% ad.7% for he lead-me segs = = = ad = = = respecvely. If s assumed ha s posve as ee e al. 000 he he average values become as hgh as 6.9% ad.7% respecvely. gure 5.4: J S bjecve fuco reduco % 5. Beef of Scearo Tables provde he resuls of he umercal vesgao. I Scearo sce he value of s cosa = oly he opmum values of are show hese ables. I hs scearo he frs level player's sadard devao of he e sock level s decal o because of he u value of. rom Tables he followg sghs may be obaed. J S J S for all values of ad lead-me segs. Ths meas ha he geeralzed UT polcy supply cha always ouperforms he radoal UT polcy supply cha. ever has u value. The value of s affeced by boh he value of ad he leadme segs. J J s acheved by alrusc behavor of he secod level S S player. Tha s by accepg.

20 Table 5.5: alues of J S : = = = Table 5.6: alues of J S : = = =

21 By usg a measure of beef of J S = J S J S / J S he beef of Scearo has bee ploed g The average beef Scearo s.9% ad.% for he lead-me segs = = = ad = = = respecvely. Wh he assumpo of posve values of hese average beefs wll crease o.0% ad 4.8% respecvely. gure 5.5: J S bjecve fuco reduco % 6 Cocluso By usg a hree-level supply cha model hree dffere scearos have bee vesgaed ad some eresg sghs have bee obaed. To oba aalycal expressos of he varaces of he ed-perod e sock levels a each level he geeralzed UT polcy supply cha a ewly developed mehod s exploed. The radoal UT polcy supply cha has bee used as a bechmark for performace Scearo. I Scearo wo proporoal corollers were corporaed oe a he frs level ad he oher a he secod level. By adjusg he values of he proporoal corollers properly a sgfca amou of beef ca be obaed. Neher of hese wo corollers akes u values; however s less ha ad oly alrusc behavor of he frs level s requred o ejoy such a beef almos all parameer segs. The quafed beefs are que large ad s show ha such beefs come from each player he supply cha dog wha s he bes for self ad he supply cha raher ha dog wha s he bes for s ow selfsh eress. I oher words a sequece of opmum polces does o provde a global mmum cos of a supply cha.

22 Scearo has show he lowes cos fuco he model segs; however o ejoy he beef he alrusc behavor a he frs level mus be acceped. Bu hs s usually where he mos expesve veory holdg coss are curred. I addo he redsrbuo of he veory coss amog players mgh be a barrer o mplemeao of Scearo as we dscussed eraure revew. Some addoal ceves for he frs level player may be ecessary sce he overall beef compleely depeds o he degree of alrusc behavor gve by he frs level player. To overcome ceve coflc ssues a supply cha Scearo s cosdered. Scearo may be a case of a hree-level supply cha ha s govered by wo orgazaos: he frs level veory s maaged by a realer ad boh secod ad hrd level veores are maaged by a suppler for example. The realer's cocer s o mmze s ow veory relaed coss. The suppler's eres s o mmze he sum of he veory relaed cos a boh secod ad hrd levels. The realer ca help he suppler by provdg up-o-dae marke demad formao. To acheve he goal depedely he realer may use he radoal UT polcy whch mmzes s ow sadard devao of e sock level ad he suppler corporaes o he UT polcy a he secod level ad employs he radoal UT polcy a he hrd level o mmze s oal veory relaed coss. Havg worked he real busess world he wo orgazao hree-level supply cha Scearo mgh become realsc. Sce he suppler behaves alruscally ad s he suppler who ejoys he beef from Scearo may be more accepable o a real busess world ha Scearo. Therefore Scearo could brg a w-w suao a supply cha easly wh less dffculy mplemeao ad operao. There mgh be some challeges o ejoy he beef. The resuls show here deped o a crucal assumpo ha all ecessary formao s shared whou delay ad exploed a proper maer o oba opmum values of. To share he formao whou delay he use of formao echologes such as Iere ad/or EI mgh be esseal. or he laer po sce he value of he objecve fuco s o so sesve o he value of see gure for example eve f he values of proporoal corollers acually used a supply cha are slghly dffere from he opmum values he supply cha sll ca reduce s oal coss by explog he geeralzed UT polcy. Appedx To opmze supply cha coss aalycal expressos of a cos fuco are esseal. I hs research aalycal expressos of varaces are

23 exploed. These expressos are able o be obaed hrough he followg seps Hosoda 005. Sep : Express he ed-perod e sock level process as a ARMAq process where q s a o-egave eger. Sep : ba he aalycal expresso of he varace of he ARMAq process. The mos sgfca advaage of hs mehod s ha s o ecessary o specfy he value of he lead-mes a supply cha o ga aalycal expressos. rom ow he deals abou how o oba wll be show. By followg he same seps s also obaable. I our model he order placed by he frs level player s expressed as ~ IP WIP. A. I s assumed here ha ca be descrbed as. rom above equao A. ca be obaed. WIP ca be expressed as WIP. A. Cosder frs he case whe s greaer ha oe. Subsug Eq. A. o Eq. A. aoher expresso of WIP s WIP. A.4 Afer corporag Eq. A. ad Eq. A.4 o he HS ad he RHS of Eq. A. respecvely some algebrac smplfcao yelds ~ IP. A.5

24 Now ca be expressed by usg. Thus sce ~ = E ~ s gve by ~. Therefore ~ ca be wre as 0 ~. A.6 ca be descrbed as. 0 0 j j Ad IP s. E IP Thus a expresso for IP becomes 0 0 j j IP. A.7 By subsug Eq. A.6 ad Eq. A.7 o Eq. A.5 he fal expresso of he ed-perod e sock level process a he frs level ca be expressed as

25 0 0 A.8 where = ad. rom Eq. A.8 ca be see ha follows ARMA process wh AuoreRressve AR coeffce ad Movg Average MA coeffces 0. I should be oed ha he case of he radoal UT polcy where = he AR coeffce becomes zero ad follows ARMA0 process. Ths resul cocdes wh Glber 005. Geerally he varace of ARMAq process a level ca be expressed as q q j 0 j0 j. A.9 Afer subsug he AR ad he MA coeffces o Eq. A.9 some algebrac smplfcao yelds Eq The same coclusos ca be obaed for he case of = where WIP = 0 by followg he same seps descrbed here. Refereces Y. Avv ad A. edergrue The operaoal beefs of formao sharg ad vedor maaged veory MI programs Workg paper Washgo Uversy S. ous M 998. R. Bellma yamc Programmg NJ: Prceo Uversy Press 957 p. 8. G. E. P. Box G. M. Jeks ad G. C. Resel Tme Seres Aalyss: orecasg ad Corol rd ed NJ: Prece Hall Eglewood Clffs 994. G. E. Colls J. R. Johso ad W. Kradck Ierval arhmec cyldrcal algebrac decomposo Joural of Symbolc Compuao S. M. sey ad. R. Towll The effec of vedor maaged veory MI dyamcs o he Bullwhp Effec supply chas Ieraoal Joural of Produco Ecoomcs 85 00a 99 5.

26 S. M. sey ad. R. Towll edor-maaged veory ad bullwhp reduco a wo-level supply cha Ieraoal Joural of peraos & Produco Maageme 00b S. Gavre Prce flucuaos formao sharg ad supply cha performace Europea Joural of peraoal Research I. Gaoccaro ad P. Poradolfo Supply cha coordao by reveue sharg coracs Ieraoal Joural of Produco Ecoomcs K. Glber A ARIMA supply cha model Maageme Scece S. C. Graves A sgle-em veory model for a osaoary demad process Maufacurg & Servce peraos Maageme T. Hosoda The prcples goverg he dyamcs of supply chas Ph dsserao Cardff Uversy UK 005. T. Hosoda ad S. M. sey The goverg dyamcs of supply chas: The mpac of alrusc behavor Auomaca 4 006a T. Hosoda ad S. M. sey varace amplfcao a hree-echelo supply cha wh mmum mea square error forecasg MEGA: The Ieraoal Joural of Maageme Scece 4 006b T. Hosoda M. M. Nam S. M. sey ad A. Poer Is here a beef o sharg marke sales formao? kg heory ad pracce Compuers & Idusral Egeerg H. Km ad J. K. Rya The cos mpac of usg smple forecasg echques a supply cha Naval Research ogscs H.. ee. Padmaabha ad S. Whag Iformao dsoro a supply cha: The bullwhp effec Maageme Scece H.. ee K. C. So ad C. S. Tag The value of formao sharg a wo-level supply cha Maageme Scece

27 J. uo Buyer-vedor veory coordao wh cred perod ceves Ieraoal Joural of Produco Ecoomcs S. Raghuaha Iformao sharg a supply cha: A oe o s value whe demad s osaoary Maageme Scece A. A. Tsay The quay flexbly corac ad suppler-cusomer ceves Maageme Scece H. J. assa Applcao of dscree varable servo heory o veory corol Joural of he peraos Research Socey of Amerca Z. K. Weg Chael coordao ad quay dscous Maageme Scece