Price Competition and Coordination in a Multi-echelon Supply Chain

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1 Engineeing Lette, 8:4, EL_8_4_0 Pice Copetition nd Coodintion in Multi-echelon Supply Chin YUN HUANG, GEORGE Q. HUANG Atct Thi ppe tudie pice coodintion pole in thee-echelon upply chin copoed of ingle upplie, ingle nufctue nd ingle etile. Thee type of chnnel tuctue e conideed, nely, the decentlized, the ei-integted, nd the integted. Two powe tuctue e tudied fo the decentlized nd the ei-integted chnnel. The lede-followe powe tuctue i odeled Stckeleg ge, whee the nufctue lwy tke the ledehip, while the independent powe tuctue i teted iultneou non-coopetive ge (iply Nh ge). We exploe the effect of powe tuctue, chnnel tuctue nd ket pete on equiliiu pice nd pofit. The eult how tht the nufctue o the integted ee hd ette tke the chnnel ledehip. We lo find tht the integtion fo the nufctue nd the etile cnnot lwy ipove thei pofit in onopoly. Beide, when poduct cot i lge thn cetin echelon, the chin ee pofit will incee the ket ecoe oe enitive to the etil pice. Index Te ulti-echelon upply chin, picing, chnnel tuctue, powe tuctue, Stckeleg ge, Nh ge. I. INTRODUCTION A the developent of upply chin ngeent, oe ephi h een put on integting upplie, nufctue, ditiuto nd etile efficiently. Mking picing ttegy in chnnel wide i not only tte concened with ech entepie individully, ut the othe chnnel ee, well the whole chnnel yte. Howeve, Peto-optil picing deciion lwy cnnot e chieved fo the chnnel ee, ince diffeent ojective of chnnel ee eult in conflict etween the, ee [4]. Hence, coodintion of diffeent echelon of the chnnel i ephized, ee [9] fo exple. Jeulnd nd Shugn ([7]) tudy the effect of coopetion etween the nufctue nd the etile coping n independent chnnel tuctue with veticlly integted chnnel nd conclude tht coopetion lwy eult in highe pofit. Choi ([4]) conide picing pole fo chnnel tuctue coniting of two copeting nufctue nd one coon etile who ell oth nufctue poduct. He tudie thee non-coopetive ge of diffeent powe tuctue etween the two nufctue nd the etile. Chle nd Mk ([]) exploe chnnel coodintion y nufctue tht ell n identicl poduct Mnucipt eceived Septee 4, 00. Yun Hung i with the Deptent of Indutil nd Mnufctuing Syte Engineeing, Univeity o Hong Kong, Hong Kong (phone: (0085) ; e-il: hungyun@hku.hk). Geoge Q. Hung i with the Deptent of Indutil nd Mnufctuing Syte Engineeing, Univeity o Hong Kong, Hong Kong (e-il: gqhung@hku.hk) to two copeting etile. Minkhi ([]) tudie chnnel copetition y nlyzing thee chnnel tuctue, the let contined of which del with two copeting nufctue nd two etile. In the ove eech, coopetive o non-coopetive picing deciion hve een de to coodinte the chnnel ee. Howeve, thee eech focu on the tditionl chnnel tuctue, lwy copoed of two echelon (uye /nufctue nd elle/etile) with diffeent powe diviion etween the. Aln nd Medini ([]) tudy picing in thee-level yte (nufctue-etile-cutoe). They conclude tht the nufctue would like to coopete with the etile to ell the poduct to the cutoe to xiize hi pofit. Although they conide ulti-level chnnel, the cutoe doe not join in king picing deciion. In fct, it i till tditionl chnnel tuctue pole. Thi ppe conide ingle poduct thee-level pice odel coniting of one upplie, one nufctue nd one etile. Two diffeent chnnel tuctue e conideed in thi upply chin. The fit i decentlized chnnel tht the nufctue ue the independent upplie nd etile, in which they optiize thei own pofit individully nd non-coopetively. The econd i tht the nufctue integte with the upplie / the etile nd ue the independent etile / the upplie iultneouly. Thi chnnel i clled y ei-integted chnnel. Lede-followe nd independent powe lnce cenio e oth conideed fo the two chnnel tuctue. Thi ppe tudie the effect of the ove chnnel tuctue, diffeent powe tuctue nd ket envionent on the equiliiu pice nd pofit of individul chnnel ee nd the upply chin yte. The einde of thi ppe i ognized follow: give the nottion nd optiizing odel fo the upplie, the nufctue nd etile. illutte two non-coopetive ge odel fo the decentlized chnnel nd give olution to the two odel. 4 tudie the ei-integted chnnel tuctue nd focue on the integtion of the nufctue nd the etile. Two ge odel e developed fo thi integtion nd olution e given. The integted chnnel tuctue i tudied in 5. 6 dicue effect of powe tuctue, chnnel tuctue nd ket pete on the equiliiu pice nd pofit. The lt ection uize jo wok nd futhe eech e. II. MODEL FORMULATION AND NOTATIONS We conide the upply chin of one upplie, one nufctue nd one etile of poduct with pice enitive dend. The upplie povide the nufctue with the ole w teil ued to poduce ingle poduct old to the etile. Then the etile ell the poduct to cutoe. Thi iple onopoly tuctue llow u to (Advnce online puliction: Novee 00)

2 Engineeing Lette, 8:4, EL_8_4_0 focu on the copetition nd coodintion etween diffeent echelon, without the ditction of ultiple poduct, ultiple upplie, nufctue nd etile. Siil uption cn e een fo [, 6, ], etc. We ue,, to index the upplie, the nufctue, the etile, epectively. Dend i ued to e function of the etile etil pice (p ) pid y end cutoe. If dend i pice enitive with contnt pice elticity, we eploy the following io-eltic dend function: Dp p, 0, 0 () whee i cling pete, nd i the pice elticity of the dend, which i lwy poitive. Thi i ecue 0 iplie tht D incee t diinihing te p decee. Thi dend function i fily coon in keting litetue (ee [, 8, 0, ]). We futhe ue tht ll cutoe dend fo the etile will e tified. We tudy one peiod ttic odel. With the deteinitic ket dend, it i ild to ue tht the nufctue h the cpcity to poduce enough to tify the etile dend nd the upplie could lo povide enough teil fo the nufctue. Given the echelon of dend, to deteine the pofit of the etile, the nufctue nd the upplie, we ue the upplie povide it w teil t pice of p nd the nufctue ell it poduct t wholele pice p. Let nd denote the nufctue pofit gin nd the etile pofit gin, epectively. Futhe, we denote the upplie pocueent cot pe unit w teil c nd the poduction cot pe unit poduct c. i ued to e the uge ount of unit w teil pe unit poduct. Thi en tht if the nufctue will poduce D unit poduct, he will puche D fo the upplie. Auing tht the etile contol the vlue of the etil pice p, the nufctue contol the vlue of the wholele pice p nd the upplie contol the vlue of the w teil pice p. Then the etile pofit function i given : p D p, () whee p p. The nufctue pofit function i: p Dp, () whee p p c. The upplie pofit function i: pp cd p (4) Uing the pofit function identified ove, we then deteine the optil picing deciion of the etile, the nufctue nd the upplie unde diffeent chnnel tuctue nd powe tuctue. III. DECENTRALIZED CHANNEL In thi ection, we conide the decentlized chnnel tuctue, in which the nufctue ue independent upplie nd etile. We conide two powe lnce cenio unde thi chnnel tuctue, lede-followe nd independent cenio. Fo the fit cenio, the nufctue tke the chnnel ledehip, while the upplie nd the etile e the followe. Fo the econd one, the upplie, the nufctue nd the etile e of independent equl ttu nd no one dointe ove othe. A hown in Figue, we ue Stckeleg ge tuctue to odel the fit cenio nd Nh ge tuctue fo the econd one. A. Mnufctue Stckeleg We ue Stckeleg ge to odel the lede-followe powe lnce cenio. In fct, it i equentil ge, copoed of two Stckeleg ge. Fo convenience, we cll thi ge odel Mnufctue Stckeleg (). The fit Stckeleg ge i etween the nufctue nd the upplie. In thi ge, the nufctue chooe it pofit gin uing the ection function of the upplie. The upplie et it w teil pice, conditionl on the nufctue pofit gin. The econd Stckeleg ge i etween the nufctue nd the etile, in which the nufctue chooe it pofit gin uing the etile ection function nd the etile deteine it pofit gin given the nufctue pofit gin. The ge ule cn e efeed fo Figue (). p p p p p Unde the ove uption, the nufctue tke the upplie nd etile ection function into conidetion fo it picing deciion. We fit olve the econd Stckeleg ge. The etile ection function cn e deived fo the fit-ode condition of (): Dp Dpp p 0 (5) p p Fo (5), the etile ection function cn e deived: p p p (6) The upplie deteine it w teil pice given the nufctue pofit gin. Uing p p c nd (6), we hve: p p p c (7) Sutituting (7) into the pofit xiiztion condition fo the upplie: Dp p p, p Dpp c 0 p p p. (8) Then we cn deive the ection function fo the upplie: ' p p p p p (9) Sutituting the upplie nd the etile ection function (6) nd (9) into the nufctue pofit xiiztion condition: p p p p p (Advnce online puliction: Novee 00)

3 Engineeing Lette, 8:4, EL_8_4_0 p D p p Dpp p c p p p p 0. (0) We cn otin the Stckeleg equiliiu of the two ge olution fo the Mnufctue Stckeleg odel. The equiliiu pice nd pofit fo thi ge tuctue cn e efeed fo Tle. B. Veticl Nh The econd independent powe lnce cenio i foulted Nh ge. In thi ge, the upplie, the nufctue nd the etile ke picing deciion iultneouly nd non-coopetively. Agin fo convenience, we cll thi ge Veticl Nh (). In thi ge, the upplie chooe it w teil pice conditionl on the nufctue pofit gin nd the etile pofit gin to xiize it pofit. The nufctue chooe it pofit gin conditionl on the upplie w teil pice nd etile pofit gin. The etile et it pofit gin o to xiize it pofit conditionl on the upplie w teil pice nd the nufctue pofit gin. The ge i plyed ccoding to the ule een fo Figue (). The Nh equiliiu fo the Veticl Nh odel cn e epeented olution fo ou picing pole. The fit-ode condition fo thi equiliiu involve the etile pofit xiiztion condition (5) nd the following two pofit xiiztion condition: Dp Dpp p c 0 () p p Dp Dpp c 0 () p p D p with io-eltic dend function Sutituting the () nd iultneouly olving (5), () nd (), we hve the eult fo optil pice nd pofit hown in Tle. IV. SEMI-INTEGRATED CHANNEL In the ei-integted chnnel, the nufctue chooe to integte with eithe the etile o the upplie fit nd then wok with the upplie o the etile independently. In effect, the upply chin with thi chnnel tuctue i two-echelon yte whee the nufctue integte with nothe echelon to e ingle deciion ke. Without lo of genelity, we inly conide the chnnel tuctue tht the nufctue integte fowd with the etile in the thee-echelon upply chin. We cll thi chnnel tuctue MR-integtion chnnel. Alo, two powe lnce cenio e conideed fo the MR-integtion chnnel, lede-followe nd independent. The fit one i the two integted chin ee (the nufctue nd the etile) ct the lede, while the independent ee (upplie) ct the followe. The econd one i tht the two integted ee nd the independent ee e of equl ttu. We foulte Stckeleg nd Nh ge fo the two cenio epectively. Since the nufctue nd the etile integte togethe, we ue tht thee in no tnfe pice etween the. Hence, thee i no need to pecify the nufctue pice in the odeling poce. A. MR-Stckeleg We fit conide the lede-followe powe lnce cenio tht the nufctue nd the etile integte nd ct the lede of the upply chin, while the upplie ct the followe. We foulte Stckeleg ge etween the integted nufctue nd etile nd the independent upplie. We cll thi ge odel MR-Stckeleg (MR-S). The nufctue nd the etile gee to ke thei own pofit gin deciion tking the upplie ection function into ccount. The upplie condition it w teil pice on the pofit gin given y the nufctue nd the etile. The ge ule i hown Figue (). p p p p The pofit function fo the nufctue nd the etile i: D p () whee p p c. i the pofit gin fo the integted nufctue nd etile. The upplie ection function cn e deived fo the fit-ode condition of (4): Dp Dpp c 0 (4) p p Then we cn otin the upplie ection function: p p p (5) Tking (5) into ccount, the nufctue cn otin it optil picing deciion though the following fit-ode condition of (): p D p Dpp p c 0 p p p. (6) D p with dend function (), we hve Sutituting the Stckeleg equiliiu eult fo thi ge tuctue on pice nd pofit in Tle. B. MR-Nh The independent powe lnce cenio hee fetue tht the integted nufctue nd etile e of equl powe with the upplie. We foulte Nh ge etween the clled y MR-Nh (MR-N). The upplie chooe it w teil pice conditionl on the pofit gin given y the nufctue nd the etile to xiize it pofit. The nufctue nd the etile integte to chooe it pofit gin conditionl on the upplie w teil pice to xiize thei totl pofit. The ge ule i hown Figue (Advnce online puliction: Novee 00)

4 Engineeing Lette, 8:4, EL_8_4_0 (). The equiliiu condition fo Nh ge cn e deived fo the fit ode condition of (4) nd (). Dp Dpp c 0 (7) p p Dp Dpp p c 0 (8) p p Siultneouly olving (7) nd (8), we hve the Nh equiliiu eult fo pice nd pofit hown Tle. V. INTEGRATED CHANNEL In thi ection, we focu on the integted chnnel (ked I). In thi chnnel, the upplie, the nufctue nd the etile integte togethe to tke deciion to xiize the entie yte pofit. The full veticl integtion of the upply chin wide pevent the nufctue fo deling with the conflicting incentive tht n independent upplie o etile would hve. We ue thee i no tnfe pice etween the upplie, the nufctue nd the etile, nd thu only ingle etil pice p to e deteined. The pofit function fo the totl thee ee i: p c cdp (9) Tking the fit ode condition of (9): Dp Dpp c c 0 (0) p p Though (0), we cn otin the optil etil pice. The othe eult fo the integted chnnel cn e efeed fo Tle. VI. DISCUSSION Thi ection dicue evel ipliction tht e oeved fo the eult. We focu pticully on the effect of powe tuctue, chnnel tuctue nd ket pete. In the following dicuion, we ue upecipt,, MR-S, MR-N, SM-S, SM-N nd I to denote the coeponding quntitie fo the (Mnufctue Stckeleg), (Veticl Nh), MR-S (MR-Stckeleg), MR-N (MR-Nh), SM-S (SM-Stckeleg), SM-N (SM-Nh) nd I (integted) ce, epectively. A. Effect of powe tuctue Choi ([4, 5]) tudie the effect of powe tuctue on the equiliiu pice nd pofit of the chnnel ee in tditionl chnnel copoed of the nufctue nd the etile nd how tht unde io-eltic dend function, when no one tke the chnnel ledehip, ech ee will loe. Hee, we will dicu the effect of diffeent powe tuctue on the equiliiu pice nd pofit in the ove thee-level upply chin. Integted chnnel i not dicued ince it doe not involve diffeent powe tuctue. The following popoition illutte the effect of the two diffeent powe tuctue of the decentlized chnnel nd MR-integtion chnnel epectively. Popoition (). Fo the decentlized chnnel, ll the upply chin ee nd the entie yte pefe the ce to the ce fo the lowe equiliiu pice nd the lge pofit. (). Fo the MR-integtion chnnel, MR-S ce i pefeed y ll the upply chin ee nd the entie yte. Poof. We ue. Cope the etil pice, the wholele pice nd the w teil pice in the ce with thoe in the ce: p p ; () p p p c c 0 p cc Hence, we hve the eltionhip: p p p p, p p. (),. The equiliiu pice fo ll upply chin ee in the ce e no highe thn thoe in the ce. Cope the etile, the nufctue, the upplie pofit nd the entie yte pofit in the ce with thoe in ce: Oviouly,. (), thi i ecue ppoche infinity, i deceent function of. When i, li. Siilly, we hve:. eche the lowet vlue. Tht. Thu, Theefoe, the pofit fo ll chin ee nd the entie upply chin yte in the ce e no le thn thoe in the ce:,,,. Thi coplete the poof of pt (). The poof of pt () i iil. Fo Popoition, we cn ee tht, when io-eltic dend function () i eployed, the ce o the MR-S ce i pefeed y the upply chin ee nd the entie yte, eing coped with the ce in the decentlized chnnel o the MR-N ce in the MR-integtion chnnel. Hence, lede-followe powe cenio i pefeed y the upply chin. Tht i, the nufctue o the integted nufctue nd etile would the tke the ledehip of the decentlized chnnel o the MR-integtion chnnel. Popoition i lo conitent with the eult fo the tditionl chnnel tuctue (Advnce online puliction: Novee 00)

5 Engineeing Lette, 8:4, EL_8_4_0 ([4]). Fo SM-S nd SM-N ce, the eult e iil with thoe of MR-S nd MR-N ce nd dicuion e oitted hee. B. Effect of chnnel tuctue We invetigte the effect of diffeent chnnel tuctue on equiliiu pice nd pofit in thi ection. Fitly, we cope the ei-integted chnnel with the decentlized chnnel. In thi uection, we tudy the effect of diffeent chnnel tuctue of the thee-level upply chin. We fit popoe the following popoition. Popoition. Coped with the decentlized chnnel, the nufctue fowd integtion with the etile cn lwy povide lge pofit fo ll the upply chin ee nd the entie yte when pice elticity tifie ( ) o.596. Poof. Popoition how tht in the decentlized chnnel, the ce povide lge pofit fo ll the chin ee nd the entie yte thn the ce nd the MR-S ce povide lge pofit thn the MR-N ce in the MR-integtion chnnel. Thu, we jut need to cope the pofit of the individul upply chin ee nd the entie yte in the MR-N ce with thoe in the ce. If the MR-N ce could povide lge pofit thn the ce, the MR-S (o MR-N) ce will lo hve lge pofit thn the (o ) ce. Tht i the integtion of the nufctue nd the etile cn lwy povide lge pofit fo ll the chin ee nd the entie yte. Cope the joint pofit of the etile nd the nufctue in the ce with tht in MR-N ce:. (4) MRN i deceent function of. Soe nueicl ethod, uch iection ethod, Newton ethod, cn e eployed to find out the oot of. Hee, we ue iection ethod nd find out the oot,.596. MR N Theefoe,, when o.596. (5) Cope the upplie pofit in the ce with tht in MR-N ce: ( ). (6) MRN ( ) It i deceent function of. When ppoche, MR N eche the highet vlue Hence, we hve MR N. Siilly, the entie yte of the ce nd tht of the MR N MR-N ce hve the following eltionhip:. Thi coplete the poof of Popoition. McGuie nd Stelin ([0]) how tht veticlly integtion cn xiize joint pofit in onopoly ut not neceily in duopoly fo chnnel copoed of the nufctue nd the etile. Fo Popoition nd 4, we cn ee tht the integtion fo the nufctue nd the etile / the upplie cn not lwy xiize the joint pofit even in onopoly. Why do McGuie nd Stelin eult diffe fo ou? The in eon i tht we conide the integtion in thee-level chnnel, which i diffeent fo the tditionl chnnel of [0]. Tke MR-integtion chnnel n exple. The upplie chge no le w teil pice when the nufctue integte with the etile coped with the decentlized chnnel. If the integtion fo the nufctue nd the etile ing enough pofit to cove the lo fo the incee of w teil pice, the integtion will e welcoe. Fo the integted chnnel, coped the etil pice nd pofit with the othe chnnel tuctue, we hve: Popoition. The integtion fo ll the upply chin ee povide the lowet etil pice nd highet yte pofit coped with the decentlized nd the ei-integted chnnel tuctue. Since the ei-integted chnnel tuctue i upeio to the decentlized chnnel tuctue in etil pice nd yte pofit, the integted chnnel h highe yte pofit thn ny of the fou ge tuctue fo the ei-integtion integted chnnel tuctue. Popoition 4. Unde io-eltic dend function, when the pice eltic, the chnnel efficiency fo decentlized chnnel fo oth Stckeleg ge tuctue nd Nh ge tuctue tend towd e nd fo Stckeleg ge tuctue nd Nh ge tuctue of the ei- integted chnnel, it tend towd e. Hee, the chnnel efficiency (ked CE) i defined the tio of the chnnel pofit to the integted chnnel pofit ([8]). The chnnel efficiency fo ll the ce i hown in the lt ow in Tle nd Tle.. Thi popoition tell u tht when the pice eltic of the dend function tend to infinite, the diffeence of chnnel efficiency etween diffeent ge tuctue fo e chnnel tuctue ecoe lle. Popoition 5. A the integtion of the upply chin incee, the chnnel efficiency ecoe highe. Refeed fo Tle nd Tle, we hve: MRN SM N MRS SM S I CE CE CE / CE CE / CE CE. (7) VII. CONCLUSION Thi ppe ttept to invetigte picing ttegie in thee-level upply chin copoed of one upplie, one nufctue nd one etile with thee type of chnnel tuctue. In the fit decentlized chnnel, the upplie, the nufctue nd the etile e independent nd they optiize thei own pofit individully. We conide two powe cenio, the lede-followe nd independent (Advnce online puliction: Novee 00)

6 Engineeing Lette, 8:4, EL_8_4_0 cenio. Stckeleg ge nd Nh ge tuctue e foulted fo the two cenio epectively. In the econd ei-integted chnnel, the nufctue could chooe to integte with the upplie o the etile to xiize thei totl pofit. Lede-followe nd independent powe cenio e oth conideed fo thi chnnel. The thid i the integted chnnel. In thi chnnel, the upplie, the nufctue nd the etile coopete togethe nd xiize thei yte wide pofit. We ke copion etween diffeent powe cenio fo decentlized nd ei-integted chnnel epectively nd etween diffeent type of chnnel tuctue. Thi ppe ke contiution in thee-fold. Fitly, we dd to the gowing litetue of chnnel tudie y odeling picing pole in ulti-level chnnel. The ge odel fo the thee-echelon upply chin i put fowd. Ech echelon i ge plye nd involved in king picing deciion. Secondly, thi ppe conide ei-integted chnnel, which i diffeent fo the fully decentlized o integted eltionhip. In ulti-level upply chin, the chin ee could chooe to integte with oe one nd non-coopete with oe othe. Unde thi cicutnce, how the integted ee nd non-coopeted ee will ehve nd when the integtion will e welcoed y the chin ee e of ou concen. Finlly, thi ppe conduct copion etween the decentlized, ei-integted nd integted chnnel tuctue nd otin oe eningful concluion. REFERENCES [] Ad, Pkh L., Supplie picing nd lot izing when dend i pice enitive, Euopen Jounl of Opetionl Reech, 78, pp4 54, 994. [] Aln G. Klton, Medini R. Singh, Picing in thee-tie nufctue-etile-cutoe yte, technicl epot, pp9-48, 99. [] Chle A. Ingene, Mk E. Py, Chnnel coodintion when etile copete, Mketing Science, 4, pp60-77, 995. [4] Choi S. Chn, Pice copetition in chnnel tuctue with coon etile, Mketing Science, 0(4), pp7-96, 99. [5] Choi S. Chn, Pice copetition in duopoly coon etile chnnel, Jounl of etiling, 7(), pp7-4, 996. [6] Hung, Y., G.Q. Hung, Ge-theoetic pice coodintion in thee-level upply chin with diffeent chnnel tuctue, Lectue Note in Engineeing nd Copute Science: Poceeding of The Wold Conge on Engineeing 00, WCE 00, 0 June - July, 00, London, U.K., pp [7] Jeulnd A. P., Shugn S. M., Mnging chnnel pofit, Mketing Science,, pp9-7, 98. [8] Li, S.X., Hung, Z., Ahley, A., Inventoy, chnnel coodintion nd gining in nufctue etile yte, Annl of Opetion Reech, 68, pp47 60, 996. [9] Mth C. Coope, Li M. Ell, Chcteitic of upply chin ngeent nd the ipliction fo puching nd logitic ttegy, The Intentionl Jounl of Logitic Mngeent, 4, pp-4, 99. [0] McGuie, Tiothy W. nd Richd Stelin, An induty equiliiu nlyi of downte veticl integtion, Mketing Science,, pp 6-90, 98. [] Minkhi Tivedi, Dituution chnnel: n extenion of excluive eltionhip, Mngeent Science, 44(7), pp , 998. [] Venktn, N., John E. Pecott, Envionent-ttegy colignent: n epiicl tet of it pefonce, Ipliction Mngeent Jounl,, pp-4, 990. Tle. Reult fo lede-followe powe tuctue Decentlized Sei- integted Mnufctue Stckeleg () MR Stckleeg (MR-S) SM Stckleeg (SM-S) p c c ( ) c c ( ) c c ( ) Integted (I) ( c c) p c c ( ) ( c c) p c c ( ) c c ( ) (Syte Pofit) c c c c c c c c c c c c () c c c c c c () c c c c c c Syte efficiency (CE) () () (Advnce online puliction: Novee 00)

7 Tle. Reult fo independent powe tuctue * * In ode to ke the eult fo Veticl Nh () ce eningful hee, we ue the pice elticity i gete thn. Decentlized Sei- integted Integted (I) Veticl Nh () MR Nh (MR-N) SM Nh (SM-N) p c c c c c c c c p c c c c p c c c c c c c c c c c c c c c c c c c c (Syte Pofit) c c c c c c c c Syte efficiency (CE) Engineeing Lette, 8:4, EL_8_4_0 (Advnce online puliction: Novee 00)

Pricing and Service Decisions of Supply Chain in an Uncertain Environment

Pricing and Service Decisions of Supply Chain in an Uncertain Environment Engineeing Lette, 4:4, EL_4_4_9 Picing and Sevice Deciion of Supply Chain in an Uncetain Envionent Shengju Sang F FAbtact In a to-echelon upply chain yte ith one anufactue and one etaile, the picing and