Assoaton for Informaton ystems AI Eletron Lbrary AIeL) WHICEB 25 Proeedngs Wuhan Internatonal Conferene on e-busness ummer 6-9-25 Behavor Coordnaton n E-ommere upply Chans Yanhong Zhang Insttute of system Engneerng of Hydraul and Hydroeletrty hool, Wuhan Unversty, Wuhan,4372, Chna, yh_zhang24@26om Xanja Wang Insttute of system Engneerng of Hydraul and Hydroeletrty hool, Wuhan Unversty, Wuhan,4372, Chna Zhje Chen hool of Management, Wuhan textle Unversty, Wuhan,4373, Chna Follow ths and addtonal works at: http://aselasnetorg/wheb25 Reommended Ctaton Zhang, Yanhong; Wang, Xanja; and Chen, Zhje, "Behavor Coordnaton n E-ommere upply Chans" 25) WHICEB 25 Proeedngs Paper 65 http://aselasnetorg/wheb25/65 hs materal s brought to you by the Wuhan Internatonal Conferene on e-busness at AI Eletron Lbrary AIeL) It has been aepted for nluson n WHICEB 25 Proeedngs by an authorzed admnstrator of AI Eletron Lbrary AIeL) For more nformaton, please ontat elbrary@asnetorg
he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton 49 Behavor Coordnaton n E-ommere upply Chans Yanhong Zhang,2 *, Xanja Wang, Zhje Chen,3 Insttute of system Engneerng of Hydraul and Hydroeletrty hool, Wuhan Unversty, Wuhan,4372, Chna 2 College of ene, the ene and ehnology of Wuhan Unversty, Wuhan,4365, Chna 3 hool of Management, Wuhan textle Unversty, Wuhan,4373, Chna Abstrat: hs paper studes the behavor oordnaton of members n e-ommere supply hans wth ooperatve game theory Under the envronment of e-ommere, the retalers and the suppler an maxmze ther profts through the ooperaton wth the nformaton provder We study ths ooperaton by means of ooperatve game theory and emphasze the mportane of the nformaton provder n the ooperaton We gve a ore alloaton and a soluton for these games Keywords: e-ommere supply hans, ooperatve game, alloaton IRODUCIO Wth the development of eletron nformaton tehnology, nformaton network have a great mpat on the tradtonal supply han he large potental mpat of the Internet on supply han management makes the study of supply han models n e-ommere tmely and mportant Robert and Horane [] argues that by upsettng the balane among the ontextual fores, t wll be the emergene of a new vson of supply han n e-ommere Wu and L [2] onstrut a randomzed prng strategy for onlne retalers by borrowng long standng promoton methods from tradtonal retalng Jayashankar et al [3] present an overvew of relevant analytal researh models that have been developed n these areas, and onlude wth a dsusson on future modelng opportuntes n ths area tudes on upply Chan Operaton Mode for Agrultural Produts under Eletron Commere have been arred out and dsussed [4],[5] E-ommere serve platform has been desgned and mplemented for the supply han management of agrultural produts [5] As we all known that the supply han management emphaszes the behavor oordnaton between the enterprses n the supply han by nformaton sharng and resoures optmzaton alloaton [6] to redue the transaton osts here's a lot of talk n the e-ommere supply han about ntegratng systems, ollaboratng wth partners [7]-[] When used approprately, the new e-ommere tehnologes allow frms to streamlne ther busness proesses to aheve lower operatng osts and n rease sales revenue, as well as to mprove flexblty n the e-ommere [] anjay G et al [] explore the oordnaton for the flexblty n e-ommere supply han In ontrast, ooperatve game theory emphaszes the ooperaton between the ompanes One of the man uestons s whether the ooperaton s stable, that s, whether there are alloatons of the total proft among the ompanes suh that no groups of ompanes would lke to ooperate on ts own [3],[4],[6] Lang, Dong and Wlhelm study the e-ommere by the negotaton [],[5] Lus, Ana and Judth [6] analyze a tradtonal supply han model by means of ooperatve game theory, they show that the orrespondng games are balaned and propose a stable soluton oneptthe mgp-soluton) for the game In ths paper, we analyze the e-ommere supply hans by means of ooperatve games We onsder one perod e-ommere supply hans wth a sngle produt In suh a supply han, the retalers know about the produt through the nformaton platform onstruted by the nformaton provder and plae one-tme orders for * Correspondng author Emal:yh_zhang24@26om
5 he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton the produt at the suppler he suppler reeves the order n the nformaton platform After produton, the suppler delvers the goods to the retalers he nformaton provder ats as an ntermedary wth revenues Every retaler and suppler pays the same nformaton ost to the nformaton provder n a perod here are no ompettons between retalers, and they sell the goods on ther own market he larger the uantty that s put on the market, the lower the pre per unt s for retalers Eah retaler hooses ts order uantty suh that ts proft s maxmzed he retaler pays the suppler a wholesale pre per unt produt ordered and delvered hs pre s a dereasng funton of the uantty ordered he regular nformaton ost s harged by the nformaton provder aordng to the number of port lked, and has nothng to do wth the number of lks on a port herefore, there exst nentves for ooperaton among retalers here are also the nentves for ooperaton between the retalers and the suppler, and the retalers or suppler wth the nformaton provder If the retalers ombne ther orders nto one large order and plae at the suppler, they enjoy a lower wholesale pre he suppler also hopes to reeve a large order to earn more profts he suppler may want to ooperate wth the nformaton provder to redue the nformaton ost Besdes, retalers may want to ooperate wth the suppler and the nformaton provder to redue the wholesale pres and the nformaton osts Obvously, the total proft under full ooperaton s larger than the sum of the ndvdual profts Beause of the nentves for ooperaton, we use ooperatve game theory to study the supply han For ths han we defne a orrespondng ooperatve game n whh the suppler, the retalers and the nformaton provder are players We adapt some propertes of the soluton provded by Lus, Ana and Judth [5] to haraterze our soluton he paper makes two ontrbutons to the e-ommere supply han Frst, we use the ooperatve game theory n e-ommere supply han; eond, we emphasze the mportane of the nformaton provder n the ooperaton n e-ommere supply han he ontents of the paper are organzed as follows eton2 we brefly ntrodue the neessary onepts of ooperatve game theory eton3 gves the model of a sngle perod e-ommere supply han and study the related ooperatve game and gve an alloaton for the game eton4 onludes 2 PRELIMIIARIE COOPERAIVE GAME HEORY A ooperatve game wth transferable utlty U game) s a par, v), where {,2,, n} s a fnte set of players and v, the haraterst funton, s a real valued funton on 2 { : } satsfyng φ) v In ths paper, the ardnalty of a fnte set s denoted by the operator,e, s the number of players n, for any ometmes we use lowerase letters to denote ardnaltes, and thus n s for any A beneft vetor, or alloaton, s denoted by x R he ore of the game, v) onssts of those alloatons v) of n whh eah oalton reeves at least ts benefts: n Core, v) { x R x v ) and x v ) for all } A ore alloaton x Core, v) s both effent, that s x x), and t satsfes the oaltonal stablty property, that s x v s) for all A game s alled balaned f ts ore s nonempty
he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton 5 A game, v) s alled monotone f for every, wth, t holds that v ) v ) We denote byg the set of all monotone games Gven, v) G, a player s a dummy f v ) v \ ) + v ) for all \, that s, f all her margnal ontrbutons are eual to v ) A player s alled a null player f she s a dummy and ) v wo players, j are symmetr f v ) v j) for all \ {, j} ontrbutons to eah oalton onde, that s, f ther margnal A sngle-valued soluton ϕ for U game, v) s a map ϕ : Γ R where Γ s the lass of U-games wth player set he payoff to player n game by ϕ v) andϕ v) ϕ v)) v Γ aordng to ths soluton s denoted 3 HE MODEL OF HE E-COMMERCE UPPLY CHAI AD RELAED COOPERAIVE GAME In ths seton, we study sngle perod models of e-ommere supply han nvolvng a sngle produt he retalers and the suppler must use the nformaton platform from dfferent ports and make transaton n the nformaton platform, whle the retalers an make allane to use the nformaton platform from a port and make transaton wth the suppler Every retaler and suppler pays a regular nformaton ost to the nformaton provder n a perod 3 he retaler suppler-nformaton provder problemri-problem) We frst onentrate on a han wth a sngle retaler he retaler plaes a one-tme order that the sze s unts through the nformaton platform he ordered goods are produed by the suppler at a ost )of per unt he ost of ths order s the wholesale pre w ) he more the retaler orders, the lower the pre per unts he has to pay o the wholesale pre funton w) s a dereasng and ontnuous funton wth w ), he expeted pre funton p : R R s dereasng and ontnuous n he retaler determnes hs order uantty suh that hs proft s maxmzed: + Max p ) w )) st Q where Q { R+ p ) w )} s the set of feasble order sze, that s, those order szes that result n a nonnegatve proft margn for the retaler from the ommodtes Gven the retaler s order sze, the suppler s proft euals Max w ) )
52 he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton he nformaton provder s proft euals 2 t 32 he retaler suppler-nformaton provder gamesri-games) ow we onsder sngle perod ooperatve models of e-ommere supply hans wth a suppler, an nformaton provder and multple retalers Eah of the retalers plaes ts order at the nformaton platform provded by the nformaton provder he retalers have the possblty to ooperate among eah other and plae a jont order, whh results n a lower wholesale pre per unt he retalers and the suppler also have the nentves to ooperate wth the nformaton provder wth the absene of the nformaton osts Let {,, n} be the set of retalers and denote the suppler by, the nformaton provder by I hen {} s the set of all retalers and the suppler and {I} s the set of all players n the han mlarly, we defne {} and {I}, for all If s denotes the total order sze by a oalton of retalers, then the jont beneft of ths oalton euals Max p )) Q : { R+ p ) w ) for all } he ooperaton among the group of retalers and the suppler s desrbed just as the jont beneft: Max p ) ) 2t he worth of the grand oalton formed by retalers, suppler and the nformaton provder euals Max p ) ) Lus, Ana and Judth [5] prove that ooperaton wth the suppler s attratve for retalers Whle the ooperaton wth the nformaton provder s also attratve for retalers and suppler sne the nformaton ost wll dsappear as long as the nformaton provder s n the ooperaton and the proft s postve When the nformaton provder s n the ooperaton or the nformaton ost s asked zero, the RI-games s the R-games that dsussed by Lus, Ana and Judth [5] o the proft funton arsng from ooperaton n e-ommere have the smlarly propertes dsussed n tradtonal supply han Lemma3 Let ret Ρ, w )) p )), Ρ, w )) w ) ), and Ρ I ) t hen sup ) Ρ ; ret ret sup I ; ) Ρ ; w )) + Ρ ; w )) + Ρ ret ret 2) Ρ ; ) Ρ ; ) ; ret ret 3) ; ) Ρ ; w )) ret ret Ρ and ; ) Ρ ; w )) Ρ Proof ) 3)follows mmedately from the defntons of Ρ, Ρ, Ρ ext we defne the ooperatve game orrespondng to the supply han n e-ommere desrbed n our ret sup I
he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton 53 stuaton that s RI-game Defnton32 he ooperatve game n e-ommereri-game), v ) s defned by and for all oaltons v ) p )), v ) p ) ) 2t v ) p ) ), and φ) v, he defnton above shows that a oalton of retalers beneft from a lower wholesale pre per unt and a lower nformaton osts, whle a oalton nludng the suppler and nformaton provder nreases ts proft due to the absene of the wholesale pres and the nformaton osts It s more attratve to ooperatve wth the nformaton provder for the retalers and the suppler sne ) v ) v >, v ) > v ), hs provdes the ompanes n the han wth suffent nentves for ooperaton and that the nformaton provder also has reasons to share the gan from ooperaton wth the retalers just as the suppler Lemma33 Let, v ) be a game n e-ommere hen ) v {I}) for all oaltons; ) v s super-addtve; ) v {I}) v ) v) for all ; v ) v{,i, }) and v ) v \ { }) v{, I, }) for all and Proof )If {}, then {I}) v{,i}) If )Let v ;, then {I}) p )) If v ; and, then {I}) p ) ) v ;, be two dsjont oaltons of retalers, then v ) + v ) p )) + p )) p )) + p )) p )) v ) Furthermore v ) + v ) p ) ) 2t + p ))
54 he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton p ) ) p ) ) and v ) + v ) p ) ) p ) ) + p ) ) p ) ) v ) + p + p ) ) v ) )hs follows from ) and the defnton of the game v)hese results follow from the defnton of the game Obvously the game s not monoton and does not satsfy the null property and symmetry he frst and thrd property n ths lemma shows the mportant role of the nformaton provder n the ooperaton 33 he ore of the game Reallng the propertes of the haratersts v, the ore of the game, v ) an be desrbed as follows: heorem 34 Let be the RI-game he ore of ths game euals Core, v ) )) n { x R x v ); x v{, I, }), ; x v ), } Proof Let x Core, v ), hen x v ) and x v \ { }) j j \{ } hus x v ) x j v ) v \ { }) v{,i, }) x j \{ } Conversely, we only need to prove the followng neualtes: x + x v ), and x + x v ), he seond neualty s obvous We now prove the frst neualty + x x x j + x v ) v{, I, j}) j \ j \ v {,I, }) v{,i, }) 2t v ) Defne the alloaton v ) I QED x by x v), x v), x v) v{,i, } ), that the alloaton x v) Core, v) We have the result: heorem 35 Let be the RI-game hen the game s balaned It s easy to see ne the suppler and the nformaton provder get nothng, the alloaton x v ) s the worst possble ore-alloaton for the suppler and the nformaton provder 34 he soluton of the game In ths seton we adjust some propertes of the soluton for the R-game to get a soluton for the RI-game
he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton 55 he soluton assgns a payoff for the suppler and the nformaton provder and s an alloaton In addton to the propertes a)-d) smlar to that desrbed by Lus, Ana and Judth [5], a sngle-value soluton for RI-game has the propertye) a)effeny: ϕ v) v ) b)tablty: v) v ) ϕ for all oalton )Retaler reduton: v ) v ) ϕ v) v{,i, }) for some oaltons and s d) Preservaton of dfferenes for retalers: ϕ v) ϕ v) v{,i, }) v{,i, j}) for all, j wth j j v ) v ) e) hare the reduton: ϕ I v) + ϕ v) s hen we have the man result n the followng theorem36: heorem36 Let, v ) be an RI-game he unue soluton v ) on the lass of RI-game, satsfynga)-e) ϕ defned by nα, ϕ v) n β α), v{, I, }) β, I,,, where α t v ) v ) max, β mn, φ s, φ s Corollary37 Let, v ) be an RI-game, v ) hen ϕ v ) Core, v ) Corollary38 Let ϕv) s the soluton of the RI-game Ift, then ϕv) ϕ s the soluton of the game, v ) s the soluton of the R-game Example39 Let {I,,,2 }, t 2, 4, p ) 2, p2 ) 2 and, w ) 8 4 +, 2 > 2, v ) s the orrespondng game hen ϕ v) 4, ϕ v) 4, ϕ v) 7, ϕ v) 55 I 2
56 he Fourteen Wuhan Intematonal Conferene on E-Busness E-Busness Management n Organzaton 4 COCLUIO he entral problem that we have ntrodued s the behavor oordnaton between the members n the e-ommere supply han wth several retalers, one suppler and an nformaton provder All players have nentves to ooperate wth eah to redue osts and nrease profts We analyze theses hans by means of ooperatve game theory he nformaton provder plays an mportant role of n the ooperaton We show that the RI-game has a nonempty ore A soluton that reognzes the mportane of the nformaton provder n ooperaton s gven hese results mply that the ompanes n an e-ommere supply han are wllng to ooperate beause there exsts stable dstrbutons of the jont proft ACKOWLEDGEME hs researh was supported by the key projet of the atonal atural ene Foundaton of Chna under Grant 7237 REFERECE [] Robert B J, Horae C M 2) An Emergng Vson of Internet-Enabled upply-chan Eletron ommere, Internatonal Journal of Eletron Commere, 44): 43-59 [2] Wu J H, L L, L D X24) A randomzed prng deson support system n eletron ommere, Deson upport ystems,58: 43 52 [3] Jayashankar M, rdhar R 23) Models for upply Chans n E-ommere, Management sene, 49):387-46 [4] Lng B, Zhu F R 26) A tudy on upply Chan Operaton Mode for Agrultural Produts under Eletron Commere, Journal of Jangx Agrultural Unversty, 5):9-94 [5] Bao L W, Huang Y C, Ma Z J 22 ) On the upply Chan Management upported by E-Commere erve Platform for Agreement based Crulaton of Fruts and Vegetables Physs Proeda, 33: 957 963 [6] MIvor R, Humphreys P, MCurry L 23) Eletron ommere: supportng ollaboraton n the supply han? Journal of Materals Proessng ehnology, 39: 47 52 [7] Davd L R, Danel F 2) Busness-to-Busness Eletron Commere, he Journal of Eonom Perspetves, 5): 55-68 [8] George M G, Ray J P, Georgos I D 999) Dynam Modelng to Assess the Busness Value of Eletron Commere, Internatonal Journal of Eletron Commere, 33): 35-5 [9] klas A, Fredrk 23) Eletron ommere, marketng hannels and logsts platforms a wholesaler perspetve, European Journal of Operatonal Researh, 44: 27 279 [] Lang P, Dong H 2) Effet of Barganng n Eletron Commere, Internatonal Journal of Eletron Commere, 43): 23-43 [] Gosan, Malhotra A, awy OAE 24) Coordnatng for Flexblty n e-busness upply Chans, Journal of Management Informaton ystems, 23): 7-45 [2] Bezalel P, Peter 27) Introduton to the theory of ooperatve games eond Edton ew York: prnger,45 [3] an C Q, Zhang Q2) Cooperatve Game heory and Applaton Be Jng: ene Press,3-22n Chnese) [4] Wlhelm R, Chu B, un R, Eletron Commere egotaton n a upply Chan Va Constrant Evaluaton [5] Lus A G, Ana M, Judth 27) Cooperaton and proft alloaton n dstrbuton hans, Deson upport ystems, 44: 7 27