Research Article Strategic Conditions for Opening an Internet Store and Pricing Policies in a Retailer-Dominant Supply Chain

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1 aheaical Pobles in Engineeing Volue 2015, Aicle ID , 15 pages hp://dx.doi.og/ /2015/ Reseach Aicle Saegic Condiions fo Opening an Inene Soe and Picing Policies in a Reaile-Doinan Supply Chain Yonghong Cheng 1,2 and Zhongkai Xiong 1,2 1 School of Econoics and Business Adinisaion, Chongqing Univesiy, Chongqing , China 2 Chongqing Key Laboaoy of Logisics, Chongqing Univesiy, Chongqing , China Coespondence should be addessed o Zhongkai Xiong; xiongzhongkai@cqu.edu.cn Received 30 ay 2014; Revised 12 Ocobe 2014; Acceped 12 Ocobe 2014 AcadeicEdio:Hai.Sivasava Copyigh 2015 Y. Cheng and Z. Xiong. This is an open access aicle disibued unde he Ceaive Coons Aibuion License, which peis unesiced use, disibuion, and epoducion in any ediu, povided he oiginal wok is popely cied. To exaine when he anufacue and doinan eaile open hei own Inene soes and how seing pices o ensue opening Inene soes ae pofiable. We conside a wo-echelon supply chain wih one anufacue and one doinan eaile. The eaile has a physical soe in a onopolis ake. Depending on whehe he Inene soes ae opened successfully by he, we fisly obain equilibiu pices and pofis unde fou possible supply chain sucues. Secondly, we idenify seveal saegic condiions when i is opial o open an Inene soe fo he anufacue and doinan eaile and discuss is iplicaions. I is ineesing o noe ha ulichannel eailing is no necessaily he bes saegy fo he doinan eaile. In addiion, we invesigae he ipacs of poble paaees (he doinan eaile s bagaining powe and consues disuiliy of puchasing a poduc fo Inene soe) on he anufacue and doinan eaile s picing policies. We find ha he anufacue s opial pice a he Inene soe is no always being lowe han he doinan eaile s. Finally, we conduc nueical exaples o illusae he heoeical esuls. 1. Inoducion The Inene envionen enables soe copanies o y o open hei own Inene soes. In pacice, he anufacues (such as Apple, IB, Hewle-Packad, Dell, Nike, and Sasung) sell hei poducs hough boh eaile s physical soe and is Inene soe. And soe eailes also open Inene soes and keep hei physical soes in place, such as Wal-a, Bes Buy, Banes & Noble, Office Depo, Saples, GOE, and Suning Appliance, aong ohes. Howeve, i is acknowledged ha soe well-known anufacues, such as Ace, Colgae, Gillee, and Tylenol, only sell hei poducs exclusively hough eaile s physical soe, and hey do no open hei Inene soe. On he eailes side, such as 7- Eleven and Caefou, hey do no povide he Inene soes, so consues can only puchase poducs fo hei physical soes [1]. Consequenly, a quesion aises. The quesion is ha why he Inene soe soeies was opened by he anufacues, wheeas in ohe cases he Inene soes ae opened by he eailes. In he anufacue s poin of view, opening an Inene soe no only oivaes he downsea eaile o pefo oe effecively bu also iigaes supply chain s double aginalizaion poble [2 7]. Howeve, soe sa consues ofen ge oe poduc infoaion and expeience fo he eailes physical soes bu shif o puchasing hei ideal poduc fo he anufacue Inene soe wih a lowe pice. Thus, hese consues buying behavio ay educe he eaile s pofi. To cope wih he above fee-iding poble, soe eailes have no choice bu o open hei own Inene soes and keep physical soes in place [8 10]. oeove, he eailes (such as Wal-a, Bes Buy, Banes & Noble, and Office Depo) sell an idenical poduc wih he sae pice acoss hei Inene soes and physical soes. In hei views, hese picing policies can eain he advanage of hei eail sevices and incease hei sales base due o cusoes puchasing fo hei Inene soes. Those successful eailes ae well known as caegoy killes o doinan eailes. Howeve, he fis paagaph illusaes ha neihe each anufacue no each eaile

2 2 aheaical Pobles in Engineeing opens hei own Inene soes. In addiion, as Iye and Villas-Boas [11], Dukes and Liu [12] poin ou ha he key easueens of supply chain ebes feaues such as he doinan eaile s bagaining powe in he supply chain and he consues disuiliy buying fo Inene soe ay influence he condiions fo opening an Inene soe. Alhough hese eeging ends ae paiculaly noiceable in he E-coece ake, hee is scan lieaue addessing he ineacions beween anufacue and doinan eaile whehe o open hei own Inene soes wih diffeen seup coss in a supply chain. To fill his gap in he lieaue, we answe he following ciical pobles faced by he anufacue and doinan eaile. (1) When should he anufacue and doinan eaile open hei own Inene soes in a supply chain? (2) How would he anufacue and doinan eaile diffeenially se eail pice beween hei Inene soes o ensue ha opening an Inene soe is pofiable in a copeiion envionen? (3) How do he anufacue and doinan eaile adjus hei picing policies accoding o he doinan eaile s bagaining powe in he supply chain and he consues disuiliy buying fo Inene soe? Ou wok is inended o develop gae-heoeic odels o gain insighs ino hese pobles. To his end, we fis foulae fou possible supply chain sucues (T-channel, RD-channel, D-channel, and -channel), which depend on whehe he Inene soes ae opened by he anufacue and doinan eaile. eanwhile, we analyse and copae he anufacue and doinan eaile s opial picing policies and equilibiu pofis aong fou supply chain sucues. Ou analysis suggess ha no ae who opens an Inene soe, he playe opening Inene soe will affec he supply chain sucue and opial picing policies in diffeen ways. I should be noed ha boh he anufacue and doinan eaile s opial choices fo opening an Inene soe ae lagely deeined by hei especive seup coss, which ae closely elaed o he doinan eaile s bagaining powe and consues disuiliy buying fo Inene soe. The eainde of his pape is oganized as follows. Secion 2 eviews he elaed lieaue and shows ou conibuions in oe deail. In Secion 3, we descibe he odels and popose soe assupions elaed o ou sudy. In Secion 4, wefispesenheequilibiuoucoesaong he diffeen supply chain sucues and hen discuss he saegic condiions fo he anufacue and doinan eaile o open an Inene soe. In Secion 5,weinvesigae he ipacs of he doinan eaile s bagaining powe and consues disuiliy of puchasing a poduc fo Inene soe on boh he anufacue and doinan eaile s picing saegies. In Secion 6, we illusae he heoeical esuls by nueical exaples. We conclude he esuls and anageial iplicaions and sugges opics fo fuue eseach in Secion 7.Allelevanpoofsaeelegaedohe appendix. 2. Lieaue Review Thee is a gowing aoun of lieaue on he Inene channel anageen saegies in eleconic coece ea. Howeve, os of he focus on he copeiive picing decisions and channel coodinaion poble, in which he anufacue sells poducs hough boh eaile s physical soe and is Inene soe, which is called dual-channel supply chain. In paicula, a lage aoun of lieaue exploe he pice-seing gae in a dual-channel envionen [13 20]. In addiion, i should be noed ha when he anufacue opens an Inene soe as is diec channel, consues have alenaives o choose soe ha is bee suied o hei needs; hen he eaile s pofi ay educe and esul in channel conflic. Theefoe, a consideable body of eseach also exiss on channel conflic and coodinaion in he dual-channel supply chain [21 27]. In hose sudies, hey show ha a anufacue would choose one conac (i.e., quaniy discouns o wo-pa aiffs, pofi shaing conac) o coodinae he disibuion channel. Howeve, all he above papes ae devoed o discussing he anufacue and eaile s picing saegies and channel coodinaion bu neglec he doinance of eaile and by defaul he eaile is unable o open an Inene soe. Alhough ou eseach is also elaed o he lieaue on he doinan eaile opening an Inene soe, he lieaue is liied. Yao and Liu [28] popose he ixed eail and e- ail disibuion channels and discuss he doinan eaile s picing saegy when opening an Inene soe. Liu e al. [29] develop a gae-heoeical odel o show ha a bick-andoaeailecanopenaninenesoeopeepheeailo s eny. Cheng and Naul [30] sudy how exising ake coveage affecs he oucoe of opening an Inene soe gae beween an exising eaile and a new enan. Zhang [31] sudies he eaile s ulichannel (beween Inene soe and physical soe) and pice adveising decisions. Huang and Swainahan [32] sudy he opial picing saegies when a poduc is sold in wo soes such as Inene soe and physical soe. I should be noed ha he auhos focus on he doinan eaile having he abiliy o open an Inene soe bu does no conside he ineacions wih anufacue in a supply chain and neglec he doinan eaile s bagaining powe in he disibuion channel. In conas o he papes ha ae invesigaed above, ou wok diffes in wo ipoan aspecs. Fis, in he ligh of he anufacue and doinan eaile having ied o open hei Inene soe, we assue ha boh of he ae able o coi whehe o open an Inene soe in asupplychainandaepopovideheoeicalinsighs ino he saegic condiions and picing policies fo he o open an Inene soe. Ineesingly, we find ha he doinan eaile opening an Inene soe can induce he anufacue o open an Inene soe o copee wih hi, and he anufacue s opial pice a he Inene soe is no always being lowe han he doinan eaile s. Second, in ode o chaaceize he doinan eaile s bagaining powe in he disibuion channel, we assue ha he wholesale pice beween anufacue and doinan eaile is deived by eans of he bagaining pocess. In

3 aheaical Pobles in Engineeing 3 R R R R PS PS RIS PS IS PS RIS IS (a) T- channel (b) RD-channel (c) D-channel (d) -channel Figue 1: The supply chain configuaion of scenaios T-, RD-, D-, and -channels. ou sudy, we noe ha he doinan eaile s bagaining poweplaysaciicaloleininfluencingequilibiupices and pofis in he disibuion syse, as well as he saegic condiions fo he anufacue and doinan eaile o open an Inene soe. 3. odel Fundaenals Conside a wo-echelon supply chain consising of one anufacue, denoed by (efeed o as she ), and one doinan eaile wih a physical soe in a onopolis ake, denoed by R (efeed o as he ), who sells he poducs of he anufacue o he consues. Wih he pevailing populaiy of consues puchasing poducs online, hey have o edesign hei disibuion channel sucues. Based on akeing cases abou he anufacue s diec channel saegy and he doinan eaile s ulichannel eailing aciviies, we assue ha each of he is able o coi whehe o open an Inene soe is faced wih diffeen seup coss. Since he anufacue and doinan eaile ay open he Inene soes successfully o no, hee ae 4 possible channel sucues. Case (A). Boh of he do no open hei Inene soes denoed by T-channel. Case (B). The anufacue does no open an Inene soe, bu doinan eaile opens an Inene soe denoed by RDchannel. Case (C). The anufacue opens an Inene soe, bu doinan eaile does no and is denoed by D-channel. Case (D). Boh of he open hei Inene soes siulaneously denoed by -channel. Figue 1 depics 4 possible cases. Fo convenience, le PS denoes he doinan eaile s physical soe; IS, he anufacue-owned Inene soe; RIS, he doinan eaile-owned Inene soe. Paaees and decision vaiables noaions used in he pape ae lised in Abbeviaions secion. Befoe esablishing he odels, we give soe assupions elaed o his sudy as follows. Assupion 1. The anufacue poduces he poduc a a consan uni (aginal) cos which is noalized o zeo and sells poduc o he doinan eaile wih a wholesale pice w j =(1 β)p j in he j-channel, which is deived by eans of he bagaining pocess, whee p j is he eail pice chaged by he doinan eaile in he j-channel, and he value of β (0, 1) denoes his bagaining powe. The wholesale pice ha is deeined in he supply chain by a negoiaion pocess is siila o he pevious eseaches such as [11, 12]. Assupion 2. The doinan eaile acs as a Sackelbeg pice leade in he disibuion channel, and his physical soe has locaed a he lef end poin of a Hoelling linea ciy bounded beween zeo and one, as seen in he pevious lieaue [29, 33 37]. Wihou loss of genealiy, we assue ha he size of he ake is one, and consues ae unifoly disibued ove he line of he ciy wih a uni avel cos ( > 0) fo aveling o he doinan eaile s physicalsoeoshop,andeachconsuebuysaosone uni of he poduc. Assupion 3. The doinan eaile ses he sae pice acoss his physical soe and Inene soe. In akeing pacice, soe doinan eailes, such as Cicui Ciy, Tiffany, Gap, and Saples, fully inegae hei offline and online opeaions, which can ake consue no figue ou whehe i is cheape o puchase fo is physical soes and Inene soes. In fac, his assupion is siila o [29, 31, 38]. Assupion 4. The value of consues willing o pay fo he poduc is sufficienly lage (V > ), so as o ensue he full ake coveage. Ohewise, he doinan eaile neve opens a physical soe o seve consues. Assupion 5. If a consue chooses o puchase he poduc fo he Inene soes (IS o RIS), he puchasing incus aunidisuiliy( > 0). Toensuehaaleasoneofhe anufacues and he doinan eaile has an incenive o

4 4 aheaical Pobles in Engineeing Table 1 s wholesale pice IS s pice PS/RIS s pice s pofi R s pofi T-channel (1 β)(v ) N/A V (1 β)(v ) β(v ) RD-channel (1 β)(v ) N/A V (1 β)(v ) β(v ) F D-channel (1 β)( + ) (2 + β) + (2 3β) + + 2β 4β 2β 2β + ( )2 12 ( + ) 2 F 16 8 Table 2 < 3 > 3 s wholesale pice IS s pice PS/RIS s pice s pofi R s pofi (1 β)( ) ( ) ( ) F β β β β F (1 β)( + ) (2 + β) + (2 3β) + + 2β 4β 2β 2β + ( )2 12 ( + ) 2 F 16 F 8 open an Inene soe, le <in ou sudy, which is siila o pevious sudies [3, 14, 17]. Consues disuiliy capuing vaious facos akes online shopping inconvenien, such as qualiy unceainy (e.g., he inabiliy o ouch and feel), discofo wih online secuiy, waiing ie unil delivey, and shipping chage. Basedonheaboveassupions,iiscleaha,foa consue locaed a x [0,1], he will ge uiliies U PS = V p xwhen puchasing he poduc fo he doinan eaile s physical soe, and U IS = V p when puchasing he poduc fo he anufacue s Inene soe, and U RIS =V p when puchasing he poduc fo he doinan eaile s Inene soe. 4. Equilibiu Oucoes and Saegic Condiions fo Opening an Inene Soe In his secion, we fis pesen he equilibiu oucoes aong he diffeen channel sucues and hen discuss he saegic condiions fo he anufacue and doinan eaile o open hei Inene soes. The equilibiu oucoes ae given by he following Leas 6 and 7, andhe poofsae povided in Appendix A Equilibiu Oucoes Lea 6. In he T-channel, D-channel, and RD-channel, he equilibiu pices and pofis fo he anufacue and doinan eaile can be suaized as shown in Table 1. Lea 7. In he -channel, he equilibiu pices and pofis fo anufacue and doinan eaile can be suaized as shown in Table 2. Fo Leas 6 and 7, we obseve ha no ae he anufacue and doinan eaile open an Inene soe will affec he supply chain sucue and equilibiu pices and pofis in diffeen ways. Le T-channel be a benchak; we noe ha he doinan eaile should lowe eail pice only when his Inene soe in he ake, and when he seup cos of opening an Inene soe F < β( ), hen he can ge oe pofi han ha of no opening an Inene soe. In addiion, we find ha when he anufacue and doinan eaile open hei Inene soes siulaneously, if consues disuiliy of puchasing a poduc fo Inene soe is low enough (i.e., </3), he anufacue can se he eail pice a he Inene soe sae o he doinan eaile s eail pice. Howeve, if consues disuiliy of puchasing a poduc fo Inene soe is elaively lage (i.e., > /3), he equilibiu pices ae sae o he case of he anufacue only open an Inene soe, ha is, D-channel. Fuheoe, he anufacue s pofi does no change, bu he doinan eaile s pofi deceases. Theefoe, we will discuss he saegic condiions fo he anufacue and doinan eaile o open an Inene soe accoding o he equilibiu pofis aong he diffeen channel sucues Saegic Condiions fo Opening an Inene Soe. Now, as one of he ciical pobles o obain he saegic condiions fo he anufacue and doinan eaile o open an Inene soe, we copae he equilibiu pofis in RDchannel, D-channel, and -channel o he equilibiu pofis in T-channel and copae he equilibiu pofis in -channel o he equilibiu pofis in RD-channel and D-channel, especively. The following poposiions and coollaies suaize he saegic condiions and is iplicaions. The poofsae given in Appendix B. Poposiion 8. Suppose ha he anufacue has no opened an Inene soe; when he seup cos of opening an Inene soe by he doinan eaile F < β( ), hecanbegino open an Inene soe. Poposiion 8 iplies ha unde he condiion of he anufacue has no opened an Inene soe, only when he seupcosofopeninganinenesoeiselaivelysall,he doinan eaile will ge oe pofi han ha of no opening an Inene soe. Ohewise, his pofi will decease due o cosly seup cos. Obviously, an iediae consequence of above poposiionsishefollowingcoollay.

5 aheaical Pobles in Engineeing 5 Coollay 9. If he anufacue has no opened an Inene soe, he doinan eaile s saegic oive fo opening an Inene soe would be weakened by inceasing consues disuiliy of puchasing a poduc fo Inene soe. Poposiion 10. Suppose ha he doinan eaile has no opened an Inene soe; when he seup cos of opening an Inene soe by he anufacue F < (+)/2β+[( ) 2 12]/16 (1 β)(v ), shecanbeginoopenan Inene soe. Poposiion 10 iplies ha, unde he condiion of he doinan eaile has no opened an Inene soe, only when he seup cos of opening an Inene soe is elaively sall, he anufacue will ge oe pofi han ha of no opening an Inene soe. Ohewise, he pofi will decease due o cosly seup cos. BasedonPoposiion 10,wehavehefollowingcoollay. Coollay 11. If he doinan eaile has no opened an Inene soe and his bagaining powe is elaively sall (i.e., β < 4/(7 )), he anufacue s saegic oive fo opening an Inene soe would be senghened by inceasing consues disuiliy of puchasing a poduc fo Inene soe. Ohewise, he saegic oive would be weakened. Poposiion 12. Thee ae wo choices fo he anufacue and doinan eaile o open hei Inene soes siulaneously, which ae suaized as follows. (1) If consues disuiliy of puchasing a poduc fo Inene soe is low enough (i.e., </3)andheseup coss of opening an Inene soe by he anufacue and doinan eaile ee F < ( )/β ( )/ (1 β)(v ) and F < ( )/ β(v ), especively, boh of he can open hei own Inene soes siulaneously. (2) If consues disuiliy of puchasing a poduc fo Inene soe is elaively lage (i.e., > /3) and he seup coss of opening an Inene soe by he anufacue and doinan eaile ee F <(+ )/2β + [( ) 2 12]/16 (1 β)(v ) and F <(+) 2 /8 β(v ), especively, boh of he can open hei own Inene soes siulaneously. Poposiion 12 iplies ha consues disuiliy of puchasingapoducfoinenesoeplaysanipoan ole fo opening Inene soes siulaneously by he anufacue and doinan eaile. And only when he seup coss of opening Inene soes by he ae elaively sall, especively,henbohwillgeoepofihanhaofno opening Inene soes. Ohewise, hei pofis will decease dueocoslyseupcoss. I should be noed ha he uppe bounds of F and F ae elaed o fo a given β in Poposiion 12, sowehavehe following coollay. Coollay 13. If boh he anufacue and doinan eaile have no opeaed hei Inene soes, hen (1) when consues disuiliy of puchasing a poduc fo Inene soe is low enough (i.e., < /3), he anufacue s saegic oive fo opening an Inene soe would be weakened by inceasing consues disuiliy of puchasing a poduc fo Inene soe, bu he doinan eaile s saegic oive fo opening an Inene soe would be senghened; (2) when consues disuiliy of puchasing a poduc fo Inene soe is elaively lage (i.e., > /3), he doinan eaile s saegic oive fo opening an Inene soe would be senghened by inceasing consues disuiliyofpuchasingapoducfoinene soe. Fo he anufacue, only if he doinan eaile s bagaining powe is elaively sall (i.e., β< 4/(7 )), he saegic oive fo opening an Inene soe would be senghened by inceasing consues disuiliy of puchasing a poduc fo Inene soe. Ohewise, he saegic oive would be weakened. Poposiion 14. Suppose ha he doinan eaile has opeaed an Inene soe, he anufacue has wo choices o open an Inene soe, which ae suaized as follows. (1) If consues disuiliy of puchasing a poduc fo Inene soe is low enough (i.e., </3), and he seup cos of opening an Inene soe by he anufacue F < ( )/β ( )/ (1 β)(v ),shecan also open an Inene soe. (2) If consues disuiliy of puchasing a poduc fo Inene soe is elaively lage (i.e., > /3), and he seup cos of opening an Inene soe by he anufacue F < ( + )/2β + [( ) 2 12]/16 (1 β)(v ), she can also open an Inene soe. Poposiion 14 iplies ha, unde he condiion of he doinan eaile has opeaed an Inene soe, consues disuiliy of puchasing a poduc fo Inene soe also plays an ipoan ole in opening an Inene soe by he anufacue. And only when he seup cos of opening an Inene soe is elaively sall, hen he anufacue will ge oe pofi han ha of no opening an Inene soe. Ohewise, he pofi will decease due o cosly se-up cos. BasedonPoposiion 14,wehavehefollowingcoollay. Coollay 15. If he doinan eaile has opeaed an Inene soe, hen (1) when consues disuiliy of puchasing a poduc fo Inene soe is low enough (i.e. < /3), he anufacue s saegic oive fo opening an Inene soe would be weakened by inceasing consues disuiliy of puchasing a poduc fo Inene soe. (2) when consues disuiliy of puchasing a poduc fo Inene soe is elaively lage (i.e. >/3), and only if he doinan eaile s bagaining powe is elaively sall (i.e. β<[(+)+ ( + ) ]/16), he anufacue s saegic oive fo opening an Inene soe would be senghened by inceasing

6 6 aheaical Pobles in Engineeing consues disuiliy of puchasing a poduc fo Inene soe. Ohewise, he saegic oive would be weakened. Poposiion 16. Suppose ha he anufacue has opeaed aninenesoe;hebeschoicefodoinaneaileisnoo open an Inene soe. Poposiion 16 iplies ha, unde he condiion of he anufacue has opeaed an Inene soe, egadless of consues disuiliy of puchasing a poduc fo Inene soe is sall o lage, i is bes fo he doinan eaile no o open an Inene soe. Ohewise, his pofi will decease due o cosly seup cos o he anufacue s low pice saegy ha aac oe consues o buy he poduc fo he Inene soe. Poposiion 17. Suppose ha he anufacue has no opened an Inene soe, if consues disuiliy of puchasing a poduc fo Inene soe is low enough (i.e., </3), and he seup cos of opening an Inene soe fo he anufacue is ineediae F [( + )/2β + [( ) 2 12]/16, ( )/β ( )/], he doinan eaile opening an Inene soecanleadohewell-knownconagion-likeeffec. Poposiion 17 iplies ha unde he condiion of he anufacue has no opened an Inene soe, when consues disuiliy of puchasing a poduc fo Inene soe is elaively sall, and he se-up cos of opening an Inene soe fo he anufacue is ineediae, he doinan eaile s Inene soe eny ay induce he anufacue o open he own Inene soe copeing wih hi. Fo Poposiion 17, we obseve ha he uppe and lowe bounds of F ae elaed o fo a given β, sowehavehe following coollay. Coollay 18. When consues disuiliy of puchasing a poduc fo Inene soe is low enough (i.e., < /3), if he doinan eaile s bagaining powe is elaively sall (i.e., β < 4/(7 )), he conagion-like effec would be expanded by inceasing consues disuiliy of puchasing a poduc fo Inene soe. Howeve, if he doinan eaile s bagaining powe is elaively lage (i.e., β > 4/(7 )), he conagionlike effec would be diinished. Based on afoeenioned poposiions, we now show when do he anufacue and doinan eaile open hei owninenesoesoaadiionalsupplychainandhowdo heysepicesafeopeninginenesoesintable Analyical Resuls on Boh Playes Picing Policies Fo Leas 6 and 7, we know ha he T-channel and RD-channel ae onopoly seings. So he doinan eaile chages he opial onopoly pice and sells he poduc o all consues. Howeve, unde he D-channel and - channel, he anufacue and doinan eaile engage in pice copeiion. To invesigae he ipacs of he doinan eaile s bagaining powe and consues disuiliy of puchasing a poduc fo Inene soe on he anufacue and doinan eaile s picing saegies, we obain he following poposiions, and he poofs ae povided in Appendix C. Poposiion 19. Supposehaonlyheanufacuecanopen an Inene soe, hen (1) p D / β = pd / β = ( + )/2β 2 <0; (2) p D / = 1/2β > 0, and p D and if β (0, 2/3),hen p D hen p D / < 0; (3) if </3,henp D p D / = (2 3β)/4β, / > 0,ifβ (2/3, 1), >pd,if=/3,henp D,andif>/3,henp D <pd. = Poposiion 19 indicaes ha when he anufacue can open an Inene soe, (1) she should also lowe he pice o induce consues o puchase he poduc fo he Inene soe as he inceasing doinan eaile s bagaining powe; ohewise, he doinan eaile will also povide pice incenives fo consues o buy he poduc fo his physical soe; (2) if he doinan eaile s bagaining powe is elaively sall (i.e., β<2/3),sheshouldaisehepice in he Inene soe wih inceasing consues disuiliy; Howeve, if he doinan eaile s bagaining powe is elaively lage (i.e., β>2/3), sheshouldcu down he pice in he Inene soe wih inceasing consues disuiliy; (3) if consues disuiliy of puchasing a poduc fo Inene soe is elaively lage (i.e., > /3), she us povide song pice incenives fo consues o puchase he poduc fo he Inene soe; ohewise he pofis will cu down owing o soe consues buying he poduc fo he doinan eaile s physical soe; on he conay, he doinan eaile will povide song pice incenives fo consues o puchase he poduc fo his physical soe when consues disuiliy of puchasing a poducfoinenesoeislowenough(i.e.,< /3), hen he anufacue s eail pice is highe han he doinan eaile s. If and only if consues disuiliy of puchasing a poduc fo Inene soe saisfies =/3, he anufacue can se he eail piceobeequalohedoinaneaile s. Poposiion 20. Suppose ha boh he anufacue and doinan eaile can open hei Inene soes siulaneously, hen. (1) If </3,hen p / β = p / β = ( )/β2 <0, p / = p / = 1/β < 0. (2) If >/3,hen p / β = p / β = ( + )/2β2 < 0, p / = (2 3β)/4β, p / = 1/2β > 0,and

7 aheaical Pobles in Engineeing 7 Table 3: Saegic condiions fo opening Inene soes o T-channel and picing policies. Saegic condiions andr s aciviies Picing policies has no opened an Inene soe and F <β( ) R can open an Inene soe onopoly picing When </3, hen p D >pd When =/3, R has no opened an Inene soe and F <(+)/2β+[( ) 2 12]/16 (1 β)(v ) can open an Inene soe When </3, F < ( )/ β(v ) and F < ( )/β ( )/ (1 β)(v ) BohandRcanopenheiInenesoessiulaneously When >/3, F <(+) 2 /8 β(v ) and F <(+)/2β+[( ) 2 12]/16 (1 β)(v ) hen p D When >/3, hen p D p =p p <p =pd <pd when β (0, 2/3), hen p / > 0, buwhenβ (2/3, 1),hen p / < 0. (3) If 3/,henp =p ;if>/3,henp <p. Poposiion 20 indicaes when boh he anufacue and doinan eaile can open hei Inene soes siulaneously. (1)Ifconsues disuiliyofpuchasingapoducfo Inene soe is low enough (i.e., < /3), boh of he can se sae pice and lowe pices as he inceasing consues disuiliy. On he conay, if consues disuiliy of puchasing a poduc fo Inene soe is elaively lage (i.e., > /3), he anufacue us povide lowe pice incenives han he doinan eaile, which ay induce consues o puchase he poduc fo he Inene soe. I should be poined ou ha when he doinan eaile s bagaining powe is elaively sall (i.e., β < 2/3), he anufacue s pice inceases wih inceasing consues disuiliy, bu when he doinan eaile s bagaining powe is elaively lage (i.e., β>2/3), he anufacue s eail pice deceases wih inceasing consues disuiliy. (2) When consues disuiliy of puchasing a poducfoinenesoeislowenough(i.e., < /3), he doinan eaile s pice deceases educe wih inceasing consues disuiliy, bu when consues disuiliyofpuchasingapoducfoinene soe is elaively lage (i.e., > /3), he doinan eaile s pice deceases wih inceasing consues disuiliy. Speaking fankly, ha is he doinan eaile s sa picing saegies. The doinan eaile will aise he eail pice when os of consues wih a lage disuiliy of puchasing a poduc fo Inene soe buy he poduc fo his physical soe and lowe he eail pice when os of consues wih a sall disuiliy of puchasing a poduc fo Inene soe buy he poduc fo he anufacue s Inene soe. Poposiion 21. Given ha he doinan eaile s bagaining powe, we obain he following esuls abou he anufacue s wholesale pice unde RD-channel, D-channel, and - channel: (1) w RD / = (1 β) < 0; (2) w D / = (1 β)/2β > 0; (3) if </3,hen w / = (1 β)/β < 0;if>/3, hen w / = (1 β)/2β > 0. Poposiion 21 indicaes ha he anufacue should se he wholesale pices diffeenially acoss he RD-channel, D-channel, and -channel and aise o lowe he wholesale pices in he ligh of consues disuiliy of buying he poduc fo Inene soe. oe specifically, he anufacue can lowe he wholesale pice wih inceasing consues disuiliy of buying he poduc fo Inene soeinherd-channel,buinhed-channel,shecanaise he wholesale pice wih inceasing consues disuiliy of buying fo Inene soe. Howeve, in he -channel, when he consues disuiliy of buying fo Inene soe is low enough (i.e., < /3), she can lowe he wholesale pice wih inceasing consues disuiliy, bu when consues disuiliy of buying fo Inene soe is elaively lage (i.e., >/3), she should aise he wholesale pice wih inceasing consues disuiliy. Poposiion 22. Given ha he doinan eaile s bagaining powe, we obain he following esuls abou he anufacue s eail pice a he Inene soe unde D-channel and - channel. (1) If < /3,whenβ (0, 2/3), hen p D / = (2 3β)/4β > 0, p / = 1/β < 0, buwhenβ (2/3, 1),hen p D / = (2 3β)/4β < 0, p / = 1/β < 0. (2) If > /3,whenβ (0, 2/3), hen p D / = p / > 0, buwhenβ (2/3, 1), hen pd / = / < 0. p Poposiion 22 indicaes ha he anufacue should se he eail pices a he Inene soe diffeenially acoss he

8 8 aheaical Pobles in Engineeing D-channel and -channel and aise o lowe he pices in he ligh of consues disuiliy of buying he poduc fo Inene soe. oe specifically, if he consues disuiliy of buying fo Inene soe is low enough (i.e., </3), heanufacuecanaiseheeailpiceaheinene soe wih inceasing consues disuiliy of buying fo Inene soe when he doinan eaile s bagaining powe is elaively sall (i.e., β < 2/3) and he doinan eaile does no open Inene soe. Howeve, if he doinan eaile also opens an Inene soe, he anufacue should lowe he eail pice a he Inene soe so as o aac consues o buy he poduc fo he Inene soe. On he conay, if he consues disuiliy of buying fo Inene soe is elaively lage (i.e., > /3) and he doinan eaile also opens an Inene soe, hen he anufacue should se he sae pice wih he doinan eaile s and adjus he pice following he doinan eaile. Poposiion 23. Given ha he doinan eaile s bagaining powe, we obain he following esuls abou doinan eaile s eail pice unde RD-channel, D-channel, and -channel: (1) If </3,hen p RD / = 1 < 0, p D / = 1/2β > 0,and p / = 1/β < 0. (2) If > /3,hen p RD / = 1 < 0, p D / = 1/2β > 0,and p / = 1/2β > 0. Poposiion 23 indicaes ha no ae when he consues disuiliy of buying fo Inene soe is sall o lage, he doinan eaile should lowe he eail pice wih inceasing consues disuiliy buying fo Inene soe in herd-channel,buinhed-channel,healwaysaiseshe eail pice wih inceasing consues disuiliy. Howeve, in he -channel, when consues disuiliy buying fo Inene soe is low enough (i.e., </3), he should lowe he pice wih inceasing consues disuiliy, bu when consues disuiliy is elaively lage (i.e., >/3), he can sehepicesaeashepiceinhed-channelandaise he pice wih inceasing consues disuiliy. 6. Nueical Exaples In his secion, we pesen nueical exaples o illusae he heoeical esuls abou ipacs of consues disuiliy of buying fo Inene soe on he anufacue and doinan eaile s picing policies wih diffeen bagaining powe fo he doinan eaile s aong RD-channel, Dchannel, and -channel, which ae suaized in Figues 2 11, wheev=14, =6, (0, 6), andβ = 0.2, β=0.8. The paaees values saisfy he assupions in Secion 3 in odeoakeheodelsfeasibleandeaningful. Copaing Figue 2 wih Figue 3, wecanobseveha when he doinan eaile s bagaining powe is elaively sall (i.e., β = 0.2); boh of he can incease pices as inceasing consues disuiliy of puchasing fo Inene soe in D-channel. Howeve, when he doinan eaile s bagaining powe is elaively lage (i.e., β = 0.8), he anufacue has no choice bu o lowe he eail pice so as o aac consues o buy he poduc fo he Inene w D p D p D Figue 2: Ipacs of on pices in he D-channel when β = w D p D p D Figue 3: Ipacs of on pices in he D-channel when β = 0.8. soe. In addiion, Figues 2 and 3 show ha when consues disuiliy buying fo Inene soe is low enough (i.e., < 2), he anufacue can se he eail pice o be lage han he doinan eaile s. Howeve, when consues disuiliy buying fo Inene soe is elaively lage (i.e., > 2), he anufacue can se he eail pice o be lowe han he doinan eaile s. Figues 4 and 5 show ha when consues disuiliy buying fo Inene soe is low enough (i.e., < 2), boh he anufacue and doinan eaile should lowe pices o incease consues disuiliy buying fo Inene

9 aheaical Pobles in Engineeing w p p Figue 4: Ipacs of on pices in he -channel when β = w D w RD w Figue 6: The wholesale pices in diffeen channels when β = w p p Figue 5: Ipacs of on pices in he -channel when β = w D w RD w Figue 7: The wholesale pices in diffeen channels when β = 0.8. soe. I is noed ha he ae of change of anufacue s eail pice wih espec o consues disuiliy buying fo Inene soe is equal o ha of doinan eaile s eail pice. Howeve, when consues disuiliy buying fo Inene soe is elaively lage (i.e., >2), if he doinan eaile s bagaining powe is elaively sall (i.e., β = 0.2), he anufacue can aise eail pice following he doinan eaile as inceasing consues disuiliy buying fo Inene soe; if he doinan eaile s bagaining powe is elaively lage (i.e., β = 0.8), he anufacue should cu down he eail pice in he Inene soe wih inceasing consues disuiliy. Figues 6 and 7 show ha no ae whehe he doinan eaile s bagaining powe is sall o lage, he anufacue can aise he wholesale pice wih inceasing consues disuiliy buying fo Inene soe in he Dchannel, bu in he RD-channel, he anufacue should lowe he wholesale pice wih inceasing consues disuiliy. Howeve, in he -channel, when consues disuiliy buying fo Inene soe is low enough (i.e., < 2), he anufacue should lowe he wholesale pice wih inceasing consues disuiliy; when consues disuiliy buying fo Inene soe is elaively lage (i.e., >2), he anufacue can aise he wholesale pice wih inceasing

10 10 aheaical Pobles in Engineeing p D p Figue 8: anufacue s eail pices in diffeen channels when β = p RD p D p Figue 10: Doinan eaile s pices in diffeen channels when β= p D p Figue 9: anufacue s eail pices in diffeen channels when β = 0.8. consues disuiliy and se he wholesale pice he sae as in he D-channel. Figues 8 and 9 show ha when he doinan eaile s bagaining powe is elaively sall (i.e., β = 0.2) in he D-channel, he anufacue can aise eail pice wih inceasing consues disuiliy buying fo Inene soe, bu when he doinan eaile s bagaining powe is elaively lage (i.e., β = 0.8), he anufacue should lowe eail pice wih inceasing consues disuiliy. Howeve, in he -channel, no ae whehe he doinan eaile s bagaining powe is sall o lage, when consues disuiliy buying fo Inene soe is low enough (i.e., < 2), he anufacue should lowe eail pice wih inceasing consues disuiliy, bu when consues disuiliy buying fo Inene soe is elaively lage (i.e., > 2), if he doinan eaile s bagaining powe is elaively sall (i.e., β = 0.2), he anufacue can aise eail pice wih inceasing consues disuiliy buying fo Inene soe; if he doinan eaile s bagaining powe is elaively lage (i.e., β=0.8), he anufacue should lowe eail pice wih inceasing consues disuiliy. Figues 10 and 11 show ha no ae whehe he doinan eaile s bagaining powe is sall o lage, he always lowes he eail pice wih inceasing consues disuiliy buying fo Inene soe in he RD-channel, bu in he D-channel, he always aises he eail pice wih inceasing consues disuiliy. Howeve, in he -channel, when consues disuiliy buying fo Inene soe is low enough (i.e., < 2), he doinan eaile should lowe eail pice wih inceasing consues disuiliy, bu when consues disuiliy is elaively lage (i.e., > 2), he doinan eaile can aise eail pice wih inceasing consues disuiliy buying fo Inene soe. 7. Conclusions and Fuue Reseach To invesigae when he anufacue and doinan eaile open hei own Inene soes wih diffeen seup coss andhowsepicesoensueopeninginenesoesae pofiable in a supply chain, we fis pesen he equilibiu oucoes unde fou possible supply chain sucues and hen discuss he saegic condiions fo he anufacue and doinan eaile when i is opial o open an Inene soe. In addiion, we analyze boh playes picing policies

11 aheaical Pobles in Engineeing p RD p D p Figue 11: Doinan eaile s pices in diffeen channels when β= 0.8. afe hey open hei Inene soes and discuss he ipacs of he doinan eaile s bagaining powe and consues disuiliy of puchasing a poduc fo Inene soe on he anufacue and doinan eaile s picing saegies. Finally, we conduc nueical exaples o illusae he heoeical esuls. We obain soe new esuls diffeing fo hose in he lieaue. We find ha he opial choices fo he anufacue and doinan eaile o open an Inene soe ae lagely deeined by hei especive seup coss, which ae closely elaed o he doinan eaile s bagaining powe and consues disuiliy of buying fo Inene soe. I is woh enioning ha ulichannel eailing fo he doinan eaile is no necessaily he bes saegy. In ohe wods, if he doinan eaile opens an Inene soe, he akeing plan fo hi o aac oe consues bychagingalowepiceisipossibleoachieve,andhe can induce he anufacue o open an Inene soe o copeewihhi.onlywhenheseupcosfohedoinan eaile o open an Inene soe is sufficienly low, hen he is pofiable. Wha is oe, we also find ha he anufacue s opial pice a he Inene soe is no always being lowe han he doinan eaile s. Fo exaple, if he consues disuiliy of buying fo Inene soe is sufficienly high, he anufacue us povide song pice incenives fo consues o puchase he poduc fo he Inene soe. Alhough his eseach povides new insighs fo he anufacue and doinan eaile o open an Inene soeandsepicesinasupplychain,heeaeseveal diecions ha could be exended. Fis, his sudy assued ha all infoaion is known o he anufacue and doinan eaile in ou odel. Howeve, infoaion could be asyeic in he supply chain since boh playes have pivae infoaion abou hei own inenal vaiable coss, fo exaple, he seup cos of opening an Inene soe, cusoes puchase paens, and seach coss. Theefoe, we can exploe he copeiive equilibiu unde asyeic infoaion seings. Second, we assue ha consues disuiliy of buy fo Inene soe is independen of he uni anspoaion cos, which can be elaxed in he fuue eseach. Thid, ade cedi is widely used in pacice and has ipoan ipac on supply chain anageen [39 41]. In ecen yeas, ade cedi has becoe one of he ajo ansacions beween supplies and eailes in a value chain. Fo exaple, Wal-a, Caefou, and GOE (a lage Chinese hoe appliance chain eaile) even delayed payens o hei supplies fo as long as one yea [42]. Hence, i is wohy o undesand how he ade cedi affecs supply channel configuaion ogehe wih picing saegies in he E-coece ake. A final issue wohy of invesigaion is how diffeen ypes of cusoes affec he anufacue and doinan eaile s channel selecion saegies. We leave hese quesions fo fuue eseach. Appendices A. Equilibiu Oucoe of he Fou Channel Sucues Poof of Lea 6. (1) In he T-channel, boh he anufacue and doinan eaile do no open hei Inene soes. Thee is only he doinan eaile s physical soe in he ake. So he doinan eaile acs as a onopolis and opially chages a pice V such ha he ake is jus coveed. Fo he anufacue, given ha he doinan eaile s opial eail pice, he opial wholesale pice is w T = (1 β)(v ). Since he anufacue poduces he poduc a a consan uni (aginal) cos which is noalized o zeo, and he ake is jus coveed, ha is, he size of he ake is one, he pofi fo he anufacue is T = (1 β)(v ). Accodingly, he pofi fo he doinan eaile is T = β(v ). (2) In RD-channel, only he doinan eaile opens an Inene soe (RIS). If a consue locaes a a disance fo physical soe (PS), he will ge a ne uiliy of by puchasing he poduc fo PS, and a ne uiliy of by puchasing he poduc fo RIS. To ensue he full ake coveage, he doinan eaile chages he onopoly pice V acoss his wo soes and sells he poduc o all consues. Fo he anufacue, given he doinan eaile s opial eail pice, he opial wholesale pice is w RD = (1 β)(v ). Since he anufacue poduces he poduc a a consan uni (aginal) cos which is noalized o zeo and he size of he ake is one, he pofis fo he anufacue and doinan eaile ae RD = (1 β)(v ) and RD = β(v ),especively. (3) In D-channel, he anufacue opens an Inene soe, bu doinan eaile does no. So consues can have convenien access o he poduc hough he doinan eaile s physical soe (PS) a pice p o he anufacue s Inene soe (IS) a pice p ; hei decision abou which soe o buy evolves aound he copaison of hei ne

12 12 aheaical Pobles in Engineeing uiliy deived fo PS U PS =V p x and U IS =V p by buying he poduc fo IS. Theefoe, he aginal consues ae locaed a x=(p p + )/. Sohepofi funcions fo he anufacue and doinan eaile can be wien as =w[ (p p +) ]+p [ (p p + ) ] F, (A.1) = (p w)[ (p p +) ]. (A.2) Unde he assupion poposed in Secion 3, he doinan eaile is he pice leade and he anufacue is he followe. As befoe, he gae is solved backwads. In his ake, we fisly need o calculae he anufacue s opial pice given any doinan eaile s pice. The anufacue s eacion funcion can be deived fo he fis-ode condiion: p = [(2 β) p 2p + ] ha is p = [(2 β) p + ]. 2 Subsiuing (A.3) ino (A.2), wege =0, (A.3) = [βp (+ βp )]. (A.4) 2 Taking he fis-ode deivaive of (A.4) wih espec o p and leing he deivaive be zeo, we have p D = (+) 2β. (A.5) Given he wholesale pice bagaining pocess, we can obain he anufacue s opial wholesale pice w D = (1 β)( + )/2β and subsiuing (A.5) ino (A.3), wege he anufacue s opial eail pice: p D = (2+β)+(2 3β). (A.6) 4β Subsiuing (A.5) and (A.6) ino (A.1) and (A.2), we can obain he equilibiu pofis fo he anufacues and doinan eaile, especively: D = (+) 2β D = (+) [( ) 2 12] F 16, (A.7) Poof of Lea 7. In he -channel, boh he anufacue and doinan eaile siulaneously open hei own Inene soes; hen cusoes ae able o puchase a poduc eihe fo he doinan eaile s physical soe (PS) o fo he alenaive Inene soes (IS/RIS). They can ge a ne uiliy of U PS =V p xby buying he poduc fo PS and a ne uiliy of U IS =V p by buying he poduc fo IS and a ne uiliy of U RIS =V p by buying he poduc fo RIS. Accoding o he basic odel, we know ha he doinan eaile fis akes picing decision as he pice leade, and he anufacue is he followe. If he doinan eaile chages a pice highe han he anufacue s pice (p >p ), hen no consue will buy he poduc fo his Inene soe. Unde his condiion, he doinan eaile akes no sale in his Inene soe and akes a pofi of F. Theefoe, he deand funcions fo he anufacue s Inene soe and doinan eaile s physical soe ae given, especively, as follows: D IS = (p p + ), (A.8) D PS = (p p +). (A.9) Hence, he anufacue s pofi funcion can be wien as = [w (p p +)+p (p p + )] Fo he fis-ode condiion, we have F. (A.10) p = [(2 β) p + ]. (A.11) 2 Given he condiion of p >p, his iplies ha p >( )/β.howeve,whenp ( )/βand p >p,wealways have / p = [(2 β)p 2p + ]/>0. Theefoe, he anufacue opially ses is pice a p =p, and he opial picing schedule is as follows: { p, p = { { p α (2 β) p +, p 2 > (A.12) α. Given he anufacue s picing schedule, he doinan eaile s pofi is given as follows: { (p w) F, = {(p w) + βp F { 2, p β p > (A.13) β. Unde he condiion of p > ( )/β,hedoinan eaile s pofi is = [βp (+ βp )] 2 F. (A.14) Taking he fis-ode deivaive of (A.14) wih espec o p, and leing he deivaive be zeo, we have p =(+)/2β.

13 aheaical Pobles in Engineeing 13 Subiing i ino (A.11), wegeheanufacue s opial pice in he Inene soe p = [(2 + β) + (2 3β)]/4β. Hence, he anufacue and doinan eaile s opial pofis ae = (+)/2β+[( )2 12]/16 F and =(+) 2 /8 F,especively. Accoding o he pevious assupion p > ( )/β, which iplies ha ( + )/2β > ( )/β, us saisfy > /3.Howeve,when</3, we always have p [( )/β]( ) >0, p [( )/β](+) <0. (A.15) So he doinan eaile s opial eail pice in he - channel is p =( )/β. Theefoe, he anufacue and doinan eaile s opial pofis ae = ( )/β [( )]/ F and = [( )]/ F,especively. B. Saegic Condiions fo Opening an Inene Soe Poofs of Poposiion 8 and Coollay 9. Fo Lea 6, we analyse he equilibiu pofis fo he doinan eaile beween he T-channel and RD-channel and noe ha only when F < β( ), hen RD > T. This iplies ha as long as he seup cos of opening an Inene soe saisfies F < β( ) B 1,iisalwaysopialoopenan Inene soe fo he doinan eaile. In addiion, we noe ha B 1 / = β < 0. So he doinan eaile s saegic oive fo opening an Inene soe would be weakened by inceasing consues disuiliy of puchasing a poduc fo Inene soe. Poofs of Poposiion 10 and Coollay 11. FoLea 6, we analyse he equilibiu pofis fo he anufacue beween he T-channel and D-channel and noe ha only when he seup cos of opening an Inene soe saisfies F < ( + )/2β+[( ) 2 12]/16 (1 β)(v ) B 2,hen D > T.Inaddiion,wenoeha B 2/ = [4 β(7 )]/8β and find when 0 < β < 4/(7 ), hen B 2 / > 0, and when 4/(7 ) < β < 1,hen B 2 / < 0. Poofs of Poposiion 12 and Coollay 13.FoLeas6 and 7,weanalyseheequilibiupofisfoheanufacueand doinan eaile beween he T-channel and -channel; we noe ha unde he condiion of </3, only when he seup coss of opening an Inene soe fo he anufacue and doinan eaile siulaneously saisfy hen F < ( ) β F < [( ) ] [( ) ] > β(v ) B 4, T, (1 β)(v ) B 3, > T (B.1). (B.2) Siilaly, unde he condiion of >/3, only when he seup coss of opening an Inene soe fo he anufacue and doinan eaile siulaneously saisfy hen F < (+) 2β F < (+)2 8 + [( ) 2 12] (1 β)(v ) B 16 5, β(v ) B 6, > T, > T (B.3). (B.4) Inaddiion,wenoehaboh B 3 / = [ + β( 2)]/β < 0 and B 4 / = ( 2)/ > 0 ae held unde he condiion of </3. Fuheoe, unde he condiion of >/3,wealsofindhawhen0 < β < 4/(7 ), hen B 5 / > 0,andwhen4/(7 ) < β < 1,hen B 5 / < 0; B 6 / = 2( + )/8 > 0. Poofs of Poposiion 14 and Coollay 15. FoLeas6 and 7, we analyse he anufacue s equilibiu pofis in he RD-channel and -channel; we noe ha unde he condiion of </3, only when he seup cos of opening an Inene soe fo he saisfies F <( )/β [( )]/ (1 β)(v ) B 7,hen > RD. In addiion, we find B 7 / = [(1 + β 2 ) 2β]/β < 0. Bu unde he condiion of >/3, only when he seup cos of opening an Inene soe fo he saisfies F <(+ )/2β + [( ) 2 12]/16 (1 β)(v ) B 8,hen > RD. In addiion, B 8/ = [β(+)+4(1 2β 2 )]/8β, we find ha when 0<β<[(+)+ ( + ) ]/16, hen B 8 / > 0,andwhen[(+)+ ( + ) ]/16 < β<1,hen B 8 / < 0. Poofs of Poposiion 16. FoLeas6 and 7, weanalyse he doinan eaile s equilibiu pofis in he D-channel and -channel and noe ha when < /3,hen D = ( 3) 2 /8 F < 0,andwhen > /3, hen D = F < 0. These iply ha when he anufacue has opeaed an Inene soe, he bes choice fo doinan eaile is no o open an Inene soe. Poofs of Poposiion 17 and Coollay 18. FoLeas6 and 7, we analyse he doinan eaile s equilibiu pofis in he D-channel and -channel and noe ha unde he condiion of </3,hen D = [8( 3) β[( + ) ]/8]/16β. This iplies ha he anufacue will open he Inene soe when he doinan eaile opens an

14 14 aheaical Pobles in Engineeing Inene soe and he seup coss of opening an Inene soe fo he saisfies B 9 (+) 2β <F < ( ) β + [( ) 2 12] 16 [( ) ] B 10. (B.5) In addiion, we find ha when 0 < β < 4/(7 ),hen B 9 / > 0 and when 4/(7 ) < β < 1,hen B 9 / < 0 and B 10 / = [ + β( 2)]/β < 0. C. The anufacue/doinan Reailes Picing Policies Poof of Poposiion 19. In he D-channel, we, especively, diffeeniae beween p D and pd wih espec o β and find ha p D / β = pd / β = ( + )/2β 2 <0.Foanygiven β, diffeeniaing beween p D and pd wih espec o,we have p D / = 1/2β > 0 and p D / = (2 3β)/4β, and if β (0, 2/3), hen p D / > 0; ifβ (2/3, 1), hen p D / < 0. In addiion, we find ha pd pd =( 3)/4; iisobvioushawhen < /3,henp D > p D ; when =/3,henp D =p D,andwhen>/3,hen p D <pd. Poof of Poposiion 20. In he -channel, we, especively, diffeeniae beween p and p wih espec o β and find ha when </3,hen p / β = p / β = ( )/β2 <0 and when >/3,hen p / β = p / β = ( + )/2β2 < 0.Foanygivenβ, we, especively, diffeeniae beween p and p wih espec o and find ha when </3,hen p / = p / = 1/β < 0; when > /3,hen p / = (2 3β)/4β and p / = 1/2β > 0. I is easy o noe ha when β (0, 2/3),hen p / > 0, bu when β (2/3, 1),hen p / < 0. Poof of Poposiion 21. Fo Leas 6 and 7, wenoeha w RD / = (1 β) < 0 and w D / = (1 β)/2β > 0. In addiion, if </3,hen w / = (1 β)/β < 0; if >/3,hen w D / = (1 β)/2β > 0. Poof of Poposiion 22. Fo he poofs of Poposiions 19 and 20, wenoeha,when < /3,ifβ (0, 2/3), hen p D / > 0, p / < 0, buifβ (2/3, 1), hen p D / < 0, p / < 0; when>/3,ifβ (0, 2/3), hen p D / = p / > 0, buifβ (2/3, 1), hen p D / = p / < 0. Poof of Poposiion 23. Fo Leas 6 and 7, wenoeha p RD / = 1 < 0 and p D / = 1/2α > 0. In addiion, if </3,hen p / = 1/α < 0;if>/3,hen p / = 1/2α > 0. Abbeviaions U K : The consue s uiliy of puchasing he poduc fo K soe, K {PS, RIS, IS} V: The value of consues willing o pay fo he poduc : Theconsues disuiliyofpuchasing he poduc fo Inene soe (IS/RIS) : The pe uni anspoaion cos of puchasing he poduc fo physical soe (PS) β: The doinan eaile s bagaining powe in he disibuion channel w j : The anufacue s wholesale pice in he j-channel, j {T, RD, D, } p j : The doinan eaile s pice in he j-channel, j {T, RD, D, } p j : The anufacue s pice in he j-channel, j {D, } F /F : The seup cos of opening an Inene soe by he anufacue/doinan eaile Π j /Πj : The anufacue/doinan eaile s pofi in he j-channel, j {T, RD, D, }. Conflic of Ineess The auhos declae ha hee is no conflic of ineess egading he publicaion of his pape. Acknowledgens This eseach has been suppoed by he Naional Naual Science Foundaion of China ( ), Chongqing s Naual Science Foundaion (csc2012jja1404), and he Open Fund of Chongqing Key Laboaoy of Logisics (CQKLL12001). Refeences [1] L. Hsiao and Y.-J. Chen, Saegic oive fo inoducing inene channels in a supply chain, Poducion and Opeaions anageen,vol.23,no.1,pp.36 47,2014. [2] I. Geyskens, K. Gielens, and. G. Dekipe, The ake valuaion of Inene channel addiions, Jounal of akeing, vol.66,no.2,pp ,2002. [3] W.-Y.K.Chiang,D.Chhajed,andJ.D.Hess, Diecakeing, indiec pofis: a saegic analysis of dual-channel supplychain design, anageen Science,vol.49,no.1,pp.1 20,2003. [4] S.-H. Chun and J.-C. Ki, Picing saegies in B2C eleconic coece: analyical and epiical appoaches, Decision Suppo Syses, vol. 40, no. 2, pp , [5] S. K. ukhopadhyay, X. Zhu, and X. Yue, Opial conac design fo ixed channels unde infoaion asyey, Poducion and Opeaions anageen,vol.17,no.6,pp , 2008.

15 aheaical Pobles in Engineeing 15 [6] G. S. Cai, Channel selecion and coodinaion in dual-channel supply chains, Jounal of Reailing,vol.86,no.1,pp.22 36,2010. [7] K.Takahashi,T.Aoi,D.Hioani,andK.oikawa, Invenoy conol in a wo-echelon dual-channel supply chain wih seup of poducion and delivey, Inenaional Jounal of Poducion Econoics,vol.133,no.1,pp ,2011. [8] D. W. Calon and J. A. Chevalie, Fee iding and sales saegies fo he Inene, Jounal of Indusial Econoics, vol. 49, no. 4, pp , [9]K.D.Ania,.Begen,andS.Dua, Copeingwihgay akes, IT Sloan anageen Review,vol.46,no.1,pp.63 69, [10] J. Shin, How does fee iding on cusoe sevice affec copeiion? akeing Science, vol. 26, no. 4, pp , [11] G. Iye and J.. Villas-Boas, A bagaining heoy of disibuion channels, Jounal of akeing Reseach,vol.40,no.1,pp , [12] A. Dukes and Y. Liu, In-soe edia and disibuion channel coodinaion, akeing Science, vol. 29, no. 1, pp , [13] H. Ahn, I. Duenyas, and R. Zhang, Pice copeiion beween eailes and anufacue-owned soes, Woking Pape, Univesiy of Califonia a Bekeley, [14] K. Caani, W. Gilland, H. S. Heese, and J. Swainahan, Boiling fogs: picing saegies fo a anufacue adding a diec channel ha copees wih he adiional channel, Poducion and Opeaions anageen, vol.15,no.1,pp.40 56, [15] K.-Y. Chen,. Kaya, and Ö. Öze, Dual sales channel anageen wih sevice copeiion, anufacuing and Sevice Opeaions anageen, vol. 10, no. 4, pp , [16] G. Hua, S. Wang, and T. C. E. Cheng, Pice and lead ie decisions in dual-channel supply chains, Euopean Jounal of Opeaional Reseach, vol. 205, no. 1, pp , [17] W. S. Yoo and E. Lee, Inene channel eny: a saegic analysis of ixed channel sucues, akeing Science, vol.30,no.1, pp , [18] Y. Xiong, W. Yan, K. Fenandes, Z.-K. Xiong, and N. Guo, Bicks vs. clicks : he ipac of anufacue encoachen wih a deale leasing and selling of duable goods, Euopean Jounal of Opeaional Reseach,vol.217,no.1,pp.75 83,2012. [19] Q. Lu and N. Liu, Picing gaes of ixed convenional and e-coece disibuion channels, Copues and Indusial Engineeing,vol.64,no.1,pp ,2013. [20] Q. Xu, Z. Liu, and B. Shen, The ipac of pice copaison sevice on picing saegy in a dual-channel supply chain, aheaical Pobles in Engineeing, vol.2013,aicleid , 13 pages, [21] C. A. Ingene and. E. Pay, Channel coodinaion when eailes copee, akeing Science,vol.14,no.4,pp , [22] A. A. Tsay and N. Agawal, Channel conflic and coodinaion in he E-coece age, Poducion and Opeaions anageen,vol.13,no.1,pp ,2004. [23] J. Raju and Z. J. Zhang, Channel coodinaion in he pesence of a doinan eaile, akeing Science,vol.24,no.2,pp , [24] K. L. Webb and C. J. Labe, Inenal uli-channel conflic: an exploaoy invesigaion and concepual faewok, Indusial akeing anageen,vol.36,no.1,pp.29 43,2007. [25] S. K. ukhopadhyay, D.-Q. Yao, and X. Yue, Infoaion shaing of value-adding eaile in a ixed channel hi-ech supply chain, Jounal of Business Reseach, vol. 61, no. 9, pp , [26] R. Yan, anaging channel coodinaion in a uli-channel anufacue-eaile supply chain, Indusial akeing anageen,vol.40,no.4,pp ,2011. [27] E. Cao, Y. a, C. Wan, and. Lai, Conacing wih asyeic cos infoaion in a dual-channel supply chain, Opeaions Reseach Lees, vol. 41, no. 4, pp , [28] D. Q. Yao and J. J. Liu, Copeiive picing of ixed eail and e-ail disibuion channels, Oega,vol.33,no.3,pp , [29] Y. Liu, S. Gupa, and Z. J. Zhang, Noe on self-esain as an online eny-deeence saegy, anageen Science,vol.52, no. 11, pp , [30] Z. Cheng and B. R. Naul, Inene channel eny: eail coveage and eny cos advanage, Infoaion Technology and anageen,vol.8,no.2,pp ,2007. [31] X. Zhang, Reailes ulichannel and pice adveising saegies, akeing Science,vol.28,no.6,pp ,2009. [32] W. Huang and J.. Swainahan, Inoducion of a second channel: iplicaions fo picing and pofis, Euopean Jounal of Opeaional Reseach,vol.194,no.1,pp ,2009. [33] H. Hoelling, Sabiliy in copeiion, The Econoic Jounal, vol.39,no.153,pp.41 57,1929. [34] J. Zhang, The peils of behavio-based pesonalizaion, akeing Science, vol. 30, no. 1, pp , [35] T. Kabiaj and C. Lee, Licensing conacs in hoelling sucue, Theoeical Econoics Lees, vol. 1, no. 3, pp , [36] H. Wang and T. Naiu, Disibuion channel anageen in an inene age: equilibiu and social welfae, Jounal of Indusy, Copeiion and Tade, vol. 12, no. 3, pp , [37]. Lijesen, Hoelling s webshop, Jounal of Econoics,vol.109, no. 2, pp , [38] R. Gulai and J. Gaino, Ge he igh ix of bicks & clicks, Havad Business Review,vol.78,no.3,pp ,2000. [39] K.-J. Chung, S.-D. Lin, and H.. Sivasava, The coplee soluion pocedues fo he aheaical analysis of soe failies of opial invenoy odels wih ode-size dependen ade cedi and deeinisic and consan deand, Applied aheaics and Copuaion,vol.219,no.1,pp ,2012. [40] K.-J. Chung, S.-D. Lin, and H.. Sivasava, The invenoy odels unde condiional ade cedi in a supply chain syse, Applied aheaical odelling. Siulaion and Copuaion fo Engineeing and Envionenal Syses, vol.37,no.24,pp , [41] K.-J. Chung, S.-D. Lin, and H.. Sivasava, The invenoy odels fo deeioaing ies in he discouned cash-flows appoach unde condiional ade cedi and cash discoun in a supply chain syse, Applied aheaics and Infoaion Sciences, vol. 8, no. 5, pp , [42] J. Luo and Q. Zhang, Tade cedi: a new echanis o coodinae supply chain, Opeaions Reseach Lees, vol. 40, no.5,pp ,2012.

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