Supply Chain Coordination for Strong Retailer with Extended Warranty under Network Externality

Transcription

1 Journal of Service Science an Management, 015, 8, Publihe Online June 015 in SciRe. htt:// htt://x.oi.org/10.436/jm Suly hain oorination for Strong Retailer with Extene Warranty uner Networ Externality Yan-Fei Tan, Yu-Yin Yi, Jun-Jiang Yao Management School, Jinan Univerity, Guangzhou, hina Receive 11 March 015; accete June 015; ublihe 6 June 015 oyright 015 by author an Scientific Reearch Publihing Inc. Thi wor i licene uner the reative ommon Attribution International Licene ( BY. htt://creativecommon.org/licene/by/4.0/ Abtract Thi aer contructe a retailer-leaing uly chain ytem coniering the extene warranty (EW with ingle manufacturer an ingle retailer to tuy the influence of networ externality on retailer-leaing uly chain coorination. Firt of all, we analyze an comare the retail rice, EW rice, EW quality, an the total ytem rofit in centralize an ecentralize moel reectively. Then we analyze the influence of networ externality on eciion variable an ytem rofit. We foun that the networ externality increae the lo of eciion efficiency. After that, we coniere the coorination of the uly chain ytem with extene warranty. Finally, ome numerical examle were reente for further analyi. Keywor Extene Warranty, Networ Externality, ontract oorination, Game Moel, Two-Part Tariff 1. Introuction In recent year, a the exanion of giant electric equiment retailer uch a Gome, Suning an o forth, ome retailer have more icoure ower in uly chain. An change of the ominant force in the uly chain have imortant imact on the noe enterrie an the erformance of the uly chain ytem. However, the intene cometition mae rofit of aliance retail o le that retailer tart looing for new rofit growth oint, one of which i after-ale ervice. Among the after-ale ervice, exten warranty ervice by aying which i alo calle extene warranty, i note wiely. Reearche on extene warranty mainly icu the rationality an the relate influence factor of the extene warranty from the theoretical an emirical erective [1] []. Scholar focue on the following a- How to cite thi aer: Tan, Y.-F., Yi, Y.-Y. an Yao, J.-J. (015 Suly hain oorination for Strong Retailer with Extene Warranty uner Networ Externality. Journal of Service Science an Management, 8, htt://x.oi.org/10.436/jm

2 ect: one i the eign of the extene warranty, which i reearche from the oint of view uch a cot of extene warranty [3], range of extene warranty [4], cutomer ri reference [5], erio of extene warranty [6], the aitive eman [7] an o forth. The econ i about the election of uly chain extene warranty moe an it otimization. eai an Pamanabhan [8] tuie the coorination of extene warranty itribution channel from manufacturer tanoint an it reearch reult howe that the hybri channel wa manufacturer otimal choice. Wang an Hu [9] tuie how attractive inex of extene warranty influence manufacturer choice of roviion moe of extene warranty in the form of moeling. In aition, Zhang et al. [10] tuie the effect of ervice level on uly chain an manufacturer otimal choice of extene warranty ale channel. Obviouly, the aer above rovie ome goo iea for the relate reearche of extene warranty, but currently the tuie are confine to the ituation of manufacturer ominating the uly chain. The roblem of uly chain coorination that trong retailer ominate the uly chain an rovie extene warranty (uch a Gome an Suning ecribe above i not yet coniere. In the meantime, many rouct, uch a mobile hone, comuter an o on, have the characteritic of networ externality in the networ economy era. An in the reality, the commoitie uch a mobile hone, comuter with networ externality are the target cutomer of extene warranty. Katz an Srairo [11] efine networ externality a that a ingle conumer utility increae with the increae of the total number who buy the ame rouct. Shanar an Bayu [1] umme u that the influencing factor of networ externality were networ cale an the intenity of networ externality. An the intenity of networ externality refer to the marginal effect of the networ cale increaing er unit on eman. They alo ointe out that the intenity of networ externality eene on the factor uch a cutomer reference, characteritic of conumer bacgroun, cutomer loyaltie an o on. After their reearche, cholar carrie out extenive reearche an they mainly focue on toic about networ externality uch a rice maing trategy [13] [14], rouct eveloment trategy [15] [16], technology licening an eciion of comatibility [17] [18], etc. Being ifferent from traitional economy of cale, networ externality erform more lie economy of cale on the eman ie. Networ externality influence conumer buying eciion by influencing conumer exectation o that manufacturer an retailer mut tae the change of maret eman caue by the change of conumer exectation into account while maing eciion. onequently, the exitence of networ externality will affect the uly chain ytem o that the eciion-maing an coorination of uly chain ytem have new characteritic an law. Furthermore, the otential conumer grou of extene warranty een on ale of rouct o that the influence of networ externality on ale of rouct further affect the eman of extene warranty. An the imact of networ externality on extene warranty majorly i rovier ervice ricing, ervice quality an other eciion-maing. However, reviou tuie rarely conier the influence of networ externality on the uly chain an it coorination. Yi et al. [19] tuie uly chain coorination for extene warranty from the erective of networ externality an the reult howe that uner the influence of networ externality, the imrove revenue haring contract coul mae uly chain ytem to obtain the Pareto imrovement an coorinate uly chain. In concluion, at reent there i no reearch involving uly chain coorination for extene warranty rovie by trong retailer uner networ externality. Therefore, thi aer have built a uly chain moel that trong retailer rovie extene warranty uner networ externality an have analyze the imact of networ externality on eciion-maing of rouct ricing, extene warranty ricing an extene warranty quality an the eciion-maing efficiency. We alo have icue how to coorinate the uly chain ominate by trong retailer who rovie extene warranty uner networ externality.. Problem ecrition an Aumtion We conier a two-tage uly chain ytem comoe of ingle manufacturer an ingle retailer who rovie extene warranty. Retailer i a leaer in the uly chain ytem an manufacturer i the follower. Bae on the real cae of the retail giant uch a Gome, Suning an o on, we aume that the retailer beie elling goo, he alo rovie extene warranty for conumer. onumer may chooe to buy ingle rouct or urchae the combination of goo an extene warranty. Thi aer introuce the following arameter: w rereent manufacture wholeale rice of unit goo; c rereent manufacture rouction cot of unit goo; rereent retailer retail rice of unit commoity; rereent retailer unit rice of extene warranty; q rereent the quality level of extene warranty an 394

3 the correoning cot of extene warranty i q, rereent the average cot factor of extene warranty an that i the level of control of retailer average cot roviing extene warranty; g rereent the unit i rofit of commoity, an g w; π j rereent the rofit of noe enterrie or uly chain ytem, the uercrit i, reectively rereent centralize eciion-maing moel an ecentralize eciionmaing moel, ubcrit j r, m, c reectively rereent retailer, manufacturer an the uly chain ytem. e Auming that conumer forme the execte maret ize of the rouct Q, an their exectation etermine their willing to ay for the maret ize f ( Q. Accoring to the connotation of networ externality e- e fine by Katz an Srairo [11], we have the following retailer linear invere eman function coniering the networ externality (A imilar eman function eign alo can be foun in the aer [11] [14] [18] [19], an that eman function cature the fact that if conumer believe that high ale of the rouct increae their utility, then uner a given rice they nee more rouct. Among them, a i the maret ize, an a e we further aume that f ( Q e µ Q, ( 0,1 e a Q+ f ( Q > c. In orer to analyze it conveniently, referencing ocument [18], µ i the coefficient meauring the intenity of networ exter- nality. The intenity of networ externality een on factor uch a conumer eronal reference, conumer characteritic of bacgroun, cutomer loyalty an o on. In aition, uner retailer avertiing an e conumer rational exectation, we have Q Q. A a reult, the retailer invere eman function i: ( 1 µ a Q An then, by uing the formula we have the following retailer commoity eman function uner the conition of networ externality: a Q 1 µ Referencing ocument [7] [9], the eman of extene warranty i influence by three factor an they reectively are ale of commoity Q, extene warranty rice an quality of extene warranty q.thu, the eman function of extene warranty i a follow: Q Q β + q Among them, β an reectively rereent the enitive coefficient of extene warranty rice an the quality of extene warranty β > 0, > 0. By Q Q we now that, when β > q, it mean art of conumer who buy the rouct with the extene warranty, hereinafter referre to a art of the extene warranty; when β q, it mean all conumer who buy the rouct with the extene warranty, hereinafter referre to a all the extene warranty. 3. entralize eciion-maing Moel (Moel The retailer an manufacture fully cooerate in thi attern. They ell commoity an rovie extene warranty an alo jointly ecie the retail rice of commoity, extene warranty rice an extene warranty quality. The rofit function of the uly chain ytem i: 1 max π ( c Q+ Q q (1,, q t β q. By contructing the Lagrange function, we will olve the above otimal value roblem with inequality contraint. The function i a follow: a a 1 L µ 1 µ The otimal trategy of uly chain ytem nee to meet the following: ( c β q q + λ ( β q c ( 395

4 L c L c q a+ c Lc a 0; β + q + λβ 0; 1 µ 1 µ ( q λ 0; λ β q 0; λ 0; β q (1 When λ 0, β > q, that art of extene warranty. In orer to juge the ufficient conition of the exitence of the otimal olution, we contruct the correoning Hee matrix: L L L 1 0 q 1 µ 1 µ L L L 1 A β q 1 µ L L L 0 q q q If an only if orer rincial minor eterminant A µ <, ( ( ( ( ( ( ( ( 1 µ 4β 1 µ 1 A > 0, β 1 µ β 1 µ A3 < < 0 hol, the otimal olution exit. It eay to now 1 µ 1 µ 1 that when 0< µ < 1, A > 0 ; when 0< µ < 1 4β β < β, we have 0 < 1 1 β < 1 4β, A 3 < 0 hol. Moreover, when β > 1,. Therefore, the following conition (I: when β > 1, 0< µ < 1 hol, then A 1 < 0, A > 0, A 3 < 0 hol, the otimal olution exit. β The correoning otimal trategy of the uly chain ytem i: ( ( ( 1 ( ( ( ( ( ( ( ( a+ c β µ a a c a c ; ; q β µ β µ β µ < β, ( When λ 0, β q, that i all the extene warranty. We orer q β, an ubtitute it into Equation (1. Then we have: a a 1 β L ( c c + 1 µ 1 µ In orer to juge the ufficient conition of the exitence of the otimal olution, we contruct the correoning Hee matrix: A L L 1 1 µ 1 µ. If an only if orer rincial minor eter- L L 1 β 1 µ minant A µ <, ( ( ( ( β 1 µ β 1 µ A > > 0 hol, the otimal olution exit. It 1 µ 1 µ eay to now that when the following conition (II: β > 1, A > 0 hol, the otimal olution exit. β β < <, 0< µ < 1 hol, A 1 < 0, β 396

5 Uing the ame metho, we can attain that uner the conition (I an (II in thi aer, all moel have the otimal olution. It i not tate anymore ue to limite ace. The correoning otimal trategy of the uly chain ytem i a the following: ( ( 1 ( ( ( ( a c ( a+ c β µ a a c β q β 1 µ β 1 µ β 1 µ ; ; Furthermore, a we have hown in Table 1, we can obtain the value of ale of commoity, the ale of extene warranty, rofit of noe enterrie an total rofit of the ytem. 4. Non-ooerative-ecentralize eciion-maing Moel (Moel In thi attern, the retailer firtly ecie the retail rice of the commoity, extene warranty rice an extene warranty quality. Then the manufacturer ecie the wholeale rice. The manufacturer rofit function i a the following: w m ( w c Q ( w c 1 maxπ The retailer rofit function i a the following:,, q a µ 1 max π r ( w Q+ Q q (4 t β q. (3 Table 1. Equilibrium value ummary heet. Part of extene warranty: β > 1, < β, 0< µ < 1 β All of extene warranty: β > 1, β < < β, 0< µ < 1 β Moel Moel Moel Moel Q c( β ( β ( µ 1 c( β ( β ( µ 4 1 c ( β β 1 µ c ( β 4β 1 µ Q c β ( β ( µ 1 c β ( β ( µ 4 1 c ( β β 1 µ c ( β 4β 1 µ ( ( β ( 1 µ ( β ( 1 µ a + c a ( 3 ( β ( 1 µ 4( β ( 1 µ a+ c a ( a c ( 1 ( 1 + β µ a β µ ( 3 ( 1 4 ( 1 a+ c β µ a β µ c ( β ( µ 1 c ( β ( µ 4 1 c ( β 1 µ c ( 4β 1 µ q c ( β ( µ 1 c ( β ( µ 4 1 c ( β β 1 µ c ( β 4β 1 µ π r c ( β ( β ( µ 4 1 c β 4β ( 1 µ π m c ( β ( 1 µ 4( β ( 1 µ 4 c β ( 1 µ 4β ( 1 µ π c c ( β ( β ( µ 1 c ( β ( 6( β ( 1 µ ( 4( β ( 1 µ c β β ( µ 1 4 c β 6β ( 1 µ 4β ( 1 µ 397

6 Accoring to bacwar inuction, we orer w+ g. The manufacturer wholeale rice can be obtaine a follow: w( a+ c (5 We ut Equation (5 into Equation (4 an contruct Lagrange function about retailer rofit: a a 1 L a+ c + β + β 1 µ 1 µ ( q q + λ ( q r Retailer otimal trategy ha to meet the following: Lr Lr Lr 0; 0; 0; λ ( β q 0; λ 0; β q q (1 When λ 0, β > q, that art of extene warranty. By atifying conition (I we can obtain retailer correoning equilibrium trategy: ( 3 ( ( 1 ( ( ( ( ( ( a c ( ( a+ c β µ a a c ; ; q 4 β 1 µ 4 β 1 µ 4 β 1 µ Then by utting into Equation (3, we can obtain manufacturer wholeale rice of the commoity uner the otimal eciion: w ( 3 ( β ( 1 µ 4( β ( 1 µ a+ c c ( When λ 0, β q, that all of extene warranty. Being imilar to the analyi metho of the firt art (1, by atifying conition (II we can obtain the correoning otimal eciion: q ( 3a c ( 1 ( ( ; ( ( ( ( 3 ( 1 ( + β µ a a c ;, 4β 1 µ 4β 1 µ a c β c+ a β µ c 4β 1 µ 4β 1 µ w Furthermore, a we have hown in Table 1, we can obtain the value of ale of commoity, the ale of extene warranty, rofit of noe enterrie an total rofit of the ytem. 5. Equilibrium Analyi In thi ection, bae on the content of Table 1, we will comare the ifference of the equilibrium value of the uly chain with the extene warranty uner centralize eciion-maing moel an ecentralize eciion-maing moel an emhatically analyze the affection of networ externality on the equilibrium reult an ifference of equilibrium. oncluion 1: Whether all conumer urchae extene warranty or not, in the ituation of centralize eciion-maing moel an ecentralize eciion-maing moel, all the following are etablihe: extene warranty rice, extene warranty quality q, commoity ale Q an extene warranty ale Q have oitive correlation with the intenity of networ externality µ while commoity retail rice have negative correlation with µ. emontration: In the cae of centralize eciion-maing moel, when art of conumer buy extene warranty, which i < β, 0< µ < 1. It eay to juge the following equation: β ( c( β > 0, µ ( β ( 1 µ ( q c( β µ ( β ( 1 µ > 0 398

7 ( Q ( a c( β µ 1 ( β ( µ > 0, ( Q βc( β µ ( c( β µ < 0 ( β ( 1 µ ( β ( 1 µ The ame theory rove that it true when all conumer buy extene warranty. In the cae of ecentralize eciion-maing moel, that concluion i alo true. oncluion : Whether all conumer urchae extene warranty or not, all the following are etablihe: >, <, q < q. Secially, the value of their ifference i relate to the intenity of networ externality µ. emontration: We tae the ituation of art of conumer buying extene warranty a an examle, we orer U U U an we can obtain q c( β ( 1 µ ( β ( µ ( β ( µ, c ( β ( µ 1, 4( β ( 1 µ ( β ( 1 µ c ( β ( µ 1 q q, 4( β ( 1 µ ( β ( 1 µ β ( β µ ( µ ( ( ( 1 4( ( 1 ( ( ( ( ( U 4a c µ β µ β µ ( ( ( U ( ( β 8 ( β ( 1 µ a c, µ β µ β µ ( ( ( 1 4( ( 1 ( ( ( U ( ( β 8 ( β ( 1 µ a c q µ β µ β µ Becaue of < β an 0< µ < 1 β ( U ( 0 µ >, U < 0 an ( ( ( 1 4( ( 1 ( U q (, > 0, it eay to juge that U > 0, U < 0, U < 0, < 0, then the concluion above i rove. In the ame way, it true µ µ when all conumer buy extene warranty. oncluion 3: Whether all conumer urchae extene warranty or not, rofit of noe enterrie an uly chain ytem are relate to the intenity of networ externality µ. emontration: We tae the ituation of art of conumer buying extene warranty for examle, when < β, 0< µ < 1, then we can obtain β ( π ( 3 4 r a c β > 0, µ 4 1 µ ( ( β ( q 399

8 ( π m c ( β µ ( 4( β ( 1 µ ( π c c ( β > 0, ( β β 4( β ( 1 µ ( π ( ( c µ ( 3 ( ( β ( µ 4 a c + + > 0, 4 1 µ > 0. In the ame way, it true when all conumer buy extene warranty. ( β ( 1 µ oncluion 4: Whether all conumer urchae extene warranty or not, uner the influence of ouble-marginalization, uly chain ytem rofit of the ecentralize eciion-maing moel i alway le than the otimal ytem rofit uner centralize eciion-maing moel. Secially, their ifference i relate to the intenity of networ externality µ. emontration: We tae the ituation of art of conumer buying extene warranty for examle, we orer π π π L c c c 3 c ( β ( µ 1 ( 4( β ( 1 µ ( β ( 1 µ ( 3 4 ( ( ( ( ( 3 ( 4( β ( 1 µ ( ( β ( 1 µ L ( π c L ( π ( ( ( ( ( c µ becaue of 4 a c β 1 µ β 1 µ + 1 µ 16β β + 4 L < β an 0< µ < 1, it eay to juge that π c > 0, β, µ, > 0, then the concluion i rove. In the ame way, it true when all conumer buy extene warranty. The concluion 1 an 3 how that imly from the erective of the noe enterrie, networ externality increae the rofit of the noe enterrie, which lay a oitive an active role. However, from the erective of uly chain oeration, concluion an 4 how that comaring with the ituation of centralize eciion-maing moel, networ externality increae the efficiency lo of ecentralize eciion-maing an wien the ga of uly chain total rofit of centralize eciion-maing an ecentralize eciion-maing. 6. Two-Part Tariff (Moel From the reviou ection we now that networ externality increae the efficiency lo of uly chain eciion-maing. In thi ection, we attemt to ue two-art tariff to coorinate the uly chain ytem with extene warranty. Becaue of retailer leaing role, we aume that a a rincial the retailer han over rouct to manufacturer for manufacturing what they nee an rovie a contract (, T to manufacturer. It mean that the re- tailer get a fixe fee T (uch a lotting allowance an fee from manufacturer by etting a lower retail rice. After that, the manufacturer will ecie whether to accet the contract an ecifically mae otimal eciion. The above iea can be moele a follow: 1 max π r ( w Q+ Q q + T (6,, q t β q. ( w arg max π w cq T (7 m ( R* R* w cq T π m ( w cq T π m (8 In the above moel, Equation (7 i manufacturer incentive comatibility conition an Equation (8 i R* manufacturer iniviual rationality contraint (articiation contraint conition. Among them, π m i manufacturer otimal rofit uner ecentralize eciion-maing moel. Similar to the metho above, we can get the equilibrium value of two-art tariff moel, a hown in Table. oncluion 6 Whether all conumer urchae extene warranty or not, all of the following are etablihe: 400

9 Table. Equilibrium value of two-art tariff moel. w Part of extene warranty ( ( β ( 1 µ ( β ( 1 µ a + c c All of extene warranty ( ( 1 ( 1 a+ c β µ c β µ ( ( β ( 1 µ ( β ( 1 µ a + c a ( ( 1 ( 1 a+ c β µ a β µ c ( β ( µ 1 c ( β 1 µ q c ( β ( µ 1 c ( β β 1 µ Q c( β ( β ( µ 1 c ( β β 1 µ Q c β ( β ( µ 1 c ( β β 1 µ π π π m r c c ( β ( 1 µ ( 4( β ( 1 µ ( ( ( β 6( β ( 1 µ ( ( β ( 1 µ ( ( β ( 1 µ ( 4( β ( 1 µ a c + c ( β ( ( β ( µ 1 4 c β ( 1 µ ( 4β ( 1 µ ( ( a c 6 ( 1 ( ( 1 ( β ( 1 µ ( 4β ( 1 µ 4 β β µ β µ + c β ( β ( µ 1,, q q, π c π, π c r < π, π r m π. emontration: The equal equilibrium value can be een irectly. We tae retailer rofit π r uner the ituation of art of conumer buying extene warranty for examle, by < β an 0< µ < 1, β we can obtain U π π m 3 c ( β ( µ 1 1 r r ( ( β ( 1 µ 4( β ( 1 µ ( > 0. It true when all conumer buy extene warranty. oncluion 6 tate that two-art tariff can otimize the eciion-maing efficiency of uly chain ytem an obtain the uly chain ytem Pareto imrovement an can alo achieve the erfect coorination of uly chain ( πc πc. But in that ituation, the manufacturer only obtain retaine rofit an retailer grab uer rofit. 7. Analyi of Examle Next, we further analyze the above concluion by an examle. Without lo of generality, we aume that a 1000, c 100, β 4, an (1 when art of conumer buy extene warranty, accoring to conition (I we aume 1 10, 0 < µ < ; ( when all of conumer buy extene warranty, accoring to conition (II,we aume 8 10, 0 < µ < Then we reectively mae comarion iagram of ro- 401

10 uct rice, extene warranty rice, extene warranty quality, commoity ale, extene warranty ale, rofit of noe enterrie an uly chain ytem uner moe (centralize eciion-maing, moel (ecentralize eciion-maing an moel (two-art tariff a follow: (1 omarion figure of retailer retail rice an rouct ale about µ uner each moel. Figure 1-4 how that whether all conumer urchae extene warranty or not, the retail rice an ale are influence by networ externality uner, an moel. It concretely how: along with the augment of µ, retail rice ecreae an commoity ale increae with the increae of the intenity of networ externality µ. Thi mean that in the maret environment with tronger networ externality, the retailer ten to increae ale by lower the commoity rice in orer to exan the follow-u otential conumer of extene warranty. ( omarion iagram of retailer extene warranty rice, extene warranty quantity an extene warranty ale about µ uner each moel. Figure 5-10 how that whether all conumer urchae extene warranty or not, the rice, quantity an ale of extene warranty are influence by networ externality uner, an moel. It concretely how: the rice, quantity an ale of extene warranty increae with the increae of the intenity of networ externality µ. It how that in the maret environment of tronger networ externality, the retailer will refer extene warranty ricing trategy with higher quality an higher rice. On the one han, roviing high quality extene warranty can attract more conumer to buy extene warranty. On the other han, it will obtain higher extene warranty ale revenue by etting higher rice. Figure 1. omarion of retail rice when art of conumer buy extene warranty an µ change. Figure. omarion of retail rice when all conumer buy extene warranty an µ change. 40

11 Figure 3. omarion of rouct ale when art of conumer buy extene warranty an µ change. Figure 4. omarion of rouct ale when all conumer buy extene warranty an µ change. Figure 5. omarion of extene warranty rice when art of conumer buy extene warranty an µ change. 403

12 Figure 6. omarion of extene warranty rice when all conumer buy extene warranty rice an µ change. Figure 7. omarion of extene warranty quantity when art of conumer buy extene warranty an µ change. Figure 8. omarion of extene warranty quantity when all conumer buy extene warranty quantity an µ change. 404

13 Figure 9. omarion of extene warranty ale when art of conumer buy extene warranty an µ change. Figure 10. omarion of extene warranty ale when all conumer buy extene warranty quantity an µ change. Throughout the above illutration, by comaring moel with moel, we foun that equilibrium value uner the ecentralize eciion-maing moel eviate from the otimal value of centralize eciion-maing moel an the ifference of them increae with the increaing of the intenity of networ externalitie µ. Thi howe that the eciion-maing efficiency of uly chain uner ecentralize eciion-maing moel wa inferior to the ituation of centralize eciion-maing moel an networ externality intenifie the efficiency lo. At the ame time, by comaring moel, moel with moel, we foun that the rice, quantity an ale of extene warranty uner two-art tariff were better than the equilibrium value uner ecentralize eciion-maing moel an agree with the otimal value uner centralize eciion-maing moel. That howe two-art tariff coul erfectly imrove the eciion efficiency of uly chain noe enterrie. (3 omarion figure of the rofit of manufacturer, retailer an the uly chain about µ uner each moel. Figure howe that whether all conumer urchae extene warranty or not, rofit of the manufacturer, the retailer an the uly chain ytem uner, an moel were influence by networ externality. It concretely howe: rofit of the manufacturer, the retailer an the uly chain ytem increae with the increae of the intenity of networ externality µ. At the ame time, we foun that (1 Whether all conumer urchae extene warranty or not, rouct rice, extene warranty rice an quantity uner the ecentralize eciion-maing moel eviate from otimal value of centralize eciion-maing moel an the manufacturer an retailer mae eciion from the oint of maximizing their elf-interet o that the ytem rofit uner the ecentralize eciion-maing moel wa alway lower than otimal value of centralize eciion-maing 405

14 Figure 11. omarion of manufacturer rofit when art of conumer buy extene warranty an µ change. Figure 1. omarion of manufacturer rofit when all conumer buy extene warranty quantity an µ change. Figure 13. omarion of retailer rofit when art of conumer buy extene warranty an µ change. 406

15 Figure 14. omarion of retailer rofit when all conumer buy extene warranty quantity an µ change. Figure 15. omarion of rofit of uly chain when art of conumer buy extene warranty an µ change. Figure 16. omarion of rofit of uly chain when all conumer buy extene warranty quantity an µ change. 407

16 moel an the ifference of them increae with the increaing of the intenity of networ externality µ ; ( Uner two-art tariff, the uly chain ytem coul obtain the Pareto imrovement an manufacturer only obtaine retaine income, while retailer coul obtain higher rofit; (3 Two-art tariff coul erfectly coorinate the uly chain ytem with extene warranty. The ame a the otimal value of centralize eciion-maing moel, ytematic total rofit uner the contract wa better than rofit uner ecentralize eciion-maing moel. 8. oncluion Uner the conition of networ externality, we tructure a two-tage uly chain ytem with extene warranty an the leaing retailer. Firtly, in the centralize eciion-maing an ecentralize eciion-maing moe, we reectively icue an comare commoity ricing, extene warranty ricing, ervice quality eciion-maing an ytem rofit of the noe enterrie an we analyze the effect of networ externality on each eciion variable an rofit. Then we trie to ue the two-art tariff to coorinate the uly chain ytem. Finally, we further analyze it by the examle. We got the following concluion. (1 The intenity of networ externality ha an imortant imact on the otimal eciion of two-tage uly chain ytem with extene warranty. The extene warranty rice, the extene warranty quality, rouct ale, extene warranty ale, noe enterrie rofit an the ytematic total rofit were oitive relate to the intenity of networ externality µ an commoity retail rice ha negative correlation with µ. ( Networ externality exacerbate the efficiency lo of eciion-maing. (3 Two-art tariff coul erfectly coorinate the uly chain ytem with extene warranty. A the otimal value in the centralize eciion-maing moel, ytematic total rofit uner the contract wa better than rofit uner ecentralize eciion-maing moel. Becaue of retailer ominant oition an tronger bargaining ower, manufacturer only obtaine retaine income, while retailer grabbe the exce rofit. In thi aer,there are ome hortcoming, for examle: (1 We only coniere the ituation of commoity ale affecte by rice an extene warranty affecte by rice an quality uner the networ externality, without coniering the ituation of goo an extene warranty affecte by the romotional effort; ( We only coniere comlete rationality of the noe enterrie in uly chain with the goal of maximizing rofit, without coniering the ituation of uly chain noe enterrie affecte by fairne. Thoe are irection which can be extene an finihe later. Acnowlegement The tuy of thi aer i uorte by Natural Science Founation of Guangong Province (014A an Key iciline an Project eveloment Founation for Management School, Jinan Univerity (GY Reference [1] Pamanabhan, V., Rao, R.. (1993 Warranty Policy an Extene Service ontract: Theory an an Alication to Automobile. Mareting Science, 1, htt://x.oi.org/10.187/mc [] Pamanabhan, V. (1995 Uage Heterogeneity an Extene Warrantie. Journal of Economic & Management Strategy, 4, htt://x.oi.org/ /j x [3] Lam, Y. an Kwo Wai Lam, P. (001 An Extene Warranty Policy with Otion Oen to onumer. Euroean Journal of Oerational Reearch, 131, htt://x.oi.org/ /s ( [4] Jac, N., Murthy,.N.P. (007 A Flexible Extene Warranty an Relate Otimal Strategie. The Journal of the Oerational Reearch Society, 58, htt://x.oi.org/ /algrave.jor.6036 [5] Hartman, J.. an Laana, K. (009 eigning an Pricing Menu of Extene Warranty ontract. Naval Reearch Logitic (NRL, 56, htt://x.oi.org/10.100/nav.0333 [6] Gallego, G., Wang, R., War, J., Hu, M. an Beltran, J.L. (014 Flexible-uration Extene Warrantie with ynamic Reliability Learning. Prouction an Oeration Management, 3, htt://x.oi.org/ /om.1178 [7] Li, K.P., Malli, S. an hhaje,. (01 eign of Extene Warrantie in Suly hain uner Aitive eman. Prouction an Oeration Management, 1, htt://x.oi.org/ /j x [8] eai, P.S. an Pamanabhan, P. (004 urable Goo, Extene Warranty an hannel oorination. Review of Mareting Science,, 1-5. htt://x.oi.org/10.0/

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