Buyback Contract Coordinating Supply Chain Incorporated Risk Aversion

Transcription

1 Reseach Jounal of Applied Sciences, Engineeing and echnology 5(5): , 13 ISSN: ; e-issn: Maxwell Scientific Oganization, 13 Sumitted: July 31, 1 Accepted: Septeme 3, 1 Pulished: Feuay 11, 13 Buyack Contact Coodinating Supply Chain Incopoated Risk Avesion 1 Guangxing, 1 Xin Deng, 1 Yanhong Qin and Qing Wu 1 Depatment of Management, Chonging Jiaotong Univesity, Chonging 474, China Depatment of Economics and Management, Univesity of Electonic Science and echnology of China, Chengdu 6154, China Astact: his eseach studies the uyack contact of a supply chain system composed of a isk-neutal supplie and a isk-avese etaile. he uyack contact is divided into two cases, the cedit fo all unsold goods and the cedit fo a patial etun of goods, which ae theoetically analyzed and simulated numeically espectively. he esults show that when the etaile is isk avese, the supply chain system is ale to achieve coodination. he uyack pice is an inceasing function of and the uyack atio is also an inceasing function of, while the wholesale pice is a deceasing function of the isk avesion. Keywods: Buyack contact, isk avesion, supply chain coodination INRODUCION heoetical analysis has dawn the conclusion that contacts such as the uyack contact, the evenueshaing contact and the uantity-flexiility contact can coodinate supply chain and optimize the pofit of the whole supply chain and those of each chain meme (Cachon, 3). Howeve, in the pactice the coodination of supply chain often lose efficiency. One of the pimay easons is the isk-neutal assumption that the pio eseaches have supposed. But, the isk attitude has a ig influence. Fo example, Luca et al. (1) consideed the picing polem when a iskavese etaile facing an uncetainty demand and pointed out that the pice y a isk-avese etaile was lowe than that y a isk-neutal etaile. hus, it is necessay to investigate the isk attitude of the supply chain paticipants. his study studies the uyack contact fo the supply chain with a isk-neutal supplie and a iskavese etaile. Pastenack (1985) fistly discussed the etun policy y developing a model of fixed pice and used optimal picing and etun policy to ensue channel coodination. It found that the patial etun policy with full pice could ensue channel coodination in single etailes and single supplie system, while the full etun policy with pat pice could make the multi-etailes system channel coodination. Acelus et al. (1) evaluated the picing and odeing policies of the etaile facing a picedependent stochastic demand unde diffeent degees of isk toleance. Choi and Chiu (1) exploed the Mean- Downside-Risk (MDR) and Mean-Vaiance (MV) newsvendo models unde oth the exogenous and endogenous etail picing decision cases and showed that the analytical solution fo oth the MDR eualed that of MV polems. Choi and Ruszczynski (11) consideed a multi-poduct newsvendo using an exponential utility function and poved that when this atio appoached zeo the isk-avese solution conveged to the coesponding isk-neutal solution, while when the poduct demands wee positively (negatively) coelated the isk avesion leaded to a lowe (highe) optimal ode uantities than the solution with independent demands. Ozgun and Chen (11) poed a isk-avese etaile, fomally modeled the isk avesion y adopting the Conditional-Value-at-Risk (CVaR) decision citeion and dawn the conclusion that the manufactue s pefeed eate type depended on whethe the etaile is isk neutal o sufficiently isk avese. Chiu et al. (11) caied out a MV analysis unde SR contacts and found that the supplie could coodinate the channel with flexile SR contacts. Wu and Wang (1) analyzed the impact of isk avesion on the manufactue s decisions, otained esults that chaacteized the explicit elationship etween the manufactue s isk attitude and his optimal decision. Wei and Choi (1) exploed the use of a Wholesale Picing and Pofit Shaing scheme (WPPS) fo coodinating supply chain unde the MV decision famewok and showed that thee existed an uniue euiliium of the Stackeleg Game with WPPS in the decentalized case. Wang and Weste (9) used a utility function to descie the decision-making ehavio of a isk avese etaile, concluded that a isk avese etaile s ode uantity would e less than a aitaily small volume when sales pices was highe than a theshold value. Choi and Li (8) poposed an MV fomulation fo a single supplie and a single etaile, Coesponding Autho: Guangxing, Depatment of Management, Chonging Jiaotong Univesity, Chonging 474, China 1744

2 Res. J. Appl. Sci. Eng. echnol., 5(5): , 13 studied oth cases of centalized and decentalized supply chains and illustated how a etun policy could e applied fo managing the supply chain to addess the issues such as channel coodination and isk contol. Lin and Zhang (1) discussed the effect of uyack pice and the maket uncetainty on decision vaiales and the ojective function and gave the deteminant conditions of the size of the optimal ode uantity fo the etaile when the demand satisfied the second-ode stochastic dominance citeia and then caied out numeical simulation analysis, which showed that the uyack pice had the effect that should not e neglected on etaile s inventoy decision-making. Qin and Zhao (11) analyzed the effect of supplie s loss avesion on poduction capacity and the pofits of supply chain memes in the consignment contact, which founded that the pofit of the supply chain memes is a deceasing function of the loss avesion. his study will design full and patial uyack contact to coodinate the supply chain system composed of a isk-neutal supplie and a isk-avese etaile, espectively. NOAIONS AND MODEL D> = he maket demand duing the selling season F(x) = he distiution function of the demand, which is diffeentiale, stictly inceasing. Let Fx 1 Fx and F() = F(x) = he density function of the demand. Let E( D). hen, xf( x) p = he etail pice w = he wholesale pice c = he supplie s poduction cost pe unit = he ode uantity of the etaile = he pice that the supplie pays the etaile pe emaining at the end of the season = he popotion that the supplie uy ack the emaining at the end of the season k = he isk avesion coefficient. Especially, when k =, the etaile is isk neutal Moeove, the net salvage value of a unit is supposed to e and the case of stock out is impossile. It is clea that p w c, w, 1. hen, the etaile s expected sales is: F( x) S ( ) xf ( x ) f ( x ) [1 F( x)] F ( x ) (1) he expect inventoy of the etaile is: I ( x) f( x) S () he pofit of the supply chain is: ps c (3) Sustituting (3) into (1), gets: (4) p F x c Oviously, the supply chain optimal ode uantity is: ag max p F( x) c o F ( ) (5) c (6) p 1 c 1 p c F F (7) p p Supply chain coodination means that in ode to achieve the maximum of the whole pofit of the supply chain, the supplie povides a pope contact to the etaile to make the etaile s ode uantity euals the aove. FULL BUYBACK CONRAC Unde the full uyack contact, the supplie chages the etaile w pe unit and pays the etaile pe unit emaining at the end of the season. he isk-neutal etaile: he etaile s expected pofit is: ( w,, ) ( p) Fx ( w ) he decision polem of the etaile is: ag max (, w, ) (8) (9) ( p ) F( x) ( w) 1745

3 Res. J. Appl. Sci. Eng. echnol., 5(5): , 13 o F w [ (,, )] w p w (, w, ) F p 1 (1) (11) Compaing (7) and (11), it can e poved that in ode to achieve supply chain coodination, the wholesale pice w and uyack pice must meet: w c p p y which thee is <<1 simultaneously meeting: and (1) p- = p (13) w- = c (14) Sustituting (13) and (14) into (8): ( w,, ) ps c (15) On the asis of (5): (, w, ) (16) y which: ( ) p w f x [( p) F( x) ( w) ] ( ) { p F x xf x Fx (19) [ ] } Va( ) ( p ) { F( x) F F F F( x) } p F F x () So, the fist deivative of ( ) U aout is: U E kva E Va k ( p) F ( w ) k p F F x ( p ) 1 F 1 k ( p) F( x) ( w ) (1) In summay, with the full uyack contact, the etaile s expected pofit is a linea function of the centalized supply chain pofit. hen, in the pusuit of the maximum expected pofit, the etaile also achieves the maximum expected pofit of the supply chain. heefoe, the full uyack contact which satisfies the conditions (1) o (13) and (14) can achieve supply chain coodination. he isk-avese etaile: he paticipants in the supply chain have diffeent isk attitude. In the supply chain system which composed with a supplie and a etaile, the small and medium-sized etailes may pefe isk avesion. In this case, the etaile s utility function is: U E( ) k Va( ) (17) whee, U. he etaile s expected pofits is: E (, w, ) ( p) F( x) ( w) (18) whee, ( ) [ ( ) ] Va px w x f x 1746 Let (1) =. hen, F 1 F 1 1 w p k p F x w p k p F x ( ) ( ) () When of () euals that of (7), the supply chain coodination is ealized. Accoding to (), if the othe values emain unchanged, will e educed gadually with the inceasing of k. heefoe, in ode to keep e the optimal, the wholesale pice w should decease with k and the uyack pice should incease with k. PARIAL BUYBACK CONRAC Unde the patial uyack contact, the supplie sells poducts to the etaile in the wholesale pice w, then etaile sells goods to customes in the etail pice p and finally the supplie uy ack the goods not selling in a cetain popotion of in the wholesale pice of w, whee <<1.

4 Res. J. Appl. Sci. Eng. echnol., 5(5): , 13 he isk-neutal etaile: he expected pofit of the etaile is: ( w,, ) pxw( xw ) f( x ) ( p w) f ( x) ( pw) p F( x) w F( x) (3) he decision polem of the etaile is: (, w, ) ag max (, w, ) ( p w) p F( x) w F( x) (4) Let fist ode deivative eual zeo. hen: namely: ( w,, ) ( pw) pf wf 1 p w (, w, ) F p w (5) In ode to coodinate the supply chain, the wholesale pice w and the uyack popotion must meet: pw pc p w p (6) y which: ( ) p w f x [( pw) p F( x) w F( x) ] ( ) { F x p w F x xf x [ ] } (9) Va( ) ( p w) [ F( x) F F F F ( x) ] p w F F x (3) ( ) So, the fist deivative of U aout is: U E( ) kva( ) E Va k ( pw) pf wf k ( p w) F F( x) ( p w) [1 k ( pw) F( x) ]( p wf ) k( pw) F( x ) (31) Let (31) =. hen, [1 k ( pw) F( x) ]( pw) F ( ) pw k p w F x pw pc pw wc (7) Accoding to (7), the optimal uyack popotion is an inceasing function of the wholesale pice w. he isk-avese etaile: he expected pofit of the etaile is: whee, E (, w, ) ( p w) p F( x) w F( x) (8) Va( ) px w ( x) w f ( x) 1747 ( ) ( ) p w k p w F x F ( p w) k ( p w) F( x) So, the optimal ode uantity is: ( p w) k 1 p w F x F ( p w) k ( p w) F( x) ( p w) 1 k 1 p w F x F ( p w) 1 k ( p w) F( x) (3) (33) When of (33) euals to that of (7), supply chain coodination is achieved.

5 ale 1: he effect of the isk avesion k on the uyack pice in full uyack contact k k Res. J. Appl. Sci. Eng. echnol., 5(5): , 13 ale : he effect of the isk avesion k on the wholesale pice w in full uyack contact k w k w ale 3: he effect of the isk avesion k on the uyack popotion in the patial uyack contact k k Fig. 1: he elation etween the isk avesion k and the uyack pice in full uyack contact ale 4: he effect of the isk avesion k on the wholesale pice w in the patial uyack contact k w k w Because (p-w) < (p-nw), when the othe values emain unchanged, will e educed gadually with k. heefoe, in ode to keeping e the optimal, the wholesale pice w should decease with k and the uyack popotion should incease with k. Fig. : he elation etween the isk avesion k and the wholesale pice w in full uyack contact NUMERICAL EXAMPLES In ode to give a moe diect eflection of the aove, a numeical simulation analysis using MALAB 7. is given as follows. Let p =.1, c =.4, F (1, 1 ). If w =.6, y sustituting the paametes into the model of full uyack contact, ale 1 and Fig. 1 ae It can e dawn that in ode to coodinate the supply chain, the uyack pice should incease with the isk avesion k. Especially, fo a isk neutal etaile, the uyack pice eaches the minimum. If =.33, y sustituting the paametes into the model of full uyack contact, ale and Fig. ae It can e dawn that in ode to coodinate the supply chain, the wholesale pice w should decease with the isk avesion k. Especially, fo a isk neutal etaile, the wholesale pice w eaches the maximum. If w =.6, y sustituting the paametes into the model of patial uyack contact, ale 3 and Fig. 3 ae It can e dawn that in ode to coodinate the supply chain, the uyack popotion should incease with the isk avesion k. Especially, fo a isk neutal etaile, the uyack popotion eaches the minimum. If =.56, y sustituting the paametes into the model of patial uyack contact, ale 4 and Fig. 4 ae 1748 Fig. 3: he elation etween the isk avesion k and the uyack popotion in the patial uyack contact Fig. 4: he elation etween the isk avesion k and the wholesale pice w in the patial uyack contact It can e dawn that in ode to coodinate the supply chain, the wholesale pice w should decease with the isk avesion k. Especially, fo a isk neutal etaile, the wholesale pice w eaches the maximum.

6 Res. J. Appl. Sci. Eng. echnol., 5(5): , 13 CONCLUSION his eseach studies the uyack contact of a supply chain system composed of a isk-neutal supplie and a isk-avese etaile. he uyack contact was divided into two cases, the cedit fo all unsold goods and the cedit fo a patial etun of goods, which ae theoetically analyzed and simulated numeically espectively. he conclusion is dawn that when the etaile pefes isk avesion, the supply chain system can still e achieved coodination. In the full uyack contact, the uyack pice should e highe than the pice of the isk neutal case, while the wholesale pices should e less than the pice of the isk neutal case. he uyack pice is the inceasing function of the iskavesion, while the wholesale pice is the deceasing function of the isk-avesion. In the patial uyack contact, the uyack popotion should highe than the popotion of the isk neutal case, while the wholesale pice should e less than the pice of the isk neutal case. he uyack popotion is an inceasing function of the isk-avesion, while the wholesale pice is a deceasing function of the isk-avesion. ACKNOWLEDGMEN his study is suppoted y the National Natual Science Foundation of China unde Gant No REFERENCES Acelus, F.J. and S. Kuma, 1. Risk toleance and a etaile s picing and odeing policies within a newsvendo famewok. Omega, 4(): Cachon, G.P., 3. Supply chain coodination with contacts. Handooks in Opeation and Managements Science, Supply Chain Management: Design, Coodination and Opeation, 11: Chiu, C.H.,.M. Choi and X. Li, 11. Supply chain coodination with isk sensitive etaile unde taget sales eate. Automatica, 47(8): Choi,.M. and D. Li, 8. Mean-vaiance analysis of a single supplie and etaile supply chain unde a etuns policy. Eu. J. Ope. Res., 184(1): Choi, S.Y. and A. Ruszczynski, 11. A multi-poduct isk-avese newsvendo with exponential utility function. Eu. J. Ope. Res., 19(1): Choi,.M. and C.H. Chiu, 1. Mean-downside-isk and mean-vaiance newsvendo models: Implications fo sustainale fashion etailing. Int. J. Pod. Econ., 14(): Lin, Z.B. and Q.S. Zhang, 1. Supply chain model with uyack contact unde isk avese assumption. Foecasting, 9(6): Luca, C. and L. Paola, 1. A note on picing with isk avesion. Eu. J. Ope. Res., 16(1): Ozgun, C.D. and Y.H. Chen, 11. Custome and etaile eates unde isk avesion. Int. J. Pod. Econ., 133(): Pastenack, B.A., Optimal picing and etun policies fo peishale commodities. Maket. Sci., 4(): Qin, J.J. and D.Z. Zhao, 11. Supply chain consignment contact in context of asymmetic isk pefeence infomation. Chinese J. Manage., 8(): Wang, C.X. and S. Weste, 9. Would a isk-avese newsvendo ode less at a highe selling pice? Eu. J. Ope. Res., 196(): Wei, Y. and.m. Choi, 1. Mean-vaiance analysis of supply chains unde wholesale picing and pofit shaing schemes. Eu. J. Ope. Res., 4(): Wu, J. and S.Y. Wang, 1. Impact of isk avesion on optimal decisions in supply contacts. Int. J. Pod. Econ., 18():