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An incentive model of partialinformation sharing in supply chain

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An incentive model of partialinformation sharing in supply chain

  1. 1. An Incentive Model of Partial Information Sharing in Supply Chain Xiongwei Zhou, Feicheng Ma, Xueying Wang Abstract- Considering one manufacturer and two retailers in supply chain based on part of retailers to participate in information sharing, we use price discrimination strategy to design an incentive mechanism which motivates retailers to share uncertain demand information with manufacturer. The research results show that information sharing may be value-added to add their profits only in under certain conditions using price discrimination strategies. And then we put forward the strict constraints and improve the information sharing incentive model under demand uncertain environment. When the retailers' external environment and their capacity are the same, i.e., they are perfect competition, the full information sharing is stable Pareto optimal equilibrium in the improved incentive model. I. INTRODUCTION There is always not the actual consuming demand information for upstream enterprise in the supply chain. Known as the bullwhip effect [1,2] is the phenomenon caused by demand information distortion to expand demand variability. How to reduce the bullwhip effect in supply chain has become a hot study issue, and information sharing is seen as the main strategy to offset the bullwhip effect. Many researchers have pointed out that information sharing can offset the "bullwhip effect" and improve performance to reduce costs and inventory [3,4,5] in supply chain. According to master-slave Stackelberg game model, through considering the upper suppliers' profits and approximately calculating by the expectations of uncertain demand information with normal distribution in supply chain, the literature [6] draws the conclusions that information sharing doesn't need make the whole supply chain optimal performance, and the total revenue does not increase but also strictly decreases with sharing uncertain demand information, and the value of information sharing must be specifically analyzed. But the optimal constraint conditions are not given in the literature. Information sharing can often be divided into full information sharing and partial information sharing from the company quantity of participating in information sharing. The partial information sharing refers to that not all retailers are involved in participating in information sharing, but only partial retailers to participate in information sharing. The partial information sharing becomes a new research direction. Literature [4,5] simulate the partial retailers to share demand Manuscript received February 22, 2009. This work was supported in part by the National Natural Science Foundation ofChina under Grant 70833005. x. Z. is with the School ofInformation Management ofWuhan University Wuhan, Hubei 430072 China (corresponding author to provide phone: 086-027-61091616; fax: 086-027-68457571; e-mail: daweycs@126.com,). F.M. is with the School ofInformation Management ofWuhan University Wuhan, Hubei 430072 China (e-mail: fchma@whu.edu.cn). X.W.is with the School ofInformation Management ofWuhan University Wuhan, Hubei 430072 China (e-mail:wangsusie@hotmail.com). 978-1-4244-3541-8/09/$25.00 ©2009 IEEE information in supply chain, and demonstrate that information sharing is beneficial to manufacturers and wholesalers to increase their income, but almost no impact on retailers. So retailers are not willing to share their private information, and we must design an appropriate incentive mechanism to make retailers willing to participate in information sharing. Literature [7] firstly puts forward using price discrimination strategy on partial retailers to share information, but the authors believe that suppliers have not incentive to use this strategy in the one-sided pursuit of their maximizing profits, and in order to motivate retailers to participate in the demand information sharing they pay certain information cost and achieve the optimal balance policy through calculating expectations. Considering suppliers' profits and two level decentralized supply chain composed of one supplier and many retailers, The literature [8] further uses price discrimination strategy to encourage retailers to participate in information sharing based on maximizing corporate profits, which can lead to achieve the final stability Pareto optimal equilibrium ofthe overall supply chain effectiveness. However, the study does not analyze what private information to share can add members' profits in supply chain. Literature [9] further study that the manufacturers adopt price discrimination strategy to share information from them to partial retailers, and the results show that manufacturers are more willing to share information demand information with partial retailers when information sharing need dissemination costs. II. THE PARTIAL INFORMATION SHARING INCENTIVE MODEL In this study, we consider one manufacturer and two retailers, only one of retailers to participate in uncertain demand information sharing in supply chain systems. The price discrimination strategy is used in the information sharing incentive model. The price discrimination strategy refers to that retailers to participate in information sharing can win at lower wholesale prices than retailers not to participate in information sharing. We assume our notation in the model as follows: 1!} is the profits of retailer R}, 1!2 is the profits of retailer R2, 1!3 is profits ofmanufacturer R3; d1 is the demand ofretailer R1, d2 is the demand ofretailer R2;PJ is the sales price ofretailer R1, P2 is the sales prices of retailer R2; Cl is the marginal cost of retailer R1, C2 is the marginal cost of retailer R2, C3 is the marginal cost of manufacturer R3; WI is the wholesale prices of retailer R1 to provide information sharing, W2 is the wholesale prices of retailer R2 not to provide information sharing; t, reflects the retailer's market signal of demand uncertainty, where its value is also small when the demand is 58
  2. 2. small. t, is random variable of i.i.d. normal distribution with mean zero and variance 0'2 , namelyti '"" N (0, a), i = 1,2. The demand function of retailer RI to participate in information sharing can be expressed as dl = DI (PI,/I) = 01 - bPI +II· The demand function of retailer R2 not to participate in information sharing can be expressed as d2 =D2(P 2, /2)=a2 -bp2 +t2· The profit function of retailer RI to participate in information sharing is fulfilled with 1fI = (PI - WI - cI)dl • The profit function of retailer R2 to participate in information sharing is fulfilled with !i2 =(P2 -w2 -c2)d 2· The profit function ofmanufacturer R3 is fulfilled with !i3 = (WI -c3)d I +(W2 -c3)d 2· Where, a., b is positive constants, PI, P21 CI, C2, C3, WI and W2 are positive constants and their relationships meet to make III ,1l2 and 113 are all positive. The game process of partial information sharing model is the process of repeated games, in which every game is as follows: 1) Manufacturer makes the wholesale prices decision according to maximize his own profits requirement and whether retailers participate in information sharing, in which the wholesale prices is WI for retailer to participate in information sharing while it is instead ofW2 for retailer not to participate in information sharing. 2) Retailers determine whether they participate in information sharing in accordance with the manufacturer make the wholesale price and their own capacity. 3) Retailers respectively determine the sales prices in accordance with the principle of maximizing their own profits. The sales price is PI for retailer to participate in information sharing and the sales price isP2for retailer not to share information. III. MODEL SOLUTION According to reverse analysis method in game theory and specific different uncertain private information, the following expression is fulfilled to solve the model: ma~ =wI -C3)(~ -bPi+/I)+(W2-C3)(~ -bp2) s.t, max s. = (al - bPI +tl )(PI - WI - CI ) , PI max s- =(a2-bp2 +t2)(P2-W2-c2) · P2 Because the retailer R2 owns private uncertain demand information12 and doesn't share with supplier, the supplier can not accurately gain it so that only its expectation can be used to estimate itselfwhen supplier make his decision. A. The Retailers' Decision-making As for the retailer Rl and R2 both have the private uncertain demand information, so their values are identified and it is simple to solve their sale prices of decision-making. According to reverse analysis method, we firstly separately solve max1f1 and max1f2 • Therefore, we have the PI P2 following proposition. Proposition LWhen retailer RI participates in information sharing with supplier while retailer R2 doesn't share information with supplier, their sales price of optimal * *equilibrium PI and P2 are respectively as follows: * a+bw+bc+t (1) * a2+bw+bS+t2 (2) PI = I I 2b I I P2 2 2h . B. The manufacturer's Decision-making Then we use the constraints conditions of max H 3 to solve manufacturer's decision making. The retailer R2 owns private demand information 12 and doesn't share it with supplier, while supplier can't accurately catch it, so supplier only can use its expectation to approximately calculate the demand function and the optimal price when he solves max H 3 • Proposition 2. When retailer RI participates in information sharing with supplier while retailer R2 doesn't share information with supplier, supplier's wholesale price of * *optimal equilibrium WI and w2 based on price discrimination strategies and the retailers' optimal polices are respectively as follows: * al -b(cI-C3 )+tI * a2 -b(c2 -c3 ) W= w=-----I 2b 2 2b * 3aI +b(CI +C3 ) +311 * 3a2 +b(C2 +C3 ) +212 ~ = 4b P2= 4b . Proof. Because £(t2 ) =0, * a2+bw +bc2+t2 a2 +bw +bc2E(p ) = E( 2 ) = 2 , 2 2b 2b E(d2) =E(a2- bp2 + t2) =a2- bp2· Retailer RI shares information with supplier, so uncertain demand information sharing t1 can directly substitute into demand function and the optimal price. Then K 3 can be calculated as follows: 113 =(111-S)(q-bn+tI)+(~ -S)(~-bR) =(lIj ---s)~-.!.(q+blf+b,,+t)+t)+(~---s)~-.!.(t;+bw+bC;))(3). 2 2 2 1 1 =2(lIj---s)qnf+b,,-q-tJt 2(~ ---s)(b~+bc;-t;) Then a1i3 =a+tl -b(2w1 +c -C3 ) , a21i 3 =-b < 0 a~ 2 a~2 59
  3. 3. alr3 =a2 -b(2w2 +C2 -c3 ) , (j2 ff; = -b < o· aW2 2 dW2 Let aJl'3 =al +tl -b(2wI +cI -c3 ) =oand aWl 2 aJl'3 =a2-b(2w2+C2-C3)=oto be simultaneous aW2 2 equations and solve the WI, W2 optimal equilibrium ofmax 1r3 • * al - b(CI - c3 ) +II * a2 - b(C2 - c3 ) (4) WI = 2b w2 = 2b Substitute the values of WI, W2 into the front of(1) and (2) to get the optimal equilibrium solution ofPI and P2: P * _ 3al +b(cI +c3)+3/1 p* 3a2 +b(c2 +c3)+212 (5). 1- 4b 2 4b C. The Profit Distribution Mechanism Proposition 3. The optimal profits ofthe manufacture and the retailers are: * (al - b(cI + c3 ) + tl ) 2 Jr=----.;;.---"""'------~ I 16b * (a2 - b(c2 +c3 ) +212)2 Jr - ----=.----=--=----~ 2 - 16b * (al -b(CI +C3)+tl ) 2 +(b(c2 +c3)-a2 ) 2 Jl'3 8b IV. MODEL ANALYSIS AND DISCUSSION A. The Equilibrium Conditions' Stability Based on Price Discrimination Strategy Proposition 4. The price discrimination strategy achieves a stable incentive and restrictive equilibrium conditions for retailer only if (al -a2 )- b(cI -C2 )+tl <0 (6) 2b ((al -a2)-b(cI -C2)+tl -2t2 ) ) (7). (al +a2 -b(cI +c2 +2c3)+tl +2t2)/16b>0 The conditions (6) satisfy WI <W2 in order to encourage information sharing through using the price discrimination strategy. Therefore inequality (6) is the basic constraint condition in the incentive model using price discrimination strategy to meet information sharing incentives for retailers. The retailer to participate in information sharing enjoys preferential policies to get a lower purchase price because his information sharing can reduce manufacturer's costs to increase his profits; while retailer not to participate in information sharing accepts that he catch a higher purchase price and maintain cost unchanged. The information sharing incentive model makes price discrimination strategy achieve a stable equilibrium, that is 111 > 1l2 , only if the profits of retailer to participate in information sharing is greater than the profits ofretailer not to participate in information sharing. The condition (7) is more incentive and restrictive condition to satisfy 111 >112 • B. When al = a2 andc1 =c2 ' the Effective Analysis to the Information sharing Incentive Mechanism Proposition 5. When al = a2 and CI = c2 ' II < 0 is satisfied. When al = a2 and CI = C2 ' that is to say the environment and entrepreneurial capacity retailer Rl and retailer R2 are almost identical, II < 0 can be deduced from the basic conditions (6) of the price discrimination strategy to motivate retailers information sharing. In other words, only if II < 0 is the condition of WI <W2 satisfied. This illustrates that if using price discrimination strategy sets up an incentive mechanism to share uncertain demand information with normal distribution, only when the retailer's demand information to reflect the uncertain signal is negative can information sharing make lower wholesale prices for retailer; otherwise retailers to provide information sharing obtain rather than higher wholesale prices, which is not in line with the purposes of the price discrimination strategy to stimulate information sharing. Hence the information sharing incentives mechanism must be appropriately amended. V. THE IMPROVED INFORMATION SHARING INCENTIVE MECHANISM According to Proposition 5, we improve the information sharing incentives mechanism as follows: When II ~ 0, let w* = al -b(cI -c3 ) to satisfy w; = w; in order to motivate I 2b retailers to participate in information sharing. Besides, the mechanism does not allow retailers to participate in information sharing in order to obtain low-cost wholesale prices to inform tl < 0 instead of tl ;;::: 0 because (I is the actual needs ofthe retailer, and then false information reduces their sales and their own profits. That is, * _ al -b(cI -c3 ) t > O· WI - 1- , 2b * al -b(cI -C3 )+tl 0 WI = 11 < . 2b Because the role ofinformation sharing is mainly to reduce production and inventory costs in the supply chain, manufacturer and retailer can increase their effectiveness. If II < 0, the demand information is critical for manufacturer to reduce production and make manufacturer and retailer reduce inventory costs, thereby increasing the overall efficiency, so the manufacturer shares the profit-added of information sharing with retailer to participate in information sharing. If tl ;;::: 0, on the contrary, the demand information is not so important during the overproduction, and it plays almost little role to reduce production and inventory costs, so that manufacturer does not have incentive to use price discrimination strategy. Therefore the improved mechanism is also fully consistent with the actual situation. Proposition 6. When al = a2 and CI = C 2 ' the improved information sharing incentive mechanism is effective to use price discrimination strategy in supply chain. 60
  4. 4. Proof. According to the improved information sharing incentive mechanism, when II ~ 0, then w; =w;, in fact it does not use price discrimination strategies to incentive information sharing, and retailers comply with the same policy to obtain the same benefits whether they participate in information sharing. Therefore, we only need to consider if 11 < 0 whether III > 112 • Then only if * * (al -b(ci +C3) +tl ) 2 (a2 -h(c2 +C3) +2t2 ) 2 JZi >112 161 > 161 Because al = a2 and CI = C2 ' then al -b(cI +C3) =a2 -b(c2 +C3) • Also because dl = al - bPI +II >0 , PI - WI - cI > 0 and WI - C3 > 0 as well as d2 =a2 - bp2 +12 >0 , and P2 - w2 - c2 > 0 and W2 - C3 > 0, So it can be launched al -b(cI +C3)+/1 > Oandzz, -b(c2 +C3)+/2 > O. It is apparently al - b(cI +c3 ) =a2 - b(c2 +c3 ) > 0 by 11 < o. So as long as al -b(cI + C3) + /I >1 a2-b(c2 + C3) + 2/2 1,it meets 111 > 1l2 • Assume tl =t2 ' then the real value of a2 - b(c2 +c3 ) +2/2 is often greater than 0, so it is obvious for 111 > 112 .Therefore it is effective to design information sharing incentive mechanism using price discrimination strategy in supply chain. Proposition 7. When al = a2 and C I = C 2 ' the improved information sharing incentive mechanism make both retailers eventually reach complete information sharing stable equilibrium. Proof.At the same time it can be seen by the optimal retail price of the retailer Rl and R2, that is the expression of (5), when al =a2 and c1 =c2 ' and 11 < 0 : * 3~ +b(cI +C3) +3/1 * 3~ +b(c2 +C3)+2t2 A ~ <A ~ . And WI <W2 and 1l1 >112 based on Proposition 6, there is directly perfect competition between the retail Rl andR2. So the price ofretailer Rl to participate in information sharing is obvious competition advantages, which attracts more customers for retailer Rland ultimately forces the retailer R2 to participate in information sharing, and eventually reaches complete information sharing stable equilibrium of both retailers to participate in information sharing. VI. CONCLUSION Information asymmetry in the supply chain is very common. Retailers often have uncertain demand private information. But many studies show that information sharing does not improve the effectiveness of retailers. How to motivate retailers willing to share their private information has become a hot research issue. In this paper, we design the information sharing incentive mechanism based on partial retailers to participate in information sharing and price discrimination strategy. In the study we use the actual value rather than approximate expectations to solve. The solution further demonstrates that only when information sharing is strictly bound in certain conditions does it add profit ofsupply chain. This result shows that information with value-added is very important whether retailers share information in the supply chain. We design information sharing incentive mechanism and improve it based on price discrimination strategy according to the certain range and conditions of information sharing with value added. The analysis shows they are effective. The next step is to conduct empirical research and introduce our research methods into the electronic direct marketing environment to design information sharing incentive mechanism in a dual-channel supply chain. REFERENCES [I] H. L. Lee, V. Padmanabhan, S. Whang.(1997,April)Information distortion in a supply chain: the bullwhip effect. Management Science, 43(4).pp.546- 558. [2] H. L. Lee, V. Padmanabhan, S. Whang. (1997,July)The bullwhip efffect in supplychain. Sloan Managment Review, l8(3).pp.93-102. [3] Z.Huang, A.Gangopadhyay.( 2004,July) A simulation study of supply chain management to measure the impact of information sharing. Information Resource Management Journal, 17(3).pp. 20-31. [4] Z.Huang, A.Gangopadhyay. "Information sharing in supply chain management with demand uncertainty". In Advanced Topics in Information Resource Manangement, vol.5, K.P.Mehdi, Ed. Hertfordshire:Idea Group, 2005,pp.45-45. [5] X. Zhou, F.Ma, L. Zhang, X. Wang. "The impact of information sharing strategies in multi-level supply chain". in 2008 Proc. IEEE Int. Conf. Conf. SOLI, pp.2045-2050. [6] Y. Zhang, J. Chen. (2004,July )Study based on Stackelberg game about the information sharing coordination in supply chain. Journal of Industrial Engineering Engineering Management, 18(3) .pp.118-120 [7] L. Li .(2002,)Information sharing in a supply chain with horizontal competition. Management Science, 48(9) .pp. 1196- 1212. [8] K. Liu, Z. Zhang.(2007, January)Information Sharing Incentive in Supply Chain: A Pricing Mode. Journal of industrial engineering / engineering management. 27(1) .pp.131-133. [9] G.O.Esther, G. Tansev.(2008,July) Information Sharing in a Channel with Partially Informed Retailers. Maketing science, 27(4).pp.642 - 658. 61

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