Coordinating strategy of supply chain contract based on price discount and quantity buyback

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1 ISSN (Print), (Online) Journal of System and Management Sienes Vol. 1 (2011) No. 4, pp Coordinating strategy of supply hain ontrat based on prie disount and quantity buybak Ping Shi 1, Lu Liu 1, Xuelong Zhang 2, 3 1 Shool of Eonomis and Management, Beijing University of Aeronautis & Astronautis 2 Shool of Eonomis and Management, University of Siene and Tehnology Beijing, China 3 Shool of Business, Guilin University of Eletroni Tehnology, Guangxi, China sinbazhu@163.om, zhxl2006@126.om Abstrat: The oordinating deision model of supply hain ontrat is developed with the ontrats of prie disount and quantity buybak, irrespetive of shortage ost. It obtains the optimal ordering strategy of retailer and quantity buybak poliy of supplier. Finally, numerial example is given to illustrate the feasibility of this model, and a onlusion is obtained that orresponds to pratie. Keywords: Prie Disount, uantity Buybak, Supply Chain Contrat 1. Introdution Pasternak (1985) first brought up the onept of supply hain ontrat. It refers to a kind of artiles through the provision of appropriate information and inentives. It ould ensure oordination of buyers and sellers, and optimize the performane of the relevant provisions of the sales hannels. It is a form of expression of eonomi ontrat theory in supply hain. Then, some studies on supply hain ontrat have a onsiderable progress in many aspets. It falls into four major types: wholesale prie ontrat, buybak ontrat, revenue sharing ontrat and quantity flexibility ontrat. Among them, the wholesale prie ontrat and buybak ontrat were studied early and they were the most ommon type of ontrat, while revenue sharing ontrat and quantity flexibility ontrat studied the ore of the supply hain: member revenue and produt quantity. In Supply Chain Management (SCM), suppliers and sellers form a supply 19

2 hain alliane through the ontrat and they onstitute the Stakelberg Game. The supplier is the host, the seller is seondary. The suppliers maximize the benefit through the reasonable ontrat, and the sellers maximize their inome through hard-working after aepting the ontrat. Therefore the ways they obtaining the profit are inonsistent. In supply hain, deentralized deisionmaking model is more ommon than the mode of entralized deision-making. The ontat between the supply hain nodes is the link to build the supply hain. The unertainty of market leads to a lak of oordination. Starting from the unertain market demand, through the researh of supply hain ontrat, it an ahieve the oordination of supply hain. It is an important part of the supply hain study. In SCM, the basi struture is the seondary single-yle supply hain behavior omposed of suppliers and sellers. The study on the ontrat and oordination of this basi struture onstitutes the basi elements of SCM researh. Prie disounts and quantity buybak is an important tool to researh the ontrat and the oordination. Pasternak (1985) proposed the uantity Buybak whih is used to oordinate the behaviors of suppliers and sellers. Cahon (1999) has studied that under the sole wholesale prie the supplier use quantity buybak in order to enable the order amount ahieve the demand quantity whih keep the supply hain oordinated. In the deentralized deision-making model of supply hain, it is obvious for the seller that the supplier wants to maximize the benefit through the ontrat. It is lear that the sellers not only have to strive for the advantageous provision in the ontrat stipulation, but also work hard if they want to make the inome maximization. Thus quantity buybak ontrat relates to the inspiration of sellers hard working. Larivee (1999) studied the relationship of quantity buybak strategy and inentive. Krishnan (2004), Zhang Juliang (2004) and Chenjian (2006) also disussed the inentive problems in the supply hain. On the basis of those literatures above, this paper revises some assumptions of studies, establishes oordinating strategy of supply hain ontrat for distributors whih is under the irumstane that the suppliers fix the prie disounts and the quantity buybak, thus further improve oordinating model of supply hain. This makes the model more pratial, and lets suppliers and the sellers know how to alulate the maximization of benefits in the two irumstanes. 2. Symbols and Assumptions Used in the Model 20

3 Supply hain ontrat (generally speaking) is a two-stage supply hain whih is omposed of one supplier (manufaturer) and one distributor (retailer) shown in Figure 1. w p Supplier Retailer Min[,D(p)] D(p) Capital flows Logistis Information flow Figure 1: Typial supply hain model Retailers fae a market in whih the demand is random. Produts are seasonal and order a long period. Aording to the theory study of LF Game (Leader- Follower Game) on the interation between suppliers and retailers, suppliers are the leaders and retailers follow them. Suppliers set ontrat parameters, whereby retailers determine optimal order quantity of produts. At the same time it shows that the market is open. Suh information as the produt pries of related market, demand distribution and inventory ost is symmetri. Therefore, as a leader, a vendor an get all the neessary information, infer the order quantity of retailer, and thus make the best deision. Suppliers and retailers are risk-neutral or fully rational. They are based on the priniple of expeted maximum profit. In order to study easily, the symbols of the model used in the paper are shown in Table 1. Table 1: Symbols of the mode Symbol Meaning Symbol Meaning Eah ordering of the retailer v Eah prie of retailer deals stok, v D Market demand r Prie of supplier buybak from retailer, r v Mean of the market demand Ratio of return and order, 0 1 Eah prodution produt ost S Expetant sales of retailer t Eah prodution sales ost I Expetant stoks of retailer w Trade prie of supplier to R retailer Expetant returns of retailer 21

4 p Eah prodution retail ost S e Eah stok ost S q F x f x Prodution quantity supplier produts Demand distribution 0, x funtion, The paper studies on the two-stage supply hain ontrat system whih is omposed of one supplier and one retailer and only fouses on the operation of a single produt yle. The assumptions of the model are given as follows: (1) the market demands of produts D 0, the market prie of produts p the same. (2) demand distribution funtion F x is ontinuous and differentiable; (3) Supply hain implement a distributed deision-making; (4) time interval is infinite; (5) do not onsider the losses of out of stok. 3. Constrution of the Model 3.1. the Basi Model of Supply Chain Contrat Based on these assumptions above, there are establishments of the following relationship: u xf ( x) dx (1) 0 S( ) ( x) f ( x) dx 0 x dyf ( x) dx 0 0 f ( x) dxdy F( x) dx 0 y 0 Among the formula, means that it take the small one in two numbers. The inventory funtion expeted by retailers: Profit funtion expeted by retailers: Profit funtion expeted by suppliers: (2) I( ) E( x) S( ) (3) R ps( ) vi ( ) ei ( ) w (4) S ( w ) (5) Expetant returns of supplier Expetant returns of supplier Balaned produt quantity F Balaned produt quantity funtion Probability density funtion, x 0, R Optimal order quantity of retailer 22

5 The expetations of the whole supply hain profit funtion as: Aording to (4), (5) and (6) get: I( ) E( x) S( ) (6) T ( p e v) S( ) ( e v) (7) Aording to the Leibniz rule, we an see T is a onave funtion, and T gets partial differential oeffiient of : T ' ( e ) ( ) e p v S v ( p v) F( ) v 0 The equilibrium order funtions of supply hain ontrat: e p F ( ) p e v The above formula has got inverse funtion. That is the balaned order quantity. 1 p F ( ) p e v The optimal order quantity of retailers: R e (9) (10) arg max (11) R From funtion (11), we an find that researhes of ollaborating supply hain ontrat fous on two major points: First, the retailer order quantity to the optimal effiieny of the supply hain; seond, how suppliers and retailers alloate the profits of the supply hain Contrat Model with Prie Disount When there is prie disount, then use the wholesale prie ontrat. The retailer's profit funtion is: T ps( ) vi ( ) I( ) w R ( p v) S( ) ( w v) Similarly, aording to Leibniz rule, we an see e e e R (8) (12) is a onave funtion. gets partial derivative of, and make the equation equal to zero, we obtain the optimal order quantity for the retailer: 1 p w R F ( ) p e v (13) 23

6 In order to ahieve oordination, it must be R, w. Now the supplier will not gain profit. It is ertainly wrong in the ommon sense. Therefore, a simple wholesale prie ontrat annot oordinate the supply hain the Contrat Model of Taking into Aount the Prie Disount and uantity Buybak Spengler (1950) first disovered that a simple wholesale prie ontrat annot ahieve oordinating supply hain mainly due to double marginal benefit of suppliers and retailers. They only onsider the marginal benefits unilaterally, without onsidering the overall marginal benefits. Even so, the prie disount ontat has been widely used in pratie beause it is simple and less ostly. As for the double marginalization of suppliers and retailers, Chao and others have made a more detailed analysis on it. There are many studies on quantity buybak ontrat too. Padmanabhan (1997), Tagaras (1992), Anupindi (2001) et al have studied on the motivation of quantity buybak ontrat. Padmanabhan (1997) et al studied the following situation: in order to ontrol the exessive ompetition among retailers, suppliers adopt the quantity buybak strategy. Thus they found that suppliers gain more. But in the ase of fixed demand, quantity buybak strategy will result in non-rational order quantity. To solve the problems above, the prie disount and quantity buybak ontrat model will lead to the maximization of marginal benefit of whole supply hain. When there is a quantity buybak strategy, that is, suppliers repurhase bak the remaining produts with supply a reasonable ommerial prie r( r v), so as to stimulate retailers to inrease the order quantity and expand produt sales. Now the retailer s profit funtion is: The retailer s profit funtion is: R ps( ) ri( ) w ts( ) ps( ) r ( S( ) w ts( ) ( p r t ) S( ) ( w r) S ( w ) r( S( )) ( w r) rs( ) (14) (15) The expetations of the whole supply hain profit funtion: T R S p ( t ) F( x) p ( t ) p( F( x)) F( x) (16) 24

7 Under the above assumptions, in order to ahieve the oordination state of the supply hain, suppliers hoose r, w, value, and make the expeted value of R maximum under the onditions of oordinating supply hain. Sellers hoose and make the expeted values of S maximum. From (16), the overall revenue of supply hain is deided by the order quantity of sellers. The parameter rw,, is the parameter for optimal deision. 4. Model Solving and Coordination Analysis 4.1. Model solving From (14) and (15), we know, the expeted profit of suppliers and vendors is omposed of two parts: the first part is the sales revenue when the order quantity is ; the seond part is prodution, sales and ordering osts. From (16), we an see that the revenue of the whole supply hain only depends on the ordering quantity, nothing to do with the buybak strategy. Similarly, aording to Leibniz rule, we an see R is a onave funtion. T gets partial derivative of, and make the equation equal to zero: The retailer order funtion: dr( ) ' ( p r t ) S ( ) ( w r) D ( p r t ) F( ) ( w r) 0 w r F ( R) p t r Retailer's optimal order quantity is: 1 w r R F ( ) p t r Similarly, aording to Leibniz rule, we an see (18) (19) (17) T is a onave funtion, gets partial derivative of, and make the equation equal to zero: dt ( ) ' ( p r t ) S ( ) ( w r) D ' ( w r) rs ( ) 0 The supply hain ontrat equilibrium order funtion: F ( ) p t (21) (20) T 25

8 Balaned order quantity of supply hain is: 1 F ( ) p t In order to ahieve oordination, it must : w r ( p r ) p t (22) t (23) Put (23) into equation (14), after finishing, it an get retailers profit: The profit of suppliers is: In the equation, p t r R T p t r S T R T T p t r p t r p t Beause of 0 1. (24) (25), 0 1, so the quantity buybak strategy an ahieve oordinating supply hain. Aording to equation (25), through seleting the repurhase prie of the size and the proportion of quantity buybak, vendors determine their own possession of the entire supply hain profit share, and aording to the type (23) to determine the optimal prie w. In order to oordinate the supply hain and also enables suppliers maximize their profit, the parameter of quantity buybak ontrat fixed by vendors should be optimal solution of the following planning problems. E( S) w t r F( x) dx (1 ) rw,, max s. t. t p w ( p r) F( ) (1 ) rf((1 ) ) r 0 1 w 0 1 The equation (17) is the ondition of retailers profit maximization, and the vendor must onsider their own maximum profit. The equation (26) is the whole profit of the supply hain. Aording to the planning problems, get that when r (26) gain the maximum profit. And from the equation (14) and (21), get: w, 1, the suppliers 26

9 t w p 1 F( ) 1 F( ) The equation (27) shows that in order to oordinate the supply hain and also maximize the overall revenue, suppliers should allow the retailers return all order produts that ouldn t be sold with the wholesale prie. The formula (27) beomes deformed: pw (28) 1 F ( ) From equation (28), it an be seen that the market prie p of produts is divided into two parts: the first part is w, the seond part is reeived by 1 F ( ) the retailers. Thus, the optimal deision ondition whih maximizes the overall profit of supply hain ontrat is: r wand 1. (27) 4.2. Examples The following example shows the feasibility of the model. Set a retailer to develop a produt order poliy for a supplier, as the following data: p =450, w =400, =150, e =30, t =15, S ( ) =2000, =2600. When r wand 1, after alulating available: this point, the total profit values of supply hain are: R =7000, S =740000, at T = Adjust r and, we an get other results, onrete results are shown in table 2. Table 2: Effet of whole supply hain profit aording to the hange of and r R S T Conlusion < < < From the analysis of available data in Table 2,we an get a suh result: As the supplier to retailer's number returns the value of the ontrat inrease r, Even more than the wholesale prie of repurhase, In the not too suppliers profit values, The retailer's return values appear larger trends, But the vendor number returns poliy should be raised with the repurhase prie should be redued, Or you may make vendor profit deline, But no matter what ombination of 27

10 strategy, Still in r w and 1, Supply hain's total profit value is the maximum, At this point, the supply hain to ahieve better oordination. Therefore the model and onlusions of the paper orrespond with the pratie. 5. Conlusion In the supply hain ontrat, prie disount ontrat has been extensively used in pratie beause of its simple and low ost of implementation. But it doesn t overall onsider the marginal benefit of the entire supply hain; in the ase of fixed demand, quantity buybak ontrat will lead to the retailer's order irrational. Therefore, without onsidering the loss out of the premise, the paper established a supply hain management model whih is a single-yle behavior and ontains only one supplier and one retailer. It ontains two ontratual relationships of prie disounts and quantity buybak. This kind of model is more lose to reality. Model analysis shows that the ontrat an ahieve supply hain oordination. Meanwhile, it verifies the feasibility of the model and the onlusions math to the reality by examples alulation. Referenes Anupindi, R., Bassok, Y. & Zemel, (2001). E. A General framework for the study of deentralized distribution systems. Manufaturing and Servie Operations Management, 3(4), Cahon, G. P. (1999). uantitative models for supply hain management. Klumer Aademi Publishers, London Cho, R. & Gerhak, Y. (2001). Effiieny of endependent downstream firm ould ounterat oordination diffiulties. University of Waterloo Working Paper, Krishnan, H., Kapusinski, R., &Butz, D. A. (2004). Coordinating ontrats for deentralized supply hains with retailer promotional effort. Management Siene, 50(1), Lariviee, M. A. (1999). uantitative models for supply hain management. Klumer Aademi Publishers, London Lariviere, M. F. (2001). Selling to the newsvendor: An analysis of prie-only ontrats. Manufaturing Servie Operational Management, 3(4),

11 Padmanabhan, V. & Png, I. P. L. (1995). Returns poliies: Make money by making good. Sloan Management Review, Fal1, Padmanabhan, V. & Png, I. P. L. (l997). Manufaturer s returns poliy and retail ompetition. Marketing Siene, 16(1), Pasternak, B. A. (1985). Optimal priing and returns polies for perishable ommodities. Marketing Siene, 4, Spengler, J. (1950). Vertial integration and antitrust poliy. Journal of Politial Eonomy, 8, Tagaras, G. & Cohen, M. A. (1992). Pooling in two loation inventory systems with no negligible replenishment lead times. Management Siene, 38(8), l Vagstad, S. (2000). Centralized VS. deentralized prourement: Does dispersed information all for deentralized deision-making?. International Journal of Industrial Organization, 18(6), Wang, X. Y. & Xiao, Y. M. (2009). Researh on supply hain oordination and risk sharing based on buybak poliy. Chinese Journal of Management Siene, 12(3), Yang, D. L., Guo,., & He, Y. et a1. (2006). Review of supply hain ontrats. Chinese Journal of Management, 3(1), 1l Zhang, J. L. & Chen, J. (2004). A oordinating ontrat of supply hain with sale-effort dependent demand. Chinese Journal of Management Siene, 12(4),