2011 International Conference on Electronic & Mechanical Engineering and Information Technology

The Pricing Model Construction of Reverse Supply Chain Based on Game theory

Xiangyan Zhang, Chunhua Jin School of Economics and Management

Beijing Information Science & Technology University Beijing, China

e-mail: x-yzhang@hotmail.com

Abstract—The pricing model of reverse supply chain (RSC) is based on the basic knowledge of closed-loop supply chain and game theory. By constructing non-cooperative and co­operative models, distributions and changes of profits among manufacturers, retailers and recyclers can get from the comparative analysis of those two cases. These will help manufacturers, retailers and recyclers make their own decisions to achieve their maximum benefits.

Keyword—Game theory; Reverse Supply Chain; Cooperation Game; Non-cooperation Game

I. INTRODUCTION

As countries pay more attention to sustainable development and recycling economy attention, the problems about closed-loop supply chain become important issues in the international academia for nearly 10 years. At the same time, in industrial circles, more and more enterprises also have that in its strategic vision moving forward. Closed Loop Supply Chain (CLSC) not only includes the traditional positive Supply Chain, also contains reverse Supply Chain. Through the positive delivered and a reverse recycling, Closed-loop supply chain changes the open-loop process-'resource-production-consumption-abandoned' into a close-loop feedback type cycle -'resource-production-consumption-renewable resources'. After consumers get the products, they retrieve waste materials and packaging. After classification, inspection and disassembly process, these waste materials and packaging return back to their initial manufacturers' hand again.

The Reverse Supply Chain (RSC) initially originated in legal and it was put forward against the positive Supply Chain. Because of its short development history, RSC is still in the exploration and development stages. Guide thinks: "Reverse Supply Chain is a series of necessary activities in order to recycle the used product from customers, and its purpose is to process or to recycle the recyclables."

According to the definition of the supply chain and reverse logistics, the reverse supply chain refers to recycle used product from the user's hand, then recycles, classifies and tests the product until the final disposal or reuse. The reverse supply is also a network that mainly constitutes by the user, recycler, traders and original manufacturers (OEMs), suppliers, service providers and distributors from the traditional supply chain. Its purpose is to get the value of the recovery products. Positive supply chain profit is the diffidence between sales revenue and raw material costs, and the added value gets out of the processing and sales stage from materials to finished products, and the goal of RSC is to

realize the value of products and services. In contrast, the profit of RSC is originated in the low cost recovery of product. In reverse supply chain, its value added in recovery stage.

II. THE PRICING MODELS OF REVERSE SUPPLY CHAIN

A. Selecting a Template The structure of RSC pricing model shows in figure 1.

Manufacturers entrust recovery contractor recycling waste product from the consumer market at a certain price. Then the manufacturers reprocess the used product, form regeneration, regenerate products on the market and meet the needs of the consumers. Recycling trader retrieve waste products from consumer market at a certain price, then deliver them to manufacturers.

These models are based on the following assumptions and prerequisite conditions:

• Manufacturers and recycler have a clear idea of each other's cost, pricing, strategy and so on.

• The market supply of waste is the increasing function of the market recycle price.

• The meanings of parameters in the RSC pricing model are showed in Table 1.

The profit from which manufactures sell recycled products:

*m= ( w - v m - w m ) rQ0

The profit from which recyclers retrieve the waste products:

^0= ( w„ ' o ) Q o The profit of the RES:

71 — 71 m + Ttr,

And assuming hypothesis parameters satisfied:

V 0 ^ P o < P o + V 0 ^ W < W m ^ Wm + V „

(2)

(3)

978-1-61284-088-8/11/S26.00 ©2011 IEEE 12-14 August, 2011

v0

w

Qo

Do

>le I. Symbolic descriptions of RSC pricing model The marginal cost of production recycled by the manufacturer processing Unit operation (including inventory transportation) cost of the recycling waste product manufacturers pay Unit the collection price at which Manufacturers purchased waste product from recyclers, the decision variables for manufacturers Unit the recycling price at which recyclers purchased waste product from the consume market, the decision variables for recyclers Unit sales price of recycling products The recovery quantity when the recycling price is P. According to the assumptions: Q 0 = a + b p 0 ( a > 0, b > 0 ) ,a is conversion

constant, b is the coefficient of elasticity of the market recycling price, also called recycling elastic coefficient Maximum ownership of the waste market, and Qo<Do;

success rate of turning the waste into recycled products, that r=l means there is no waste treatment

B. non-cooperative games In non-cooperative circumstances, as independent

decision makers, manufacturers and recyclers' goal is to achieve their profit maximization. But both sides in the RSC channel have different position. Manufacturers entrust recovery contractor recycling waste product, so in normally, Manufacturers give priority to recovery from merchants. Manufacturers make decisions first, then recyclers make their strategies based on manufacturer's decisions. Both sides constitute Stackelberg game. But sometimes it also exist these situations: when the recyclers get the equal status with the manufacturers, they will not depend on manufacturers' decisions. Then both sides will not consider each other when they make decisions. This is static game which is also called Nash Equilibrium. The analyses of these two cases are as follows: • Stackelberg game

Make the relationship between manufacturers and recyclers into a non-cooperative Model, in which manufacturers have the leading position while recyclers are subordinates. The decision-making process is as follows: manufacturers make the collection price first pricing decisions according to the market information. Recyclers make their own decisions to their market price following manufacturers' decisions. Obviously, manufacturers could consider recyclers reaction when they make strategies. Once they make decisions, manufacturers will retrieve waste products from recyclers at a certain

price, and recyclers recover the waste product on an established the collection price. Using backward induction to solve the Stackelberg game and the solving process are as follows:

By (2)

To: *"m/Po

Po=[b(wm-v0)-a]/2b (5)

Therefore: p0 is positively correlated with wm. This means that the market collection price increases while the collection price increases and reduces with the reduction of recycling priced. Take formula (5) into (1), we get:

^ m = ( w - v m - w m ) r [ b ( w m - v 0 ) - a ] / 2 b

Because

nm I ww = 0 ;

(7)

Therefore:

wm= [ b ( w - w m + v 0 ) - a ] / 2 b (6)

Take formula (6) into (5), we get Stackelberg equilibrium : in RSC, when Stackelberg is equilibrium, The optimal pricing of manufacturers and recyclers are :

Wm= [b(w-wm+v0)-a]/2b

p0=[b(w-wm-vo)-3a]/4b At this pricing strategy, the profit of manufacturers and

recyclers are:

7rm= r [ b ( w - w m - v 0 ) + a]2/8b (8)

TT0= [ b ( w - w m - v 0 ) + a]2/16b (9)

n = nm+n0 (io)

Nash Equilibrium Recyclers' influence in RSC is growing, assuming that recovery contractor and manufacturers have equal relations. Both sides make their profit maximization in non-cooperation at the same time. Manufacturers' optimization problem is:

max w - ■ w , ,)rQ0 (11)

1881

S.t. (2X4) From (11), we get:

d*m /dwm<0 This means wm is smaller, it is more favorable for manufacturers, but wm could not endless reduce. So by constraint conditions:

From d 7Tm 19p0 , we get:

a

W m = P o + V 0 (13)

Take formula (5) into (1), we get: 7T0 = 0 This shows, if recyclers make decisions without

considering manufacturers' profit, manufacturers will bring down the recycling price and make the recyclers' interests tend to zero at the same time. Then manufacturers possess all the profits in RSC and recyclers have no interests. Under such circumstances, recyclers won't accept the entrustment of the manufacturer. The TSC of these will dissolve into nothingness.

Therefore, in the RSC, although recovery contractor's influence can be appropriately increase, but the manufacturers' decision may make recyclers' interests tend to zero when this kind of influence endanger the manufacturer's dominant position. Therefore, the rational recyclers don't make decisions independently with manufacturers meanwhile. In reality, the static game does not exist.

C. Cooperative games In cooperative circumstances, both manufacturers and

recyclers have the same goal to get the maximum profit in the RSC. They make the pricing strategy together. This is an ideal situation in the RSC and is also the state to obtain the biggest profit in the RSC. In reality, the composition of the RSC members is independent economic entity. Both sides, they will cooperate on conditions that they will pursue their own benefit maximization. So this cooperation is limited.

In cooperative conditions, the model is structured as follows:

max7r

S.t. Formula (3)(4)

From (3), we get:

( w - v m - w m ) r Q 0 + ( w m - p 0 - v 0 ) Q 0

Because

S; r / aw m =( l - r )Q 0 >0 , So it means 7T is positively correlated with W m .

And when

W m = W - V m

We get the maximum value of 7T.

(14)

P0=[rw+ ( l - r ) w m - r v m - v 0 - - ] (15)

By formula (14) (15) we get: in RSC, when they are

cooperative, the optimal pricing of manufacturers and

recyclers are:

Wm*=w-vm

Po'= [b(W-Vm-Vo)-a] / 2 b (16)

Under this pricing strategy, the profit of manufacturers,

recyclers and the RSC are as follows:

< = [ b ( w - v m - v 0 ) + a]2/4b (17)

n = [ b ( w - v m - v 0 ) + a]2/4b

III. ANALYSES

Making a comparison between the Stackeberg game and cooperation game, we can see:

First, comparing with the state of non-cooperation, both the collection price and the market recycling price has increases when manufacturers and recyclers have cooperation with each other. Cooperation not only mobilizes the initiative to recycle the waste products, but also prompts consumers to sell waste product more actively. These will help to increase recyclers' profits

Second, when manufacturers and recyclers have cooperation with each other, the recycler's profits increase, and the manufacturer's profits was reduced and almost reduced to zero. In this case, the recycler has the channels exclusive profits. Obviously, the manufacturer cannot accept this cooperation. Make sure that the manufacturer's profits in cooperation are not lower than in non-cooperation, then the manufacturer could accept this cooperation. Clearly, it needs both of them to coordinate their respective interest.

IV. CONCLUSION

In this paper, we introduced basic knowledge of the reverse supply chain which contains the manufacturer and the recycler firstly. Then, using the game theory, we instruct the pricing models of the waste products. The pricing models include non-cooperative game and cooperative game. The non-cooperative game contains Stackelberg game and Nash Equilibrium. Through the study of the non-cooperation game, we point that Nash Equilibrium is not exist in reality, because the recycler has no profit in this state. So in non-cooperation there is only Stackelberg game. The study of cooperative game points that the manufacturer's profit is

1882

lower than in the state of non-cooperation. The manufacturer will not accept cooperation if there is no coordination. This paper demonstrates that if the manufacturer and the recycler want to have the maximum profit, both of them must consider each other when they make strategies. These conclusions complete the theory of the reverse supply chain and it will promote the development and application of the reverse supply chain.

ACKNOWLEDGMENT This research is supported by the Social Science

Research Common Program of Beijing Municipal Commission of Education, China under Grant No.SM201010772002.

REFERENCES [1] Canan R..Savaskan.,Shantanu B., Closed-Loop supply chain models

with product remanufacturing,Management science,2004,50(2),pp.239-252.

[2] ZHANG Qian-fan,FANG Chao-long,HU Dan-dan, The Incentive Mechanism of Supply Chain Technological Innovation Based on Game Theory,Commercial Research;2007, 9,pp.46-50

[3] QIU Ruo-zhen,HUANG Xiao-yuan,Coordination Model for Closed-Loop Supply Chain with Product Recycling,Journal of Northeastern University(Natural Science);2007,6 ,pp.22-26

[4] TENG Chun-xian,YAO Feng-min,LIU Zhi-yong,The Coordination of Pricing in A Supply Chain with Stackelberg Game,Systems Engineering,2007-07,pp .10-15

[5] Zhou Ming,Guan Xin-guo,The Impact of Remanufacturability on the Total Profits of Close-loop Supply Chains,Industrial Engineering Journal;2009,l,pp:51-56

[6] ZHANG Jian-jun,HUO Jia-zhen~l,ZHANG Yan-xia,Coordination Strategy Designing in Closed-loop Supply Chain Based on Pricing Game,Journal of Industrial Engineering and Engineering Management;2009,2, pp.43-47

[7] GE Jing-yan,HUANG Pei-qing,LI Juan,Social Environmental Consciousness and Price Decision Analysis for Closed-loop Supply Chains—Based on Vertical Differentiation Model,Industrial Engineering and Management,2007,4,pp.38-42

[8] HUANG Ymg-ymg,ZHOU Gen-gui,CAO Jian,Study on Price and Incentive Mechanism of Three-level Reverse Supply Chain for Electronic Products,Industrial Engineering and Management,2009,3, pp.88-97

[9] Anna Nagurney,Fuminori Toyasaki,Reverse supply chain management and electronic waste recycling: a multitiered network equilibrium framework for e-cycling . Transportation Research Part E: Logistics and Transportation Review,Volume 41, Issue 1, January 2005,pp. 1-28

[10] K.K. Pochampally, S.M. Gupta, A multi-phase mathematical programming approach to strategic planning 5 an efficient reverse supply chain network, Electronics and the Environment, 2003. IEEE International Symposium on, 2003, pp.72-78

[11] Michael P. Johnson,Bryan.Tutorials in operations research: models, methods, and applications for Innovative Decision Making,Presented at the INFORMS Annual Meeting, November 5-8,2006,pp:200-233

Manufacturers Manufacturers buy the waste Recyclers Retrieve the waste from consumer market Consumers

Manufacturers entrust recycler retrieve the waste

The Reverse Supply Chain

Figure 1. The structure of RSC pricing model

1883