Coordination and competition in a closed loop supply chain
Sarat Kumar Jena S P Sarmah [email protected]
Department of Industrial Engineering & Management, IIT Kharagpur, India
Abstract This paper studies coordination and competition issues in a closed-loop supply chain. The supply chain consists of two competing manufacturers who collect the used-product for remanufacturing through a common retailer. We obtain the optimal wholesale prices, and the optimal fraction of collection for the two cases: case1 (uncoordinated system) and case2 (channel-coordinated system). Furthermore, by comparing the optimal results, it is found that channel coordination system is the best for two competitive closed-loop supply chains. At the end, we illustrate the model by a numerical example. Also sensitivity analysis is performed to see the impact of market size and acquisition cost on total channel profit. Keywords: Remanufacturing, Coordination, Competition
Introduction The importance of environmental performance of product is increasingly being recognized by the business organizations. Among the various factors, globalization of business, increased market competition, information technology, awareness of customers, and increased demand for the value added product/service have largely contributed to the changes in the environment. In the light of increasing environmental consciousness and stricter legislation, remanufacturing has become a vital process to overcome this environmental issue. Remanufacturing is the process where some components of used products are disassembled, cleaned, reprocessed, inspected, and reassembled to be used again. Customer may return their product due to variety of reasons during and after the product life cycles such as due to warranty, repair return, end-of-use return, and end-of-life returns. The product take-back system and reuse of outdated product depends on the product characteristics. According to a recent survey made by Kelly Service analysis (2012), remanufacturing in Indian automotive industry is growing at 13%, and by 2016, it is forecasted to reach US $120 -159 billion. Similar trend of growth in remanufacturing is also present in other industries, such as computer and accessories (Jorjani et al. 2004, Shi et al. 2011), camera
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(Savaskan and Van Wassenhove2006), electrical equipments, consumer electronics, and furniture etc. This paper considers a two stage closed-loop supply chain distribution channel where two different manufacturers producing substitutable product compete to sell and collect the used products through a common retailer. The price of one product can affect the sales of the other product. We have studied two cases for the above described system (i) when all the three members individually maximize their profit (un-coordinated system). (ii) Secondly, both the manufacturers coordinate separately with the retailer and both the integrated channel compete on choosing the product prices in response to the other channel to maximize the profit (channel-coordinated system). The paper is organized as follows. A brief review of literature is provided in the next section. After that, mathematical models are developed and subsequently numerical study and sensitivity analysis are made. Finally, conclusions, and future scope of study are presented. Review of literature The literature here can broadly be divided into three categories: management of supply chain with competing manufacturer, secondly, management of supply chain with competing retailers and finally, literatures related to competition between supply chains to supply chain. In the management of supply chain with competing manufactures. Choi (1991) reported that the price competition between differential products plays a major role in determining the channel structure. The author has analyzed the market structure through two competing manufacturers and one common retailer. Ha, Li, and Ng (2003) considered a supply chain in which two suppliers compete to supply to a customer. Further, Gu and Gao(2012) addressed on the wholesale prices and the retailer prices and collecting prices for two competitive closed- loop supply chains. In the management of supply chain with competing retailers, Ingene and Parry (1995) studied the coordination among the retailers under price competition in supply chain. Iyer (1998) examined the coordination of the supply chain with one manufacture and two retailers competing in price and service. Tsay and Agrawal (2000) have studied the supply chain considering two competing retailers with a common manufacture where both the retailers provide the same products as well as service to the customer at a competitive price and service. Bernstein and Fedegruen(2005) examined the equilibrium behavior of decentralized supply chain with competing retailers and a single supplier under demand uncertainty in a two-echelon distribution systems. They have considered that retailers are non-identical in nature. Savaskan and Van Wassenhove (2006) addressed the interaction between a manufacture’s reverse channel choice to collect used product and a strategic product pricing decision in the forward channel in retail competition.
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In the management of supply chain with chain-to-chain competition, Kurata et al (2007) have investigated channel pricing in multiple channel distribution considering competition between a national and a store brand product where the national brand product can be distributed through both direct and indirect channel whereas store brand product can be distributed only through indirect channel. Xia and Gilbert (2007) developed a model considering two substitutable products in which the product service level was decided by the manufacturer whereas, the prices were determined by the retailer. Guide et al. (2009) addressed a single closed-loop supply chain that consists of one manufacturer and one retailer. Wu (2012) has studied price and service competition among the manufacturer and remanufacture with a common retailer. In the study, author has investigated the profits of the chain members by considering different interactions between price and service. Many models have been developed on competition of used product, but till date, to our knowledge, no work has been reported in the literature about the effect of market size and acquisition cost on total channel profit considering coordination under price competition in a CLSC problem.
Model development The following notation are used for the development of the mathematical models (i, j=1, 2, i≠j) Di : demand of product i per unit time cm : per unit production cost of new product cr : per unit remanufacturing cost of return product w i : per unit wholesale price of product i p i : per unit sale price at the retailer end of product i
i : fraction of products i remanufactured from return units. i.e., 0≤ ≤1
bi : per unit transfer price of product i A : fixed price made to the customer who returns a used product. I: production collection effort I C L C : scaling parameter. cc L mr
r : profit of the retailer
mi : profit of the manufacturer i where i=1,2 The demand functions of the substitutable products produced by two manufacturers are continuous and assumed to be of the following form
Di( i p i pwherep j ), i (1),(,1,2, rwij i ij ) This function is a variation of more general class linear demand functions used in many aforementioned studies (Choi 1991). The two parameters β and γ are 3
independent in nature. It is assumed, αi and β > 0 so that demand for each product decreases with the increase in price. Further for substitute product, γ >0; and for complementary product γ < 0 Following are the assumptions in the development of the model: Single period is considered here. Demand for each product is deterministic and price sensitive. Each manufacturer has infinite capacity.
ccrm So >0, It is a realistic assumption that remanufacturing cost of production is less than the cost of manufacturing of new product. There is no difference between the new and remanufactured product. We have developed the mathematical model for the following two cases. Case1: Uncoordinated system Here, the two manufactures compete to sell the new product in the market and also at the same time compete to collect the used product through a common retailer (see Figure.1). The competition for selling of new product is called here as forward price competition where as the competition to collect the used product for remanufacturing is termed as inward (reverse) price competition. In the, uncoordinated system, each individual member tries to maximize his own profit ignoring the impact of his decision on the other members of the system.
(D1τ1) b1 Manufacturer1 Pi Di Retailer Market W1
W2 (Di τi ) A
Manufacturer2 (D2τ2)b2
Figure.1-Wholesale price duopoly without system coordination The retailer collects the used product from the market at a certain fixed price A and then the retailer adds his own margin to sell it to the respective manufacturer. Manufactuere1 and manufacture 2 simultaneously set the wholesale price w1 and w2 to sell the new product. The retailer adds his own margin on each wholesale price to set the final market price as p11 w(1 r ) and p22 w(1 r ) Retailer’s problem The profit equation of the retailer can be written as Retailer’s profit = Sales revenue from new product 1 and 2 + Revenue earned by selling the used product to both the manufacturers – Cost of purchasing of new product– Cost of acquisition of used product– Cost incurred to collect the used product. DpDp bDbD DwDw ADADC 22 C (1) r11 22111222 11 22 11 22 L 1 L 2 4
Since the objective function is concave in nature, it is solved by first-order condition (see Appendix A for proof) and the solution is given as: r 0 1
1 w 1(1 r ) w 2 (1 r ) ( b 1 A ) 2 CL 1 0 w**(1 r ) w (1 r ) ( b A ) * 1 1 2 1 1 2CL ** * D1( w 1 , w 2 )( b 1 A ) 1 (2) 2CL Similarly, D( w** , w )( b A ) * 2 1 2 2 (3) 2 2C L Manufacturer’s problem The profit equation of the manufacturer can be written as Profit of manufacturer i = Sales revenue from product i + Savings due to remanufacturing of product i – Cost of manufacturing/remanufacturing the product i – Cost of acquiring the used product from the retailer.
1 D 1[ w 1 1 cm b 1 )] (1 w 1 (1 r ) w 2 (1 r ))[ w 1 cm 1 ( b 1 )] (4)
Substituting the values of τ1 in (4), one gets
1 w 1(1 r ) w 2 (1 r ) ( b 1 A ) 1(,)(w 1 w 2 1 w 1 (1)(1)) r w 2 r w 1 cm () b 1 (5) 2CL
Since 1 is a concave function, the simultaneous solution of the first-order condition gives
(1w 2 (1 r )) 1 2 X 1 cm (b11 A )( b ) (1 r ) w1 where X1 (6) 2 (1r )(1 X11 ) 2(1 X ) 2CL
Similarly, the wholesale price of the manufacture 2 can be written as
(2 w 1 (1 r ) 1 2 X 2 cm (1 r ) (b22 A )( b ) (1 r ) w2 = where X 2 (7) 2 (1rX )[12 ] 2CL * Solving (6) and (7) simultaneously, the optimal wholesale price ( ww12,*) can be derived as
* (1 2X1 )(2 1 cmm ) 2 (1 X 2 )( c 2 2 z (1 X 1 )) w1 4 (1X21 )(1 X )[1 z (1 r )] (1 2XX )(1 2 ) z 21 and 2 (8) 4 (1r )(1 X21 )(1 X )
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* (1 2X2 )(2 2 cmm ) 2 (1 X 1 )( c 2 1 z (1 X 2 )) w2 (9) 4 (1X21 )(1 X )[1 z (1 r )] Substituting the value of w1 and w2 in equation (1) and (2), one can obtain the * * optimal value of 1 and 2 Case2: Channel-coordinated system In this case, we have studied the problem where each manufacturer individually coordinates with the retailer to form a coordinated channel. Here, manufacturer 1 and the retailer together coordinate and it is called as channel l. Similarly, manufacturer 2 and retailer together constitute an integrated channel and is called as channel 2. Both the channels compete with each other in terms of setting the whole sale price and corresponding fraction of collection of used product (see Figure.2). This model can be considered as a case of inter supply chain competition under intra supply chain coordination.
Manufacturer 2 Manufactuer1
c Retailer D1 c D2
c c c A, τ1D1 A, τ2D2 c
Market
Figure.2-Wholesale price duopoly with system coordination
In the channel 1, the manufacturer 1 sets an integrated pricing policy of (w1 , τ1) in response to the channel 2 pricing policy of (w2 , τ2). The profit function of channel 1 is the summation of profit of the retailer and the manufacturer 1 and can be written as 22 r Dpw111111[][] bDCL 1 ADDpw 11222 bDCL 222 2 AD 22 (10)
mm1 D 1[ w 1 c 1 ( b 1 )] (11) The objective function of channel 1 is,
Maxcc11 r m 12 w11, Since the objective function is concave in nature, it is solved by first-order condition (see Appendix B) and the solution is given as
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(cA ( )) 1 wm 1 w(1 2 r ) ( b A ) (13) 12(1rr ) 2 (1 ) 1 2 2 2
DA1() 1 (14) 2CL
Solving (13) and (14) simultaneously, the optimal solution (w1, τ1) can be derived corresponding to the other channel’s policy (w2, τ2). Similar to the earlier case, solving the objective function of the channel 2, one gets, (cA ( )) 1 wm 2 ( w (1 2 r ) ( b A )) (15) 22(1rr ) 2 (1 ) 2 1 1 1
DA2 () 2 (16) 2CL
Again, solving (15) and (16) simultaneously, the optimal solution (w2, τ2) can be derived corresponding to the policy (w1, τ1) of channel 1. ** The value of equilibrium price (,)wwijand fraction of collection of used product ** (,)ijcan be derived by iterative procedure and once optimal **** (,,,)wi w j i and j are derived, corresponding channel profit can be determined.
Finally, the total profit of the system can be written as * sys ch ch ij Numerical example and managerial insights In this section, a numerical study is conducted to illustrate the model. The parameters are set as follows
A30,1 100, 2 150, 1, 0.7, cmL 100, b 1 45, b 2 40, 40, r 0.15, and C 1000
Table1: Results of two different cases of system
System τ1 τ2 w 1 w 2 Π m1 Π m2 Π r Π ch1 Π ch2 Π ch Un coordinated 0.28 0.45 181 179 2838 7094 4161 14093
system coordinated 0.31 0.41 154 170 6816 9196 16012 system
The results in Table1 show that the wholesale prices of the product are more in un-coordinated system whereas, it is less in the coordinated system. The total collection of current generation of used product is more in uncoordinated system compared to coordinated system (See Table1). The total profit is substantially higher in channel-coordinated system compared to uncoordinated system (see Table1).
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Sensitivity analysis Impact of acquisition cost (A) Here, we have studied the impact of acquisition cost (A) on total channel profit * (ch ) in both the systems. From Figure.3, it is observed that the value of total channel profit decreases as the acquisition cost increases in an un-coordinated system. The reason is that retailer collects used product from market by paying certain fixed amount. After that the retailer sells the same product to manufacture by keeping some margin. The manufacture sells the new product to the retailer with low wholesale price due to price competition. Therefore, the total cost of manufacturer increases as acquisition cost increases, and the manufacturer make lesser profit in the uncoordinated system. Again, from Figure.3, it is observed that the total channel profit is not affected by acquisition cost in channel-coordinated system. In this system, if acquisition cost of used product increases then manufacturer will sell their product at a higher price. Therefore, the total channel profit looks straight line as acquisition cost increases. Impact of market size (α) Here, we have studied the impact of market size α on total channel profit ( ). From Figure.4, it is found that total channel profit marginally increases in the both the system as the market size increases. When market size increases, channel- coordinated system makes more profit compared to uncoordinated system. In the uncoordinated system, manufacturers sell the product with higher wholesale price and due to the presence of double marginalization; it makes less profit compared to the coordinated system.
Conclusion In this paper, the issue of price competition and coordination in a closed-loop supply chain has been investigated where two manufacturers compete to sell their products through a common retailer. It is observed that, manufacturer gets more profit considering price competition under channel coordination. In the channel- coordination system, the total channel profit increases than uncoordinated system as the market price increases. The total channel profit nearly remains same as the acquisition cost increases under channel-coordinated system. But in the uncoordinated system, total channel profit decreases as the acquisition cost increases. Price competition normally increases the manufactures profit under channel-coordination. There are several directions for further study; a linear demand curve can be modified to include many other possible non-linear curves. Price competition has been considered here which can be extended to service and price competition among the manufacturers under coordination system.
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18000 16500 15000 13500 12000 10500 9000 7500 UC 6000 4500 CC 3000 1500
Total channel profit Totalchannel 0
A
Figure.3.The total channel profit of three cases in different values of acquisition price (A)
50000 45000 40000 35000 30000 25000 20000 UC 15000 10000 CC 5000 Total channel profit channel Total 0 60 70 79 89 99 108 118 128 137 147 157 166 176 186 195 α
Figure.4-The total channel profit of three cases in different values of market size
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Appendix A
22 rL(1ppwrbA 121111 )[ ] ( 2 ppwrb 212222 )[ AC ] [ 12 ]
22 rr 2 1 12 20CL H (,) 12 2202 C rr L 2 21 2 This hessian matrix shows negative definite and also principal diagonal elements are negative, so it follows concave. Appendix B
ch111( wrwrwrc (1 ) 2 (1 ))[ 1 (1 ) m 111111 ( bb )] ( wrwr (1 ) 2 (1 )) w11, 2 CAL1111( wrwr (1 ) 2 (1 )) ( 22 wrwrwrb (1 ) 1 (1 )) 22222 ( wr (1 ) 2 w1(1 r )) CL 2 A 2 ( 2 w 2 (1 r ) w 1 (1 r )) Hessian matrix
22 ch11 ch 2 w w Hw(,) 1 11 11 22 ch11 ch 2 11w 1 2 (1 r )2 (1 r )( A ) (1 r )( A ) 2 C L Since, from the operating conditions, D1>0 and D2>0, the members of the principal diagonal are negative. Hence, the objective function is a concave function
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