Reused Product Pricing and Stocking Decisions in Closed-Loop Supply Chain

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1 Reused Product Pricing and Stocking Decisions in Closed-Loop Supply Chain Yuanjie He * California State Polytechnic University, Pomona, USA Abolhassan Halati California State Polytechnic University, Pomona, USA Sustainability in supply chains is increasingly becoming one of the main themes in operations and supply chain management literature and business practices. Within the framework of Sustainable Supply Chain Management (SSCM), this paper studies the sequential pricing and stocking decisions in a closed-loop supply chain when the firm makes its sourcing decisions in dual supply channels including both a reliable supplier and an unreliable recycle/reuse channel. We use analytical modeling approach and obtain the optimal decisions under uncertainties in both supply and demand. Numerical examples are utilized to demonstrate the application and provide managerial insights. Keywords: sustainability, sustainable supply chain management, closed-loop supply chain, dual supply channels, random yield * Corresponding Author. address: he@csupomona.edu I. INTRODUCTION Sustainability has recently become one of the main focuses in Operations, Supply Chain Management and various other technical fields (Souza, G 2013),(Linton, et. al. 2007), (Tatichi, P. 2013), and (Guide and Van Wassenhove 2009). Kleindorfer et. al. (2005) surveyed the literature in sustainable operations management and categorized the related publications in the journal of Production and Operations Management into three areas consisting of green product and process development, lean and green OM, and remanufacturing and closed-loop supply chain. Our paper contributes to the third research stream by studying the joint price and quantity decision in a two echelon closed-loop supply chain with dual supply channels and a focal firm. A closed-loop supply chain, extends the forward chain to include the reverse supply chain with channels for product recycling/recovery and rese/remanufacturing. Within the context of SSCM there are two primary aspects in closing the supply chain and extending the producer responsibility to product lifecycle: one is reduction in economic cost and capturing the added value of the recycled products, and the second is lowering the adverse impact on the environment through reduction of waste, emissions and promotion of sustainable use of resources. When companies take lifecycle responsibility of their products, they may also take the potential cost advantage from recycling and reuse. The economics of closed loop supply chains has been studied by (Chen J. M. and Chang C. I. 2012), (Ferrer, G. 1997a, 1997b), (Ferrer G., and Ayres, R. U. 2000), (Geyer R. et. al. 2007), and (Chen J. M. and Chang C. I. 2012). 41

2 Sustainable initiatives in reducing waste and emissions, and environmental management can also have significant impact on companies financial performances (Klassen and Mclaughlin 1996), (Dowell et.al. 2000), and (Wang, Z. and Sarkis, J. 2013). These studies have concluded that sustainable supply chains may contribute to increased competitive advantage and thus not surprisingly there is a growing interest both in academia and industry in this area. One of the main challenges in the operation of closed loop supply chain systems is the establishment and reliability of the recycling channels. This paper studies the operational characteristics of the recycling channels and specifically focuses on the reliability issue of the recycling channels of a sustainable supply chain. We apply the random yield concept from production and operations literature (Yano and Lee 1995) (Gerchak 1992) to model the inherent uncertainty of these channels. Interested readers are referred to Li et. al. (2013) for the most recent development in random yield related literature. Another important dimension of closed loop supply chain operations involves developing pricing strategies for collection and disposition of both reused (cores) and the new products. Researchers have examined optimal pricing strategies in sustainable supply chains under different channel settings and assumptions (Gu et. al., 2005; Guide et. al., 2003; Ray et. al., 2005; Gu and Shi, 2005; Liang et. al., 2009; and Xu and Zhu, 2011). This paper primarily contributes to the literature in the above two areas. First, the paper enriches the sustainability supply chain literature by introducing the concept of recycling channel reliability issue, which has not received much attention in the literature. Secondly, it provides insights on how pricing decision in a recycling channel affects the supply chain performance, which adds value to the close-loop supply chain literature as studies in this area remains sparse. The remainder of the paper is organized as following. Section 2 presents the modeling assumptions and the results. Section 3 provides some numerical examples to demonstrate the findings with managerial discussions and section 4 concludes the paper with discussion of future research. II. MODEL SEQUENTIAL PRICING AND STOCKING DECISIONS IN CLOSED-LOOP SUPPLY CHAIN Consider a retailer of recyclable product with a dual source of supply. The product can either be purchased from the new product supplier at wholesale price c per unit, or obtained through the established recycling channels. We assume the recycled quantity that can be purchased depends on the retailer s recycling price policy. Therefore, every selling season, the retailer needs to decide on the quantity Q to purchase from the new product supplier and the recycling price v for the core product. The two supply channels differ in their cost and reliability. The supplier of the new product has a higher cost but is highly reliable due to previously established relationship between the main supplier and the retailer. The recycling channel exhibits a lower variable cost (v < c) for purchasing the core products, but it is unreliable and thus the quantity that can be obtained through this channel is uncertain. To model this uncertainty, we assume that the yield u from recycling channel follows a general distribution with density function g(u) and cumulative function G(u) on support [0,1]. The mean of the yield u is, i.e.. Also, the maximum potential yield Y(v) is a function of the recycling price v. For simplicity, we assume that Y(v) = a+bv (with a>0 and b>0) suggesting that the maximum potential yield increases in recycle price v. Using the 42

3 multiplicative form of random yield model, the realized recycled quantity is thus Y(v)u which depends on the realization of yield u. Furthermore, we assume that the product demand is stochastic and follows general distribution f(.) and F(.) with mean and support on ). With the early reveal of yield information, the retailer makes stocking decision Q thus resulting in a two-stage sequential decision process. At stage 1 (early stage), assuming zero beginning inventory, the retailer decides on the recycling price v. Based on the pricing decision, the maximum recycled quantity is Y(v). At the end of stage 1 the yield u is realized and observed. At the beginning of stage 2 (late stage), the retailer decides on the order quantity Q based on the revealed information of yield u. At the end of stage 2, the demand uncertainty is resolved and the revenue and costs are incurred accordingly. At stage 2, given recycling price v and the random yield u s realization U, the retailer s expected profit function based on demand uncertainty can be expressed as, ( )] ( )] (1) Notice that at stage 2, the recycle product cost is sunk cost and the retailer only considers the new product acquisition cost as the main cost. For simplicity, we have ignored the holding cost and penalty cost as the addition of these inventory costs does not alter the problem structure and properties of the solution; and with redefined selling price p and c, similar results in this paper can be achieved with holding costs and penalty costs added. Furthermore we have assumed perfect substitution between the core and the new product and the market willingness to pay the same unit price p for both products. The following proposition describes the optimal solution to the stage 2 problem. Proposition 1: The retailer s expected profit function is a concave function in stocking decision with the optimal stocking decision determined by the following equation. { (2) Proof of proposition 1: At stage 2, the retailer s expected profit function follows (1). After expansion, we have, ( )] ] ] ] ( ) The first order solution corresponds to the standard newsvendor solution,. Therefore,. When, the yield from recycled channel exceeds the newsvendor optimal stocking quantity determined by the critical fractile. Hence, it is optimal not to order, which satisfies the non-negative assumption of order quantity Q. The proof for proposition 1 is complete. Proposition 1 has an intuitive economic explanation. With the revealed yield information U, if the recycling yield is lower than the newsvendor critical fractile, the optimal stage 2 decision is to order up to the optimal newsvendor solution. On the other hand, if the recycling yield is higher than the newsvendor solution clearly it is optimal not to order additional new products. It should be 43

4 noted that the inclusion of penalty cost ( ) and/or holding cost (h) does not alter the structure of the solution. By Redefining and, similar results to proposition 1 is obtained with and substituting for p and c. Under the optimal decision structure illustrated in proposition 1, we can further analyze stage 1 problem with the given response function from stage 2. The expected profit function for stage 1 can be expressed as, ( )] ( )] ] ] (3) The first term represents the expected revenue with the optimal response function and under joint uncertainties of demand and yield. The next two terms represent the purchasing cost from the new product supply channel and the purchasing cost from the recycling channel respectively. The expected purchasing cost of the new product depends on the yield distribution as the optimal stocking decision depends on the realization of the yield u. Expand (3), and we have, ( )] The first four terms of this expected profit function represents the revenue terms under different scenarios of uncertainty realization. The first term is the revenue term under low yield and low demand, thus and there will be unsold products due to low demand; similarly, the second term is the revenue under high yield and low demand ( ), the third term is the revenue under low yield and high demand, and the fourth term is the revenue under high yield and high demand. The fifth term is the new product expected purchasing cost which happens only under low yield scenario with. The last term is the expected purchasing cost from the recycling channel. Proposition 2: ( )] is concave in v. The optimal stage 1 decision on recycling price v is determined by the first order equation ] Proof of proposition 2: (5) The first order derivative of ( )] with respect to v is given by, ( )] [ ] (4) [ Reorganizing the terms, ] 44

5 ( )] ] Taking second order derivative with respect to v, and plugging in for, results in, ( )] ] The optimal solution v and can be found by solving the first order equation. The proof for proposition 2 is complete. ]. Proposition 2 suggests that under the optimal response function, the retailer s optimal stage 1 pricing decision can be obtained by solving equation (5), which yields the highest expected profit under recycle yield randomness and demand uncertainty. III. NUMERICAL EXAMPLES AND DISCUSSION Numerical analysis was performed assuming uniform distribution for demand and recycling yield to demonstrate the results and further gain managerial insights. The recycle yield is assumed to follow a uniform (0, 1) distribution, thus. Figures 1 and 2 demonstrate how recycling channel parameters (a, b) affect the optimal pricing decision and the expected retailer profit. As a, the baseline for the potential quantity of products available through the recycling channel increases, the retailer s expected profit also increases. It is always beneficial to the retailer to maintain a larger recycling channel when the recycle channel price v* (in this example, less than 20) is less than the supplier channel price c (in this example, c=20). At the same time, with a larger recycling channel (higher a), it is optimal for the retailer to offer lower recycling price to enlarge the recycle yield. Similarly, Figure 2 shows that as the market exhibits higher sensitivity to recycling price (i.e., b increases), the retailer benefits from the increased awareness and sensitivity with higher expected profit due to lower cost of the recycle channel. We also notice from Figure 2 that this positive impact on expected profit slowly deteriorates as b increases. The recycle channel price v* decreases in b, indicating that as the market becomes more sensitive to the recycling price, the retailer would lower v * to reduce the acquisition cost of the core products. Figure 3 shows the impact of exogenous market parameters on the optimal decision and retailer s profit. As the ratio c/p increases, which can either result from increasing supplier channel cost (c) or reduced market price (p), the business environment worsens and the expected profit reduces. At the same time, the recycling price v* decreases, which follows the intuition that the higher supplier channel cost results in a lower newsvendor optimal critical fractile and hence the retailer dependency on the recycling channel to meet the demand is reduced It is optimal for the retailer to reduce v* accordingly. 45

6 Profit & Recycling Price Profit & Recycling Price Yuanjie He, Abolhassan Halati 25 Demand ~uniform (50,150), p=25, c=20, b= v* profit/ a FIGURE 1: RECYCLING CHANNEL PARAMETER a IMPACTS v* AND PROFIT (IN $100) Demand ~uniform (50,150), p=25, c=20, a= b v* profit/100 FIGURE 2: RECYCLING CHANNEL PARAMETER b IMPACTS v* AND PROFIT (IN $100) 46

7 Profit & Recycling Price Profit & Recycling Price Yuanjie He, Abolhassan Halati Demand ~unif(50,150), p=25, a=25, b= C/P v* Profit/100 FIGURE 3: CRITICAL FRACTILE IMPACTS v* AND PROFIT (IN $100) 30 p=25, c=15, a=50, b= v* Profit/ cv/cv 0 FIGURE 4: DEMAND RISK IMPACT v* AND PROFIT (IN $100) 47

8 Figure 4 demonstrates the effect of increased demand uncertainty on the retailer s optimal core product pricing and profit. The results exhibited corresponds to a constant demand mean, with increase in the uniform distribution range from [150,250] to [100, 300]. Hence, the coefficient of variation is increased, which demonstrates the increment in both absolute and relative demand risks. represents the base coefficient of variation when the demand distribution is Uniform(150, 250). The results show that that as the demand uncertainty increases, the external market condition worsens and the retailer s profit deteriorates. Simultaneously, the retailer offers lower recycling channel price as a measure to reduce risk exposure from the recycling channel and becomes more dependent on the more reliable supply channel to meet market demand. IV. CONCLUSION AND FUTURE RESEARCH This paper studied the sequential pricing and stocking decisions within the context of a simple closed-loop supply chain under both stochastic demand and stochastic yield from the recycling channel. A two stage sequential decision model was proposed and the closed form solutions of the optimal decisions were developed for the optimal joint stocking and pricing decisions. To further gain managerial insights, numerical examples were conducted to investigate how external parameters affect the closed-loop supply chain performance and the optimal decisions. The parameters studied included recycling channel potential yield (Y(v) described by a and b), retailer s cost structure (described by p and c), and market demand variation. The results suggest that despite the lower reliability, the retailer normally shows preference for the recycle channel over the main supply channel due to a lower cost. With improved recycling market (higher baseline recycling amount a and/or higher price sensitivity b), the closedloop supply chain exhibited better performance manifested in increased retailer profit. At the same time, a worsening cost structure (higher c and/or lower p) results in reduced profitability and thus lower performance. When demand uncertainty was increased, the retailer was worse-off and showed decreasing profit and lowered the recycling price for the purpose of risk control. The model can be further expanded in a number of directions. First, the recycling channel model may be refined by considering other channel costs such as processing, reverse logistic, and remanufacturing costs etc. We conjecture that inclusion of additional supply channel costs would not alter the structure and the characteristics of the solutions provided. Another potential expansion is to study the problem under different decision sequences and different information revealing sequences similar to (He 2013). Future research may also investigate the joint impact of w the yield and demand uncertainty on the focal firm s decisions and profit. It would be interesting to explore how reduction on the recycling yield risk affect double marginalization in a more complex supply chain setting. V. References Chen, J. M., and Chang C. I. (2012). The economics of hybrid manufacturing systems in a closed-loop supply chain. Netnomics, Vol. 13, Chen, J. M., and Chang C. I. (2012). The economics of a closed-loop supply chain with remanufacturing. Journal of the Operational Research Society, Vol. 63, Dowell, G., Hart, S. and Yeung, B. (2000). Do corporate global environmental standards create or destroy market value? Management Science, 46 (8), Ferrer, G. (1997a). The economics of personal computer remanufacturing. Resources, 48

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