Choosing the right exchange-old-for-new programs for durable goods with a rollover

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Production, Manufacturing and Logistics

Choosing the right exchange-old-for-new programs for durable goods with a rollover Yongbo Xiao∗ Research Center for Contemporary Management, Key Research Institute of Humanities and Social Sciences at Universities, School of Economics and Management, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 26 January 2016 Accepted 1 November 2016 Available online xxx Keywords: Supply chain management Trade-in rebates Remanufacturing Customer choice behavior Optimal pricing

a b s t r a c t By offering to trade-in one unit of old product at a discounted price while selling new products, “exchange-old-for-new” (EON) programs have been considered efficient ways of expanding market for durable goods. Starting from the choice behavior of customers, this paper studies optimal pricing and remanufacturing decisions for firms that adopt the EON program. Specifically, considering a supply chain that consists of one manufacturer and one retailer, we investigate two business models: (i) in the manufacturer-initiated scenario, the manufacturer launches an EON program and owns all the old items that are returned; he remanufactures all (or a portion) of the old items and sells them to a secondary market. (ii) In the retailer-initiated scenario, any old items that are returned belong to the retailer; she remanufactures the old items and sells them to the secondary market. An in-depth comparison between the optimal decisions in the two models is conducted in this paper. We show it is possible that a firm may be even more profitable from being a “free-rider”, instead of offering an EON program by himself/herself. Based on a centralized supply chain as a benchmark, an exchange-discount-sharing contract is proposed to coordinate the supply chain and to improve the overall welfare of customers. Numerical experiments are conducted to show the profit impact for the supply chain members, which uncover some interesting managerial insights for the proper adoption of the most efficient EON programs. © 2016 Elsevier B.V. All rights reserved.

1. Introduction It has been challenging for firms involved in the production and distribution of durable products (such as furniture, household electrical appliances, computers, etc.) to continuously expand the market in a competitive environment. This is because, unlike consumer goods, a durable product can usually be used for a rather long period of time, whereas advances in technology accelerate the development of new products. Therefore, marketing a new generation of durable products has become increasingly difficult, especially when the market is highly saturated. For example, given that a customer already owns an old but fully functional air-conditioner, he/she would be reluctant to buy a newly-launched high-frequency model that is more energy-efficient, if he/she must resell the old one at a markedly low residual value or discard it even by paying a disposal cost. To stimulate the sales volume of new products, various forms of “exchange-old-for-new” (or simply “old-for-new”, abbreviated as EON) programs have been widely adopted, in which

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manufacturers or retailers offer a trade-in rebate to customers seeking replacements to hasten their purchase decisions (Ray, Boyaci, & Aras, 2005). A typical example is Apples iPhone trade-in program, which was rolled out in August 2013 to increase the uptake of the iPhone 5 (Burrows, 2013; Fiegerman, 2013). After the bolstered sales in the U.S, Apple also extended the trade-in program for iPhones to China in association with the Foxconn Technology Group in March 2015 (Culpan & Higgins, 2015). In an EON program such as the one offered by Apple, the credit received by customers can, generally, be only used toward the purchase of a new product (Fiegerman, 2013). As a result, a direct benefit of this program is to support the sales of new products in more-developed markets such as the U.S. or Japan (Walsh, 2013). For example, it was estimated that about half the people buying iPhones in the U.S. during the final quarter of 2014 traded in their older phones (Culpan & Higgins, 2015). In fact, the EON program represents a win-win solution for customers and firms. On the one hand, it provides an additional option for customers that already possess old items. By receiving a credit and paying a discounted price, replacement customers can “upgrade” their product without worrying about their obsolete generation of product. As a result, it increases the purchasing frequency (Van Ackere & Reyniers, 1995).

http://dx.doi.org/10.1016/j.ejor.2016.11.002 0377-2217/© 2016 Elsevier B.V. All rights reserved.

Please cite this article as: Y. Xiao, Choosing the right exchange-old-for-new programs for durable goods with a rollover, European Journal of Operational Research (2016), http://dx.doi.org/10.1016/j.ejor.2016.11.002

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On the other hand, while expanding the market of new products by launching an EON program, a firm can generate additional revenue from the returned old items by refurbishing and selling them to less-developed countries or regions. This provides an opportunity to boost a firm’s secondary market (Graham & Molina, 2013). Even if the returned old items do not have any monetary value, they can be disassembled in an environmentally friendly manner, and the recyclable components and materials can be sold to other firms at a reasonable price. Recognizing its benefits, an increasing number of companies have adopted various forms of EON program to stimulate demand. For example, a few years before the iPhone trade-in program, Apple has initiated a “Reuse and Recycling program” (see http://www. apple.com/recycling/), which allows a customer to bring his/her old iPod to an Apple retail store and get 10% off a new one (Boehret, 2012). The major Chinese smart phone manufacturers, including Huawei, Xiaomi, Letv, Lenovo, and Qiku, all have rolled out their EON programs in recent years.1 It is worth mentioning that, besides the aforementioned manufacturers, an increasing number of retailers are adopting their EON programs as well. For example, kindle owners can trade in their old models and receive credit for a new one, or anything else that Amazon sells (Sorrel, 2011). One of the largest online retailers in China, JD.com, offers a EON program for a variety of household electrical appliances.2 Note that the EON program of the retailer will benefit the upper-stream manufacturer as well because it induces more new product sales. The effectiveness of EON programs has been promising: as reported in China Daily, from September 1, 2009 to December 31, 2011, China’s household appliance replacement policy, which has been proposed by The Ministry of Commerce, “drove sales of 342 billion yuan, around 22% of the expenditure in the sector as a whole during the period (Liu, 2012).” One of the key factors that determine the profitability of an EON program is the exchange discount (or trade-in rebate) that is offered to replacement customers. Although a high exchange discount may induce more customers to engage in the program and therefore increase the sales of new products, it may harm profitability by the so-called “demand dilution” effect. That is, a portion of customers who have intended to buy a new product may turn to exchange their on-hand old product for a new one at a discounted price. As a result, the firm may lose money from this specific transaction. A second key factor relates to how the firm generates additional revenue from the returned old items. Given the old items being perfectly usable, they can be remanufactured and sold to a secondary market in less developed countries/regions (like Apple’s iPhone). Or, they can be manufactured into a totally different product; for example, a U.S. startup, Xavage Technologies, has created a phone-housing-plus-app combo (i.e., Xentry) that turns an old iPhone or Galaxy S Fascinate into a door-mounted callerdisplay (for more information, visit xavagetech.com). Therefore, considering the choice behavior of customers and the revenues from the exchange sales and the secondary market, is an EON program always profitable? If so, how should a firm make the trade-off between the sales volume and unit revenue, and balance the revenue from selling new and returned old products, so as to maximize the profitability from the EON program? In particular, what is the impact of an EON program on other firms involved in the supply chain? Moreover, is it possible to motivate the supply chain members to act in a coordinated way so that the maximal profit potential from EON programs can be realized? In this paper, we seek to provide answers to the above questions and investigate 1 For more detailed information regarding their trade-in policies, please visit their respective websites. 2 For more details about JD’s EON program, please visit http://jmall.jd.com/ p192319.html.

the problem of how an EON program should be implemented in a more efficient way. Specifically, we study a stylized supply chain that consists of one manufacturer and one retailer facing an uncertain demand. This is a common setting in the supply chain optimization and coordination literature (Cachon, 2003; Chen, 2003). The upperstream firm sells a new generation of product through a wholesale price contract with the down-stream firm. Given that the market is becoming increasingly mature, they are considering expanding the market by adopting some form of EON program. Note that both supply chain members have incentive to adopt an EON program. Depending on the program-initiator, we consider two variants of decentralized business models in this paper: (i) in the manufacturer-initiated scenario, the manufacturer launches an EON program and owns all the old items that are returned; he remanufactures all (or a portion) of the old items and sells them to a secondary market. We consider the setting in which the collecting of old items is conducted by the retailer because the manufacturer does not have direct access to the market. (ii) In the retailerinitiated scenario, any old items that are returned are the property of the retailer; she remanufactures and sells them to the secondary market. As we will show, each supply chain member may benefit from the EON program offered by the other member. Therefore, the retailer and the manufacturer will act as a “free-rider” in the two business models, respectively. Starting from the choice behavior of customers, we will study the optimal decisions for the supply chain members under the two business models, and then provide an in-depth comparison between them. Based on a centralized supply chain as a benchmark, we will propose to adopt a collaborative EON model to coordinate the supply chain. Numerical experiments will be conducted to show the profit impact by adopting different forms of EON programs. Our major findings include the following. (1) The comparison between the two decentralized business models shows that the supply chain member (i.e., the manufacturer or the retailer) will offer a higher exchange discount if his/her takes a higher profit margin in selling new product (Proposition 1). Consequently, the optimal exchange discount in each decentralized scenario is lower than that of the centralized system (Proposition 3). (2) Each supply chain member may prefer to wait for the other firm to launch an EON program, instead of initiating the program by himself/herself, for example, when the new product is associated with a high selling price. (3) If the manufacturer and the retailer agree to adjust their wholesale price according to a pre-specified formula [i.e., Eq. (28)], an exchange-discount-sharing contract, which is incentive compatible, can be adopted to coordinate the supply chain. In particular, the coordinated contract may help improve the welfare of customers as compared to the decentralized system. The numerical experiments show that coordination between the supply chain members could improve their overall profit rather significantly, especially when the substitution level is high, when the size of existing customer is medium, and/or when the size of the secondary market is relatively large. We hope that our research provides useful insights for firms that are considering managing demand of durable goods by choosing the right EON program. To model the demand for durable goods has been extensively studied in the marketing literature. For example, Cripps and Meyer (1994) examine the process by which individuals make recurrent decisions about when to replace durable goods. Melnikov (20 0 0) provide a theoretical and empirical description of consumer behavior in a dynamic market for differentiated durable goods. Gowrisankaran and Rysman (2009) specify a dynamic model of consumer preferences for new durable goods with persistently heterogeneous consumer tastes, rational expectations, and repeat purchases over time. For a more detailed overview of the representative models that study consumers’ micro replacement decisions,

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please refer to Fernandez (2001). In our work, following the literature in operations management (e.g., Akçay, Natarajan, & Xu, 2010), we characterize the demand from the choice behavior of customers (for an overview of choice models, refer to Ben-Akiva and Lerman, 1985). The concept of “exchange-old-for-new” is not new at all, and its benefit has been investigated from the perspective of economics in the early literature (e.g., Fudenberg & Tirole, 1998; Klemperer, 1987; Levinthal & Purohit, 1989). However, in recent years, the frequent release of upgraded versions of products in many industries has arisen the interest of academic researchers towards the rollover-related strategies. For example, several papers, including those by Arslan, Kachani, and Shmatov (2009), Koca, Souza, and Druehl (2010), Liang, Cakanyildirim, and Sethi (2014), and Lobel, Patel, Vulcano, and Zhang (2015), investigate whether a single or dual rollover strategy should be adopted, by considering factors, such as cannibalization effect, product introduction and phase-out times, and choice behavior of forward-looking customers. However, how to implement the EON program has been paid less attention. To the best of our knowledge, quite a few papers have considered the EON program from the perspective of operations management, which we review in the following. Ray et al. (2005) is one of the earliest papers that study the optimal pricing/trade-in strategies for durable and remanufacturable products. They consider a market consisting of first-time-buyers and replacement customers, with the later customer having an existing product of different ages. Three pricing schemes (i.e., a uniform price for all customers, age-independent price differentiation, and age-dependent price differentiation) are studied and the most favorable pricing strategy are identified. Chen (2015) considers three trade-ins policies (i.e., no trade-ins, trade-ins to replacement consumers with high-quality used goods, and trade-ins to all replacement consumers) by optimizing the pricing and/or tradein rebate, and the strategic choice among the three options for the firm is studied. Chen and Hsu (2015) investigate when and how a durable goods firm should offer a trade-in rebate to collect and recover used products to achieve successful price discrimination and to weaken competition from third-party remanufacturers. Yin and Tang (2014) examine the effectiveness of trade-in programs by considering two successive generations of products. In their model, customers can participate in the trade-in program in the first period by paying a nonrefundable up-front fee. Thus, customers can opt to trade-in their first-generation product, and a pre-specified trade-in value to be used for the purchase of the second-generation product in the second period can be received. In another study, Yin, Li, and Tang (2015) consider the interactions between forward-looking consumers and a firm when a trade-in program is offered. They also optimize the selling prices of two successive-generation products in equilibrium, and the conditions under which trade-in programs are beneficial to the firm are examined. By considering a competitive setting with two firms, Desai, Purohit, and Zhou (2016) model two exchange promotions (i.e., within-category and multicategory) and analyzes their similarities and differences. Zhu, Wang, Chen, and Chen (2006) study a twoperiod model in which a firm makes new products in the first period and collects used products through trade-in, along with new product sale, in the second period. By considering a competitive environment, they investigate the equilibrium decisions. The above literature mainly focus on the optimal trade-inrelated decisions for a single firm or two competing firms. Our model, however, investigates the trade-in strategy from the perspective of supply chains. In particular, we are interested in comparing the manufacturer-initiated EON program with the retailerinitiated EON program. Given that each firm may benefit from the EON program offered by the other firm, the prisoner’s dilemma may apply to the supply chain under consideration. That is, it is

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likely that both firms would prefer to be a free-rider, instead of initiating the EON program by himself/herself. When this happens, it is extremely important to motivate the manufacturer and the retailer to launch a joint EON program that could improve the overall performance of the supply chain and the respective performance of each supply chain member. Therefore, our research follows the framework of supply chain optimization and coordination, which is a well-studied topic in the area of operations management, and seeks to devise an EON-based coordinating contract that is incentive compatible. For more literature on supply chain coordination, please refer to the excellent survey paper by Cachon (2003) and Chen (2003), and the references therein. We believe, our model is a useful supplement to the existing supply chain coordination literature. Moreover, by assuming that all the old products collected from the EON program can be remanufactured and sold to a secondary market, our model is relevant to the body of literature on remanufacturing, reverse logistics, and closed-loop supply chains. The majority of this literature concentrates on inventory management (e.g., Bhattacharya, Guide, & Wassenhove, 2006; Robotis, Bhattacharya, & Wassenhove, 2005), pricing (e.g., Ferrer & Swaminathan, 2006; Guide, Teunter, & Wassenhove, 2003), and channel design (e.g., Savaskan, Bhattacharya, & Wassenhove, 2004; Savaskan & Wassenhove, 2006) models; interested readers are referred to Atasu, Guide, and Wassenhove (2008), who provides an overview of analytic research on the business economics of product reuse. The majority of the remanufacturing literature considers a two-period model, in which the product is sold in the first stage and returned/remanufactured in the second stage. Our model differs from them by considering the interaction between the old and new generation of products. Therefore, like Ray et al. (2005), our model is a useful supplement to the existing remanufacturing literature as well. The remainder of the article is organized as follows: in the next section we will introduce the models and notation. In Section 3 we study the optimal decisions for the manufacturer and the retailer in the two business models and conduct a comparative analysis between them. In Section 4 we propose a collaborative EON model and develop a contract to coordinate the supply chain. We present the numerical results and analysis in Section 5 and conclude the paper in Section 6.

2. The models and notation We consider a supply chain that consists of one manufacturer and one retailer. The manufacturer produces a new type of durable product (i.e., the “new” product) and sells them to the end customers via the retailer. We assume that the transaction between the manufacturer and the retailer is based on a wholesale price contract; i.e., the retailer purchases the products at a unit cost w and sells at a unit price p ( p > w). Both w and p are assumed to be exogenous. The unit production cost of the manufacturer is denoted by c1 (c1 < w). The potential market of the new product, which we call the “primary market”, consists of two parts: customers that do not have any old product (i.e., new customers) and customers that already hold an old generation of product (i.e., existing customers). Note that we only consider one generation of old product in the model; it is natural to extend the model to more general cases with multiple new and old products in the future research direction. Given the selling price being exogenous, the actual demand from the first part is represented by D0 , which is a general random variable with mean value μ0 = E[D0 ]. The potential size of the second part is denoted by D1 , which is a continuous random variable with probability density function (PDF) and cumulative

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distribution function (CDF) being f1 (x) and F1 (x), respectively. For notational convenience, we let μ1 = E[D1 ]. Suppose the primary market is relatively saturated, i.e., random variable D0 is relatively small as compared to D1 . To increase sales and therefore improve profitability, the manufacturer and the retailer are considering launching certain EON programs that are targeted at the potential existing customers. In the program, customers can get a discount of α (α ≤ p) while they purchase the new products, if they are willing to return one unit of old product to the retailer/manufacturer. That is, while purchasing one unit of new product, customers can “sell” their old product to the retailer or manufacturer at a price α . It is expected that the manufacturer and the retailer can benefit from demand induction by offering this additional option. Note that we assume the introduction of an EON program will not affect the regular selling price p; this is consistent with the selling practice of many products including iPhone. As to the old products collected from existing customers, they can be remanufactured and sold to a secondary market located in a less-developed area. Following the newsvendor models, the demand is represented by a continuous random variable D2 , whose PDF and CDF functions are f2 (x) and F2 (x), respectively. We assume the secondary market is independent of the primary market. This is consistent with the case of iPhone, because “......used iPhones collected in the U.S. will only be resold in emerging markets......That way, the resale of Apples older models wont cannibalize iPhone 5 sales in the U.S.” (Burrows, 2013). Depending on the actual business model being adopted, the remanufacturing process may be associated with different cost structure. For example, the manufacturer can have the old products remanufactured by using his own capacity; or, he can outsource to an OEM. For comparison purposes, in this paper we assume the unit remanufacturing cost, denoted as c2 , is identical for both the manufacturer and retailer. This applies to the scenario in which the manufacturer and the retailer will collaborate with a common third-party OEM in the remanufacturing link,3 or the scenario in which the refurbishing cost is determined by the market. The selling price of the remanufactured old product, denoted as r, is supposed to be greater than c2 , i.e., we have r > c2 . Without loss of generality, we assume the salvage value of any excess old product is zero. 2.1. Choice behavior of potential customers To model the demand from the primary market, we start from the choice behavior of existing customers. Note that the new and old products are substitutable, with different qualities (or functionalities) from the point view of customers. Therefore, we follow the vertical-differentiation model proposed by Tirole (1988) to characterize the utilities towards the two types of products. Specifically, suppose the “quality” indices of the new and old products are represented by v1 and v2 (v1 > v2 ); and a potential customer’s utility is vi , i = 1, 2, where  follows a uniform distribution within domain [0, 1] and denotes the customers’ sensitivity towards the product quality. Given the selling price of the new product being p and the EON discount being α , each existing customer makes his/her choice decision to maximize the respective “net utility” (i.e., utility minus costs). Unlike Ray et al. (2005), who assume that “the replacement customers are only interested in trade-ins”, we consider a more general scenario. That is, each customer faces three options: either to keep using the existing old product (i.e., buy nothing), to exchange the old product for a new one, or to buy another unit of

3 Note that this is quite common in the electronics industry. For example, many Chinese firms collaborate with Foxconn Technology Group in remanufacturing.

Fig. 1. EON program’s impact on existing customers.

new product; their corresponding net utilities are:

U0 = v2 , U1 = v1 − p + α , and U2 = [v1 + (1 − s )v2 ] − p, (1) where s ∈ [0, 1] represents the level of substitutability of the old and new products (Calzada & Valletti, 2012). When s = 0 the products are independent, when 0 < s < 1 the products are partial substitutes, and s = 1 corresponds to the standard case in the literature, where existing customers will never buy another new product while keeping the old one. To avoid the trivial cases, in the following we assume 0 ≤ s < 1. By the definition of utilities, we can see that v1 (and v2 ) can also be seen as the maximal utility of a unit of new (and old) product to any existing customers. Clearly, if we denote the portion of existing customers that will engage in the EON program by γ e (α ), and the portion of customers that will buy another unit of new product by γ n (α ), then we have:

γe (α ) = P[U1 ≥ max(U0 , U2 )] = P

 p−α  α ≤≤ , v1 − v2 ( 1 − s )v2

γn (α ) = P[U2 ≥ max(U0 , U1 )]    p α = P  ≥ max , . ( 1 − s )v2 v1 − sv2

(2)

Naturally, the portion of customers that will not buy the new product is given by [1 − γe (α ) − γn (α )]. As can be seen from Eq. (2), the detailed formulations of γ e (α ) and γ n (α ) are dependent on the value of α . To avoid trivial cases and to simplify the analysis, we make the following assumption: Assumption 1. Suppose the parameters hold the following rela(1−s )v tionship: (i) p < v1 − sv2 ; and (ii) v −sv 2 p ≤ α ≤ (1 − s )v2 . 1

2

The intuition behind Assumption 1 can be explained by the following: (i) The selling price of the new product cannot be greater than v1 − sv2 , because otherwise no existing customer will choose to buy any new product when the EON program is not offered. We impose this assumption to better reflect the real practice. (ii) From Eq. (2) we know that γ n (α ) reduces to zero if α > (1 − s )v2 . We impose the constraint α ≤ (1 − s )v2 to warrant the concurrence of exchanges and buy-news when the EON program is being launched. Moreover, Eq. (2) suggests that, if the exchange dis(1−s )v count α is sufficient low (i.e., α ≤ v −sv 2 p), the EON program will 1 2 have no attraction at all, because no existing customer will join this program. Therefore, if the exchange discount is set lower than (1−s )v2 v1 −sv2 p, the manufacturer or the retailer’s expected profit will be (at least) sub-optimal. By Assumption 1, we can easily have, when the EON program is launched, the portion of existing customers that will engage in the exchange program γ e (α ), and the portion of existing customers that will buy a new product γ n (α ) are formulated as (see Fig. 1):

γe (α ) =

p−α α α − and γn (α ) = 1 − . ( 1 − s )v2 v1 − v2 ( 1 − s )v2

(3)

As a result, the total demand that will engage in the program (i.e., the “exchanges”, denoted as D1e (α )) and the total demand that will

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Fig. 2. The manufacturer-initiated scenario.

buy a new product (i.e., the “buy-news”, denoted as D1n (α )) are:

D1e (α ) = D1 γe (α ) and D1n (α ) = D0 + D1 γn (α ). As compared to the scenario in which EON program is not launched (see Fig. 1), the availability of the EON program will have two-fold impacts on existing customers: On the one hand, cusp α tomers whose  value is within interval ( v −s v , (1−s )v ] will be 1

2

2

attracted to engage in the EON program from buying new products (i.e., demand dilution); on the other hand, customers whose  α value is within interval [ vp− , p ) will be induced to engage 1 −v2 v1 −sv2 in the EON program from buying nothing (i.e., demand induction). As can be seen quite intuitively, as the value of α increases, the number of expected exchanges will increase whereas the number of expected buy-news will decrease, resulting in an increase in the total sales of the new products. Therefore, the manufacturer and/or the retailer seek to make a trade-off between the unit revenues and magnitude of demands, by adjusting the value of α , so as to improve their respective profits. 2.2. Two exchange-old-for-new programs We consider two variants of EON programs in this paper: the manufacturer-initialized and retailer-initialized programs. (i) The manufacturer-initialized EON program: In this scenario, the EON program is launched by the manufacturer. That is, the manufacturer authorizes the retailer to collect returned old products while selling new products (see Fig. 2). Any old products returned from the EON program are the property of the manufacturer, who in turn, remanufactures and sells to the secondary market. Note that in this model, the retailer will earn a unit profit of ( p − w ) from any sale of new products, regardless of whether it is an “exchange” or a “buy-new”. Therefore, the unit retail price of “exchanges” is ( p − α ), and the corresponding wholesale price is (w − α ). The manufacturer faces a two-stage optimization problem: in the first stage, he determines the exchange discount, α , and sells the products to the primary market; in the second stage, observing the realized quantity of returned old products, he determines the remanufacturing quantity Q to be offered to the secondary market. Owing to the capacity constraint of the secondary market, it may not be necessary for the manufacturer to remanufacture all of the old products. Suppose the manufacturer may simply discard the rest of the old products, because they can hardly generate any profit. (ii) The retailer-initialized EON program: In this scenario, the EON program is launched by the retailer. That is, the retailer sells the new product to two segments of customers with price p and

( p − α ), respectively. Any old products collected from the EON program are the property of the retailer. She remanufactures all or a portion of the old products and sells them to the secondary market. The retailer faces a two-stage decision problem as well: in the first stage she determines the exchange discount α ; in the second stage, observing the realized quantity of returned old products, she determines the remanufacturing quantity Q. Again, the retailer will simply discard any remaining old products. Fig. 3 provides an illustration of the retailer-initialized EON program. Note that in the above two business models, we assume the unit remanufacturing costs for the manufacturer and the retailer are both equal to c2 , because both of them can outsource the remanufacturing process to a same OEM. Moreover, we assume the manufacturer and retailer are risk-neutral; they seek to maximize their respective expected profit by making the optimal decisions. Following the literature in supply chain management, we suppose all the information is common knowledge to the manufacturer and retailer. In the rest of the paper, as a convention we call the manufacturer as a “he” and the retailer as a “she”. For notational clarity we use subscripts “m” and “r” in the decision variable α and the profit functions for the manufacturer-initiated and retailer-initiated EON programs respectively. Moreover, we denote x+ := max(x, 0 ) and x∧y := min (x, y), and list the major notation used in this paper in Table 1. Table 1 List of notation. Symbol

Description

p w

Retail price of the new product in the primary market Wholesale price of the new product between the manufacturer and the retailer Actual demand of new customers, with μ0 = E[D0 ] Potential size of existing customers, with μ1 = E[D1 ], PDF f1 (x), and CDF F1 (x) Demand of the secondary market, with PDF f2 (x) and CDF F2 (x) Unit production cost of the new product of the manufacturer Unit remanufacturing cost of the returned old product Selling price of the remanufactured old product in the secondary market Quality index of the new product Quality index of the old product Substitutability level of the old and new products Customers’ sensitivity towards the product quality, ∼ U[0, 1] Maximal remanufacturing quantity of the manufacturer and/or the retailer Exchange discount in the manufacturer-initiated scenario Exchange discount in the retailer-initiated scenario Exchange discount in the centralized supply chain

D0 D1 D2 c1 c2 r

v1 v2 s

 q

αm αr αc

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Fig. 3. The retailer-initiated scenario.

3. The optimal decisions In this section, we investigate the optimal decisions involved in the two variants of EON programs, and conduct a comparison between them. Firstly, if the optimal exchange discount, αi∗ (i = m, r), (1−s )v

in the two scenarios equals to the lower-bound value v −sv 2 p, 1 2 then the expected profits of the manufacturer and the retailer, denoted as V0 and R0 , are

   p μ0 + μ1 1 − , and v1 − sv2    p R 0 = ( p − w ) μ0 + μ1 1 − , v1 − sv2

products, as represented by γ e (α m )D1 , is random as well. Anticipating all possible profits that could be collected from the secondary market, the manufacturer chooses a best level of exchange discount α m , to maximize his total expected profit. The profit function, denoted as Vm (α m ), is the summation of expected profits from the primary and secondary markets. That is, we have:



Vm (αm ) = E (w − c1 )D1n (αm ) + (w − c1 − αm )

V0 = (w − c1 )

× D1e (αm ) + (D1e (αm ))



   p − αm μ0 + μ1 1 − v1 − v2  α  p−α

= ( w − c1 )

(4)

respectively. In later sections we will use them as benchmarks to evaluate profit improvement by launching the EON programs. For each scenario, we solve the two-stage decision problems in reverse order. First, we consider the remanufacturing quantity decision (Q) of the manufacturer (in the manufacturer-initiated scenario) and retailer (in the retailer-initiated scenario) in the second stage. Given the actual quantity of returned products being y ≥ 0 in either scenario, the manufacturer and/or retailer need to optimize his/her expected profit from the secondary market. Let (y) be the optimal expected profit function, i.e.:

−αm μ1 − ( 1 − s )v2 v1 − v2

∞   +  xγe (αm ) f1 (x )dx, m

q = F¯2−1

c  2

r

.

That is, if the quantity of returned old products is greater than q, the manufacturer and/or the retailer will have to discard a portion of them, because their marginal production cost c2 is greater than the marginal expected revenue. Therefore, we have:





(r − c2 )y − r 0y (y − x ) f2 (x )dx (y ) = q yes(r − c2 )q − r 0 (q − x ) f2 (x )dx

if y ≤ q otherwise,

(6)

where function γ e (α m ) is given by Eq. (3). The first derivatives of Vm (α m ) is readily shown to be

Vm (αm ) =

(y ) = max E r (D2 ∧ Q ) − c2 Q . The above is, apparently, a typical newsvendor problem. The optimal quantity to be remanufactured, denoted as Q∗ (y), is intuitively given by Q ∗ (y ) = min(q, y ), where q is

m

0



0≤Q≤y



 v1 − sv2 2αm μ1 − v (v − v2 )(1 − s )    2 1  r F¯2 xγe (αm ) − c2 x f1 (x )dx . p + w − c1 μ1 − v1 − v2



q

γe ( α m )

0

(7)

Note that γ e (α m ) is increasing in α m ; it is not difficult to show Vm (αm ) is decreasing in α m . Therefore, Vm (α m ) is a concave (1−s )v

function. Considering that the feasible domain αm ∈ [ v −sv 2 p, (1 − 1 2 s )v2 ∧ p] is convex, the Karush–Kuhn–Tucker (KKT) conditions, which are sufficient and necessary for optimality, can be used to find the optimal exchange discount that maximizes Vm (α m ). That is, if λ1 and λ2 are the respective dual variables corresponding to (1−s )v boundary conditions αm − v −sv 2 p ≥ 0 and (1 − s )v2 ∧ p − αm ≥ 0, 1 2 then the manufacturer’s optimal exchange discount within interval p [ v v2 , v2 ∧ p], is the unique solution of the following equations: 1

(5)

which is, clearly, continuous and concave in y. In the following, we investigate the optimal exchange discount decision for the manufacturer-initiated and retailer-initiated scenarios respectively. 3.1. The manufacturer-initiated scenario Recall that the size of the existing customers, D1 , is random. Therefore, given an exchange discount α m , the quantity of returned

⎧ V (αm ) = −λ1 + λ2 , ⎪ ⎨ m  )v2 λ1 αm − (1−s v1 p = 0, ⎪ ⎩ λ2 [(1 − s )v2 ∧ p − αm ] = 0;

(8)



where Vm (αm ) is given by (7). To characterize the structure of the above equations’ solution, we introduce a function h(r, γ ):

h(r, γ ) :=



q/γ 0





r F¯2 (xγ ) − c2 x f1 (x )dx,

(9)

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where r ≥ c2 and 0 ≤ γ ≤ 1. For notational convenience, when γ = 0, we let

h(r, 0 ) = lim {h(r, γ )} = γ →0



0

∞

(r − c2 )x f1 (x )dx = (r − c2 )μ1 .

Lemma 1. Function h(r, γ ) has the following properties: (i) for any γ ∈ [0, 1], h(r, γ ) is increasing in r; and (ii) for any r ≥ c2 , h(r, γ ) is decreasing in γ . Proof. (i) On the one hand, for any x ∈ [0, γq ], we have

(1−s )v

∗ equals the lower-bound ∗ 2 That is, αm v1 −sv2 p if and only if r ≤ r1 ; αm ∗ equals the upper-bound (1 − s )v2 ∧ p if and only if r ≥ r2 ; αm equals α 1 if and only if r ∈ (r1 , r2 ).

Proof. We only prove for the case p ≤ (1 − s )v2 (the case p > (1 − s )v2 can be proven similarly). We first show the necessary part. Recall that v2 < v1 ; clearly, in the solution of Eqs. (8), the dual variables λ1 and λ2 cannot be both positive. We discuss based on the following three possibilities: •

r F¯2 (xγ ) − c2 ≥ r F¯2 (q ) − c2 = 0; that is, the integrand in (9) is always non-negative. On the other hand, the upper-limit of the integration is increasing in r (recall that q is increasing in r). Therefore, h(r, γ ) is increasing in r. (ii) For a given r, as γ decreases, both the integrand and upperlimit of the integration in (9) will increase. Therefore, h(r, γ ) is decreasing in γ . This completes the proof.  By Lemma 1, we know that given two constants γ 0 and z0 , if h(r, γ0 ) = z0 , then the value of r can be uniquely determined. For notational convenience, we denote it as r = h−1 (z0 |γ = γ0 ). Before presenting the main result (Theorem 1) in this subsection, we define the following two critical values:

 v (1 − s )( p − w + c )    2 1 r1 := h−1 μ1 γ = 0 v1 − sv2 ( 1 − s )v2 = c2 + ( p − w + c1 ), v1 − sv2 ⎧  )v2 ⎪ h−1 2 pμ1 − (v11−s ( p + w − c1 ) ⎪ −sv2 ⎪ ⎪   ⎪  ⎪ p ⎨ μ1 γ = (1−s )v2  r2 := )v2 −1 ⎪ h 2(1 − s )v2 μ1 − (v11−s ⎪ −sv2 ⎪ ⎪   ⎪ ⎪ ⎩ ( p + w − c1 )μ1 γ = v1 −p−sv2 v 1 −v 2

•

•

1

•

(10) •

(11) otherwise.

•



≤ h ( r1 , 0 ) < h r2 ,



p , ( 1 − s )v2

from which we know r1 < r2 . [Recall from Lemma 1 that h(r, (1−sp )v ) is increasing in r.] 2

The case p > (1 − s )v2 can be proven in a similar way. This completes the proof.  The following theorem shows that the optimal exchange discount (i.e., the solution of Eq. (7)), is characterized depending on the value of r. Theorem 1. Define α 1 as the unique solution of the first-order condi tion Vm (αm ) = 0. In the manufacturer-initiated scenario, the optimal ∗ , exhibits the following structure: exchange discount, denoted as αm

⎧ (1−s)v2 ⎨ v1 −sv2 p αm∗ = α1 ⎩ ( 1 − s )v2 ∧ p

i f r ∈ [c2 , r1 ], i f r ∈ ( r1 , r2 ), otherwise;

If r ≤ r1 , because h(r, 0) is increasing in r, we can easily (1−s )v have Vm ( v −sv 2 p) ≤ 0. Note that Vm (α m ) is concave, therefore, 1

2

1

2

(1−s )v

If r ≥ r2 , because h(r, (1−sp )v ) is increasing in r, we can easily 2 have Vm ( p) ≥ 0. Note that Vm (α m ) is concave, therefore, Vm (α m ) is increasing in the entire domain [ v −sv 2 p, p]. As a result, the 1 2 ∗ = optimal exchange rate that maximizes Vm (α m ) is given by αm p. If r1 < r < r2 , by conducting a similar analysis, we know (1−s )v that Vm ( v −sv 2 p) > 0 and Vm ( p) < 0. Due to the concavity of 1

( 1 − s )v2 ( 1 − s )v2 pμ1 − ( p + w − c 1 ) μ1 v1 − sv2 v1 − sv2   ( 1 − s )v2 p < 2 pμ1 − ( p + w − c 1 ) μ1 = h r 2 , . v1 − sv2 ( 1 − s )v2



2

(1−s )v

h ( r1 , 0 ) = 2

p ( 1 − s )v2

1

Vm (α m ) is decreasing in the entire domain [ v −sv 2 p, p]. As a re1 2 sult, the optimal exchange rate that maximizes Vm (α m ) is given ( 1 −s ) v ∗ = 2 by αm v −sv p.

(12)

2

(1−s )v

Vm (α m ), we know that Vm (α m ) is increasing in [ v −sv 2 p, α1 ] 1 2 ∗ = whereas it is decreasing in [α 1 , p]. As a result, we have αm α1 .

Proof. We first consider the case p ≤ (1 − s )v2 . By the definition of r1 and r2 , we have



2

We next show the sufficient part.

Lemma 2. r1 and r2 have the following relationship: r1 < r2 .

h r1 ,

(1−s )v

If αm = v −sv 2 p, we have λ1 ≥ 0 and λ2 = 0; substitut1 2 ing which into the first equation in (8), we know that (1−s )v Vm ( v −sv 2 p) ≤ 0, which reduces to r ≤ r1 . 1 2 If αm = p, we have λ1 = 0 and λ2 ≥ 0, substituting which into the first equation in (8), we know that Vm ( p) ≥ 0, which reduces to r ≥ r2 . (1−s )v If v −sv 2 p < αm < p, we have λ1 = λ2 = 0, substituting which 1 2 into the first equation in (8) we know that αm = α1 . To warrant (1−s )v (1−s )v that α 1 is within ( v −sv 2 p, p), we need to have Vm ( v −sv 2 p) > 0 and Vm ( p) < 0, which reduces to r1 < r < r2 .

if p ≤ (1 − s )v2 ,

Because h(r1 , γ ) is decreasing in γ , we have

7

This completes the proof.



Theorem 1 shows that the profitability of the secondary market has a direct impact on the manufacturer’s best selling strategy. That is, given the demand from the secondary market being exogenous, the manufacturer tends to offer a higher exchange discount (so as to induce more exchanges) if the unit revenue from remanufactured products is high. More specifically: (i) if the unit revenue is sufficient low (i.e., r ≤ r1 ), the manufacturer will choose the lowest available exchange discount, such that the portion of exchanges reduces to zero; (ii) if the unit revenue is sufficient high (i.e., r ≥ r2 ), the manufacturer will choose to offer the highest available exchange discount, such that a maximal portion of exchanges can be realized. (When this happens, no existing customers will choose to buy a new product if (1 − s )v2 ≤ p, and every existing customers will either engage in the EON program or buy a new product if p < (1 − s )v2 .) ∗ equals the lower bound (1−s )v2 p, the manRecall that if αm v1 −sv2 ufacturer actually does not launch any EON program. Therefore, Theorem 1 suggests, under certain conditions, the manufacturer could be even less profitable if the EON program is offered. Specifically, only when the unit profit from the secondary market, r − (1−s )v c2 , is above a non-negative threshold value, v −sv 2 ( p + c1 − w ), 1 2 should the EON program be profitable. This implies, if the profitability from the secondary market is zero (or even negative), then the EON program will never be optimal for the manufacturer. This

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seems counter-intuitive, because one might expect that the manufacturer would benefit from the demand induction effect, even if he could not generate any profit from the secondary market. We could explain this phenomenon from the trade-off between the marginal revenue and marginal cost associated with the EON program. Supposing that the profit function (·) ≡ 0 in Eq. (6), then (1−s )v we can show Vm (αm ) < 0 for any αm ≥ v −sv 2 p. Therefore, ignor1 2 ing the profit from the secondary market, any increase in the exchange discount will, indeed, decrease the profit of the manufacturer. Note that the threshold value r1 is decreasing in s. This implies the manufacturer would be more likely to benefit from the EON program when the level of substitutability is high. In other words, there exists a critical value for the substitution level, such that the manufacturer should adopt the EON program only when s is above this critical level. We will show this through numerical experiments in Section 5. In particular, when the old products are completely substitutable by the new one (i.e., s = 1), the EON program should be adopted by the manufacturer as long as he can generate a positive profit from the secondary market. For ease of later comparison, we denote the expected profits of the manufacturer and the retailer under the optimal decision as Vm and Rm respectively; i.e., ∗ Vm = Vm (αm ), and

Rm = ( p − w )

  ∗  p − αm μ0 + μ1 1 − . v1 − v2

(13)

By comparing Rm with R0 in Eq. (4), we clearly have Rm > R0 if )v2 αm∗ > (v11−s −sv2 p. Therefore, the EON program will always benefit the retailer; this is because, as a free-rider, the retailer expands her total sales while incurring no additional cost at all.

When the EON program is supposed to be launched by the retailer, she determines her exchange discount α r , with the objective of maximizing her total expected profit. Note that given the quantity of returned products being y, her maximal expected profit from the secondary market is (y) as well. Therefore, the retailer’s total expected profit as function of α r , denoted as Rr (α r ), is:







+ ( p − w − αr )D1 γe (αr ) + (D1e (αr ))

   p − αr μ0 + μ1 1 − v1 − v2  α  p−α



r3 := h−1

 



wμ1 γ = 0 = c2 +

( 1 − s )v2 w, v1 − sv2

(17)

if p ≤ (1 − s )v2 , (18) otherwise.

Theorem 2. Define α 2 as the unique solution of the first-order con dition Rr (αr ) = 0. In the retailer-initiated scenario, the optimal exchange discount, denoted as αr∗ , exhibits the following structure:

⎧ (1−s)v2 ⎨ v1 −sv2 p αr∗ = α2 ⎩ ( 1 − s )v2 ∧ p

i f r ∈ [c2 , r3 ], i f r ∈ ( r3 , r4 ),

(19)

otherwise;

That is, αr∗ equals the lower-bound v −sv 2 p if and only if r ≤ r3 ; αr∗ 1 2 equals the upper-bound (1 − s )v2 ∧ p if and only if r ≥ r4 ; αr∗ equals α 2 if and only if r ∈ (r3 , r4 ). Proof. We only prove for the case p ≤ (1 − s )v2 (the case p > (1 − s )v2 can be proven similarly). We first show the necessary part. Recall that v2 < v1 ; clearly, in the solution of Eqs. (16), the dual variables λ1 and λ2 cannot be both positive. We discuss based on the following three possibilities:

r

•

(14)

Note that the retailer’s profit function Rr (α ) differs from Vm (α ) only in the profit from the primary market. Therefore, by conducting a similar analysis as that in Section 3.1, we can characterize the optimal exchange discount αr∗ for the retailer. Specifically, the first derivative of Rr (α r ) is

 v1 − sv2 2αr μ1 − v (v − v )(1 − s )   2 1  2  r F¯2 xγe (αr ) − c2 x f1 (x )dx .



(1−s )v

If αr = v −sv 2 p, we have λ1 ≥ 0 and λ2 = 0; substituting which 1 2 (1−s )v into the first equation in (16), we know that R r ( v −sv 2 p) ≤ 0, 1 2 which reduces to r ≤ r3 . If αr = p, we have λ1 = 0 and λ2 ≥ 0, substituting which into the first equation in (16), we know that R r ( p) ≥ 0, which reduces to r ≥ r4 . (1−s )v If v −sv 2 p < αr < p, we have λ1 = λ2 = 0, substituting which 1 2 into the first equation in (16) we know that αr = α2 . To warrant (1−s )v (1−s )v that α 2 is within ( v −sv 2 p, p), we need to have R r ( v −sv 2 p) > 1

2

0 and R r ( p) < 0, which reduces to r3 < r < r4 .

1

2

We next show the sufficient part. •

If r ≤ r3 , because h(r, 0) is increasing in r, we can easily have (1−s )v Rr ( v −sv 2 p) ≤ 0. Note that Rr (α r ) is concave, therefore, Rr (α r ) 1

q

2

(1−s )v

is decreasing in the entire domain [ v −sv 2 p, p]. As a result, the 1 2 optimal exchange rate that maximizes Rr (α r ) is given by αr∗ =

γe ( α r )

0

(15)

(1−s )v2 v1 −sv2 p.

•



Because Rr (αr ) is decreasing α r , the retailer’s profit function Vr (α r ) is concave. As a result, her optimal exchange discount within do(1−s )v main [ v −sv 2 p, (1 − s )v2 ∧ p], is uniquely determined by the KKT 1

2

Following a similar analysis as that of Lemma 2, we can show r3 < r4 . The following theorem characterizes the optimal exchange discount decision of the retailer.

0

2p − w Rr (αr ) = μ − v1 − v2 1

 ( 1 − s )v

⎧ v1 − sv2 )v2 ⎪ h−1 2 pμ1 − (v11−s (2 p − w ) ⎪ −sv2 ⎪ ⎪   ⎪  ⎪ p ⎨ μ1 γ = (1−s )v2  r4 := )v2 −1 ⎪ h 2(1 − s )v2 μ1 − (v11−s ⎪ −sv2 ⎪ ⎪   ⎪ ⎪ ⎩ (2 p − w )μ1 γ = v1 −sv2 −p v 1 −v 2

•

− αr μ1 − ( 1 − s )v2 v1 − v2

∞   +  xγe (αr ) f1 (x )dx.



(16)

where Rr is given by (15). To describe the solution of the above equations, we define the following two critical values:

•



= ( p − w)

r

⎧ ⎨Rr (αr ) = −λ1 + λ2 , )v2 λ1 αr − (v11−s p = 0, −sv2 ⎩ λ2 ((1 − s )v2 ∧ p − αr ) = 0;

(1−s )v

3.2. The retailer-initiated scenario

Rr (αr ) = E ( p − w ) D0 + D1 γn (αr )

conditions. Again, if λ1 and λ2 are the respective dual variables (1−s )v corresponding to boundary conditions αr − v −sv 2 p ≥ 0 and (1 − 1 2 s )v2 ∧ p − αr ≥ 0, then the retailer’s optimal exchange discount, αr∗ , is the unique solution of the following equations:

2

If r ≥ r4 , because h(r, (1−sp )v ) is increasing in r, we can eas2 ily have Rr ( p) ≥ 0. Note that Rr (α r ) is concave, therefore, Rr (α r ) (1−s )v

is increasing in the entire domain [ v −sv 2 p, p]. As a result, the 1 2 optimal exchange rate that maximizes Rr (α r ) is given by αr∗ = p.

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If r3 < r < r4 , by conducting a similar analysis, we know that (1−s )v Rr ( v −sv 2 p) > 0 and Rr ( p) < 0. Due to the concavity of Rr (α r ), 1

2

(1−s )v

we know that Rr (α r ) is increasing in [ v −sv 2 p, α2 ] whereas it is 1 2 decreasing in [α 2 , p]. As a result, we have αr∗ = α2 . This completes the proof.



Theorem 2 shows that when the EON program is launched by the retailer, her optimal exchange discount has a similar structure as that in the manufacturer-initiated scenario. However, the detailed values and corresponding boundary conditions could be different. Similar to the manufacturer-initiated scenario, the magnitude of the unit revenue from the secondary market determines whether or not it is profitable to launch the EON program on the retailer side. Specifically, only when the unit profit (denoted by (1−s )v r − c2 ) is greater than a positive value, v −sv 2 w, should the retailer 1 2 launch the EON program. Therefore, if the secondary market does not have any profit potential, it would be never optimal for the retailer to launch the EON program; this result can be obtained by conducting marginal analysis as well. Again, the threshold value is decreasing in s, which means the retailer is more likely to benefit from the EON program when the old and new products are highly substitutable with each other. Denote the expected profits of the manufacturer and the retailer under the optimal decision as Vr and Rr respectively; i.e.,

Rr = Rr (αr∗ ), and Vr = (w − c1 )

   p − αr∗ μ0 + μ1 1 − . v1 − v2

(20)

By comparing Vr with V0 in Eq. (4), we clearly have Vr > V0 if )v2 αm∗ > (v11−s −sv2 p. Therefore, the EON program launched by the retailer will always benefit the manufacturer because the manufacturer becomes a free-rider in the retailer-initiated scenario. 3.3. Comparisons of the two business models Having obtained the optimal decisions for the manufacturerand retailer-initiated scenarios in the previous subsections, we now conduct a comparison between them and show how the initiator of the EON program will impact on the profitability of respective supply chain members. First, by the assumption that the remanufacturing cost (c2 ) are identical in the two scenarios, the remanufacturing quantity decisions in the second stage are the same for the manufacturer and the retailer, for any given quantity of returned products. The relationship between the optimal exchange ∗ and α ∗ , are presented in the following discount decisions, αm r Proposition. Proposition 1. The optimal exchange discounts in the two EON mod∗ and α ∗ , have the following relationship: (i) if w − c ≥ p − w, els, αm 1 r ∗ ≥ α ∗ ; and (ii) otherwise if w − c ≤ p − w, we have we have αm 1 r αm∗ ≤ αr∗ . Proof. From Eqs. (7) and (15), the difference between the derivatives of Vm (α ) and Rr (α ) is:



Vm (α ) − Rr (α ) =

( w − c1 ) − ( p − w ) μ1 . v1 − v2



Considering the case w − c1 ≥ p − w, we have Vm (α ) − Rr (α ) ≥ 0. (1−s )v

∗ ≥ α ∗ . (ii) Therefore: (i) If αr∗ = v −sv 2 p, we apparently have αm r 1 2 (1−s )v Otherwise if αr∗ > v −sv 2 p, from the proof of Theorem 2 we know Rr (αr∗ )

1

2

Vm (αr∗ ) ≥ Rr (αr∗ ) ≥ 0; i.e., Vm (α ) is ∗ αr . Therefore, αm∗ ≥ αr∗ . This com-

that ≥ 0. As a result, non-decreasing at point α = pletes the proof for part (i). Part (ii) can be proven in a similar way. This completes the proof. 

9

Note that (w − c1 ) is the unit profit of the manufacturer, and ( p − w ) is the unit profit of the retailer. Proposition 1 implies that when the EON program is launched by a supply chain member that has a higher unit profit, a higher exchange discount should be offered to existing customers. This is because a higher unit profit provides sufficient room for the manufacturer (or retailer) to discount the exchange sales. We remark that if the unit remanufacturing costs in the two EON models are not identical, the comparison ∗ and α ∗ may be much more complicated than that of between αm r Proposition 1. This is because the maximal remanufacturing quantity for the two models will be different. From the characterization of the optimal decisions in the two scenarios, clearly, the manufacturer (or retailer) will be better off (or, at least not worse-off) if he (or she) launches the EON program. A natural question is: as compared to being a free-rider, will the manufacturer/retailer still be better off if he/she personally launches the EON program? That is, is Rr always no less than Rm and Vm always no less than Vr ? One might expect so because being a program initiator, the manufacturer/retailer gains control over the EON program and optimizes his/her decisions more proactively. However, a simple analysis could show that this intuition might not be true. For example, consider the case p − w < w − c1 : if the unit revenue in the secondary market r lies between r1 and r3 , i.e., r1 < r < r3 , from Theorems 1 and 2 we know that the EON program will be effective only in the manufacturer-initiated scenario. Therefore, the retailer’s expected profits satisfies

Rm > R0 and Rr = R0 , which induces to Rr < Rm . We can also show that in certain conditions, the manufacturer might even benefit more if he is a freerider, instead of being the initiator of the EON program. In particular, if Vm < Vr and Rr < Rm , then both supply chain members will choose to wait for the other firm to launch the EON program. As a result, nobody will actually launch the program at all and neither firm benefits. A next question is, from the perspective of the entire supply chain, which of the two decentralized business models will be more profitable? For comparison purposes, let (α ) be the total expected profit of the manufacturer and retailer in the two scenarios, given that the exchange discount is α ; i.e.,

(α ) = Vm (α ) + Rm (α ) = Vr (α ) + Rr (α )   = E ( p − c1 )D1n (α ) + ( p − c1 − α )D1e (α ) + (D1e (α ))    p−α = ( p − c 1 ) μ0 + μ1 1 − v1 − v2   p−α α − αμ1 − ( 1 − s )v2 v1 − v2

∞   +  xγe (α ) f1 (x )dx. (21) 0

∗ ) := V + R and (α ∗ ) := V + R The relationship between (αm m m r r r is presented in the following Proposition.

Proposition 2. When the EON program is launched by a supply chain member that has a higher unit profit, the total profit of the manufacturer and retailer would be higher; that is: ∗ ) ≥ (α ∗ ); and (i) if w − c1 ≥ p − w, we have (αm r ∗ ) ≤ (α ∗ ). (ii) if w − c1 ≤ p − w, we have (αm r

Proof. By comparing Eq. (21) with (6), we have, for i = m, r:

  p − αi∗  (αi∗ ) = ( p − w ) μ0 + μ1 1 − + Vm (αi∗ ). v1 − v2 ∗ ) and (α ∗ ) is: Therefore, the difference between (αm r ∗ ∗ αm − αr ∗ ∗ ∗ (αm ) − (αr ) = ( p − w ) μ + V (α ) − Vm (αr∗ ). v1 − v2 1 m m

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Consider the case w − c1 ≥ p − w. On the one hand, by ∗ ≥ α ∗ ; on the other hand, Proposition 1 we know that αm r ∗ ∗ ) ≥ V (α ∗ ). Theresince αm = argmax{Vm (α )} we have Vm (αm m r ∗ ) − (α ∗ ) ≥ 0. This completes the proof of part (i). Part fore, (αm r (ii) can be proven in a similar way.  Proposition 2 implies that from the supply chain’s perspective, it’s better that the EON program be launched by the firm that has a higher unit profit in selling new products. Given that customers always enjoy a higher exchange discount, we know that the social welfare is also better off if the EON program is launched by the high-profit firm. In cases when the firm with a higher unit profit prefers to be a free-rider (instead of launching the program by himself/herself), we can show that the other firm will choose to wait to be a free-rider as well (otherwise a contradictory to Proposition 2 occurs). That is, both firms may fall into a prisoner’s dilemma by choosing to wait for the other firm to launch the program. When this happens, it would be extremely important to motivate the supply chain members to actually initiate the program. Even if the equilibrium is that the higher-profit firm launches the EON program, the supply chain may still have potential in improving the overall profit. Therefore, an interesting question is: could the manufacturer and retailer adopt some form of coordinating contract so as to make the best from an EON program? We will investigate this question in the next section.

4. A collaborative EON program In this section we will devise a modified version of the EON program to motivate the manufacturer and retailer to coordinate in the decentralized supply chain. As a benchmark we first study the optimal decisions for the centralized supply chain where the manufacturer and retailer seek to optimize their joint profit.

⎧  )v2 ⎪ h−1 2 pμ1 − (v11−s ( 2 p − c1 ) ⎪ −sv2 ⎪ ⎪   ⎪  ⎪ p ⎨ μ1 γ = (1−s )v2  r6 := )v2 −1 ⎪ h 2(1 − s )v2 μ1 − (v11−s ⎪ −sv2 ⎪ ⎪   ⎪ ⎪ ⎩ (2 p − c1 )μ1 γ = v1 −sv2 −p v 1 −v 2

if p ≤ (1 − s )v2 , (23) otherwise.

The optimal exchange discount α c shares a similar structure as that ∗ and α ∗ , as presented in Theorem 3. of αm r Theorem 3. Define α 3 as the unique solution of the first-order condi tion  (α ) = 0. In the centralized supply chain, the optimal exchange discount α c exhibits the following structure:

⎧ (1−s)v2 ⎨ v1 −sv2 p αc = α3 ⎩ ( 1 − s )v2 ∧ p

i f r ∈ [c2 , r5 ], i f r ∈ ( r5 , r6 ),

(24)

otherwise; (1−s )v

That is, α c equals the lower-bound v −sv 2 p if and only if r ≤ r5 ; α c 1 2 equals the upper-bound (1 − s )v2 ∧ p if and only if r ≥ r6 ; α c equals α 3 if and only if r ∈ (r5 , r6 ). Clearly, the critical value r5 is less than r1 and r3 . This implies that the centralized system only requires a relatively mild condition to have the EON program adopted in practice, as compared to the manufacturer- and retailer-initiated scenarios. Therefore, even if the EON program is not profitable for the manufacturer and/or the retailer in the scenarios studied in Section 3, however, it could have potential in improving the profit of the entire supply chain. By comparing (α ) with Vm (α ) and Rr (α ), we know that for any given exchange discount α ,







 (α ) > Vm (α ) and  (α ) > Rr (α ) will always hold; this leads to the following proposition.

4.1. The centralized system as a benchmark Like the manufacturer- and retailer-initiated scenario, the centralized decision maker faces a two-stage decision problem: in the first stage, he/she determines the exchange discount to be offered to existing customers; and in the second stage, after observing the quantity of returned products, he/she determines the remanufacturing quantity and sells to the secondary market. Given the unit remanufacturing cost being c2 and the unit revenue of remanufactured products being r, the second-stage decision problem is the same as that studied in Section 3. Therefore, if the actual quantity of returned products is y, the optimal expected profit from the secondary market is (y). Conditioning upon the size of the existing customers D1 , the centralized decision maker’s expected profit as function of the exchange discount α , is therefore given by (α ) [refer to Eq. (21)]. Let

αc :=

{(α )}

argmax

)v2 α ∈[ (v1−s −sv p, (1−s )v2 ∧ p] 1

2

be the optimal exchange discount in the centralized system. It is trivial that (α ) differs from functions Vm (α ) and Rr (α ) in a linear function of α . Therefore, (α ) is concave, and its maximizer α c can be determined directly by using the KKT conditions. More specifically, (α ) is equivalent to Vm (α ) by replacing w with p in Eq. (6) or Rr (α ) by replacing w with c1 in Eq. (14). Once again, we need to define two critical values, r5 and r6 as follows:

r5 := h−1

 ( 1 − s )v

2

v1 − sv2

 



c1 μ1 γ = 0 = c2 +

( 1 − s )v2 c , v1 − sv2 1

(22)

Proposition 3. Compared to the manufacturer- and retailer-initiated scenarios, the decision maker will offer a higher exchange discount in ∗ , α ∗ ). the centralized supply chain; i.e., we have αc ≥ max(αm r ∗ (or α ∗ ) and α well explains why the deThe gap between αm c r centralized systems are not optimal from the perspective of the entire supply chain. Given that (α ) is concave, the chain performance would be even worse off if the exchange discount departs more significantly from the centralized decision α c . This implies, it is even worse that the EON program be launched by the firm that has a lower profit margin (Proposition 2). By offering a lower exchange discount, the program initiators in the two decentralized systems would capture less demand (i.e., less existing customers will become exchanges) and generate less profit from the secondary market (because less old products will be returned). In particular, given other parameters being fixed, the supply-chain profit in the retailer-initiated model will be even worse-off when the wholesale price w is high, and that in the manufacturer-initiated model will be even worse-off when the wholesale price w is low.

4.2. A collaborative EON program By Proposition 3, we know that to improve the performance of the supply chain, one need to induce the manufacturer or retailer to offer a higher exchange discount. More specifically, only when the exchange discount is increased to α c , would the maximal profit potential of the supply chain be realized. Similar to the majority of the coordination contracts proposed in the literature (refer to the survey paper by Cachon, 20 03 and Chen, 20 03), a possible direction for coordinating the supply chain is to share the

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market or supply risk among the supply-chain members so that the double-marginalization effect could be erased. Therefore, naturally, to motivate the manufacturer (or the retailer) to increase the exchange discount, the other firm (i.e., the retailer or the manufacturer) could offer to share a portion of the cost and risk involved in the EON program. In this section, we propose to adopt a collaborative business model. That is, the EON program is jointly launched by the manufacturer and retailer, instead of by a single party. By doing so, the decision makers are expected to maximize the total expected profit while improving their respective profits in the decentralized system. The collaborative business model can be regarded as a combination of the manufacturer- and retailer-initiated models studied in Section 3, which contains an exchange-discount-sharing contract and is introduced as follows. Suppose the manufacturer and the retailer launch an EON program together, and the exchange cost (i.e., the exchange discount α ) is shared between the two firms, with each party bearing a portion of β and 1 − β respectively (0 ≤ β ≤ 1). That is, while collecting one unit of old products at price α , α × β will be paid by the manufacturer and the rest be paid by the retailer. By doing so, the old products returned from the EON program would be jointly owned by the two firms. Naturally, any profit collected from the secondary market should be shared between them as well. Suppose given y units of old products are returned, in the corresponding expected profit (y), a portion of β goes to the manufacturer and the rest goes to the retailer. Clearly, the above contract is incentive compatible, because for each firm, his/her profit from the secondary market is in proportional to the corresponding exchange cost. Implementation of the contract could have two forms, depending on which firm is the decision maker. Specifically, if the exchange discount α and remanufacturing quantity Q are determined by the manufacturer, then we call the scenario as the manufacturer-led EON program, because it is a variant of the manufacturer-initiated model; otherwise if the decisions are made by the retailer, then the scenario is called the retailer-led EON program. In the following we investigate how the contract will impact the optimal decisions of the manufacturer and/or the retailer. We consider the manufacturer-led scenario first. In the second stage, because the profit from the secondary market is shared between the manufacturer and retailer, therefore, given y units of old products are returned, the manufacturer’s optimization problem is to maximize β E{r (D2 ∧ Q ) − c2 Q }, whose optimal solution is clearly Q∗ (y). Note that the manufacturer only pays βα for each exchange, his expected profit, denoted as V(α ), is

V (α ) = E{(w −c1 )D1n (α ) + (w −c1 − βα )D1e (α ) + β (D1e (α ))}    p−α = ( w − c 1 ) μ0 + μ1 1 − v1 − v2   p−α α − βαμ1 − ( 1 − s )v2 v1 − v2

∞   +β  xγe (α ) f1 (x )dx. (25) 0

Alternatively, if the decisions are to be made by the retailer (i.e., in the retailer-led scenario), the retailer’s expected profit as function of the exchange discount α , is

R ( α ) = E{ ( p − w ) D1n ( α ) + [ p − w − ( 1 − β ) α ]D1e ( α ) + (1 − β )(D1e (α ))}

   p−α μ0 + μ1 1 − v1 − v2   p−α α − (1 − β )αμ1 − ( 1 − s )v2 v1 − v2

∞   + (1 − β )  xγe (α ) f1 (x )dx.

= ( p − w)

0

(26)

11

Clearly, if β = 1, then the manufacturer-led scenario reduces to the manufacturer-initiated scenario; and if β = 0, then the retailerled scenario reduces to the retailer-initiated scenario. The following Theorem shows that the proposed exchange-discount-sharing contract, while being implemented in both the manufacturer- and retailer-led scenarios, could motivate the manufacturer and retailer to act in a coordinated manner. Theorem 4. Suppose the exchange-discount-sharing contract is adopted. If the factor β is set at

β=

w − c1 , p − c1

(27)

then, in both the manufacturer- and retailer-led scenarios, the optimal exchange discount should be set at α c . As a result, the maximal profit potential of the supply chain could be realized; i.e., the total profit of the manufacturer and retailer is equal to (α c ). Proof. We first consider the manufacturer-led scenario. By substituting (27) into (25), we have

V (α ) = β × (α ). Therefore, the optimal exchange discount that maximizes V(α ) is exactly α c (note that β is independent of α ). As a result, the entire supply chain will perform the same as the centralized system. The retailer-led scenario can be proven in a similar way. This completes the proof.  Theorem 4 shows that by adopting the exchange-discountsharing contract in either scenario, as long as the sharing factor β satisfies relationship (27), the manufacturer and the retailer’s expected profits, V(α c ) and R(α c ), are

V (αc ) = β (αc ), and R(αc ) = (1 − β )(αc ); i.e., the contract will induce the manufacturer and retailer’s share of profit in the entire supply chain to be β and (1 − β ), respectively. w−c We have shown that if β is set at p−c 1 , the exchange-discount1 sharing contract would align the decentralized system with the centralized one. However, this contract might not necessarily be accepted by the supply chain members. For example, if β (α c ) is even less than Vm , then the manufacturer would be unwilling to launch the collaborative EON program together with the retailer. Instead, he would prefer to launch the program by himself. Similarly, if (1 − β )(αc ) is less than Rm , then the retailer would be unwilling to share the exchange discount cost and secondary profit with the manufacturer; instead, she would prefer to allow the manufacturer launch the program and become a freerider. Therefore, to guarantee that the contract be acceptable, both supply chain members should benefit from coordination. Motivated by the formula in (27), we suggest that the manufacturer adjust his wholesale price while implementing the exchangediscount-sharing contract. That is, suppose the wholesale price, de˜ , is given by formula noted as w

˜ = c1 + β˜ ( p − c1 ), 0 ≤ β˜ ≤ 1, w

(28)

where the value of β˜ is determined in the negotiation process between the manufacturer and retailer. Specifically, if the manufacturer has a relatively stronger bargaining power, then β˜ will be even closer to 1; otherwise β˜ will be even closer to zero. Once β˜ is determined, then the manufacturer and retailer are suggested to adopt the exchange-discount-sharing contract while launching the EON program (in either the manufacturer- or retailer-led scenario), during which the sharing factor β is set at β˜ . Apparently, this contract will coordinate the supply chain. Moreover, in the manufacturer-led scenario, as long as

Vm

(αc )

≤ β˜ ≤ 1 −

Rm

(αc )

,

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Table 2 Numerical results with different level of substitution. s

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Without EON

Manufacturer-initiated

Retailer-initiated

R0

αm∗

Manufacturer

Retailer

αr∗

Manufacturer

Retailer

αc

Improvement

294.44 282.56 269.51 255.13 239.19 221.43 201.52 179.03 153.45 124.07

88.33 84.77 80.85 76.54 71.76 66.43 60.45 53.71 46.03 37.22

1.131 1.088 1.039 0.982 0.913 0.827 0.723 0.594 0.399 0.199

1.84% 2.70% 3.97% 5.85% 8.68% 12.97% 19.57% 30.06% 40.41% 42.30%

7.40% 8.85% 10.46% 12.23% 13.96% 15.35% 16.38% 16.65% 10.69% 4.67%

1.022 0.963 0.907 0.866 0.820 0.765 0.688 0.576 0.399 0.199

0.00% 0.00% 0.67% 3.14% 6.19% 9.75% 12.90% 14.63% 10.69% 4.67%

0.00% 0.00% 0.05% 1.16% 4.75% 13.26% 30.84% 63.63% 109.77% 130.11%

1.194 1.144 1.086 1.019 0.939 0.846 0.735 0.599 0.399 0.199

3.63% 4.59% 5.89% 7.67% 10.16% 13.72% 18.97% 27.05% 33.55% 33.62%

then both the manufacturer and retailer will benefit from the coordinating contract (as compared to the manufacturer-initiated scenario). Similarly, in the retailer-led scenario, as long as

Vr

(αc )

Centralized

V0

≤ β˜ ≤ 1 −

Rr

(αc )

,

then both the manufacturer and retailer will benefit from the coordinating contract (as compared to the retailer-initiated scenario). Finally, we remark that by adopting a coordinated EON contract, the welfare of customers will be improved (compared to the two decentralized supply chain) as well; this is because the existing customers can enjoy a higher exchange discount (Proposition 3). 5. Numerical results and discussion In this section, we report the results of our computational studies, which we have conducted to evaluate the profit potential by launching an EON program. The magnitude of some of the major parameters are designed, roughly, in proportional to the real data of Apple’s iPhone. As was estimated in Sherman (2013), in the total cost (or, the selling price) of 650 dollars inside an iPhone 5 (i.e., the “new product” in our model), the manufacturing, operating expenses, wholesale to retail markup are 226.85 dollars, 61.18 dollars, and 68.90 dollars, respectively. By normalizing the unit production cost (= 226.85 dollars + 61.18 dollars) to 1, we set the parameters in the base numerical experiment at ( p, w, c1 ) = (2.3, 2.0, 1.0 ) to approximate the price/cost structure. When Apple first offered a trade-in program for iPhone 5 in early 2013, the selling price of the refurbished iPhone 4s (i.e., the “old product” in our model) was around 300 dollars. Therefore, we let r = 1.0 in the numerical experiments. Given that the refurbishing costs are largely labor costs, we let c2 = 0.2. We suppose the size of potential existing customers (D1 ) and the secondary market demand (D2 ) follow normal distributions, with mean and standard variance being (μ1 , σ 1 ) and (μ2 , σ 2 ) respectively. The values of other parameters are the following: (v1 , v2 ) = (4.5, 2.0 ); s = 0.6; (μ0 , μ1 , μ2 ) = (50, 500, 200 ); and (σ1 , σ2 ) = (100, 50 ). Our nu∗ merical result indicates that the optimal exchange discount (αm ∗ and αr ) of the base model is around 0.7; this is almost consistent with the actual trade-in price of iPhone 4s of about 200 dollars (Burrows, 2013). Within each group of experiments, we alter the value of one parameter and calculate the optimal performance for the scenario without launching an EON program, the manufacturer- and retailer-initiated scenarios, and the centralized system, respectively. Due to the space limitations, besides listing the optimal exchange discount for different scenarios, we simply report the profit improvement (in percentage) of the manufacturer (and retailer) over V0 (and R0 ) for the two decentralized systems, and the overall profit improvement of the entire supply chain (over V0 + R0 ) for the centralized system.

5.1. Impact of the substitution level We first evaluate the impact of the level of substitution between the old and new products; a sample of the numerical results with different values of s is reported in Table 2. As can be seen intuitively, as the level of substitution increases, the decision maker in all of the scenarios will be less inclined to offer a high exchange discount. This is because, for any given exchange discount, more customers will choose to engage in the EON program and less customers will choose to buy a new product(see Fig. 1) when the value of s is high. Therefore, a lower exchange discount should be adopted to balance the overall demands. As compared to the scenario without launching an EON program, the manufacturer and retailer will benefit more significantly from the program in both scenarios when s is high; this is consistent with the analysis presented in Sections 3.1 and 3.2. In particular, the optimal exchange discount may even exceed the selling price of the remanufactured product in the secondary market. This is because the program initiator can still benefit from selling more new products. Note that in this group of experiments, the manufacturer has a much higher profit margin in selling new products. As a result, the manufacturer is better off by launching an EON program by himself, instead of waiting to be a free-rider. The retailer, however, prefers to launch an EON program only when the substitution level s is high. The results show that when s ≤ 0.1, the retailer will suffer from a loss if she launches an EON program. Another interesting pattern uncovered from Table 2 is that the free-rider’s profit improvement may not necessarily to be increasing in s. In fact, when s is high, they will only benefit slightly from being a free-rider. For example, when s = 0.9, both the manufacturer and the retailer will prefer to launch the EON program by himself/herself, because being a free-rider only increases profit by 4.67%. When this happens, the coordinating contract as proposed in Section 4.2 would be even more useful in motivating the two parties to jointly launch the EON program. The last column of Table 2 shows that a coordinated EON program would be much more profitable, from the perspective of the supply chain, when the substitution level is high. This is because a higher s implies the existing customers are less inclined to buy a new product in regular selling; as a result, the EON program would be more efficient in inducing more sales of new products. 5.2. Impact of the prices In the second group of experiments, a sample of the numerical results with different values of p and w is reported in Table 3, which reveals the following findings. On the one hand, given the wholesale price w being fixed, retail price p is one of the major factors that determines the demand in the primary market. By Fig. 1, when p is high, a higher exchange discount is needed to induce the same level of new product sales. As a result, the optimal exchange

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13

Table 3 Numerical results with different values of p and w. p

2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.3 2.3 2.3 2.3 2.3 2.3 2.3

w

2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.6 1.7 1.8 1.9 2.0 2.1 2.2

Without EON

Manufacturer-initiated

Retailer-initiated

Centralized

V0

R0

αm∗

Manufacturer

Retailer

αr∗

Manufacturer

Retailer

αc

Improvement

231.82 216.67 201.52 186.36 171.21 156.06 140.91 120.91 141.06 161.21 181.36 201.52 221.67 241.82

23.18 43.33 60.45 74.55 85.61 93.64 98.64 141.06 120.91 100.76 80.61 60.45 40.30 20.15

0.682 0.702 0.723 0.743 0.762 0.781 0.800 0.705 0.709 0.714 0.719 0.723 0.727 0.731

19.93% 19.74% 19.57% 19.41% 19.28% 19.18% 19.13% 22.29% 21.22% 20.48% 19.95% 19.57% 19.30% 19.10%

14.93% 15.60% 16.38% 17.28% 18.22% 19.35% 20.58% 14.59% 14.99% 15.48% 15.98% 16.38% 16.77% 17.17%

0.639 0.663 0.688 0.712 0.736 0.760 0.785 0.709 0.705 0.699 0.694 0.688 0.682 0.675

11.22% 12.00% 12.90% 13.95% 15.19% 16.66% 18.45% 14.99% 14.59% 13.99% 13.50% 12.90% 12.31% 11.61%

80.42% 43.02% 30.84% 25.01% 21.78% 19.91% 18.90% 21.22% 22.29% 23.89% 26.43% 30.84% 39.97% 68.01%

0.686 0.710 0.735 0.759 0.783 0.799 0.800 0.735 0.735 0.735 0.735 0.735 0.735 0.735

19.49% 19.11% 18.97% 19.05% 19.35% 19.84% 19.73% 18.97% 18.97% 18.97% 18.97% 18.97% 18.97% 18.97%

Table 4 Numerical results with different values of v1 and v2 .

v1

4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.5 4.5 4.5 4.5 4.5 4.5 4.5

v2

2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.7 1.8 1.9 2.0 2.1 2.2 2.3

Without EON

Manufacturer-initiated

Retailer-initiated

Centralized

V0

R0

αm∗

Manufacturer

Retailer

αr∗

Manufacturer

Retailer

αc

Improvement

166.67 179.03 190.63 201.52 211.76 221.43 230.56 219.54 213.74 207.74 201.52 195.06 188.36 181.41

50.00 53.71 57.19 60.45 63.53 66.43 69.17 65.86 64.12 62.32 60.45 58.52 56.51 54.42

0.769 0.753 0.737 0.723 0.709 0.696 0.683 0.612 0.648 0.685 0.723 0.760 0.798 0.837

21.54% 20.75% 20.11% 19.57% 19.12% 18.74% 18.40% 23.02% 21.87% 20.72% 19.57% 18.42% 17.26% 16.09%

21.27% 19.31% 17.70% 16.38% 15.26% 14.22% 13.32% 13.26% 14.21% 15.27% 16.38% 17.52% 18.70% 19.92%

0.728 0.714 0.700 0.688 0.675 0.664 0.653 0.591 0.623 0.656 0.688 0.718 0.748 0.777

15.68% 14.57% 13.66% 12.90% 12.17% 11.54% 11.00% 11.55% 12.04% 12.59% 12.90% 13.03% 12.93% 12.40%

28.14% 29.14% 30.03% 30.84% 31.57% 32.23% 32.84% 47.78% 42.08% 36.43% 30.84% 25.36% 20.05% 15.02%

0.782 0.766 0.749 0.735 0.720 0.707 0.694 0.620 0.658 0.696 0.735 0.773 0.813 0.854

21.69% 20.60% 19.71% 18.97% 18.34% 17.80% 17.34% 20.85% 20.20% 19.58% 18.97% 18.38% 17.79% 17.22%

∗ , α ∗ , and α ) is increasing in p; discount in each scenarios (i.e., αm c r this is consistent with Table 3. In particular, the table shows that as p increases, the EON program initiator (i.e., the manufacturer or the retailer) will benefit less from the program because she has to pay more to motivate existing customers to upgrade their product. However, the free-rider (i.e., the retailer or the manufacturer) will benefit more significantly as p increases. Therefore, when the selling price is sufficiently high, both supply chain members prefer to be a free-rider, instead of launching the EON program by himself/herself. On the other hand, given the retail price p being fixed, wholesale price w only impacts the unit profit of both supply chain members. Because the manufacturer has a higher margin and the ∗ is retailer has a lower margin when w is high, we know that αm increasing and αr∗ is decreasing in w; this is consistent with the intuition behind Proposition 1. Consequently, the manufacturer is more willing to launch the EON program when w is low, but the retailer is more willing to launch the EON program when w is high. Note that w is an internal transfer payment between the supply chain members; as a result, it does not impact the optimal decisions in the centralized supply chain at all. The last column shows that the profit potential by adopting a coordinated EON program is rather significant, with all of the improvements being around 19%.

5.3. Impact of the quality indices In the third group of experiments, we alter the values of v1 and

v2 , and report a sample of the results in Table 4.

It can be seen that as the “quality gap” between the old and new products increases (i.e., as v1 increases or v2 decreases), the

manufacturer and/or the retailer will be less inclined to offer a high exchange discount in either scenario. This is because when v1 is high or when v2 is low, the decision maker can achieve a same level of total demand (refer to Fig. 1) by offering a lower discount exchange. In this group of experiments, when the manufacturer launches the EON program, he enjoys a higher profit improvement (in percentage) when v1 and v2 is low. This implies the relative profit improvement of the manufacturer does not necessarily to be monotonic in the quality gap between the two generations of products. This phenomenon is due to the fact that v0 is increasing in v1 and decreasing in v2 . Again, the last column in Table 4 shows that the maximal profit potential by adopting an EON program is rather significant, with the average improvement being 19.10%. In particular, if we measure the profit improvement of the centralized system over the two decentralized scenarios, we can see that the improvement is more significant when v1 is low and/or v2 is high. This implies that coordination could be even more necessary when the new generation of product is only mildly superior to the old one. 5.4. Impact of the market size In the last group of experiments, we investigate the impact of the market size, as measured by the mean value of D1 and D2 ; the results with different values of μ1 and μ2 are reported in Table 5, which reveals the following findings. First, as can be seen, in each scenario the optimal exchange discount is decreasing in μ1 and increasing in μ2 . This can be explained by the following. Suppose the size of the potential existing market becomes larger, then more customers will engage in

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Table 5 Numerical results with different values of μ1 and μ2 .

μ1 200 300 400 500 600 700 800 500 500 500 500 500 500 500

μ2 200 200 200 200 200 200 200 50 100 150 200 250 300 350

Without EON

Manufacturer-initiated

Retailer-initiated

Centralized

V0

R0

αm∗

Manufacturer

Retailer

αr∗

Manufacturer

Retailer

αc

Improvement

110.61 140.91 171.21 201.52 231.82 262.12 292.42 201.52 201.52 201.52 201.52 201.52 201.52 201.52

33.18 42.27 51.36 60.45 69.55 78.64 87.73 60.45 60.45 60.45 60.45 60.45 60.45 60.45

0.785 0.765 0.744 0.723 0.707 0.692 0.679 0.601 0.645 0.686 0.723 0.756 0.782 0.796

17.62% 19.56% 20.17% 19.57% 19.29% 18.46% 17.56% 3.10% 9.74% 15.74% 19.57% 22.50% 23.78% 24.23%

16.42% 17.63% 17.38% 16.38% 15.43% 14.31% 13.24% 4.27% 8.63% 12.70% 16.38% 19.65% 22.23% 23.62%

0.717 0.709 0.700 0.688 0.679 0.669 0.660 0.581 0.623 0.659 0.688 0.709 0.716 0.717

11.50% 12.86% 13.27% 12.90% 12.53% 11.86% 11.16% 2.28% 6.45% 10.02% 12.90% 14.99% 15.68% 15.78%

25.96% 29.28% 31.13% 30.84% 31.56% 30.87% 29.92% 2.69% 14.85% 25.74% 30.84% 34.00% 34.44% 34.49%

0.800 0.784 0.758 0.735 0.716 0.700 0.686 0.609 0.654 0.696 0.735 0.771 0.800 0.800

17.52% 19.31% 19.68% 18.97% 18.51% 17.59% 16.66% 3.47% 9.58% 15.16% 18.97% 22.02% 23.64% 24.18%

the EON program if the exchange discount remains unchanged; as a result, more returned old items will have to be discarded (because the firm will remanufacture up to a level q, which is independent of the size μ1 ). Based on the trade-off between the primary and secondary market, the decision makers will naturally decrease the optimal exchange discount. Similarly, a higher value of μ2 implies the secondary market has greater profit potential and the remanufacturing-up-to-level will be high; consequently, a higher exchange discount should be offered so that more old items could be collected to satisfy customers from the secondary market. Second, as the size of the existing customers μ1 increases, both program initiators’ profit improvement are shown to be first increasing and then decreasing. This can be explained by the following. When μ1 is relatively small, the quantity of collected old items is the dominating factor that determines the profit in the secondary market. As a result, an increase in μ1 leads to a significant profit improvement in the secondary market. However, when μ1 is relatively large, an increasing in μ1 hardly increases the profit in the secondary market because the remanufacturing-up-to-level q is the dominating factor that determines the profit in the secondary market. On the other hand, as the size of the secondary market μ2 increase, both program initiators’ profit improvement are shown to be monotonically increasing; however, the improvement becomes flat when μ2 is sufficiently large. The reason behind this is similar: when μ2 is low, the remanufacturing-up-tolevel q is the bottle neck of the secondary market, and when μ2 is high, the quantity of collected old items becomes the bottle neck. Moreover, the benefit from coordination could be rather significant, especially when the size of existing customers is medium and/or the size of the secondary market is relatively large; this is consistent with one’s intuition. 6. Concluding remarks In this paper we have considered the practice of exchange-oldfor-new, in which the manufacturer/retailer offers to trade-in one unit of old product, at a specified exchange discount, so as to expand the demand for new product generation. By considering a decentralized supply chain consisting of one manufacturer and one retailer, we investigate two variants of models, in which the EON program is launched by the manufacturer and retailer, respectively. Based on the trade-off between the revenue from the primary market and the secondary market, we characterize the optimal exchange discount and remanufacturing quantity decisions for each model and conduct an in-depth comparison between them.

It is shown that each supply chain member may prefer to wait for the other firm to launch an EON program, because he/she can benefit more significantly from being a free-rider. Moreover, compared to the centralized supply chain, the decision maker in the manufacturer- and retailer-initiated EON programs tends to offer a lower exchange discount; this impacts the profit of the entire supply chain. Therefore, we propose to adopt a collaborative EON program to induce the manufacturer and retailer to act in a coordinated way so as to improve the overall performance. In the proposed exchange-discount-sharing contract, the wholesale price is determined by negotiation, together with two parties sharing the exchange cost and corresponding secondary profit. Major findings from the numerical experiments include: (1) the exchange discount offered by each firm may even exceed the selling price of refurbished products in the secondary market; (2) each firm may be more willing to be a free-rider, for example, when the new product is associated with a high selling price; and (3) coordination between the supply chain members could improve their overall profit rather significantly, especially when the substitution level is high, when the size of existing customer is medium, and/or when the size of the secondary market is relatively large. Using EON programs to manage the demand provides vast opportunities for future research. First, in this study we only consider one type of old products, which can be returned for a price discount. In reality, however, different customers may have different types of old products. Therefore, it would be much more interesting to extend our model to a general case with multiple old products, which have different qualities and could be traded-in at different prices. Also, the new generation of product can have more than one type, like the case of iPhone 6 and iPhone 6+. The choice behavior of customers will be more complicated. Second, our model is targeted at a make-to-order or assemble-to-order scenario, therefore the manufacturing quantity of new products is not taken as a decision variable. Studying the exchange-related decisions considering production lead-time is of considerable research interest. Third, considering the choice behavior of customers, we know that the demand is jointly determined by the selling price of new products and exchange discount. Therefore, if the prices could be jointly optimized, instead of supposing the selling price p being exogenous, the manufacturer/retailer could, apparently, improve his/her performance. Specifically, it would be interesting to figure out how the incorporation of an EON program will impact the selling price of the new products. Finally, the model could be extended to more complicated situations, including multiple competing manufacturers, multiple competing retailers, and multiple periods (in which the value of products may vary over time).

Please cite this article as: Y. Xiao, Choosing the right exchange-old-for-new programs for durable goods with a rollover, European Journal of Operational Research (2016), http://dx.doi.org/10.1016/j.ejor.2016.11.002

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ARTICLE IN PRESS Y. Xiao / European Journal of Operational Research 000 (2016) 1–15

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Please cite this article as: Y. Xiao, Choosing the right exchange-old-for-new programs for durable goods with a rollover, European Journal of Operational Research (2016), http://dx.doi.org/10.1016/j.ejor.2016.11.002