The optimal pricing for a trade-in program in remanufacturing supply chain

We develop a model to investigate the optimal pricing for a trade-in program in remanufacturing supply chain. Customer choice behavior is introduced, and the generalized Nash bargaining framework is adopted to model the sale agent’s trade-in program in the business-to-business (B2B) market. Moreover, we analyze the impacts of bargaining power of customers on equilibrium decisions and firm profits.


Introduction
A trade-in program is an arrangement in which customers purchase a new product at a reduced price by returning an old product [1], and it is a popular approach to expanding product sales and stimulating market demand [2,3]. For example, Apple provides trade-in programs both in-store and online to encourage customers to exchange used products for credits to purchase new iPads,iPhones and Macs [4]. In China, Suning, JD.com and other online retailers offer digital products, computers, televisions, and other home appliances for trade-in programs. Other examples can be found on a wide variety of company websites, ranging from the highly desirable luxury durable goods manufacturers such as Audi, BMW, and Mercedes-Benz to the producers of the quasi-durable goods like HP, IBM, and Xerox [5].
Recently, with the increase in the acceptance of remanufactured products and supported by the push-up policy, the remanufacture of used products has become an important production activity for many companies. As the remanufacturing industry and trade-in strategy continue to grow, but the retailers/sale agents are strongly opposed to the presence of remanufacturing products, thus the optimal pricing policy for a trade-in program is an important question.
In this paper, we develop a model for this scenario: the OEM produces both the new and remanufactured products, and the sale agent is responsible for sales of the remanufactured products and lauch a trade-in program.  [6] argued that trade-in rebates can improve an original equipment manufacturer's competitive position in a duopoly. Rao et al. [7] demonstrated that trade-in rebates can alleviate the inefficiencies arising from the lemon problem. Zhu et al. [8] and Kim et al. [9] investigated the effects of trade-in programs on customers' willingness to pay (WTP). In addition to the above basic research, some researchers have examined pricing policy and the potimal decisions under different scenarios. Li et al. [10] studied trade-in programs in B2B markets where trade-in rebates are granted up front. Ray et al. [11] took agedependent revenues into account, provided firms with insights to determine the optimal price and trade-in rebates. Yin and Tang [1] and Yin et al. [3] analyzed a two-period dynamic game to determine the optimal price and trade-in decisions by strategic consumers given the absence/presence of an upfront fee. Chen [12] considered three trade-in policies by optimizing pricing and/or trade-in rebates.

Literature Review
The aforementioned studies obtained some interesting findings for firms with trade-in programs. However, most of them do not consider the relationship between trade-in and remanufacturing. In recent years, trade-in programs have become firms' main strategy to acquire used products for repair, remanufacture and recycling. Agrawal et al. [13] analyze when and how the OEM should provide trade-in program. Zhang et al. [4] investigated the effect of consumers' purchase behavior on the economy and environment under a trade-in program with remanufacturing. Agrawal et al. [14] shows that trade-in program can help firms achieve successful price discrimination and weaken competition from third-party remanufacturers (3PRs). Ma et al. [15] studied firms' optimal pricing decisions and provide offers a reference for providing "trade old for new" (TON) and "trade old for remanufactured" (TOR) simultaneously. Miao et al. [16] investagted the problem of remanufacturing with trade-ins and analyzed optimal pricing and remanufacturing decisions under the carbon tax policy and the cap and trade program. Xiao [17] studied optimal pricing and production decisions for manufacturers/retailers that adopt an exchange-old-for-new (EON) program.
The above papers regard trade-in programs as an effective recovery method for remanufacturing. Our paper, however, regards trade-in programs as a price discrimination method. This is a significant difference, because the trade-in program in our context is initiated by a sale agent and is operated independently of remanufacturing. In addition, most assumed that the used product is functional and can be resold, and thus has residual value for customers. In our paper, the used product could not be sold in the secondary market and have no residual value for the customers. This represents a significant difference when determining trade-in rebates. Moreover, to the best of our knowledge, only Agrawal et al. [14] and Li et al. [18] took the B2B market's characteristic into consideration. We extend Agrawal et al. [14]'s model to investigate the optimal pricing for a remanufaturing supply chain that consists of one OEM and one sale agent.

Assumptions and Notations
A supply chain that consists of one OEM (the leader, player M), one sale agent (the follower, player S), and consumers (the corporate customers, player C). The OEM sells products through the sale agent. The sale agent can provide trade-in program for consumers.

Product Life Cycle
The product life duration is one period. After one period of use, the product ceases to provide functionality and use to the consumers. Used products can be either collected for materials recovery or remanufactured.

Customer Characteristics
Customers are heterogeneous, and each customer buys one unit at most in a period and the size of potential customers is normalized to 1. We set v to represent the customer's WTP for a new product and assume uniform distribution in [0,1]. We set the WTP for a remanufactured product as v  , where 0,1  () . The above assumptions have been used by many scholars, such as Ferrer et al. [20], Yenipazarli [21] and so on. context like our setting, which has been shown by Agrawal et al. [14].
We apply the GNBS model to our case as follows. Let   is the customer's bargaining power and 1  − is the sale agent's bargaining power.

Selling Price, Wholesale Price and Cost Structure
Let the selling price, wholesale price and unit production cost for a new product be denoted by

Specification of The Game
Our problem is a single-period game to determine firms' optimal pricing decisions to maximize their profits. Specifically, the OEM sets the wholesale price and the sale agent optimally sets both the selling price and the customized trade-in price. We begin with customers' purchasing decisions based on their WTP and then solve for the sale agent's optimal price decisions. After characterizing the sale agent's optimal responses to the wholesale prices, we solve the problem of the OEM that maximizes its profits by optimally choosing the wholesale prices. For ease of reference, we summarize the model's parameters in Table 1. Table 1 Table 2: , the price of new products, the trade-in price and the profits of sale agent decrease with the bargaining power of customers; the quantity of new products and trade-in products increase with the bargaining power of customers; the bargaining power of customers has no impact on the price of remanufacturing products, wholesale prices and the profits of OEM.
(2)When * r c l  , the price of new products, the price of remanufacturing products, wholesale prices and the quantity of trade-in products decrease with the bargaining power of customers; the trade-in price, the quantity of new products and remanufacturing products, the profits of firms increase with the bargaining power of customers.

Conclusions
Motivated by the fact that trade-in programs and remanufacturing have been matters of widespread concern in practice, we analyze optimal price strategy of trade-in programs in a decentralized supply chain consisting of one OEM and one sale agent, and analyze the effects of bargaining power of customers on the optimal solutions. We first characterize customer choice behavior based on the consumer's WTP and develop four supply chain models under four scenarios. Next, we derive the optimal price for each member and compare the firms' optimal solutions. Our study fill in the gap on the research of trade-in program in B2B market and Supply Chain management. Some interesting findings are obtained: (1) the unit cost of remanufacturing is crucial to the optimal policy decisions of the supply chain.