# Distribution Channel and Remanufacturing Strategy Selection

Authors: Xunbo Wu; Yi Wang; Lingjie Meng; Wenqi Jiang; Ming Wang
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Remanufacturing has become an important and fast-growing industry. Many original equipment manufacturers (OEMs) cooperate with third-party remanufacturers (3PRs) through either outsourcing or licensing. They sell the new and remanufactured products either directly to the consumer or indirectly through a retailer. Our study compares the OEM’s remanufacturing strategy selection in different distribution channel structures. We demonstrate that outsourcing remanufacturing benefits the OEM when the new products are sold directly and remanufactured products, with a relatively low valuation, are sold indirectly; otherwise, licensing remanufacturing is more beneficial for the OEM. We further find that when consumers perceive the remanufactured products with a sufficiently high value, the selection of remanufacturing strategies benefits consumers, society, and the environment.


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## Body

## 1. Introduction

Remanufacturing, from both a quality and performance perspective, is a controlled and reproducible industrial process by which previously used, worn, or nonfunctional products or parts are revamped to the like-new or better-than-new condition [1]. There is a general consensus both in academic and industrial fields that remanufacturing, a key part in circular economy, could significantly reduce the discharge of greenhouse gas and energy consumption [1]. As a $160 billion industry, remanufacturing generates more than 450,000 jobs worldwide [2]. By recycling and reclaiming products, it saves 85% of energy, water, and material use, as well as reduces greenhouse gas emissions between 79% and 99% compared to traditional manufacturing process [2]. As a crucial conjunction in the circular economy where materials can be part of a continual re-use and recycling system, the remanufacturing sector in the US is estimated to grow at a compound annual growth rate of 6.6% from 2017 to 2025 [3].In practice, original equipment manufacturers (OEMs) often rely on third-party remanufacturers (3PRs) to perform remanufacturing operations. Furthermore, there are two different strategies for OEM’s remanufacturing operation. One is outsourcing remanufacturing operations, in which the OEM only outsources the remanufacturing operations to a 3PR and retains the sales of remanufactured products. For example, Land Rover appointed Caterpillar, one of the world’s largest remanufacturers, as the preferred provider of global remanufacturing services [4]. The other is licensing remanufacturing business, in which the OEM licenses the whole remanufacturing business (i.e., both remanufacturing and marketing the remanufactured products) to a 3PR. For example, Dell licenses remanufacturing operations and sales of desktop, notebook, server, and storage systems at its Lebanon, TN facility to GENCO ATC [5, 6]. Foxconn, as a remanufacturer of Apple, not only obtained the right to remanufacture iPhone mobile phones but also got authorization to sell the remanufactured iPhone in China [4]. Besides the different remanufacturing operation strategies, the OEM and 3PR may choose different distribution channels for their products. Specifically, both new and remanufactured products may be sold either directly or indirectly through a retailer. For example, Canon sells its remanufactured products, including PowerShot Digital Cameras, VIXIA Camcorders, and EOS Digital SLR Cameras through Canon’s online website [7, 8]. Panasonic sells its remanufactured Toughbook computers through several reseller partners, including Bizco, BAYCOM, and Daly Computers [8, 9]. Motivated by the above practices, we raise our research questions as follows:(1)
What are the implications of the distribution channel (direct selling or indirect selling) on remanufacturing strategy selection (outsourcing or licensing)?(2)
What are the optimal product prices and resulting product sales and profits of different entities?(3)
How does this selection affect consumer surplus, social welfare, and environmental impacts?To answer our research questions, we build a model wherein an OEM produces a new remanufacturable product and chooses remanufacturing strategies (i.e., outsourcing remanufacturing operation and licensing remanufacturing business). In addition, we consider four distribution channel structures for the marketing of new and remanufactured products: both new and remanufactured products are sold directly, both new and remanufactured products are sold indirectly through a retailer, new products are sold directly (indirectly), and remanufactured products are sold indirectly (directly).The analysis of our model reveals that the OEM chooses different remanufacturing strategies in different channel structures. Specifically, when the new products are sold directly and remanufactured products, with a relatively low valuation, are sold indirectly, outsourcing remanufacturing is more beneficial for the OEM; otherwise, the OEM prefers to license the remanufacturing business. Furthermore, when consumers perceive the remanufactured products with a sufficiently high value, the selection of remanufacturing strategies benefits consumers, society, and the environment.The remainder of this study is organized as follows. In Section2, we briefly summarize the related literature. In Section 3, we describe our model. In Section 4, we derive the optimal equilibrium results and discuss the impact of the distribution channel (direct selling or indirect selling) on remanufacturing strategy selection (outsourcing or licensing). In Section 5, we conclude with a summary of our findings. All proofs and technical details are presented in the appendix.


## 2. Literature Review

Our work studies the remanufacturing strategies in different distribution channel structures, pertaining to three fields of research: remanufacturing strategies, environmental policies, and distribution channel.The existing literature on remanufacturing strategies can be classified into the following two types: outsourcing remanufacturing operation and licensing remanufacturing business. In terms of outsourcing remanufacturing operations, Savaskan and Bhattacharya [10] studied three modes of collection of used products: direct collection by a manufacturer, outsourcing to an existing retailer, and outsourcing to a third party. They found that the retailer is the most effective undertaker of product collection. Sun et al. [11] compared OEM’s in-house remanufacturing with outsourcing remanufacturing to a 3PR. They found that it is more profitable for the OEM to perform remanufacturing operations in-house, but it is more friendly to the environment to outsource remanufacturing to a 3PR. In terms of licensing remanufacturing business, Huang et al. [12] considered a retailer-dominated closed-loop supply chain in which the retailer was licensed to remanufacturing and found that it is crucial for the retailer to reduce the reverse logistic cost coefficient. Ma et al. [13] studied whether an OEM can license a 3PR to remanufacture the used products and found that although it is profitable for an OEM to license the remanufacturing business, it is not always necessary for a 3PR to accept OEMs’ authorization. Zou et al. [14] proposed that remanufacturing by technology licensing only benefits the manufacturer but may hurt the supplier and environment. Furthermore, it is more beneficial for remanufacturing to consider customers’ environmental awareness. The work by Zou et al. [4] is closely related to our article and worth special mentioning. Zou et al. [4] compared outsourcing remanufacturing with authorization remanufacturing and found that the OEM always obtains higher profit in outsourcing strategy than authorization strategy. However, in our model setting, we find that outsourcing strategy may not always be beneficial to OEM. Zou et al. [4] also found that the 3PR prefers the outsourcing strategy when consumers perceive a high-value remanufactured products, whereas we find that the 3PR may prefer the outsourcing strategy when consumers perceive a low-value remanufactured product or even regardless of the value of the remanufactured products.The second stream of literature related to this work is on environmental policies. See Atasu and Van Wassenhove [15] for a comprehensive overview of this topic. Atasu et al. [16] discussed the economic and environmental impacts of extended producer responsibility type of legislation and identified efficiency conditions. Plambeck and Wang [17] investigated the impact of e-waste regulation on new product introduction in a stylized model of the electronics industry. Atasu and Subramanian [18] investigated the implications of collective and individual producer responsibility models of product take‐back laws for e‐waste on manufacturers’ design for product recovery choices and profits and on consumer surplus in the presence of product competition. Esenduran et al. [19] considered three levels of legislation, no take‐back legislation, legislation with collection targets, and legislation with collection and reuse targets, characterized the optimal solution for the manufacturer, and analyzed how various levels of legislation affect manufacturing, remanufacturing, and collection decisions. Esenduran et al. [20] examined the effects of environmental policies on three key factors: remanufacturing levels, consumer surplus, and OEM profit.The other related literature stream investigates the distribution channel choice of a firm. Chiang et al. [21] demonstrated that a manufacturer’s direct channel not only increases the profit of the manufacturer by reducing the double marginalization but also benefits the retailer by reducing the wholesale price. Cai [22] investigates the influence of channel structures and channel coordination on the supplier, the retailer, and the entire supply chain in the context of two single-channel and two dual-channel supply chains. In terms of channel selection in the closed-loop supply chain, previous literature focuses on the collection of used products from end uses [10, 23–25]. However, there is little research that focuses on the distribution channel structure for the new and remanufactured products’ selling. Yan et al. [8] showed that although a manufacturer markets remanufactured products through its own e-channel is greener than through a third party, both manufacturer and retailer may be worse off. Shi et al. [6] considered a firm with separate manufacturing and remanufacturing divisions and an independent retailer and showed that a decentralized firm can benefit from indirect selling through the retailer. In such a channel structure, the firm has more incentive to design a remanufacturable product. In our analysis, we consider the remanufacturing strategy selection when the OEM sells both new and remanufactured products directly, only sells the new products directly, only sells the remanufactured products directly, and sells both products indirectly through a retailer. We compare various circumstances to investigate how the distribution channel (direct selling or indirect selling) affects remanufacturing strategy selection (outsourcing or licensing). To the best of our knowledge, this study is the first to study the impact of the distribution channel on remanufacturing strategy selection.


## 3. Model Setup

We consider the interaction among three profit-maximizing firms: an original equipment manufacturer (OEM or he), a third-party remanufacturer (3PR or she), and a retailer (it).


### 3.1. The OEM

The OEM, denoted asM, designs and produces a new remanufacturable product which has a product cost cn. The OEM has two alternative strategies for the remanufacture business:(1)
Outsourcing remanufacturing operation to a 3PR (denoted as strategyj=O), in which the 3PR collects and remanufactures the returned products at cost cr per unit. However, the remarketing operation is still reserved by the OEM. The OEM only pays an outsourcing fee po to the 3PR for the remanufacturing operation.(2)
Licensing remanufacturing business to a 3PR (denoted as strategyj=L), in which the 3PR not only collects and remanufactures the returned products but also remarkets the remanufactured products. The 3PR pays a licensing fee pl to the OEM for the remanufacturing business.The remanufacturing operations also include cleaning and reassembling the products. All these costs are abstracted by the remanufacturing costcr. To model the sustainability and the environmental friendliness of the remanufacturing operations, we assume cr<cn [6, 23, 24]. This assumption signifies that savings from materials (except for the essential input that needs to be replaced) and assembly of subsystems within the new product dominate the additional costs of disassembly and remanufacturing.Following the convention in the literature [4, 24, 26, 27], we define en and er as the environmental impact of one unit of new product and remanufactured product, respectively. The environmental impact reflects how the products impact the environment in all stages of the product life cycle, including production, use by customers, and end of life. Usually, the environmental impact of a new product is higher than that of a remanufactured product because more material and energy are consumed in the manufacturing operations. Therefore, we assume en>er.


### 3.2. The 3PR

The 3PR, denoted asR, collects and remanufactures the returned products at cost cr. To derive the key economic insights without introducing unnecessary mathematical complexity, we normalize all other costs to zero.For modeling convenience and analytical tractability, we consider a single-period model, in which both new and remanufactured products are being sold in the same period. This model can be applied to cases where similar products are introduced to the market repeatedly [10] or where a product’s life cycle has reached its maturity stage so that prices, demands, and collection rate are stable [6, 24].


### 3.3. The Retailer

The retailer, denoted asT, can sell both new and remanufactured products (if the OEM and the 3PR choose to indirectly sell their products through the retailer) and set the retail prices pn for the new products and pr for the remanufactured products.We consider four alternative distribution channel structures:(1)
Both the new and remanufactured products are sold directly (denoted as structures=DD). Specifically, in strategy O, the OEM direct sells both the new and remanufactured products (take Figure 1(a) as a visual illustration). In strategy L, the OEM sells the new products directly and the 3PR sells the remanufactured products directly (see Figure 1(b)).(2)
Only the new products are sold directly (denoted as structures=DD¯). Specifically, in strategy O, the OEM direct sells the new products and indirectly sells the remanufactured products through the retailer. In strategy L, the OEM sells the new products directly and the 3PR sells the remanufactured products through the retailer. Figures 1(c) and 1(d) provide the visual illustration of the two models, respectively.(3)
Only the remanufactured products are sold directly (denoted as structures=D¯D). Specifically, in strategy O, the OEM sells the new products through the retailer and sells the remanufactured products through his direct channel. In strategy L, the OEM sells the new products through the retailer and the 3PR sells the remanufactured products directly. The two models are illustrated in Figures 1(e) and 1(f).(4)
Both the new and remanufactured products are sold indirectly (denoted as structures=D¯D¯). Specifically, in strategy O, the OEM sells both the new and remanufactured products through the retailer (see Figure 1(g)). In strategy L, the OEM sells the new products indirectly and the 3PR sells the remanufactured products indirectly (see Figure 1(h)).Figure 1
Distribution channel structures and decisions.
(a)(b)(c)(d)(e)(f)(g)(h)


### 3.4. Consumers

Consumer willingness-to-pay (WTP) for a new product is heterogeneous and uniformly distributed in the interval [0, 1]. The market size is normalized to 1. Consumers typically value the remanufactured product less than the new product [6, 28–30]. Thus, we assume that if a consumer is willing to pay θ for a new product, then his WTP for a remanufactured product is δθ, where δ0<δ<1 is a discount factor for the remanufactured product. This value discount arises for several reasons. Customers may have an inherent distrust for recovered products. Some customers care about the newness of the product, and thus, they will pay less for a product that is essentially a used one. Moreover, the value discount may also reflect some customers’ concern for fairness because product recovery typically costs less than new production.Each consumer purchases at most one unit of one product (either new products or remanufactured products), i.e., there is no value from consuming a second product. Each consumer chooses the product offering that maximizes her expected surplus which is the difference between WTP and the price. Specifically, consumerθ has three choices:(1)
Purchasing a new product and realizing the surplusθ−pnjs, where pnjs is the price of the new products(2)
Purchasing a remanufactured product and realizing the surplusδθ−prjs, where prjs is the price of the remanufactured products(3)
Purchasing nothing and realizing zero surplusBased on the above assumptions, similar to Zou et al. [4], Shi et al. [6], and Chen and Chen [29], the demand functions for new and remanufactured products are dnjs=1−pnjs−prjs/1−δ and drjs=δpnjs−prjs/δ1−δ, where dnjs and drjs are the demand for new products and the demand for remanufactured products, respectively.We assume all the parameters are common knowledge for these three players. The key notations are summarized in Table1.Table 1
Table of key notation.
NotationDescriptionSuperscriptsjType of remanufacturing strategy,j=O (outsourcing remanufacturing operation to a 3PR) and L (licensing remanufacturing business to a 3PR)sType of distribution channel structure,s=DD (direct sell the new and remanufactured products), DD¯ (direct sell the new products and indirect sell the remanufactured products), D¯D (indirect sell the new products and direct sell the remanufactured products), and D¯D¯ (indirect sell the new and remanufactured products)SubscriptshType of product,h=n (new product) and r (remanufactured product)gType of player,g=M (original equipment manufacturer), R (third-party remanufacturer), and T (retailer)ParameterscnManufacturing cost per unitcrRemanufacturing cost per unitθConsumer willingness-to-pay for a productδWTP discount factor for a remanufactured productehUnit environmental impact from a producthDecision variableswhjsWholesale price of producth in strategy j and channel structure sphjsRetail price of producth in strategy j and channel structure spoOOutsourcing fee for remanufacturing operationplLLicense fee for remanufacturing businessAuxiliary variablesdhjsProduct demand for producth in strategy j and channel structure sCSjsConsumer surplus in strategyj and channel structureSWjsSocial welfare in strategyj and channel structure sEIjsTotal environmental impact in strategyj and channel structure sObjective function valuesΠMjsOEM’s profit in strategyj and channel structure sΠRjs3PR’s profit in strategyj and channel structure sΠTjsRetailer’s profit in strategyj and channel structure s


## 3.1. The OEM

The OEM, denoted asM, designs and produces a new remanufacturable product which has a product cost cn. The OEM has two alternative strategies for the remanufacture business:(1)
Outsourcing remanufacturing operation to a 3PR (denoted as strategyj=O), in which the 3PR collects and remanufactures the returned products at cost cr per unit. However, the remarketing operation is still reserved by the OEM. The OEM only pays an outsourcing fee po to the 3PR for the remanufacturing operation.(2)
Licensing remanufacturing business to a 3PR (denoted as strategyj=L), in which the 3PR not only collects and remanufactures the returned products but also remarkets the remanufactured products. The 3PR pays a licensing fee pl to the OEM for the remanufacturing business.The remanufacturing operations also include cleaning and reassembling the products. All these costs are abstracted by the remanufacturing costcr. To model the sustainability and the environmental friendliness of the remanufacturing operations, we assume cr<cn [6, 23, 24]. This assumption signifies that savings from materials (except for the essential input that needs to be replaced) and assembly of subsystems within the new product dominate the additional costs of disassembly and remanufacturing.Following the convention in the literature [4, 24, 26, 27], we define en and er as the environmental impact of one unit of new product and remanufactured product, respectively. The environmental impact reflects how the products impact the environment in all stages of the product life cycle, including production, use by customers, and end of life. Usually, the environmental impact of a new product is higher than that of a remanufactured product because more material and energy are consumed in the manufacturing operations. Therefore, we assume en>er.


## 3.2. The 3PR

The 3PR, denoted asR, collects and remanufactures the returned products at cost cr. To derive the key economic insights without introducing unnecessary mathematical complexity, we normalize all other costs to zero.For modeling convenience and analytical tractability, we consider a single-period model, in which both new and remanufactured products are being sold in the same period. This model can be applied to cases where similar products are introduced to the market repeatedly [10] or where a product’s life cycle has reached its maturity stage so that prices, demands, and collection rate are stable [6, 24].


## 3.3. The Retailer

The retailer, denoted asT, can sell both new and remanufactured products (if the OEM and the 3PR choose to indirectly sell their products through the retailer) and set the retail prices pn for the new products and pr for the remanufactured products.We consider four alternative distribution channel structures:(1)
Both the new and remanufactured products are sold directly (denoted as structures=DD). Specifically, in strategy O, the OEM direct sells both the new and remanufactured products (take Figure 1(a) as a visual illustration). In strategy L, the OEM sells the new products directly and the 3PR sells the remanufactured products directly (see Figure 1(b)).(2)
Only the new products are sold directly (denoted as structures=DD¯). Specifically, in strategy O, the OEM direct sells the new products and indirectly sells the remanufactured products through the retailer. In strategy L, the OEM sells the new products directly and the 3PR sells the remanufactured products through the retailer. Figures 1(c) and 1(d) provide the visual illustration of the two models, respectively.(3)
Only the remanufactured products are sold directly (denoted as structures=D¯D). Specifically, in strategy O, the OEM sells the new products through the retailer and sells the remanufactured products through his direct channel. In strategy L, the OEM sells the new products through the retailer and the 3PR sells the remanufactured products directly. The two models are illustrated in Figures 1(e) and 1(f).(4)
Both the new and remanufactured products are sold indirectly (denoted as structures=D¯D¯). Specifically, in strategy O, the OEM sells both the new and remanufactured products through the retailer (see Figure 1(g)). In strategy L, the OEM sells the new products indirectly and the 3PR sells the remanufactured products indirectly (see Figure 1(h)).Figure 1
Distribution channel structures and decisions.
(a)(b)(c)(d)(e)(f)(g)(h)


## 3.4. Consumers

Consumer willingness-to-pay (WTP) for a new product is heterogeneous and uniformly distributed in the interval [0, 1]. The market size is normalized to 1. Consumers typically value the remanufactured product less than the new product [6, 28–30]. Thus, we assume that if a consumer is willing to pay θ for a new product, then his WTP for a remanufactured product is δθ, where δ0<δ<1 is a discount factor for the remanufactured product. This value discount arises for several reasons. Customers may have an inherent distrust for recovered products. Some customers care about the newness of the product, and thus, they will pay less for a product that is essentially a used one. Moreover, the value discount may also reflect some customers’ concern for fairness because product recovery typically costs less than new production.Each consumer purchases at most one unit of one product (either new products or remanufactured products), i.e., there is no value from consuming a second product. Each consumer chooses the product offering that maximizes her expected surplus which is the difference between WTP and the price. Specifically, consumerθ has three choices:(1)
Purchasing a new product and realizing the surplusθ−pnjs, where pnjs is the price of the new products(2)
Purchasing a remanufactured product and realizing the surplusδθ−prjs, where prjs is the price of the remanufactured products(3)
Purchasing nothing and realizing zero surplusBased on the above assumptions, similar to Zou et al. [4], Shi et al. [6], and Chen and Chen [29], the demand functions for new and remanufactured products are dnjs=1−pnjs−prjs/1−δ and drjs=δpnjs−prjs/δ1−δ, where dnjs and drjs are the demand for new products and the demand for remanufactured products, respectively.We assume all the parameters are common knowledge for these three players. The key notations are summarized in Table1.Table 1
Table of key notation.
NotationDescriptionSuperscriptsjType of remanufacturing strategy,j=O (outsourcing remanufacturing operation to a 3PR) and L (licensing remanufacturing business to a 3PR)sType of distribution channel structure,s=DD (direct sell the new and remanufactured products), DD¯ (direct sell the new products and indirect sell the remanufactured products), D¯D (indirect sell the new products and direct sell the remanufactured products), and D¯D¯ (indirect sell the new and remanufactured products)SubscriptshType of product,h=n (new product) and r (remanufactured product)gType of player,g=M (original equipment manufacturer), R (third-party remanufacturer), and T (retailer)ParameterscnManufacturing cost per unitcrRemanufacturing cost per unitθConsumer willingness-to-pay for a productδWTP discount factor for a remanufactured productehUnit environmental impact from a producthDecision variableswhjsWholesale price of producth in strategy j and channel structure sphjsRetail price of producth in strategy j and channel structure spoOOutsourcing fee for remanufacturing operationplLLicense fee for remanufacturing businessAuxiliary variablesdhjsProduct demand for producth in strategy j and channel structure sCSjsConsumer surplus in strategyj and channel structureSWjsSocial welfare in strategyj and channel structure sEIjsTotal environmental impact in strategyj and channel structure sObjective function valuesΠMjsOEM’s profit in strategyj and channel structure sΠRjs3PR’s profit in strategyj and channel structure sΠTjsRetailer’s profit in strategyj and channel structure s


## 4. Model Analysis

### 4.1. Distribution Channel StructureDD

In this section, we consider the structureDD, in which both the new and remanufactured products are sold directly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM and the 3PR, which are given by(1)ΠMODD=pnODD−cndnODD+prODD−poODDdrODD,ΠRODD=poODD−crdrODD.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoODD. Sequentially, the OEM determines the retail prices pnODD and prODD of the new and remanufactured products, respectively.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLDD. Then, the OEM and the 3PR maximize their profits by optimizing the retail prices of new and remanufactured products, respectively. The profits of the OEM and the 3PR, which are given by(2)ΠMLDD=pnLDD−cndnLDD+plLDDdrLDD,ΠRLDD=prLDD−cr−plLDDdrLDD.We solve the game backward to ensure subgame perfection. Proposition1 states the equilibrium solutions in strategy O and strategy L.Proposition 1.
In the channel structureDD, the equilibrium solutions are summarized in Table 2.Proposition1 states the equilibrium solutions in structure DD. According to this, we compare the OEM’s equilibrium results, which lead to Corollary 1. For easy interpretation, we define the unit marginal profits of new products for the OEM as mpnODD=pnODD−cn in strategy O and mpnLDD=pnLDD−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprODD=prODD−poODD in strategy O and mprLDD=plLDD in strategy L, respectively.Table 2
Equilibrium solutions in structureDD.
Optimal solutionsStrategyOStrategyLpoODDplLDDδcn+cr/2δ21−cn+8δ−cr/28+δpnODDpnLDD1+cn/21+cn/2+δcn−cr/8+δprODDprLDD2δ+δcn+cr/4δ/2+δ2cn+4δcn+4cr/28+δdnODDdnLDD2−cn/4−cn−cr/41−δ1/2+δ2cn+δcn−8cn+6cr/21−δ8+δdrODDdrLDDδcn−cr/41−δδ2+δδcn−cr/8+δ1−δδΠMODDΠMLDDδcn−cr2/161−δδ+1−cn2/4δcn−cr2/8+δ1−δδ+1−cn2/4ΠRODDΠRLDDδcn−cr2/81−δδ2+δ2δcn−cr2/8+δ21−δδCorollary 1.
In the channel structureDD,(1)
The unit marginal profit of new products for the OEM in strategyO is lower than the profit in strategy L. Formally, mpnODD−mpnLDD=−δcn−cr/8+δ<0.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is lower than the profit in strategy L. Formally, mprODD−mprLDD=−8−δδcn−cr/48+δ<0.(3)
The demand for new products in strategyO is higher than the demand in strategy L. Formally, dnODD−dnLDD=4−δδcn−cr/48+δ1−δ>0.(4)
The demand for remanufactured products in strategypnODDO is lower than the demand in strategy L. Formally, drODD−drLDD=−3δcn−cr/48+δ1−δ<0.Corollary1 demonstrates that, for the OEM, when he chooses to license the whole remanufacturing business to the 3PR rather than only outsource the remanufacturing operations, he can get higher unit marginal profits from both the new and remanufactured products. Furthermore, the 3PR produces more remanufactured products, which further increases the OEM’s profit from licensing. The cons of licensing for the OEM is licensing leads to the 3PR gains the whole control for the remanufacturing business. Thus, the new product would face more intense retail competition. The OEM cuts back on the production of new products.Next, we characterize the conditions for the OEM to choose different remanufacturing strategies in structureDD. By comparing strategy O with strategy L, we derive the following proposition.Proposition 2.
In the channel structureDD,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L. Formally, ΠMODD−ΠMLDD=−8−δδcn−cr=2/16δ+81−δδ<0.(2)
The 3PR’s profit in strategyO is higher than the profit in strategy L. Formally, ΠRODD−ΠRLDD=32−7δ2−16δδcn−cr2/8δ+821−δδ>0.According to Proposition2, we find that the OEM always chooses to license the remanufacturing to the 3PR in the channel structure DD. The reason is, as demonstrated in Corollary 1, licensing can lead to higher marginal profits from both new and remanufactured products and larger production from remanufactured products. However, the OEM’s choice makes the 3PR get worse (i.e., ΠRLDD−ΠRODD<0).


### 4.2. Distribution Channel StructureDD¯

In this section, we consider the structureDD¯, in which only the new products are sold directly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM, the 3PR, and the retailer, which are given by(3)ΠMODD¯=pnODD¯−cndnODD¯+wrODD¯−poODD¯drODD¯,ΠRODD¯=poODD¯−crdrODD¯,ΠTODD¯=0prODD¯−wrODD¯drODD¯.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoODD¯. Secondly, the OEM determines the retail price pnODD¯ of the new products and the wholesale price wrODD¯ of the remanufactured products to the retailer. Finally, the retailer determines the retail price prODD¯ of the remanufactured products.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLDD¯. Then, according to plLDD¯, the 3PR maximizes her profit by optimizing the wholesale price wrLDD¯ of the remanufactured products to the retailer. Thirdly, the retailer determines the prices of the new and remanufactured products, respectively. The profits of the OEM, the 3PR, and the retailer, which are given by(4)ΠMLDD¯=pnLDD¯−cndnLDD¯+plLDD¯drLDD¯,ΠRLDD¯=wrLDD¯−cr−plLDD¯drLDD¯,ΠTLDD¯=prLDD¯−wrLDD¯drLDD¯.Similarly, we use backward induction to ensure subgame perfection. Proposition3 states the equilibrium solutions in strategy O and strategy L.Proposition 3.
In the channel structureDD¯, the equilibrium solutions are summarized in Table 3.According to Proposition3, we compare the OEM’s equilibrium results, which lead to Corollary 2. Similarly, we define the unit marginal profits of new products for the OEM as mpnODD¯=pnODD¯−cn in strategy O and mpnLDD¯=pnLDD¯−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprODD¯=wrODD¯−poODD¯ in strategy O and mprLDD¯=plLDD¯ in strategy L, respectively.Table 3
Equilibrium solutions in structureDD¯.
Optimal solutionsStrategyOStrategyLpoODD¯plLDD¯δcn+cr/2δ1−cn/2+2−δ8−3δδcn−cr/2δ3−3δ2−5δ+16wrODD¯wrLDD¯2δ+δcn+cr/4δ+cr/2+8−3δδcn−cr/2δ3−3δ2−5δ+16pnODD¯pnLDD¯1+cn/21+cn/2+3−δ2−δδcn−cr/2δ3−3δ2−5δ+16prODD¯prLDD¯4δ+3δcn+cr/8δ1+cn/2−2−δ2δcn−cr/2δ3−3δ2−5δ+16dnODD¯dnLDD¯1−cn/2−δcn−cr/81−δ1−cn/2−2−δ5−2δδcn−cr/2δ3−3δ2−5δ+161−δdrODD¯drLDD¯δcn−cr/81−δδ2−δ2−δ2+2δδcn−cr/2δ3−3δ2−5δ+161−δδΠMODD¯ΠMLDD¯1−cn2/4+δcn−cr2/321−δδ1−cn2/4+2−δ2δcn−cr2/4δ3−3δ2−5δ+161−δδΠRODD¯ΠRLDD¯δcn−cr2/161−δδ2−δ4−δδ2−2δ−22δcn−cr2/4δ3−3δ2−5δ+1621−δδΠTODD¯ΠTLDD¯δcn−cr2/641−δδ2−δ2δ2−2δ−22δcn−cr2/4δ3−3δ2−5δ+1621−δδCorollary 2.
In the channel structureDD¯,(1)
The unit marginal profit of new products for the OEM in strategyO is lower than the profit in strategy L. Formally, mpnODD¯−mpnLDD¯=−3−δ2−δδcn−cr/2δ3−3δ2−5δ+16<0.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is lower than the profit in strategy L. Formally, mprODD¯−mprLDD¯=−δ3−9δ2+23δ−16δcn−cr/4δ3−3δ2−5δ+16<0.(3)
The demand for new products in strategyO is higher than the demand in strategy L. Formally, dnODD−dnLDD=δ3−11δ2+31δ−24δcn−cr/8δ−1δ3−3δ2−5δ+16>0.(4)
The demand for remanufactured products in strategypnODDO is lower than the demand in strategy L. Formally, drODD−drLDD=−3δ2+131−δδcn−cr/81−δδ3−3δ2−5δ+16<0.As the same as the structureDD, the OEM can get higher unit marginal profits from both new and remanufactured products and a larger demand from remanufactured products in strategy L and structure DD¯. Interestingly, we find that the OEM may not always choose to license the whole remanufacturing business to the 3PR. This is summarized in the following proposition.Proposition 4.
In the channel structureDD¯,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L if δ>δ1; otherwise, the profit in strategy O is higher than that in strategy L. Formally, ΠMODD¯−ΠMLDD¯=−δ3−11δ2+27δ−16δcn−cr2/32δ3−3δ2−5δ+161−δδ<0 if δ>δ1 and ΠMODD¯−ΠMLDD¯≥0 if δ≤δ1, where δ1∈0,1 is defined as the real root of the cubic equation: δ3−11δ2+27δ−16=0.(2)
The 3PR’s profit in strategyO is lower than the profit in strategy L if δ>δ2; otherwise, the profit in strategy O is higher than that in strategy L. Formally, ΠRODD¯−ΠRLDD¯=−3δ6−34δ5+129δ4−158δ3−105δ2+320δ−128δcn−cr2/16δ3−3δ2−5δ+1621−δδ<0 if δ>δ2 and ΠRODD¯−ΠRLDD¯≥0 if δ≤δ2, where δ2∈0,1 is defined as the real root of the sixth degree equation: 3δ6−34δ5+129δ4−158δ3−105δ2+320δ−128=0.(3)
The retailer’s profit in strategyO is lower than the profit in strategy L. Formally, ΠTODD¯−ΠTLDD¯=−15δ5−122δ4+321δ3−190δ2−377δ+416δcn−cr2/64δ3−3δ2−5δ+1621−δ<0.Proposition4 illustrates that, in the structure DD¯, when the WTP discount factor for a remanufactured product is sufficiently low (i.e., δ≤δ1), the OEM chooses to only outsource the remanufacturing operation to the 3PR. The reason is that the OEM produces larger new products when he adopts strategy O and the benefits of larger new products outweigh the disadvantages of lower margin profits when the WTP discount factor is low. From the 3PR’s perspective, the OEM’s choice makes the 3PR worse when the WTP discount factor is in a midrange (i.e., δ2<δ<δ1). Specifically, when the WTP discount factor is sufficiently low (i.e., δ≤δ2), the OEM adopts strategy O and the 3PR realizes a higher profit (i.e., ΠRODD¯−ΠRLDD¯>0 when δ≤δ2). When the WTP discount factor is sufficiently high (i.e., δ≥δ1), the OEM adopts strategy L and the 3PR realizes a higher profit (i.e., ΠRLDD¯−ΠRODD¯>0 when δ≥δ1). From the retailer’s perspective, the OEM’s choice makes the retailer worse when the WTP discount factor is low (i.e., ΠTODD¯−ΠTLDD¯<0).


### 4.3. Distribution Channel StructureD¯D

In this section, we consider the structureD¯D, in which only the remanufactured products are sold directly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM, the 3PR, and the retailer, which are given by(5)ΠMOD¯D=wnOD¯D−cndnOD¯D+prOD¯D−poOD¯DdrOD¯D,ΠROD¯D=poOD¯D−crdrOD¯D,ΠTOD¯D=pnOD¯D−wnOD¯DdnOD¯D.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoOD¯D. Secondly, the OEM determines the retail price prOD¯D of the remanufactured products and the wholesale price wnOD¯D of the new products to the retailer. Finally, the retailer determines the retail price pnOD¯D of the new products.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLD¯D and the wholesale price wnLD¯D. Sequentially, the 3PR maximizes her profit by optimizing the retail price prLD¯D of the remanufactured products. Simultaneously, the retailer determines the price pnLD¯D of the new products. The profits of the OEM, the 3PR, and the retailer, which are given by(6)ΠMLD¯D=wnLD¯D−cndnLD¯D+plLD¯DdrLD¯D,ΠRLD¯D=prLD¯D−cr−plLD¯DdrLD¯D,ΠTLD¯D=pnLD¯D−wnLD¯DdnLD¯D.Similarly, we use backward induction to ensure subgame perfection. Proposition5 states the equilibrium solutions in strategy O and strategy L.Proposition 5.
In the channel structureD¯D, the equilibrium solutions are summarized in Table 4.According to Proposition5, we compare the OEM’s equilibrium results, which lead to Corollary 3. In the same manner, we define the unit marginal profits of new products for the OEM as mpnOD¯D=wnOD¯D−cn in strategy O and mpnLD¯D=wnLD¯D−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprOD¯D=prOD¯D−poOD¯D in strategy O and mprLD¯D=plLD¯D in strategy L, respectively.Table 4
Equilibrium solutions in structureD¯D.
Optimal solutionsStrategyOStrategyLpoOD¯DplLD¯D1+cn−δδ/22−δ+cr/2δ−cr/2wnOD¯DwnLD¯D1+cn/21+cn/2pnOD¯DpnLD¯D6−δ+cn+cr/8+2cn−δ/82−δ6−3δ+2cn+cr/24−δprOD¯DprLD¯Dcr/4+−3δ2+5δ+δcn/42−δ5+δcn+2cr−2δ2/24−δdnOD¯DdnLD¯D1/8+1−2cn/42−δ−cn−cr/81−δcn−2δ−2cn+cr+2/24−δ1−δdrOD¯DdrLD¯Dδ−cr/8δ+δcn−cr/81−δδ1+cn+crδ−δ2−2cr/24−δ1−δΠMOD¯DΠMLD¯Dδ2−1+cn+crδ+2cr2/322−δ1−δδ+1−cn2/42−δ1−cn22−δ/44−δ1−δ+δ2−2cn+crδ+2crδ−cr/44−δ1−δδΠROD¯DΠRLD¯Dδ2−1+cn+crδ+2cr2/162−δ1−δδδ2−1+cn+crδ+2cr2/44−δ21−δδΠTOD¯DΠTLD¯Dδ2−1+cn+crδ+2cr+41−δ1−cn2/642−δ21−δcn−2δ−2cn+cr+22/44−δ21−δCorollary 3.
In the channel structureD¯D,(1)
The unit marginal profit of new products for the OEM in strategyO is the same as the profit in strategy L.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is higher than the profit in strategy L if δ<δ3 and is lower than the profit in strategy L if δ≥δ3. Formally, mprOD¯D−mprLD¯D=δ2−cn+cr+1δ+2cr/42−δ>0 if δ<δ3 and mprOD¯D−mprLD¯D≤0 if δ≥δ3, which is defined as the real root of the quadratic equation: δ2−cn+cr+1δ+2cr.(3)
The demand for new products in strategyO is lower than the demand in strategy if δ<δ3 and is higher than the demand in strategy L if δ≥δ3. Formally, dnOD¯D−dnLD¯D=−δ2−cn+cr+1δ+2crδ/84−δ2−δ1−δ<0 if δ<δ3 and dnOD¯D−dnLD¯D≥0 if δ≥δ3.(4)
The demand for remanufactured products in strategyO is higher than the demand in strategy L if δ<δ3 and is lower than the demand in strategy L if δ≥δ3. Formally, drOD¯D−drLD¯D=δ2−cn+cr+1δ+2cr/84−δ1−δ>0 if δ<δ3 and drOD¯D−drLD¯D≤0 if δ≥δ3.Different from the structureDD and DD¯, in the channel structure D¯D, the OEM earns a constant unit marginal profit from new products no matter what remanufacturing strategy the OEM chooses. With a low WTP discount factor (i.e., δ<δ3), the OEM earns a higher unit marginal profit from remanufactured products in strategy O and the demand for remanufactured products is higher in strategy O. However, the OEM produces smaller new products in strategy O. With a high WTP discount factor (i.e., δ≥δ3), the OEM earns a lower unit marginal profit from remanufactured products in strategy O and the demand for remanufactured products is lower in strategy O. However, the OEM produces larger new products in strategy O. An intriguing result is that different changes in unit marginal profit and demand may cause the OEM to always choose the same remanufacturing strategy, as Proposition 6 presents.Proposition 6.
In the channel structureD¯D,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L. Formally, ΠMOD¯D−ΠMLD¯D=−δ2−cn+cr+1δ+2cr24+δ/324−δ2−δ1−δδ<0.(2)
The 3PR’s profit in strategyO is higher than the profit in strategy L. Formally, ΠROD¯D−ΠRLD¯D=δ2−1+cn+crδ+2cr2δ2−4δ+8/164−δ22−δ1−δδ>0.(3)
The retailer’s profit in strategyO is higher than the profit in strategy L if δ4<δ<δ5; otherwise, the profit in strategy O is lower than that in strategy L. Formally, ΠTOD¯D−ΠTLD¯D=δ2−1+cn+crδ+2cr321−δ1−cn+4−δ2cr−16−δ1−δδ−7δcn+2crδ/644−δ22−δ21−δ>0 if δ4<δ<δ5 and ΠTOD¯D−ΠTLD¯D≤0 if δ≤δ4 or δ≥δ5, where δ4∈0,1 and δ5∈0,1 are defined as the smaller and larger real root of the quintic equation: δ2−1+cn+crδ+2cr321−δ1−cn+4−δ2cr−16−δ1−δδ−7δcn+2cr.According to Proposition6, we find that, in the structure D¯D, the OEM always chooses to license the remanufacturing to the 3PR in the channel structure DD. However, the OEM’s choice makes the 3PR get worse (i.e., ΠRLDD−ΠRODD<0). And, the retailer also gets worse when the WTP discount factor is in a midrange (i.e., ΠTLDD−ΠTODD<0 when δ4<δ<δ5).


### 4.4. Distribution Channel StructureD¯D¯

In this section, we consider the structureD¯D¯, in which both the new and remanufactured products are sold indirectly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM, the 3PR, and the retailer, which are given by(7)ΠMOD¯D¯=wnOD¯D¯−cndnOD¯D¯+wrOD¯D¯−poOD¯D¯drOD¯D¯,ΠROD¯D¯=poOD¯D¯−crdrOD¯D¯,ΠTOD¯D¯=pnOD¯D¯−wnOD¯D¯dnOD¯D¯+prOD¯D¯−wrOD¯D¯drOD¯D¯.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoOD¯D¯. Secondly, the OEM determines the wholesale price wnOD¯D¯ of the new products to the retailer and the wholesale price wrOD¯D¯ of the remanufactured products. Finally, the retailer determines the retail price pnOD¯D¯ and prOD¯D¯of the new and remanufactured products, respectively.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLD¯D¯. Sequentially, the 3PR maximizes her profit by optimizing the wholesale price wrLD¯D¯ of the remanufactured products. Simultaneously, the OEM determines the wholesale price wnLD¯D¯ of the new products. Finally, the retailer determines the retail price pnLD¯D¯ and prLD¯D¯ of the new and remanufactured products, respectively. The profits of the OEM, the 3PR, and the retailer, which are given by(8)ΠMLD¯D¯=wnLD¯D¯−cndnLD¯D¯+plLD¯D¯drLD¯D¯,ΠRLD¯D¯=wrLD¯D¯−cr−plLD¯D¯drLD¯D¯,ΠTLD¯D¯=pnLD¯D¯−wnLD¯D¯dnLD¯D¯+prLD¯D¯−wrLD¯D¯drLD¯D¯.Similarly, we use backward induction to ensure subgame perfection. Proposition7 states the equilibrium solutions in strategy O and strategy L.Proposition 7.
In the channel structureD¯D¯, the equilibrium solutions are summarized in Table 5.We define the unit marginal profits of new products for the OEM asmpnOD¯D¯=wnOD¯D¯−cn in strategy O and mpnLD¯D¯=wnLD¯D¯−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprOD¯D¯=wrOD¯D¯−poOD¯D¯ in strategy O and mprLD¯D¯=plLD¯D¯ in strategy L, respectively. According to Proposition 7, we compare the OEM’s equilibrium results, which lead to Corollary 4.Table 5
Equilibrium solutions in structureD¯D¯.
Optimal solutionsStrategyOStrategyLpoOD¯D¯plLD¯D¯δcn+cr/2δ/2−δ2cn+8cr/28+δwnOD¯D¯wnLD¯D¯1+cn/21+cn/2+δcn−cr/8+δwrOD¯D¯wrLD¯D¯δ/2+δcn+cr/4δ/2+δ2cn+4δcn+4cr/28+δpnOD¯D¯pnLD¯D¯3+cn/43+cn/4+δcn−cr/28+δprOD¯D¯prLD¯D¯3δ/4+δcn+cr/83δ/4+δ2cn+4δcn+4cr/48+δdnOD¯D¯dnLD¯D¯2−cn/8−cn−cr/81−δ1/4−3+δ2−δcn+2cn−cr/48+δ1−δdrOD¯D¯drLD¯D¯δcn−cr/81−δδ2+δδcn−cr/28+δ1−δδΠMOD¯D¯ΠMLD¯D¯1−cn2/8+δcn−cr2/321−δδ1−cn2/8+δcn−cr2/28+δ1−δδΠROD¯D¯ΠRLD¯D¯δcn−cr2/161−δδ2+δ2δcn−cr2/28+δ21−δδΠTOD¯D¯ΠTLD¯D¯1−cn2/16+δcn−cr2/641−δδ2+δ2δcn−cr2/48+δ21−δδ+1−cn8+δ−2δcn−cr2/168+δ2Corollary 4.
In the channel structureD¯D¯,(1)
The unit marginal profit of new products for the OEM in strategyO is lower than the profit in strategy L. Formally, mpnOD¯D¯−mpnLD¯D¯=−δcn−cr/8+δ<0.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is lower than the profit in strategy L. Formally, mprOD¯D¯−mprLD¯D¯=−8−δδcn−cr/48+δ<0.(3)
The demand for new products in strategyO is higher than the demand in strategy. Formally, dnOD¯D¯−dnLD¯D¯=4−δδcn−cr/88+δ1−δ>0.(4)
The demand for remanufactured products in strategypnODDO is lower than the demand in strategy L. Formally, drOD¯D¯−drLD¯D¯=−3δcn−cr/88+δ1−δ<0.Corollary4 illustrates that, as the same as the structure DD and DD¯, the OEM can get higher unit marginal profits from both new and remanufactured products and a larger demand from remanufactured products in strategy L and structure D¯D¯.Next, we characterize the conditions for the OEM to choose different remanufacturing strategies in distribution channel structureD¯D¯. By comparing strategy O with strategy L, we derive the following proposition.Proposition 8.
In the channel structureD¯D¯,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L. Formally, ΠMOD¯D¯−ΠMLD¯D¯=−8−δδcn−cr2/328+δ1−δδ<0.(2)
The 3PR’s profit in strategyO is higher than the profit in strategy L. Formally, ΠROD¯D¯−ΠRLD¯D¯=32−16δ−7δ2δcn−cr2/168+δ21−δδ>0.(3)
The retailer’s profit in strategyO is lower than the profit in strategy L if δ>δ6; otherwise, the profit in strategy O is higher than that in strategy L. Formally, ΠTOD¯D¯−ΠTLD¯D¯=−16−17cnδ2+112−48cn+crδ+128cn−64cr−128δcn−cr/648+δ21−δ<0 if δ>δ6 and ΠTOD¯D¯−ΠTLD¯D¯≥0 if δ≤δ6, where δ6∈0,1 is defined as the real root of the quadratic equation: 16−17cnδ2+112−48cn+crδ+128cn−64cr−128.Proposition8 demonstrates that when both new and remanufactured products are sold through the retailer, the OEM licenses the whole remanufacturing business to the 3PR no matter what the WTP discount factor is. Compared with strategy O, the 3PR realizes a lower profit in strategy L. The sign of the retailer’s profit change depends on the WTP discount factor. Specifically, with a high WTP discount factor, the retailer gets better (i.e., ΠTLD¯D¯−ΠTOD¯D¯>0 when δ>δ6) and the retailer gets worse with a low WTP discount factor (i.e., ΠTLD¯D¯−ΠTOD¯D¯≤0 when δ≤δ6).


### 4.5. Consumer Surplus, Social Welfare, and Environmental Impact

In this section, we extend the analysis from pure profit orientation to include a consumer surplus perspective, a social welfare perspective, and an environmental impact perspective.For the consumer of typeθ, the surplus of an individual consumer who purchases a new product is θ−pnjs and the surplus of an individual consumer who purchases a remanufactured product is δθ−prjs. Therefore, the total consumer surplus is given by(9)CSjs=∫1−dnjs−drjs1−dnjsδθ−prjsdθ+∫1−dnjs1θ−pnjsdθ.Correspondingly, the social welfare in strategyj and channel structure s is given by(10)SWjs=CSjs+ΠMjs+ΠRjs+ΠTjs.From the environmental impact perspective, when the OEM producesdnjs units and the 3PR remanufactures drjs units, the total environmental impact in strategy j and channel structure s is given by(11)EIjs=dnjsen+drjser.The next lemma shows the consumer surplus, social welfare, and environmental impact in different strategies and channel structures.Lemma 1.
In the strategyj and channel structure s, the consumer surplus, social welfare, and environmental impact are summarized in Tables 6–8, respectively.Proposition9 demonstrates the important relationships we derive from Lemma 1.Table 6
Consumer surplus in strategyj and structure s.
Strategy and structureConsumer surplusODD1−cn2/8+δcn−cr2/321−δδLDD2+δ2δcn−cr2/28+δ21−δδ+1−cn8+δ−2δcn−cr2/88+δ2ODD¯1−cn2/8+δcn−cr2/1281−δδLDD¯1−cn2/8+2−δ2δcn−cr23δ3−15δ2+17δ+4/8δ3−3δ2−5δ+1621−δδ−3−δ1−cn/4δ3−3δ2−5δ+16OD¯Dδ2−1+cn+crδ+2cr24−3δ/1282−δ21−δδ+1−cn2+1−cnδ−cr/162−δLD¯D1−cn24+δδ+4δ−cr2/84−δ2δ+δcn−cr2/84−δ21−δOD¯D¯1−cn2/32+δcn−cr2/1281−δδLD¯D¯2+δ2δcn−cr2/88+δ21−δδ+1−cn8+δ−2δcn−cr2/328+δ2Table 7
Social welfare in strategyj and structure s.
Strategy and structureSocial welfareODD31−cn2/8+7δcn−cr2/321−δδLDD1−cn2/4+32+δ2+28+δδcn−cr2/28+δ21−δδ+1−cn8+δ−2δcn−cr2/88+δ2ODD¯31−cn2/8+15δcn−cr2/1281−δδLDD¯31−cn2/8+2−δ2δcn−cr25δ3−21δ2+7δ+36/8δ3−3δ2−5δ+1621−δδ+2−δ3−δδ2−2δ−22δcn−cr2/2δ3−3δ2−5δ+1621−δδ−3−δ1−cn/4δ3−3δ2−5δ+16OD¯Dδ2−1+cn+crδ+2cr216−3δ/1282−δ21−δδ+51−cn2+1−cnδ−cr/162−δ+δ2−1+cn+crδ+2cr+41−δ1−cn2/642−δ21−δLD¯D1−cn22−δ/44−δ1−δ+δ2−2cn+crδ+2crδ−cr/44−δ1−δδ+δ2−1+cn+crδ+2cr2/44−δ21−δδ+cn−2δ−2cn+cr+22/44−δ21−δ+1−cn24+δδ+4δ−cr2/84−δ2δ+δcn−cr2/84−δ21−δOD¯D¯71−cn2/32+15δcn−cr2/1281−δδLD¯D¯1−cn2/8+δcn−cr2/28+δ1−δδ+72+δ2δcn−cr2/88+δ21−δδ+31−cn8+δ−2δcn−cr2/328+δ2Table 8
Environmental impact in strategyj and structure s.
Strategy and structureEnvironmental impactODD2−cnen/4+δcn−crer−δen/41−δδLDDen/2+δ2cn+δcn−8cn+6cren/21−δ8+δ+2+δδcn−crer/8+δ1−δδODD¯1−cnen/2+δcn−crer−δen/81−δδLDD¯1−cnen/2−2−δ5−2δδcn−cren/2δ3−3δ2−5δ+161−δ+2−δ2−δ2+2δδcn−crer/2δ3−3δ2−5δ+161−δδOD¯Den/8+1−2cnen/42−δ+δ−crer/8δ+δcn−crer−δen/81−δδLD¯Dcn−2δ−2cn+cr+2en/24−δ1−δ+1+cn+crδ−δ2−2crer/24−δ1−δOD¯D¯2−cnen/8+δcn−crer−δen/81−δδLD¯D¯en/4−3+δ2−δcn+2cn−cren/48+δ1−δ+2+δδcn−crer/28+δ1−δδProposition 9.
(1)
In the channel structureDD, the consumer surplus in strategy O is higher than that in strategy L if δ<δ6 and is lower than that in strategy L if δ≥δ6; the social welfare in strategy O is higher than that in strategy L if δ<δ7 and is lower than that in strategy L if δ≥δ7; the environmental impact in strategy O is higher than that in strategy L. Formally, CSODD−CSLDD=17cn−16δ2+48cn−cr−112δ−128cn+64cr+128δcn−cr/328+δ21−δ>0 if δ<δ6 and CSODD−CSLDD≤0 if δ≥δ6, where δ6∈0,1 is defined as the real root of the quadratic equation: 16−17cnδ2+112−48cn+crδ+128cn−64cr−128. SWODD−SWLDD=9cn+16δ2+16cn−25cr+112δ+128cn−cr−1δcn−cr/328+δ2δ−1>0 if δ<δ7 and SWODD−SWLDD≤0 if δ≥δ7, where δ7∈0,1 is defined as the real root of the quadratic equation: 9cn+16δ2+16cn−25cr−112δ+128cn−128cr−128. EIODD−EILDD=4−δen−3erδcn−cr/48+δ1−δ>0.(2)
In the channel structureDD¯, the consumer surplus in strategy O is higher than that in strategy L if δ<δ8 and is lower than that in strategy L if δ≥δ8; the social welfare in strategy O is higher than that in strategy L if δ<δ9 and is lower than that in strategy L if δ≥δ9; the environmental impact in strategy O is higher than that in strategy L. Formally,(12)CSODD¯−CSLDD¯=33cn−32δ6+288−342cn−crδ5+1199cn+54cr−768δ4−1138cn+431cr−224δ3−2343cn−1362cr−4256δ2+5600cn−1913cr−6592δ−3072cn+992cr+3072δcn−cr128δ3−3δ2−5δ+1621−δ>0,ifδ<δ8 and CSODD¯−CSLDD¯≤0 if δ≥δ8, where δ8∈0,1 is defined as the real root of the sixth degree equation: 33cn−32δ6+288−342cn−crδ5+1199cn+54cr−768δ4−1138cn+431cr−224δ3−2343cn−1362cr−4256δ2+5600cn−1913cr−6592δ−3072cn+992cr+3072:(13)SWODD¯−SWLDD¯=17cn+32δ6−118cn+49cr+288δ5+255cn+406cr+768δ4−402cn+1023cr−224δ3+1801cn+178cr−4256δ2−4256cn−2455cr−6592δ+3072cn−1−2336crδcn−cr128δ3−3δ2−5δ+162δ−1>0,ifδ<δ9 and SWODD¯−SWLDD¯≤0 if δ≥δ9, where δ9∈0,1 is defined as the real root of the sixth degree equation: 17cn+32δ6−118cn+49cr+288δ5+255cn+406cr+768δ4−402cn+1023cr−224δ3+1801cn+178cr−4256δ2−4256cn−2455cr−6592δ+3072cn−1−2336cr:(14)EIODD¯−EILDD¯=−enδ3+11en−3erδ2−31en+13erδ+24en−13erδcn−cr8δ3−3δ2−5δ+161−δ>0.(3)
In the channel structureD¯D, the consumer surplus in strategy O is higher than that in strategy L; the social welfare in strategy O is higher than that in strategy; the environmental impact in strategy O is higher than that in strategy L if δ>2er/en+er and is lower than that in strategy L if δ≤2er/en+er. Formally,(15)CSOD¯D−CSLD¯D=δ2−1+cn+crδ+2cr3δ4+5cn−3cr−39δ3−12cn−34cr−100δ2−88cr+64δ+64cr1284−δ22−δ2δ−1>0,SWOD¯D−SWLD¯D=δ2−1+cn+crδ+2cr13δ4−21cn+13cr+73δ3+108cn+94cr+124δ2−128cn+232cr+64δ+192cr1284−δ22−δ2δ−1>0,EIOD¯D−EILD¯D=en+erδ−2erδ2−1+cn+crδ+2cr84−δ2−δδ−1>0,ifδ>2er/en+er and EIOD¯D−EILD¯D≤0 if δ≤2er/en+er.(4)
In the channel structureD¯D¯, the consumer surplus in strategy O is higher than that in strategy L if δ<δ6 and is lower than that in strategy L if δ≥δ6; the social welfare in strategy O is higher than that in strategy L if δ<δ10 and is lower than that in strategy L if δ≥δ10; the environmental impact in strategy O is higher than that in strategy L. Formally,(16)CSOD¯D¯−CSLD¯D¯=17cn−16δ2+48cn−cr−112δ−128cn+64cr+128δcn−cr1288+δ21−δ>0,ifδ<δ6 and CSOD¯D¯−CSLD¯D¯≤0 if δ≥δ6, where δ6∈0,1 is defined as the real root of the quadratic equation: 16−17cnδ2+112−48cn+crδ+128cn−64cr−128:(17)SWOD¯D¯−SWLD¯D¯=cn+48δ2−16cn+49cr+336δ+384cn−1−−320crδcn−cr1288+δ2δ−1>0,ifδ<δ10 and SWOD¯D¯−SWLD¯D¯≤0 if δ≥δ10, where δ10∈0,1 is defined as the real root of the quadratic equation: cn+48δ2−16cn+49cr+336δ+384cn−320cr−384:(18)EIODD−EILDD=4−δen−3erδcn−cr88+δ1−δ>0.Proposition9 illustrates that, in the different channel structures, the optimal remanufacturing strategy may lead to higher or lower consumer surplus, social welfare, and environmental impact. More precisely, in the channel structure DD and D¯D¯, the OEM’s remanufacturing strategy benefits consumers and society when the WTP discount factor is sufficiently high and hurts them when the factor is sufficiently low. In the channel structure DD¯, the OEM’s remanufacturing strategy benefits consumers and society when the WTP discount factor is either low or high and hurts them otherwise. In the channel structure D¯D, the OEM’s remanufacturing strategy always benefits consumers and society. We present Figures 2 and 3 to provide a visual illustration of consumer surplus and social welfare in different strategies and structures, respectively.
Notes. The following parameter values are used: cn=0.4 and cr=0.1. Qualitatively, the results do not change for other values of the parameter.
Notes. The following parameter values are used: cn=0.4 and cr=0.1. Qualitatively, the results do not change for other values of the parameter.
In terms of environmental impact, we present Figure4 to clarify.
Notes. The following parameter values are used: cn=0.4, cr=0.1, en=0.8, and er=0.6. Qualitatively, the results do not change for other values of the parameter.
In the channel structureDD and D¯D¯, the OEM’s remanufacturing strategy is always friendly to the environment. However, in the channel structure DD¯ and D¯D, the strategy is environmentally friendly when the WTP discount factor is high and unfriendly to the environment when the factor is low.Figure 2
Consumer surplus in different strategies and distribution channel structures.Figure 3
Social welfare in different strategies and distribution channel structures.Figure 4
Environmental impact in different strategies and distribution channel structures.


## 4.1. Distribution Channel StructureDD

In this section, we consider the structureDD, in which both the new and remanufactured products are sold directly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM and the 3PR, which are given by(1)ΠMODD=pnODD−cndnODD+prODD−poODDdrODD,ΠRODD=poODD−crdrODD.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoODD. Sequentially, the OEM determines the retail prices pnODD and prODD of the new and remanufactured products, respectively.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLDD. Then, the OEM and the 3PR maximize their profits by optimizing the retail prices of new and remanufactured products, respectively. The profits of the OEM and the 3PR, which are given by(2)ΠMLDD=pnLDD−cndnLDD+plLDDdrLDD,ΠRLDD=prLDD−cr−plLDDdrLDD.We solve the game backward to ensure subgame perfection. Proposition1 states the equilibrium solutions in strategy O and strategy L.Proposition 1.
In the channel structureDD, the equilibrium solutions are summarized in Table 2.Proposition1 states the equilibrium solutions in structure DD. According to this, we compare the OEM’s equilibrium results, which lead to Corollary 1. For easy interpretation, we define the unit marginal profits of new products for the OEM as mpnODD=pnODD−cn in strategy O and mpnLDD=pnLDD−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprODD=prODD−poODD in strategy O and mprLDD=plLDD in strategy L, respectively.Table 2
Equilibrium solutions in structureDD.
Optimal solutionsStrategyOStrategyLpoODDplLDDδcn+cr/2δ21−cn+8δ−cr/28+δpnODDpnLDD1+cn/21+cn/2+δcn−cr/8+δprODDprLDD2δ+δcn+cr/4δ/2+δ2cn+4δcn+4cr/28+δdnODDdnLDD2−cn/4−cn−cr/41−δ1/2+δ2cn+δcn−8cn+6cr/21−δ8+δdrODDdrLDDδcn−cr/41−δδ2+δδcn−cr/8+δ1−δδΠMODDΠMLDDδcn−cr2/161−δδ+1−cn2/4δcn−cr2/8+δ1−δδ+1−cn2/4ΠRODDΠRLDDδcn−cr2/81−δδ2+δ2δcn−cr2/8+δ21−δδCorollary 1.
In the channel structureDD,(1)
The unit marginal profit of new products for the OEM in strategyO is lower than the profit in strategy L. Formally, mpnODD−mpnLDD=−δcn−cr/8+δ<0.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is lower than the profit in strategy L. Formally, mprODD−mprLDD=−8−δδcn−cr/48+δ<0.(3)
The demand for new products in strategyO is higher than the demand in strategy L. Formally, dnODD−dnLDD=4−δδcn−cr/48+δ1−δ>0.(4)
The demand for remanufactured products in strategypnODDO is lower than the demand in strategy L. Formally, drODD−drLDD=−3δcn−cr/48+δ1−δ<0.Corollary1 demonstrates that, for the OEM, when he chooses to license the whole remanufacturing business to the 3PR rather than only outsource the remanufacturing operations, he can get higher unit marginal profits from both the new and remanufactured products. Furthermore, the 3PR produces more remanufactured products, which further increases the OEM’s profit from licensing. The cons of licensing for the OEM is licensing leads to the 3PR gains the whole control for the remanufacturing business. Thus, the new product would face more intense retail competition. The OEM cuts back on the production of new products.Next, we characterize the conditions for the OEM to choose different remanufacturing strategies in structureDD. By comparing strategy O with strategy L, we derive the following proposition.Proposition 2.
In the channel structureDD,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L. Formally, ΠMODD−ΠMLDD=−8−δδcn−cr=2/16δ+81−δδ<0.(2)
The 3PR’s profit in strategyO is higher than the profit in strategy L. Formally, ΠRODD−ΠRLDD=32−7δ2−16δδcn−cr2/8δ+821−δδ>0.According to Proposition2, we find that the OEM always chooses to license the remanufacturing to the 3PR in the channel structure DD. The reason is, as demonstrated in Corollary 1, licensing can lead to higher marginal profits from both new and remanufactured products and larger production from remanufactured products. However, the OEM’s choice makes the 3PR get worse (i.e., ΠRLDD−ΠRODD<0).


## 4.2. Distribution Channel StructureDD¯

In this section, we consider the structureDD¯, in which only the new products are sold directly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM, the 3PR, and the retailer, which are given by(3)ΠMODD¯=pnODD¯−cndnODD¯+wrODD¯−poODD¯drODD¯,ΠRODD¯=poODD¯−crdrODD¯,ΠTODD¯=0prODD¯−wrODD¯drODD¯.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoODD¯. Secondly, the OEM determines the retail price pnODD¯ of the new products and the wholesale price wrODD¯ of the remanufactured products to the retailer. Finally, the retailer determines the retail price prODD¯ of the remanufactured products.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLDD¯. Then, according to plLDD¯, the 3PR maximizes her profit by optimizing the wholesale price wrLDD¯ of the remanufactured products to the retailer. Thirdly, the retailer determines the prices of the new and remanufactured products, respectively. The profits of the OEM, the 3PR, and the retailer, which are given by(4)ΠMLDD¯=pnLDD¯−cndnLDD¯+plLDD¯drLDD¯,ΠRLDD¯=wrLDD¯−cr−plLDD¯drLDD¯,ΠTLDD¯=prLDD¯−wrLDD¯drLDD¯.Similarly, we use backward induction to ensure subgame perfection. Proposition3 states the equilibrium solutions in strategy O and strategy L.Proposition 3.
In the channel structureDD¯, the equilibrium solutions are summarized in Table 3.According to Proposition3, we compare the OEM’s equilibrium results, which lead to Corollary 2. Similarly, we define the unit marginal profits of new products for the OEM as mpnODD¯=pnODD¯−cn in strategy O and mpnLDD¯=pnLDD¯−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprODD¯=wrODD¯−poODD¯ in strategy O and mprLDD¯=plLDD¯ in strategy L, respectively.Table 3
Equilibrium solutions in structureDD¯.
Optimal solutionsStrategyOStrategyLpoODD¯plLDD¯δcn+cr/2δ1−cn/2+2−δ8−3δδcn−cr/2δ3−3δ2−5δ+16wrODD¯wrLDD¯2δ+δcn+cr/4δ+cr/2+8−3δδcn−cr/2δ3−3δ2−5δ+16pnODD¯pnLDD¯1+cn/21+cn/2+3−δ2−δδcn−cr/2δ3−3δ2−5δ+16prODD¯prLDD¯4δ+3δcn+cr/8δ1+cn/2−2−δ2δcn−cr/2δ3−3δ2−5δ+16dnODD¯dnLDD¯1−cn/2−δcn−cr/81−δ1−cn/2−2−δ5−2δδcn−cr/2δ3−3δ2−5δ+161−δdrODD¯drLDD¯δcn−cr/81−δδ2−δ2−δ2+2δδcn−cr/2δ3−3δ2−5δ+161−δδΠMODD¯ΠMLDD¯1−cn2/4+δcn−cr2/321−δδ1−cn2/4+2−δ2δcn−cr2/4δ3−3δ2−5δ+161−δδΠRODD¯ΠRLDD¯δcn−cr2/161−δδ2−δ4−δδ2−2δ−22δcn−cr2/4δ3−3δ2−5δ+1621−δδΠTODD¯ΠTLDD¯δcn−cr2/641−δδ2−δ2δ2−2δ−22δcn−cr2/4δ3−3δ2−5δ+1621−δδCorollary 2.
In the channel structureDD¯,(1)
The unit marginal profit of new products for the OEM in strategyO is lower than the profit in strategy L. Formally, mpnODD¯−mpnLDD¯=−3−δ2−δδcn−cr/2δ3−3δ2−5δ+16<0.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is lower than the profit in strategy L. Formally, mprODD¯−mprLDD¯=−δ3−9δ2+23δ−16δcn−cr/4δ3−3δ2−5δ+16<0.(3)
The demand for new products in strategyO is higher than the demand in strategy L. Formally, dnODD−dnLDD=δ3−11δ2+31δ−24δcn−cr/8δ−1δ3−3δ2−5δ+16>0.(4)
The demand for remanufactured products in strategypnODDO is lower than the demand in strategy L. Formally, drODD−drLDD=−3δ2+131−δδcn−cr/81−δδ3−3δ2−5δ+16<0.As the same as the structureDD, the OEM can get higher unit marginal profits from both new and remanufactured products and a larger demand from remanufactured products in strategy L and structure DD¯. Interestingly, we find that the OEM may not always choose to license the whole remanufacturing business to the 3PR. This is summarized in the following proposition.Proposition 4.
In the channel structureDD¯,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L if δ>δ1; otherwise, the profit in strategy O is higher than that in strategy L. Formally, ΠMODD¯−ΠMLDD¯=−δ3−11δ2+27δ−16δcn−cr2/32δ3−3δ2−5δ+161−δδ<0 if δ>δ1 and ΠMODD¯−ΠMLDD¯≥0 if δ≤δ1, where δ1∈0,1 is defined as the real root of the cubic equation: δ3−11δ2+27δ−16=0.(2)
The 3PR’s profit in strategyO is lower than the profit in strategy L if δ>δ2; otherwise, the profit in strategy O is higher than that in strategy L. Formally, ΠRODD¯−ΠRLDD¯=−3δ6−34δ5+129δ4−158δ3−105δ2+320δ−128δcn−cr2/16δ3−3δ2−5δ+1621−δδ<0 if δ>δ2 and ΠRODD¯−ΠRLDD¯≥0 if δ≤δ2, where δ2∈0,1 is defined as the real root of the sixth degree equation: 3δ6−34δ5+129δ4−158δ3−105δ2+320δ−128=0.(3)
The retailer’s profit in strategyO is lower than the profit in strategy L. Formally, ΠTODD¯−ΠTLDD¯=−15δ5−122δ4+321δ3−190δ2−377δ+416δcn−cr2/64δ3−3δ2−5δ+1621−δ<0.Proposition4 illustrates that, in the structure DD¯, when the WTP discount factor for a remanufactured product is sufficiently low (i.e., δ≤δ1), the OEM chooses to only outsource the remanufacturing operation to the 3PR. The reason is that the OEM produces larger new products when he adopts strategy O and the benefits of larger new products outweigh the disadvantages of lower margin profits when the WTP discount factor is low. From the 3PR’s perspective, the OEM’s choice makes the 3PR worse when the WTP discount factor is in a midrange (i.e., δ2<δ<δ1). Specifically, when the WTP discount factor is sufficiently low (i.e., δ≤δ2), the OEM adopts strategy O and the 3PR realizes a higher profit (i.e., ΠRODD¯−ΠRLDD¯>0 when δ≤δ2). When the WTP discount factor is sufficiently high (i.e., δ≥δ1), the OEM adopts strategy L and the 3PR realizes a higher profit (i.e., ΠRLDD¯−ΠRODD¯>0 when δ≥δ1). From the retailer’s perspective, the OEM’s choice makes the retailer worse when the WTP discount factor is low (i.e., ΠTODD¯−ΠTLDD¯<0).


## 4.3. Distribution Channel StructureD¯D

In this section, we consider the structureD¯D, in which only the remanufactured products are sold directly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM, the 3PR, and the retailer, which are given by(5)ΠMOD¯D=wnOD¯D−cndnOD¯D+prOD¯D−poOD¯DdrOD¯D,ΠROD¯D=poOD¯D−crdrOD¯D,ΠTOD¯D=pnOD¯D−wnOD¯DdnOD¯D.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoOD¯D. Secondly, the OEM determines the retail price prOD¯D of the remanufactured products and the wholesale price wnOD¯D of the new products to the retailer. Finally, the retailer determines the retail price pnOD¯D of the new products.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLD¯D and the wholesale price wnLD¯D. Sequentially, the 3PR maximizes her profit by optimizing the retail price prLD¯D of the remanufactured products. Simultaneously, the retailer determines the price pnLD¯D of the new products. The profits of the OEM, the 3PR, and the retailer, which are given by(6)ΠMLD¯D=wnLD¯D−cndnLD¯D+plLD¯DdrLD¯D,ΠRLD¯D=prLD¯D−cr−plLD¯DdrLD¯D,ΠTLD¯D=pnLD¯D−wnLD¯DdnLD¯D.Similarly, we use backward induction to ensure subgame perfection. Proposition5 states the equilibrium solutions in strategy O and strategy L.Proposition 5.
In the channel structureD¯D, the equilibrium solutions are summarized in Table 4.According to Proposition5, we compare the OEM’s equilibrium results, which lead to Corollary 3. In the same manner, we define the unit marginal profits of new products for the OEM as mpnOD¯D=wnOD¯D−cn in strategy O and mpnLD¯D=wnLD¯D−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprOD¯D=prOD¯D−poOD¯D in strategy O and mprLD¯D=plLD¯D in strategy L, respectively.Table 4
Equilibrium solutions in structureD¯D.
Optimal solutionsStrategyOStrategyLpoOD¯DplLD¯D1+cn−δδ/22−δ+cr/2δ−cr/2wnOD¯DwnLD¯D1+cn/21+cn/2pnOD¯DpnLD¯D6−δ+cn+cr/8+2cn−δ/82−δ6−3δ+2cn+cr/24−δprOD¯DprLD¯Dcr/4+−3δ2+5δ+δcn/42−δ5+δcn+2cr−2δ2/24−δdnOD¯DdnLD¯D1/8+1−2cn/42−δ−cn−cr/81−δcn−2δ−2cn+cr+2/24−δ1−δdrOD¯DdrLD¯Dδ−cr/8δ+δcn−cr/81−δδ1+cn+crδ−δ2−2cr/24−δ1−δΠMOD¯DΠMLD¯Dδ2−1+cn+crδ+2cr2/322−δ1−δδ+1−cn2/42−δ1−cn22−δ/44−δ1−δ+δ2−2cn+crδ+2crδ−cr/44−δ1−δδΠROD¯DΠRLD¯Dδ2−1+cn+crδ+2cr2/162−δ1−δδδ2−1+cn+crδ+2cr2/44−δ21−δδΠTOD¯DΠTLD¯Dδ2−1+cn+crδ+2cr+41−δ1−cn2/642−δ21−δcn−2δ−2cn+cr+22/44−δ21−δCorollary 3.
In the channel structureD¯D,(1)
The unit marginal profit of new products for the OEM in strategyO is the same as the profit in strategy L.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is higher than the profit in strategy L if δ<δ3 and is lower than the profit in strategy L if δ≥δ3. Formally, mprOD¯D−mprLD¯D=δ2−cn+cr+1δ+2cr/42−δ>0 if δ<δ3 and mprOD¯D−mprLD¯D≤0 if δ≥δ3, which is defined as the real root of the quadratic equation: δ2−cn+cr+1δ+2cr.(3)
The demand for new products in strategyO is lower than the demand in strategy if δ<δ3 and is higher than the demand in strategy L if δ≥δ3. Formally, dnOD¯D−dnLD¯D=−δ2−cn+cr+1δ+2crδ/84−δ2−δ1−δ<0 if δ<δ3 and dnOD¯D−dnLD¯D≥0 if δ≥δ3.(4)
The demand for remanufactured products in strategyO is higher than the demand in strategy L if δ<δ3 and is lower than the demand in strategy L if δ≥δ3. Formally, drOD¯D−drLD¯D=δ2−cn+cr+1δ+2cr/84−δ1−δ>0 if δ<δ3 and drOD¯D−drLD¯D≤0 if δ≥δ3.Different from the structureDD and DD¯, in the channel structure D¯D, the OEM earns a constant unit marginal profit from new products no matter what remanufacturing strategy the OEM chooses. With a low WTP discount factor (i.e., δ<δ3), the OEM earns a higher unit marginal profit from remanufactured products in strategy O and the demand for remanufactured products is higher in strategy O. However, the OEM produces smaller new products in strategy O. With a high WTP discount factor (i.e., δ≥δ3), the OEM earns a lower unit marginal profit from remanufactured products in strategy O and the demand for remanufactured products is lower in strategy O. However, the OEM produces larger new products in strategy O. An intriguing result is that different changes in unit marginal profit and demand may cause the OEM to always choose the same remanufacturing strategy, as Proposition 6 presents.Proposition 6.
In the channel structureD¯D,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L. Formally, ΠMOD¯D−ΠMLD¯D=−δ2−cn+cr+1δ+2cr24+δ/324−δ2−δ1−δδ<0.(2)
The 3PR’s profit in strategyO is higher than the profit in strategy L. Formally, ΠROD¯D−ΠRLD¯D=δ2−1+cn+crδ+2cr2δ2−4δ+8/164−δ22−δ1−δδ>0.(3)
The retailer’s profit in strategyO is higher than the profit in strategy L if δ4<δ<δ5; otherwise, the profit in strategy O is lower than that in strategy L. Formally, ΠTOD¯D−ΠTLD¯D=δ2−1+cn+crδ+2cr321−δ1−cn+4−δ2cr−16−δ1−δδ−7δcn+2crδ/644−δ22−δ21−δ>0 if δ4<δ<δ5 and ΠTOD¯D−ΠTLD¯D≤0 if δ≤δ4 or δ≥δ5, where δ4∈0,1 and δ5∈0,1 are defined as the smaller and larger real root of the quintic equation: δ2−1+cn+crδ+2cr321−δ1−cn+4−δ2cr−16−δ1−δδ−7δcn+2cr.According to Proposition6, we find that, in the structure D¯D, the OEM always chooses to license the remanufacturing to the 3PR in the channel structure DD. However, the OEM’s choice makes the 3PR get worse (i.e., ΠRLDD−ΠRODD<0). And, the retailer also gets worse when the WTP discount factor is in a midrange (i.e., ΠTLDD−ΠTODD<0 when δ4<δ<δ5).


## 4.4. Distribution Channel StructureD¯D¯

In this section, we consider the structureD¯D¯, in which both the new and remanufactured products are sold indirectly. Firstly, consider that the OEM outsources remanufacturing operation. Based on the above model description, we can get the profits of the OEM, the 3PR, and the retailer, which are given by(7)ΠMOD¯D¯=wnOD¯D¯−cndnOD¯D¯+wrOD¯D¯−poOD¯D¯drOD¯D¯,ΠROD¯D¯=poOD¯D¯−crdrOD¯D¯,ΠTOD¯D¯=pnOD¯D¯−wnOD¯D¯dnOD¯D¯+prOD¯D¯−wrOD¯D¯drOD¯D¯.The sequence of events is as follows: first, the 3PR decides on the outsourcing feepoOD¯D¯. Secondly, the OEM determines the wholesale price wnOD¯D¯ of the new products to the retailer and the wholesale price wrOD¯D¯ of the remanufactured products. Finally, the retailer determines the retail price pnOD¯D¯ and prOD¯D¯of the new and remanufactured products, respectively.Secondly, we consider that the OEM licenses the whole remanufacturing business to the 3PR. In this model, the OEM first decides on the licensing feeplLD¯D¯. Sequentially, the 3PR maximizes her profit by optimizing the wholesale price wrLD¯D¯ of the remanufactured products. Simultaneously, the OEM determines the wholesale price wnLD¯D¯ of the new products. Finally, the retailer determines the retail price pnLD¯D¯ and prLD¯D¯ of the new and remanufactured products, respectively. The profits of the OEM, the 3PR, and the retailer, which are given by(8)ΠMLD¯D¯=wnLD¯D¯−cndnLD¯D¯+plLD¯D¯drLD¯D¯,ΠRLD¯D¯=wrLD¯D¯−cr−plLD¯D¯drLD¯D¯,ΠTLD¯D¯=pnLD¯D¯−wnLD¯D¯dnLD¯D¯+prLD¯D¯−wrLD¯D¯drLD¯D¯.Similarly, we use backward induction to ensure subgame perfection. Proposition7 states the equilibrium solutions in strategy O and strategy L.Proposition 7.
In the channel structureD¯D¯, the equilibrium solutions are summarized in Table 5.We define the unit marginal profits of new products for the OEM asmpnOD¯D¯=wnOD¯D¯−cn in strategy O and mpnLD¯D¯=wnLD¯D¯−cn in strategy L, respectively. The unit marginal profits of remanufactured products for the OEM are mprOD¯D¯=wrOD¯D¯−poOD¯D¯ in strategy O and mprLD¯D¯=plLD¯D¯ in strategy L, respectively. According to Proposition 7, we compare the OEM’s equilibrium results, which lead to Corollary 4.Table 5
Equilibrium solutions in structureD¯D¯.
Optimal solutionsStrategyOStrategyLpoOD¯D¯plLD¯D¯δcn+cr/2δ/2−δ2cn+8cr/28+δwnOD¯D¯wnLD¯D¯1+cn/21+cn/2+δcn−cr/8+δwrOD¯D¯wrLD¯D¯δ/2+δcn+cr/4δ/2+δ2cn+4δcn+4cr/28+δpnOD¯D¯pnLD¯D¯3+cn/43+cn/4+δcn−cr/28+δprOD¯D¯prLD¯D¯3δ/4+δcn+cr/83δ/4+δ2cn+4δcn+4cr/48+δdnOD¯D¯dnLD¯D¯2−cn/8−cn−cr/81−δ1/4−3+δ2−δcn+2cn−cr/48+δ1−δdrOD¯D¯drLD¯D¯δcn−cr/81−δδ2+δδcn−cr/28+δ1−δδΠMOD¯D¯ΠMLD¯D¯1−cn2/8+δcn−cr2/321−δδ1−cn2/8+δcn−cr2/28+δ1−δδΠROD¯D¯ΠRLD¯D¯δcn−cr2/161−δδ2+δ2δcn−cr2/28+δ21−δδΠTOD¯D¯ΠTLD¯D¯1−cn2/16+δcn−cr2/641−δδ2+δ2δcn−cr2/48+δ21−δδ+1−cn8+δ−2δcn−cr2/168+δ2Corollary 4.
In the channel structureD¯D¯,(1)
The unit marginal profit of new products for the OEM in strategyO is lower than the profit in strategy L. Formally, mpnOD¯D¯−mpnLD¯D¯=−δcn−cr/8+δ<0.(2)
The unit marginal profit of remanufactured products for the OEM in strategyO is lower than the profit in strategy L. Formally, mprOD¯D¯−mprLD¯D¯=−8−δδcn−cr/48+δ<0.(3)
The demand for new products in strategyO is higher than the demand in strategy. Formally, dnOD¯D¯−dnLD¯D¯=4−δδcn−cr/88+δ1−δ>0.(4)
The demand for remanufactured products in strategypnODDO is lower than the demand in strategy L. Formally, drOD¯D¯−drLD¯D¯=−3δcn−cr/88+δ1−δ<0.Corollary4 illustrates that, as the same as the structure DD and DD¯, the OEM can get higher unit marginal profits from both new and remanufactured products and a larger demand from remanufactured products in strategy L and structure D¯D¯.Next, we characterize the conditions for the OEM to choose different remanufacturing strategies in distribution channel structureD¯D¯. By comparing strategy O with strategy L, we derive the following proposition.Proposition 8.
In the channel structureD¯D¯,(1)
The OEM’s profit in strategyO is lower than the profit in strategy L. Formally, ΠMOD¯D¯−ΠMLD¯D¯=−8−δδcn−cr2/328+δ1−δδ<0.(2)
The 3PR’s profit in strategyO is higher than the profit in strategy L. Formally, ΠROD¯D¯−ΠRLD¯D¯=32−16δ−7δ2δcn−cr2/168+δ21−δδ>0.(3)
The retailer’s profit in strategyO is lower than the profit in strategy L if δ>δ6; otherwise, the profit in strategy O is higher than that in strategy L. Formally, ΠTOD¯D¯−ΠTLD¯D¯=−16−17cnδ2+112−48cn+crδ+128cn−64cr−128δcn−cr/648+δ21−δ<0 if δ>δ6 and ΠTOD¯D¯−ΠTLD¯D¯≥0 if δ≤δ6, where δ6∈0,1 is defined as the real root of the quadratic equation: 16−17cnδ2+112−48cn+crδ+128cn−64cr−128.Proposition8 demonstrates that when both new and remanufactured products are sold through the retailer, the OEM licenses the whole remanufacturing business to the 3PR no matter what the WTP discount factor is. Compared with strategy O, the 3PR realizes a lower profit in strategy L. The sign of the retailer’s profit change depends on the WTP discount factor. Specifically, with a high WTP discount factor, the retailer gets better (i.e., ΠTLD¯D¯−ΠTOD¯D¯>0 when δ>δ6) and the retailer gets worse with a low WTP discount factor (i.e., ΠTLD¯D¯−ΠTOD¯D¯≤0 when δ≤δ6).


## 4.5. Consumer Surplus, Social Welfare, and Environmental Impact

In this section, we extend the analysis from pure profit orientation to include a consumer surplus perspective, a social welfare perspective, and an environmental impact perspective.For the consumer of typeθ, the surplus of an individual consumer who purchases a new product is θ−pnjs and the surplus of an individual consumer who purchases a remanufactured product is δθ−prjs. Therefore, the total consumer surplus is given by(9)CSjs=∫1−dnjs−drjs1−dnjsδθ−prjsdθ+∫1−dnjs1θ−pnjsdθ.Correspondingly, the social welfare in strategyj and channel structure s is given by(10)SWjs=CSjs+ΠMjs+ΠRjs+ΠTjs.From the environmental impact perspective, when the OEM producesdnjs units and the 3PR remanufactures drjs units, the total environmental impact in strategy j and channel structure s is given by(11)EIjs=dnjsen+drjser.The next lemma shows the consumer surplus, social welfare, and environmental impact in different strategies and channel structures.Lemma 1.
In the strategyj and channel structure s, the consumer surplus, social welfare, and environmental impact are summarized in Tables 6–8, respectively.Proposition9 demonstrates the important relationships we derive from Lemma 1.Table 6
Consumer surplus in strategyj and structure s.
Strategy and structureConsumer surplusODD1−cn2/8+δcn−cr2/321−δδLDD2+δ2δcn−cr2/28+δ21−δδ+1−cn8+δ−2δcn−cr2/88+δ2ODD¯1−cn2/8+δcn−cr2/1281−δδLDD¯1−cn2/8+2−δ2δcn−cr23δ3−15δ2+17δ+4/8δ3−3δ2−5δ+1621−δδ−3−δ1−cn/4δ3−3δ2−5δ+16OD¯Dδ2−1+cn+crδ+2cr24−3δ/1282−δ21−δδ+1−cn2+1−cnδ−cr/162−δLD¯D1−cn24+δδ+4δ−cr2/84−δ2δ+δcn−cr2/84−δ21−δOD¯D¯1−cn2/32+δcn−cr2/1281−δδLD¯D¯2+δ2δcn−cr2/88+δ21−δδ+1−cn8+δ−2δcn−cr2/328+δ2Table 7
Social welfare in strategyj and structure s.
Strategy and structureSocial welfareODD31−cn2/8+7δcn−cr2/321−δδLDD1−cn2/4+32+δ2+28+δδcn−cr2/28+δ21−δδ+1−cn8+δ−2δcn−cr2/88+δ2ODD¯31−cn2/8+15δcn−cr2/1281−δδLDD¯31−cn2/8+2−δ2δcn−cr25δ3−21δ2+7δ+36/8δ3−3δ2−5δ+1621−δδ+2−δ3−δδ2−2δ−22δcn−cr2/2δ3−3δ2−5δ+1621−δδ−3−δ1−cn/4δ3−3δ2−5δ+16OD¯Dδ2−1+cn+crδ+2cr216−3δ/1282−δ21−δδ+51−cn2+1−cnδ−cr/162−δ+δ2−1+cn+crδ+2cr+41−δ1−cn2/642−δ21−δLD¯D1−cn22−δ/44−δ1−δ+δ2−2cn+crδ+2crδ−cr/44−δ1−δδ+δ2−1+cn+crδ+2cr2/44−δ21−δδ+cn−2δ−2cn+cr+22/44−δ21−δ+1−cn24+δδ+4δ−cr2/84−δ2δ+δcn−cr2/84−δ21−δOD¯D¯71−cn2/32+15δcn−cr2/1281−δδLD¯D¯1−cn2/8+δcn−cr2/28+δ1−δδ+72+δ2δcn−cr2/88+δ21−δδ+31−cn8+δ−2δcn−cr2/328+δ2Table 8
Environmental impact in strategyj and structure s.
Strategy and structureEnvironmental impactODD2−cnen/4+δcn−crer−δen/41−δδLDDen/2+δ2cn+δcn−8cn+6cren/21−δ8+δ+2+δδcn−crer/8+δ1−δδODD¯1−cnen/2+δcn−crer−δen/81−δδLDD¯1−cnen/2−2−δ5−2δδcn−cren/2δ3−3δ2−5δ+161−δ+2−δ2−δ2+2δδcn−crer/2δ3−3δ2−5δ+161−δδOD¯Den/8+1−2cnen/42−δ+δ−crer/8δ+δcn−crer−δen/81−δδLD¯Dcn−2δ−2cn+cr+2en/24−δ1−δ+1+cn+crδ−δ2−2crer/24−δ1−δOD¯D¯2−cnen/8+δcn−crer−δen/81−δδLD¯D¯en/4−3+δ2−δcn+2cn−cren/48+δ1−δ+2+δδcn−crer/28+δ1−δδProposition 9.
(1)
In the channel structureDD, the consumer surplus in strategy O is higher than that in strategy L if δ<δ6 and is lower than that in strategy L if δ≥δ6; the social welfare in strategy O is higher than that in strategy L if δ<δ7 and is lower than that in strategy L if δ≥δ7; the environmental impact in strategy O is higher than that in strategy L. Formally, CSODD−CSLDD=17cn−16δ2+48cn−cr−112δ−128cn+64cr+128δcn−cr/328+δ21−δ>0 if δ<δ6 and CSODD−CSLDD≤0 if δ≥δ6, where δ6∈0,1 is defined as the real root of the quadratic equation: 16−17cnδ2+112−48cn+crδ+128cn−64cr−128. SWODD−SWLDD=9cn+16δ2+16cn−25cr+112δ+128cn−cr−1δcn−cr/328+δ2δ−1>0 if δ<δ7 and SWODD−SWLDD≤0 if δ≥δ7, where δ7∈0,1 is defined as the real root of the quadratic equation: 9cn+16δ2+16cn−25cr−112δ+128cn−128cr−128. EIODD−EILDD=4−δen−3erδcn−cr/48+δ1−δ>0.(2)
In the channel structureDD¯, the consumer surplus in strategy O is higher than that in strategy L if δ<δ8 and is lower than that in strategy L if δ≥δ8; the social welfare in strategy O is higher than that in strategy L if δ<δ9 and is lower than that in strategy L if δ≥δ9; the environmental impact in strategy O is higher than that in strategy L. Formally,(12)CSODD¯−CSLDD¯=33cn−32δ6+288−342cn−crδ5+1199cn+54cr−768δ4−1138cn+431cr−224δ3−2343cn−1362cr−4256δ2+5600cn−1913cr−6592δ−3072cn+992cr+3072δcn−cr128δ3−3δ2−5δ+1621−δ>0,ifδ<δ8 and CSODD¯−CSLDD¯≤0 if δ≥δ8, where δ8∈0,1 is defined as the real root of the sixth degree equation: 33cn−32δ6+288−342cn−crδ5+1199cn+54cr−768δ4−1138cn+431cr−224δ3−2343cn−1362cr−4256δ2+5600cn−1913cr−6592δ−3072cn+992cr+3072:(13)SWODD¯−SWLDD¯=17cn+32δ6−118cn+49cr+288δ5+255cn+406cr+768δ4−402cn+1023cr−224δ3+1801cn+178cr−4256δ2−4256cn−2455cr−6592δ+3072cn−1−2336crδcn−cr128δ3−3δ2−5δ+162δ−1>0,ifδ<δ9 and SWODD¯−SWLDD¯≤0 if δ≥δ9, where δ9∈0,1 is defined as the real root of the sixth degree equation: 17cn+32δ6−118cn+49cr+288δ5+255cn+406cr+768δ4−402cn+1023cr−224δ3+1801cn+178cr−4256δ2−4256cn−2455cr−6592δ+3072cn−1−2336cr:(14)EIODD¯−EILDD¯=−enδ3+11en−3erδ2−31en+13erδ+24en−13erδcn−cr8δ3−3δ2−5δ+161−δ>0.(3)
In the channel structureD¯D, the consumer surplus in strategy O is higher than that in strategy L; the social welfare in strategy O is higher than that in strategy; the environmental impact in strategy O is higher than that in strategy L if δ>2er/en+er and is lower than that in strategy L if δ≤2er/en+er. Formally,(15)CSOD¯D−CSLD¯D=δ2−1+cn+crδ+2cr3δ4+5cn−3cr−39δ3−12cn−34cr−100δ2−88cr+64δ+64cr1284−δ22−δ2δ−1>0,SWOD¯D−SWLD¯D=δ2−1+cn+crδ+2cr13δ4−21cn+13cr+73δ3+108cn+94cr+124δ2−128cn+232cr+64δ+192cr1284−δ22−δ2δ−1>0,EIOD¯D−EILD¯D=en+erδ−2erδ2−1+cn+crδ+2cr84−δ2−δδ−1>0,ifδ>2er/en+er and EIOD¯D−EILD¯D≤0 if δ≤2er/en+er.(4)
In the channel structureD¯D¯, the consumer surplus in strategy O is higher than that in strategy L if δ<δ6 and is lower than that in strategy L if δ≥δ6; the social welfare in strategy O is higher than that in strategy L if δ<δ10 and is lower than that in strategy L if δ≥δ10; the environmental impact in strategy O is higher than that in strategy L. Formally,(16)CSOD¯D¯−CSLD¯D¯=17cn−16δ2+48cn−cr−112δ−128cn+64cr+128δcn−cr1288+δ21−δ>0,ifδ<δ6 and CSOD¯D¯−CSLD¯D¯≤0 if δ≥δ6, where δ6∈0,1 is defined as the real root of the quadratic equation: 16−17cnδ2+112−48cn+crδ+128cn−64cr−128:(17)SWOD¯D¯−SWLD¯D¯=cn+48δ2−16cn+49cr+336δ+384cn−1−−320crδcn−cr1288+δ2δ−1>0,ifδ<δ10 and SWOD¯D¯−SWLD¯D¯≤0 if δ≥δ10, where δ10∈0,1 is defined as the real root of the quadratic equation: cn+48δ2−16cn+49cr+336δ+384cn−320cr−384:(18)EIODD−EILDD=4−δen−3erδcn−cr88+δ1−δ>0.Proposition9 illustrates that, in the different channel structures, the optimal remanufacturing strategy may lead to higher or lower consumer surplus, social welfare, and environmental impact. More precisely, in the channel structure DD and D¯D¯, the OEM’s remanufacturing strategy benefits consumers and society when the WTP discount factor is sufficiently high and hurts them when the factor is sufficiently low. In the channel structure DD¯, the OEM’s remanufacturing strategy benefits consumers and society when the WTP discount factor is either low or high and hurts them otherwise. In the channel structure D¯D, the OEM’s remanufacturing strategy always benefits consumers and society. We present Figures 2 and 3 to provide a visual illustration of consumer surplus and social welfare in different strategies and structures, respectively.
Notes. The following parameter values are used: cn=0.4 and cr=0.1. Qualitatively, the results do not change for other values of the parameter.
Notes. The following parameter values are used: cn=0.4 and cr=0.1. Qualitatively, the results do not change for other values of the parameter.
In terms of environmental impact, we present Figure4 to clarify.
Notes. The following parameter values are used: cn=0.4, cr=0.1, en=0.8, and er=0.6. Qualitatively, the results do not change for other values of the parameter.
In the channel structureDD and D¯D¯, the OEM’s remanufacturing strategy is always friendly to the environment. However, in the channel structure DD¯ and D¯D, the strategy is environmentally friendly when the WTP discount factor is high and unfriendly to the environment when the factor is low.Figure 2
Consumer surplus in different strategies and distribution channel structures.Figure 3
Social welfare in different strategies and distribution channel structures.Figure 4
Environmental impact in different strategies and distribution channel structures.


## 5. Conclusions

In this study, we seek insights for OEMs that consider cooperating with 3PRs. Inspired by some examples found in practice, we consider the interaction among three firms, including an OEM who produces a new remanufactured product and has two remanufacturing strategies (i.e., outsourcing and licensing), a 3PR who collects and remanufactures the returned products, and a retailer through which the OEM and 3PR sell their products. Given this construct, we derive the optimal product pricing and resulting product sales and profits of different entities in different remanufacturing strategies and channel structures. To the best of our knowledge, this study is the first to shed light on the remanufacturing strategy in the channel structure. We demonstrate that outsourcing remanufacturing benefits the OEM when the new products are sold directly and remanufactured products, with a relatively low valuation, are sold indirectly; otherwise, licensing remanufacturing is more beneficial for the OEM. In line with our findings, Panasonic sells its remanufactured products, which with relatively low valuations, through several reseller partners, including Bizco, BAYCOM, and Daly Computers, Dell licenses its remanufacturing operations and sales to GENCO ATC, and Apple licenses its remanufacturing business in China to Foxconn.In addition, we have come to several interesting results. First, we find that, in the channel structureDD, the OEM always chooses to license the remanufacturing to the 3PR and such a choice makes the 3PR get worse. Second, in the channel structure DD¯, the OEM prefers to license the remanufacturing when the consumers perceive the remanufactured products with a high value (i.e., the WTP discount factor is sufficiently high); otherwise, outsourcing remanufacturing is more beneficial for the OEM. According to the OEM’s selection, the 3PR realizes a higher profit when the discount factor is high or low and the retailer realizes a higher profit when the discount factor is high. Third, in the channel structure D¯D, the OEM prefers licensing remanufacturing whereas the 3PR prefers outsourcing remanufacturing and the retailer prefers licensing remanufacturing with a high or low discount factor. Fourth, in the channel structure D¯D¯, the OEM also prefers to license the remanufacturing to the 3PR, and such strategy selection hurts the 3PR and the retailer when consumers perceive remanufactured products with a low value. Fifth, from the perspective of consumer surplus and social welfare, the OEM’s strategy selection benefits consumers and society when the WTP discount factor is high and regardless of the channel structure. The selection also benefits them when the discount factor is low and in the channel structure DD¯. Finally, the OEM’s remanufacturing strategies are always environmentally friendly in the channel structure DD and D¯D¯. In the structure DD¯ and D¯D, the strategies benefit the environment when consumers perceive remanufactured products with a high value.Our work also has some limitations. We consider the channel structures are exogenous. Relaxing this assumption and considering the OEM not only selects the remanufacturing strategies but also selects the distribution channel structures which may derive more insights. Furthermore, it would be interesting to study how the OEM could outsource or license remanufacturing operations to the retailer.



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