Closed-loop supply chain models with product take-back and hybrid remanufacturing under technology licensing

Accepted Manuscript Closed-loop supply chain models with product take-back and hybrid remanufacturing under technology licensing Yanting Huang, Zongjun Wang PII:

S0959-6526(16)31675-4

DOI:

10.1016/j.jclepro.2016.10.065

Reference:

JCLP 8256

To appear in:

Journal of Cleaner Production

Received Date: 4 May 2016 Revised Date:

30 July 2016

Accepted Date: 13 October 2016

Please cite this article as: Huang Y, Wang Z, Closed-loop supply chain models with product take-back and hybrid remanufacturing under technology licensing, Journal of Cleaner Production (2016), doi: 10.1016/j.jclepro.2016.10.065. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Closed-Loop Supply Chain Models with Product Take-back and Hybrid Remanufacturing under Technology Licensing Yanting Huang* and Zongjun Wang School of Management, Huazhong University of Science and Technology, Wuhan 430074, China;

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*Correspondence: [email protected]; Tel./Fax:+86-27-8755-6440

Abstract: The economical and environmental benefits of remanufacturing have been widely recognized in literature and practical life. In this paper, we consider a

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closed-loop supply chain consisting of a manufacturer, a distributor and a third party, who are engaged in producing remanufactured products. Additionally, the manufacturer as the channel leader tends to cooperate with the distributor and the third

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party by technology licensing. Specifically, we develop three hybrid remanufacturing models: (1) the manufacturer collects and remanufactures used products by herself (Model M), (2) the manufacturer remanufactures a fraction of used products and licenses the distributor to remanufacture while the distributor collects used products (Model MD), (3) the manufacturer remanufactures a fraction of used products and

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licenses the third party to remanufacture while the third party collects used products (Model MT). We discuss the impacts of remanufacturing ability on the chain members and environmental sustainability, and also analyze the role of saving unit cost in the remanufacturing process. Moreover, we apply the Stackelberg game to attain the

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equilibrium strategies from the perspective of chain members’ profits. The profit of the manufacturer, the distributor and the third party reaches the most in Model M,

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Model MD and Model MT, respectively. These results can help achieve an optimal approach of hybrid remanufacturing in a closed-loop supply chain. Keywords: closed-loop supply chain; hybrid remanufacturing; technology licensing; game theory; take-back

1. Introduction Over decades, the environmental performance of products and processes in a closed-loop supply chain (CLSC) has gained considerable attention. Remanufacturing is an effective approach because it can not only mitigate the environmental burden but 1

ACCEPTED MANUSCRIPT also cut down the production costs (Atasu et al., 2008b; Wu, 2012b). Relevant literature (Ferrer and Swaminathan, 2010; Geyer et al., 2007; Guide Jr et al., 2006; Guide Jr and Van Wassenhove, 2009; Guide and Wassenhove, 2006) indicates that remanufacturing performs economically and environmentally. Many companies, such as Kodak (Geyer et al., 2007), IBM, BMW, Xerox and Home Depot (Guide Jr and Van Wassenhove,

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2009), are some good examples in this area. In practice, remanufacturing is carried out by either original equipment manufacturers (OEMs) or independent remanufacturers (Örsdemir et al., 2014). However, the growing remanufacturers would seriously affect the sale of new products. To deal with such tough issue, OEMs may enter the market by

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remanufacturing alone or cooperative remanufacturing with others (Ferrer and Swaminathan, 2006; Savaskan et al., 2004). While considering the transportation, inventory costs and such factors, OEMs would lack remanufacturing motivation.

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Therefore, OEMs tend to seek for other ways to conduct remanufacturing activities. Technology licensing, as one well-known means, has already been applied by OEMs to authorize other manufacturers to manufacture new products. It should be pointed out that, as for technology licensing, the licensor only allows the licensee to use the technology rather than transfers the ownership of the licensed technology

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(Zhao et al., 2014). In practice, many companies, such as IBM, Kodak, Dow, Hitachi actively license their technology to other firms and obtain substantial economic revenue (Arora et al., 2013). According to Bloomberg news, Microsoft Company promoted the development of a mobile system based on the Windows phone, through

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licensing technology to Nokia. On the other hand, technology licensing is also applied in remanufacturing used products. Very recently, Apple subcontracted Foxconn to

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remanufacture the End-of-life iPhone mobile phones in China (Zou et al., 2016). This case highlights the critical role of technology licensing within remanufacturing. In addition, such real-world case can also be found in fashion industry. For example, in fashion industry, many recycling companies (e.g., I: CO2) also undertake remanufacturing of new products using the collected used apparel. And fashion companies like Uniqlo, H&M, and Esprit are engaged in cooperating with companies like I: CO2 in further processing the collected products (Wang et al., 2014). Though technology licensing in manufacturing new products has been extensively studied, theoretical research on such favorable activity in the reverse flow is rarely investigated. 2

ACCEPTED MANUSCRIPT Therefore,

we

aim

to

explore the

channel

performance

within

the

remanufacturing under technology licensing. Concerning two main processes in the reverse flow, namely collecting and reprocessing of used products, we propose several remanufacturing models in such a novel scenario. As for collecting used products, similar with the work by Savaskan et al. (2004), three approaches, namely

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manufacturer collection, distributor collection and third party collection are adopted. While in the reprocessing of used products, different from most of prior studies, we consider that both the collecting and reprocessing of used products are undertaken by the distributor/the third party under technology licensing by OEMs. Up to now, most

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of the researches have focused on the retailers’ collection behaviors in remanufacturing system. In reality, it is more possible for the distributor than the retailer to undertake such reprocessing activities due to its relatively larger scale.

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Accordingly, we thus in this paper further explore three hybrid remanufacturing models: (1) the manufacturer collects and remanufactures used products (model M); (2) the distributor collects used products, while both the manufacturer and the distributor hybrid remanufacture used products (model MD); (3) the third party collects used products, while both the manufacturer and the third party hybrid

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remanufacture used products (model MT). Herein, hybrid remanufacturing means that more than one chain member undertake reprocessing returned products. We contribute to this literature by bringing a technology licensing perspective to the hybrid remanufacturing problems through a focus on used products in a CLSC. To the

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best of our knowledge, no prior research has presented hybrid remanufacturing under technology licensing in a CLSC. In this paper, we aim to address the following

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research questions:

(1) What are the equilibrium decisions and profits of each remanufacturing

model?

(2) Among the four remanufacturing models, which is the best one for the chain

members and the environment? (3) How does the remanufacturing ability influence the profit of each chain member and the environment? The remainder of this paper is structured as follows. In the next section, we briefly discuss the relevant literature; meanwhile compare those with our present work. In section 3, we outline basic assumptions and notations. Section 4 presents three remanufacturing models. And in conjunction, we make a comparison to these models 3

ACCEPTED MANUSCRIPT and obtain the equilibrium decisions. Based on these equilibrium results, we describe the interrelationship between the costs, the prices and the corresponding profits. In section 5, we conduct the numerical studies under the three remanufacturing models and discuss the influences of the remanufacturing ability on the profit of each chain member. The last section concludes the paper and promotes future research directions.

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All proofs of this paper are provided in the appendix. 2. Literature Review

This paper is related to two separated streams of researches in the literature: one examines the perspective of technology licensing, and the other explores the

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remanufacturing in a CLSC. For the first stream, most studies only pay attention on the licensing behaviors with respect to manufacturing new products, but not the

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remanufacturing process(Arora et al., 2013; Bagchi and Mukherjee, 2014; Robinson et al., 2015; Savva and Taneri, 2015; Zhao et al., 2014). For instance, Arora et al. (2013) focus on how licensing activity should be organized within large corporation. Zhao et al. (2014) explore the optimal licensing contracts with network effort, and also describe three licensing strategies: fixed-fee licensing, royalty licensing and two-part tariff licensing. While Bagchi and Mukherjee (2014) show how technology licensing affects

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product market competition in a differentiated oligopoly. In addition, Savva and Taneri (2015) analyze the impact of technology licensing on university spin-offs with asymmetric information. Furthermore, Robinson et al. (2015) recently investigate the

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brand licensing announcements and their influences in the licensor firms’ shareholder values. While the technology licensing within remanufacturing should be considered, only little study addresses this issue. Oraiopoulos et al. (2012) investigate a scenario

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where the OEM (who does not undertake remanufacturing) charges a relicensing fee from a third party remanufacturer in the secondary market. In contrast to their work, this paper considers the scenario where both the OEM and the distributor/the third party remanufacturer (under technology licensing) are engaged in the remanufacturing activities. The second stream of literature primarily examines remanufacturing in a CLSC. We refer readers to Atasu et al. (2008a), Guide Jr and Van Wassenhove (2009), and Souza (2013) for the elaborate reviews. For example, Atasu et al. (2008a) divide the literature into four parts from a business economic perspective, namely operation research, design, strategy and behavioral. Most studies focus on the part of collecting 4

ACCEPTED MANUSCRIPT used products while regard OEMs as the remanufacturers. Savaskan et al. (2004) is the first to study the remanufacturing decision by comparing different recycling channels. Further, they extend collecting problems to two retailers’ competition (Savaskan and Van Wassenhove, 2006). Considering the quality of returned products, Pokharel and Liang (2012) systematically analyze the optimal acquisition price and quantity policy

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by an analytical model. He (2015) also examines the acquisition pricing under situation of both demand and supply uncertainties. Atasu and Souza (2013) and Atasu et al. (2013) study the manufacturer’s choice under alternative collection cost structures and three forms of product recovery. Huang et al. (2013) consider dual recycling channels

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in a CLSC. In their view, there is a competitive relationship between the retailer and the third party in the recycling process. Later on, Chuang et al. (2014) investigate three collection schemes of a high-tech product which is of a short life-cycle and volatile

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demand. The above studies are built on the assumption that the OEMs play the role of channel leader. Differently, Choi et al. (2013) explore a CLSC from the perspective of supply chain members’ leadership, namely collector-led, manufacturer-led and retailer-led. In addition, with regard to the role of government, Ma et al. (2013) show the effect of government subsidy on supply chain performances.

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Taking independent third party remanufacturers into account gives rise to some other significant literature. For instance, Ferrer and Swaminathan (2006) show how various system parameters affect the competition between manufacturer and remanufacturer in a multi-period setting. Further, Örsdemir et al. (2014) study the

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production quality competition between an OEM and an independent remanufacturer in equilibrium. Similarly, Wu (2012a) discusses the price and service competition

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between a manufacturer and a remanufacturer. However, there is a lack of literature examining the case of hybrid remanufacturing

under technology licensing. Different from the previous papers, our work examines the scenario where the OEM and the distributor/the third party remanufacturer (under technology licensing) conduct hybrid remanufacturing in a cooperation way. We explore the equilibrium decisions of each model and the optimal profit of each chain member. 3. Model Assumptions and Notations

5

ACCEPTED MANUSCRIPT We consider a CLSC which consists of three supply chain members, namely a manufacturer, a distributor, and a third party. Concerning their roles in the models, we assume that: (1) The manufacturer produces new products from raw materials. She can also collect used products directly from consumers and remanufacture new products using

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returned products. In addition, the manufacturer licenses the distributor/third party to remanufacture.

(2) The distributor sells new and remanufactured products, and may collect and remanufacture a fraction of used products.

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(3) The third party collects and remanufactures a fraction of used products.

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Fig. 1. Supply Chain Models with Remanufacturing

In this paper, the distributor, who sells new and remanufactured products, is a necessary actor in our models. And to simplify the models, we only consider the case

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where there are at most two players involving in the reprocessing of returned products. Based on their individual roles, four supply chain models are presented, in which no-remanufacturing (Model N, Fig. 1a) is referred as a benchmark scenario. The

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manufacturer undertakes both collecting and remanufacturing used products (Model M, Fig. 1b). The distributor undertakes collecting all used products and remanufacturing a fraction of returned products. Meanwhile, the manufacturer produces a fraction of remanufactured products (Model MD, Fig. 1c). The third party undertakes collecting all used products and remanufacturing a fraction of returned products. And the manufacturer also produces a fraction of remanufactured products (Model MT, Fig. 1d). Table 1. Parameters and definitions Notation

w

Definition The unit wholesale price 6

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The unit retail price The unit transfer price of a returned product given by the manufacturer to the distributor/the third party The average unit cost of manufacturing new products, returned products by the manufacturer The average unit cost of remanufacturing returned products by the distributor, the third party the average saving unit cost from remanufacturing by the manufacturer, the distributor and the third party The average acquisition price for a used product from consumers The market demand function The market size

b cm , cr cd , ct

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s , s1 , s2 r

D

φ β G f t

Π

Profit

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Sensitivity of consumers to the retail price The supply function of used products The unit licensing fee given by the distributor/the third party to the manufacturer The remanufacturing ability of the distributor/the third party( 0 ≤ t ≤ 1 )

A list of related notations is presented in Table 1. In addition, Π ik represents the profit function for channel member i in Model k . Whereby, the superscript k takes the value of Model N, M, MD, MT, denoting the CLSC in no-remanufacturing, the

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manufacturer remanufacturing, the manufacturer and the distributor hybrid remanufacturing, and the manufacturer and the third party hybrid remanufacturing, respectively. Here the subscript i takes the value of M, D and T, which represents the

respectively.

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parameter corresponding to the manufacturer, the distributor and the third party,

Analogous to the work by Atasu et al. (2008b) and Savaskan et al. (2004), we

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assume that the saving unit cost from remanufacturing activities by the manufacturer, the distributor and the third party is s = cm − cr , s1 = cm − cd , and s2 = cm − ct , respectively.

According to the research by Bakal and Akcali (2006), the supply function G can

be considered to be a linear function of the acquisition price r . The general supply function of used products is given by G(r ) = u + vr ( u > 0 and v > 0 ), where u and v represent the supply quantity when r =0 and the sensitivity of consumers to the acquisition price, respectively. The supply quantity of used products obviously determines the environmental impact. Since it is commonly accepted that the remanufacturing process produces less carbon and pollutant emissions than 7

ACCEPTED MANUSCRIPT manufacturing new products ( Qiang, 2015; Yan et al., 2015). Meanwhile, for instance, in fashion industry, remanufacturing can reduce the inventory and landfill space for the damaged products, scraps, and unsold fashion products (Choi and Li, 2015). In addition, we assume that all returned products can be successfully remanufactured and resold. Therefore, we could evaluate the environmental impact based on the supply

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quantity of used products G(r ) . In our models, we assume that the distributor/the third party only remanufacture a fraction of returned products depending on their remanufacturing ability ( t ) which is decided by the damage degree of returned products, the reproduction scale and the

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remanufacturing technology and so on. And the remanufacturing ability ( t ) satisfies 0 ≤ t ≤ 1 . Especially, in the case t = 0 , the distributor/the third party can totally not be

engaged in remanufacturing activities; and when t = 1 , meaning that the distributor/the

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third party has sufficient capability to remanufacture every returned product. We assume that the remanufacturing ability of the distributor and the third party is the same under technology licensing from the manufacturer.

The primary purpose of this paper is to acquire the optimal strategies and profits in equilibrium. And there are some basic assumptions in this paper, which are as follows.

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1) There is no difference between remanufactured products and new products. That is to say the remanufactured products can attract the same consumers as the new one and can be sold in the same market. 2) The market demand is a deterministic and linear function of the retail price

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( p ) and given by D ( p ) = φ − β p ; with φ > 0 , β > 0 , and φ > β cm . Such linear demand function is quiet common in the literature (e.g., Savaskan

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et al., 2004 and Choi et al., 2013) and can facilitate mathematical formulation and analyses.

3) All chain members have access to the same information when deciding their optimal objective functions.

4) The cost of producing remanufactured products by the distributor/the third party is lower than that by the manufacturer, i.e., cd < cr < cm and

ct < cr < cm (i.e., s < s1 , s < s2 ). This assumption states that the unit cost of remanufacturing in the usage of used products is lower than that of producing new products in the usage of new cores. In practice, many manufacturers (i.e., Caterpillar, HP and Xerox) would 8

ACCEPTED MANUSCRIPT like to be engaged in producing remanufactured products, which can save 30~70% costs for them comparing with producing new products (Wu, 2012a). 5) The manufacturer acts as the channel leader, who offers contracts to the distributor/the third-party. 6) We only consider the strategies of a CLSC in one single period.

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4. Models

In this section, we consider the formulations and solutions to the no-remanufacturing model (Model N) and three CLSC models with remanufacturing (Model M, MD and MT). In addition, we analyze the results and also provide some

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guidance in this division. In Model N, Model M and Model MD, we consider two

third party is also included.

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supply chain members: the manufacturer and the distributor; while in model MT, the

4.1. Model N-- No-Remanufacturing

In this section, we consider the no-remanufacturing model (Model N), which provides a benchmark scenario to compare with the remanufacturing models with respects to the supply chain members’ profits and the reverse channel performances.

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We regard the whole supply chain decision process as a Stackelberg game, with the manufacturer as the channel leader and the distributor as the follower. Hence, the objective functions can be defined as

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MaxwΠ MN = (w − cm ) D( p) = (w − cm )(φ − β p) , Max p Π DN = ( p − w) D ( p ) = ( p − w)(φ − β p ) .

(1) (2)

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Proposition 1.

(i) The manufacturer’s profit function Π MN is concave with respect to wholesale price ( w ).

(ii) The distributor’s profit function Π DN is concave with respect to the retail price ( p ). The proofs of proposition 1 as well as the proofs of the other propositions are given

in Appendix. Since the manufacturer and the distributor’s functions are concave in w and p , the optimal value can be found through maximizing the profit function. We assume that the superscript “*” represents the equilibrium value. Then, we use 9

ACCEPTED MANUSCRIPT backward induction to acquire equilibrium decisions. The results are summarized in the following proposition 2. Proposition 2. The retail price and the wholesale price are characterized as follows: p * N = (3φ + β cm ) / (4 β ) , w* N = (φ + β cm ) / (2 β ) .

obtain the optimal profits as follows: Π*DN = (φ -β cm )2 / (16β ) , and

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4.2. Model M--Manufacturer Remanufacturing

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Π *MN = (φ − β cm ) 2 / (8 β ) .

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Substituting the values of p*N and w*N into Eq. (1) and (2) and simplifying, we

In this model, the manufacturer is engaged in the collection of used products and in the production of new and remanufactured products. While the distributor sells new and remanufactured products. The manufacturer independently decides on the wholesale price w and the acquisition price r ; while the distributor determines the

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retail price p . We first give the distributor and manufacturer’s best response functions, and then present the method to decide the Stackelberg equilibrium strategies of each member. The distributor’s optimal problem can be solved as follows: Max Π D = ( p − w)(φ − β p ) M

(3)

p

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And the manufacturer’s unique best response to the wholesale price w and the acquisition price r can be described by the followings:

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Maxw,r Π MM = ( w − cm ) [ D( p) − G (r ) ] + ( w − cm + s − r )G (r )

= (w − cm )(φ − β p) + ( s − r )(u + vr )

(4)

Proposition 3.

(i) The manufacturer’s profit function Π MM is concave with respect to its wholesale price w and acquisition price r . (ii) The distributor’s profit function Π MD is concave with respect to its retail price p .

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ACCEPTED MANUSCRIPT Proposition 3 indicates that each chain member has an optimal solution to maximize her profit. We can find the optimal solutions from the first-order conditions, which are given in the following proposition. Proposition 4. The retail price ( p*M ), the wholesale price ( w*M ) and the acquisition

p*M = (φ + β w) / (2β ) , w*M = (φ + β cm ) / (2 β ) ,

r *M = (vs − u) / (2v) .

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price( r *M ) are given as follows:

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Thus, the demand function can be described by D( p ) = φ − β p = (φ − β w) / 2 , and the supply function of used products is given by G (r ) = (u + vs) / 2 . Substituting the

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values of p*M , w*M and r *M into Eq. (3) and (4) and simplifying, we get Π*MM = (φ − β cm )2 / (8β ) + (vs + u)2 / (4v) , and

Π *DM = (φ -β cm ) 2 / (16β ) .

4.3. Model MD--Manufacturer and Distributor Hybrid Remanufacturing

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Under this reverse channel model, the manufacturer produces new products and remanufactures a fraction of returned products, and also licenses remanufacturing technology to the distributor. The distributor undertakes collection of used products and production of remanufactured products, and also sells new products and

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remanufactured products. Therefore, the decision order is that the manufacturer as the channel leader first determines the wholesale price w . Then the distributor as the

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follower decides the retail price p as well as the acquisition price r based on the manufacturer’s decision. We derive the equilibrium decisions by backward induction. The manufacturer and the distributor’s objective functions can be stated as: MaxwΠ MD （w − cm + s − b)(1 − t )G (r ) + ftG(r ) M = ( w − cm )[ D ( p ) − G ( r )] +

= (w − cm )(φ − β p) + [( f − w + cm )t +(s − b)(1 − t )](u + vr )

(5)

Max p , r Π DMD = ( p − w) D ( p ) + ( w − cm + s1 )tG ( r ) + b(1 − t )G ( r ) − rG ( r ) − ftG ( r )

= ( p − w)(φ − β p ) + [( w − cm + s1 − b − f )t + b − r ](u + vr )

(6)

In order to maximize the objective functions, we examine some propositions and Π MD regarding Π MD D . M 11

ACCEPTED MANUSCRIPT Proposition 5. is strictly concave with respect to its (i) The manufacturer’s profit function Π MD M wholesale price w . is jointly concave in its retail price (ii) The distributor’s profit function Π MD D p and acquisition price r .

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Proposition 5 shows that we can obtain the optimal values of p , w and r by and Π MD , and subsequently we obtain using only the first-order conditions of Π MD M D optimal price strategies in the following proposition.

by

w*MD =

M1 φ + , 2β 4( β + vt 2 )

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p*MD = (φ + β w) / (2β）=

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Proposition 6. The optimal retail price, wholesale price and acquisition price are given

M1 , 2 β + 2vt 2

1 1 r *MD = [( w − cm + s1 − b − f )t + b − u / v] = [ N1t + b − u / v] , 2 2 M1 = (2 f + 2cm + 2b − s − s1 )vt 2 + (s − 2b)vt − ut + β cm + φ ,

where

M1 − cm + s1 − b − f . 2β + 2vt 2

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N1 =

Also, the manufacturer’s and the distributor’s equilibrium profits can be found by

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substituting the values of p*MD , w*MD and r *MD into Eq. (5) and (6), and the results can be solved as follows:

M1 β M1 φ 1 − cm )( − ) + [( s1 − N1 − s)t + s − b](u + vN1t + vb) , 2β + 2vt 2 2 4β + 4vt 2 2

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Π *MMD = (

Π*DMD =

φ2 φ M1 β M12 1 u − + + ( N1t + b + )(u + vN1t + vb) . 2 2 2 4 β 4( β + vt ) 16( β + vt ) 4 v

4.4. Model MT--Manufacturer and Third Party Hybrid Remanufacturing In Model MT, the manufacturer also produces new products and remanufactures a fraction of returned products, which is the same with that in Model MD. Besides, the manufacturer licenses remanufacturing technology to the third party. The third party is engaged in collecting used products and remanufacturing a fraction of returned products. In this reverse channel, the distributor only undertakes distributing new and 12

ACCEPTED MANUSCRIPT remanufactured products. Therein, the manufacturer decides the wholesale price w ; the distributor decides the retail price p ; and the third party determines the acquisition price r . The manufacturer, the distributor and the third party’s problems are solved by: MaxwΠ MMT = (w − cm )[ D( p) − G(r )] +（w − cm + s − b)(1 − t )G(r ) + ftG(r )

Max p Π MT D = ( p − w)(φ − β p )

(7)

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= ( w − cm )(φ − β p ) + [( f − w + cm )t +(s − b)(1 − t )](u + vr )

(8)

Maxr ΠTMT = ( w − cm + s2 )tG (r ) − rG (r ) + b(1 − t )G (r ) − ftG (r )

Proposition 7. Π MT M

is strictly concave in the wholesale

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(i) The manufacturer’s profit function

(9)

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= [( w − cm + s2 − b − f )t + b − r ](u + vr )

price w .

(ii) The distributor’s profit Π MT is concave with respect to its retail price p . D (iii) The third party’s profit Π TMT is concave in its acquisition price r . Proposition 7 indicates that the first-order conditions characterize the best response of w , p and r .

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Proposition 8. The formulations of the optimal retail price, the optimal wholesale price and the optimal acquisition price in the CLSC are given by:

φ M2 + , 2β 4(β + vt 2 )

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p*MT = (φ + β w) / (2β）=

w*MT =

M2 , 2 β + 2vt 2

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1 1 r *MT = [( w − cm + s2 − b − f )t + b − u / v] = ( N 2t + b − u / v) , 2 2

M 2 = (2 f + 2cm + 2b − s − s2 ) vt 2 + ( s − 2b ) vt − ut + β cm + φ ,

where

N2 =

M2 − cm + s2 − b − f . 2β + 2vt 2

Subsequently, we can derive the optimal profit functions from proposition 8. The results can be simplified as follows: Π*MMT = (

M2 φ β M2 1 − cm )( − ) + [( s2 − N 2 − s)t + s − b](u + vN 2t + vb) ; 2 2 2β + 2vt 2 4β + 4vt 2

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ACCEPTED MANUSCRIPT Π*DMT =

φ2 φM2 β M 22 ; − + 4 β 4( β + vt 2 ) 16( β + vt 2 ) 2

1 u Π T*MT = ( N 2t + b + )(u + vN 2t + vb) . 4 v

4.5. Analysis of the supply chain models

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In this section we present further analyses to illustrate the aforementioned equilibrium results and study the impacts of relevant factors on equilibrium decisions. Meanwhile, due to analytical intractability, we would further employ numerical examples for more insights in section 5. Based on analyzing the equilibrium decisions

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of the three hybrid remanufacturing models, we obtain the following corollaries. *M Corollary 1. (i) In Model M, ∂r = 1 > 0 .

∂s

2

* MD

∂r *MD 1 . 1 , and 0< < 4 ∂s1 2

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(ii) In Model MD, 0 < ∂r

∂s

(iii) In Model MT, 0 < ∂r

* MT

∂ s2

<

<

1. 2

Corollary 1(i) indicates that the acquisition price r increases with increasing s . It could be due to that increasing s would motivate the manufacturer to invest more

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for the collection process of remanufacturing. Corollary 1(ii) implies that the acquisition price r increases with increasing s and s1 . With the increasing s and

s1 , more costs can be saved during the remanufacturing process; then the distributor

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would be willing to pay more in the collecting process; and eventually the recycling procedure would be sped up.

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Based on the Corollary 1(iii), it can be found that the acquisition price r increases with increasing s2 . Because remanufacturing activities is one profitable behavior, the distributor would be willing to collect more used products, which gives rise to the increase of acquisition price r . In real life, for example, used carpets, silk products, and leathers can greatly save the cost to produce a remanufactured product. Then the remanufacturer would like to increase the acquisition price r to recycle more used products. Corollary 2. In Model MD and MT, ∂r < 0 , ∂ r > 0 . ∂b

∂f

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ACCEPTED MANUSCRIPT Corollary 2 indicates that the acquisition price r decreases with the increase of the licensing fee f and increases with the increase of the transfer price b . Since the increase of the licensing fee f would increase the remanufacturing costs of the distributor or the third party, the passion of the distributor/the third party to collect used products would be attenuated. It finally leads to the decrease of acquisition price r . In

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addition, with increasing of the transfer price b , the distributor/the third party could earn more profit, which results in the increase of their willingness to collect more used products. Eventually, the distributor/the third party would raise the acquisition price r to achieve this goal.

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Corollary 3. The optimal wholesale price and retail price in our models satisfy the relations as follows: (i) w* N = w* M , p * N = p * M ;

s − 2b u φ − − , then w* MD < w* M , p * MD < p * M ; t vt β

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(ii) If s1 > 2 f + cm + 2b − s +

(iii) If s1 > s2 , then w* MD < w* MT , p * MD < p * MT .

Corollary 3 clearly shows that the wholesale price and retail price in Model N are

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equivalent with that in Model M. When the distributor’s saving unit cost s1 is relatively large (i.e., s1 > 2 f + cm + 2b − s +

s − 2b u φ − − ), the wholesale price in t vt β

Model MD is lower than that in Model M. In comparison of Model MD and MT, larger saving unit cost will result in lower wholesale price. Moreover, the wholesale

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price has direct influence on the retail price in every model. Corollary 4. The acquisition prices and supply quantities in our models are related as

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follows:

(i) In Model M and Model MD, we can get r *MD > r *M and G*MD > G*M when s1 >

R (where R = svt 3 + ( sv + u )t 2 + [(cm + 2b + 2 f ) β − φ ]t + 2 β ( s − b) ). vt + 2 β t 3

(ii) In model MD and model MT, if s1 < s2 , then r *MD < r *MT and G*MD < G*MT . Especially, if s1 = s2 , then r *MD = r *MT , G*MD = G*MT . Corollary 4 suggests that the distributor would get stronger incentive to increase

the acquisition price r *MD and to collect more used products as if the distributor’s saving unit cost s1 is large enough (i.e., s1 > 15

R ). Additionally, it can be also vt + 2βt 3

ACCEPTED MANUSCRIPT found that the distributor in Model MD and the third party in Model MT play the same role (i.e., collecting and remanufacturing a fraction of returned products). Therefore, equal saving unit cost (i.e., s1 = s2 ) suggests the same acquisition price (i.e., r *MD = r *MT ), and the acquisition price and the supply quantity would go up with the increase of saving unit cost.

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Corollary 5. (i) In Model N and Model M, Π *DN = Π *DM , Π *MN < Π *MM .

(ii) In Model MD and Model MT, if s1 = s2 , then Π*MMD = Π*MMT ,

Π*DMD =Π*DMT + Π*TMT .

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The distributor plays the same role in Model N and Model M, hence she obtains the equal profit (i.e., Π *DN = Π *DM ). However, the manufacturer undertakes dual work of

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collecting used products and remanufacturing a fraction of returned products, and producing new products in Model M. Therefore, she acquires more profits (i.e., *M ). Π *N M < ΠM

While in Model MD, the distributor instead undertakes collecting used

products and remanufacturing a fraction of returned products, besides marketing products, and enjoys dual profits. And in Model MT, the distributor only sell products and the third party is engaged in collecting used products and producing

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remanufactured products. If the saving unit cost is the same in two models (i.e.,

s1 = s2 ), the distributor’s profit in Model MD equals the distributor’s profit adding the third party’s profit in Model MT (i.e., Π *DMD =Π *DMT + Π T*MT ). In addition, the

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manufacturer’s profit in Model MD and MT is the same (i.e., Π *MMD = Π *MMT ).

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5. Numerical examples

We now perform numerical examples of the theoretical results. We focus on the

differences between no-remanufacturing model and hybrid remanufacturing models. And we analyze the impacts of the remanufacturing ability t on the acquisition price and chain members’ profits. In this section, we assume that φ = 140000 , β = 160 , u = 10000 , v = 100 , cm = 550 , s = 270 , s1 = s2 = 400 , b = 150

numerical examples are summarized in Figs. 2-6.

16

and

f = 150 .

The results of

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Fig. 2. The acquisition price with different t.

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As clearly shown in Fig. 2, the acquisition price in Model MD is higher than that in Model M when t > 0.45 . And the supply quantity G(r ) would increase with increasing r based on the previous discussion, which is beneficial to the environment. Therefore,

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assuming that the chain members have a certain ability to remanufacture used products (i.e., t > 0.45 ), we can find that it would be better for the environment to endow the remanufacturing of returned products to the distributor/the third party rather than the manufacturer. From the perspective of social welfare and environment, the government would be more willing to encourage independent third party remanufacturer to

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undertake such remanufacturing activities.

Fig. 3. The manufacturer’s profit with different t in Models N, M, and MD.

Fig. 3 demonstrably represents that no matter how much the remanufacturing

ability t is, the manufacturer’s profit in Model M would be larger than that in Model MD. As if the manufacturer is the channel leader, she would like to produce remanufactured products by herself for larger profit, rather than authorize the distributor/the third party to remanufacture. However, considering additional costs (e.g., logistics cost) and the complexity of remanufacturing process, she would not 17

ACCEPTED MANUSCRIPT hesitate to license others to remanufacture. Fig. 3 also suggests that the manufacturer’s profit in each remanufacturing model is always greater than that in no-remanufacturing model (Model N). Furthermore, the manufacturer could also share some

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remanufacturing profits through charging licensing fees.

Fig. 4. The distributor’s profit with different t in Models M, MD and MT.

Subsequently we consider the distributor’s profit in Models M, MD and MT. As shown in Fig. 4, regardless of the value of t, the distributor can always obtain some profits from remanufacturing activities. Moreover, the distributor’s profit in Model MD is larger than that in Model MT and Model M. It should be mentioned that the

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distributor’s profit in Model M is the same with that in Model N, both only originates from selling. We can also find that the distributor’s profit in both Model MD and MT increases with increasing t. Therefore, from the view of the distributor’s profit, the higher the remanufacturing ability t is, the more eager she would be to take part in the

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remanufacturing activities.

Fig. 5. The third party’s profit with different t in Model MT.

In Model MT, the third party’s profit comes from collecting used products and remanufacturing a fraction of returned products. As indicated from Fig. 5, the third 18

ACCEPTED MANUSCRIPT party’s profit increases with increasing t. It can be easily understood because the elevation of t leads to a higher remanufacturing motivation and eventually promote the

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competition of remanufacturing industry in our daily life.

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Fig. 6. The manufacturer’s profit with different t in Models MD and MT.

While in Models MD and MT, if there is a difference in the saving unit cost (viz.

s1 ≠ s2 ), the manufacturer’s profit will be different. Fig. 6 explicitly reveals that the more the saving unit cost is, the larger the manufacturer’s profit can reach. We assume that the saving unit cost in Model MD is a fixed value (i.e., s1 = 400 ). Then it becomes

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obvious that larger profit can be obtained for the manufacturer with a higher saving unit cost in Model MT (i.e., s2 > s1 ). In addition, the manufacturer’s profit would decrease with increasing t . In this case, the manufacturer would rather remanufacture by herself if she just considers her maximum profit.

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Above all, we find that the acquisition price, the distributor’s profit and the third party’s profit increase with an increase of t , and the manufacturer’s profit decreases

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with increasing t . We can clarify the remanufacturing process from the following two aspects. On the one hand, chasing for the interest, each supply chain member (namely the manufacturer, the distributor and the third party) would prefer to undertake remanufacturing work by themselves. On the other hand, from the perspective of environment protection and sustainable development, the channel leader manufacturer would like to get G ( r ) as large as possible. In this case, the manufacturer would choose to cooperate with the remanufacturer (the distributor/the third party) because larger

G (r )

can be achieved with higher remanufacturing ability t . In addition, such

cooperation would save more remanufacturing costs for the manufacturer. In return, the

19

ACCEPTED MANUSCRIPT distributor/the third party can also acquire more profits by undertaking such remanufacturing activities. 5. Conclusions and Future research In this paper, we develop three hybrid remanufacturing models with a

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manufacturer, a distributor/a third party to investigate equilibrium decisions when considering the fluctuation of remanufacturing ability and saving unit cost. We propose the equilibrium schemes for each chain member under technology licensing. Our study extends the previous works which focused on alone collecting process and on the competition between a single remanufacturer and one OEM.

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We explore the profit transfer for each chain member in each model and environmental influence in the whole supply chain. The chain members’ responses to

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the remanufacturing ability and saving unit cost are analyzed as well. Our paper yields the following insights. First, the performances of the remanufacturing ability on the supply chain are described. The increase of remanufacturing ability would elevate the acquisition price, the supply quantity of used products and the profit of the distributor/the third party. Meanwhile, the manufacturer’s profit would decrease. Second, the manufacturer’s profit is in proportion to the saving unit cost of

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remanufacturing. With the increase of saving unit cost, the acquisition price will increase. The less cost in the remanufacturing process will lead to more invest in the collection of used products and eventually elevate the acquisition price. Furthermore,

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when the saving unit cost goes beyond a threshold, the distributor/the third party in Model MD/MT would pay higher acquisition price than the manufacturer in Model M to collect used products. Last, the environmental impact is considered to be related

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with the supply quantity of used products, which is determined by the acquisition price. Therefore higher remanufacturing ability and saving unit cost would benefit for the environment. Meanwhile, Models MD and MT are definitely more favorable to the environment than Model M. In addition, our three models M, MD and MT bring the maximum benefit for the manufacturer, the distributor and the third party, respectively. And all the received profits of chain members from the remanufacturing activities in Models M, MD and MT are larger than that in Model N. Nonetheless, our study also might have some limitations. This paper has made several assumptions that must be relaxed in future research to better understand the remanufacturing systems in the CLSC. In the first place, we only consider royalty 20

ACCEPTED MANUSCRIPT licensing. A more comprehensive consideration of fixed-fee licensing and two-part tariff licensing should be conducted in future study. In another, an extension of this paper would be to presume information asymmetry to choose optimal decisions for chain members, yet this may lead to model complexity and intractable analysis. What’s more, it is insightful to suppose nonlinear demand function, which may arouse more

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interesting findings. Finally, the leadership between chain members should be taken into account. For example, that what different results can be observed if the distributor/the third party as a channel leader deserves investigations.

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Acknowledgments: This research is supported partially by the Enterprise Technology

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Innovation Soft Science Research Base of Hubei province, China (2014BDF002).

Conflicts of Interest: The authors declare no conflict of interest.

Appendix

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Proof of Proposition 1.

second-order derivative of Π MN with respect to w is 2 N 2 ∂ Π M / ∂w = − β < 0 , and thus Π MN is concave in w . (ii) Taking the second-order derivative of Π ND with respect to p , then yields ∂ 2 Π DN / ∂p 2 = −2 β < 0 . Therefore, Π ND is concave in p .

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(i) The

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Proof of Proposition 2. The first-order derivatives of the optimal price strategy can be solved as follows:

 ∂Π DN = (φ − β p) − β ( p − w)=0   ∂p  N  ∂Π M = φ − β w − β ( w − cm ) =0  ∂w 2 2

Proof of Proposition 3. (i) The Hessian matrix of Π MM with respect to w and r is  ∂ 2 Π M / ∂w2 ∂ 2 Π MM / ∂w∂r   − β H MM =  2 MM = 2 M 2   ∂ Π M / ∂r ∂w ∂ Π M / ∂r   0 21

0   −2v 

ACCEPTED MANUSCRIPT Since ∂2ΠMM / ∂w2 = −β < 0 and H MM = 2β v > 0 , Π MM is strictly jointly concave in w and r . (ii) Taking the second-order derivative of Π DM with respect to p , we can obtain ∂ 2Π MD / ∂p2 = −2β < 0 , and thus Π MD is concave in p . Proof of Proposition 4. The optimal price strategy can be solved as follows:

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∂Π MD / ∂p = (φ − β p) − β ( p − w) = 0 , p* M = (φ + β w) / (2 β )

Proposition 3 shows that Π MM has a unique optimal solution. Taking the first-order partial derivatives of Π MM with respect to w and r , and letting the derivatives be zero,

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we have

Proof of Proposition 5.

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 ∂Π MM 1 1  ∂w = − 2 β ( w − cm ) + 2 (φ − β w) = 0 .  M ∂Π  M = v( s − r ) − (u + vr ) = 0  ∂r

(i) Taking the second-order derivative of Π MD with respect to w , we M 2 have ∂ 2 Π MD , and hence Π MD is concave in w . M / ∂w = −2 β < 0 M

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(ii) Taking the second-order partial derivatives of Π MD with respect to p and r , D we have the Hessian matrix

2  ∂ 2 Π MD ∂ 2 Π DMD / ∂p∂r   −2β D / ∂p H DMD =  2 MD = 2 MD 2   ∂ Π D / ∂r ∂p ∂ Π D / ∂r   0

r.

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2 Since ∂ΠMD and HDMD = 4βv > 0 , D / ∂p = −2β < 0

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Proof of Proposition 6. Proposition 5 shows that Taking the first-order partial derivatives of

Π MD D

0   −2 v 

Π MD D

is jointly concave in p and

Π MD D

has a unique optimal solution.

with respect to p and r , we obtain

 ∂Π MD D = (φ − β p ) − β ( p − w) = 0  ∂p   MD  ∂Π D = v[( w − c + s − b − f )t + b − r ] − (u + vr ) = 0 m 1  ∂r

Subsequently, the first-order derivative of

Π MD M

with respect to w can be

rewritten as follows. ∂Π MD 1 1 1 M = (φ + β cm − 2 β w ) + vt[( f − w + cm )t + ( s − b )(1 − t )] − t[( w − cm + s1 − b − f )vt + vb + u ] ∂w 2 2 2

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ACCEPTED MANUSCRIPT = (2 f + 2 cm + 2b − s − s1 ) vt 2 + ( s − 2 b ) vt − ut + φ + β cm − 2 β w − 2 vt 2 w = 0

Proof of Proposition 7. (i) Taking the second-order derivative of Π MT with respect to w , we have M ∂ 2 Π MT 1 1 M = − β − vt − vt 2 < 0 , ∂w 2 2 2

and then Π MT is concave in w . M

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(ii) Taking the second-order derivative of Π MT with respect to p , we obtain D 2 , and thus Π MT is concave in p . ∂ 2 Π MT D / ∂p = − 2 β < 0 D

(iii)Taking the second-order derivative of Π TMT with respect to r , we get

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∂ 2ΠTMT / ∂r 2 = −2v < 0 , and hence Π TMT is concave in r .

Proof of Proposition 8. The proof of proposition 8 is similar to that of proposition 6.

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Proof of Corollary 1. Consider the following derivatives:

∂r * M 1 ∂r *MD vt 2 (1 − t ) 1 = > 0, = < , ∂s 2 ∂s 4( β + vt 2 ) 4

∂ r * MD ∂ r * MT 1 2 β + vt 2 1 = = t⋅ < . 2 ∂ s1 ∂s2 2 2 β + 2 vt 2

Proof of Corollary 2. Consider the following derivatives:

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∂r * MD ∂r *MT −β t = = , ∂f ∂f 2β + 2vt 2 ∂r * MD ∂r *MT β (1 − t ) = = . 2β + 2vt 2 ∂b ∂b

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* MD ∂r *MD ∂r *MT ∂r *MT Since 0 < t < 1 , then we can get ∂r = >0. = < 0 and

∂f

∂f

∂b

∂b

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Proof of Corollary 3.

(i) Since w* N = (φ + β cm ) / (2 β ) and w * M = (φ + β c m ) / (2 β ) , then we can get

w*N = w*M .

（ii）To prove w*MD < w*M , we have to show that w * MD [(2 f + 2 c m + 2 b − s − s1 ) vt 2 + ( s − 2 b ) vt − ut + β c m + φ ](2 β ) = < 1. w*M (φ + β c m )(2 β + 2 v t 2 )

After simplification, this reduces to showing that (2 f + 2cm + 2b − s − s1 ) β vt 2 − (φ + β cm )vt 2 + ( s − 2b) β vt − u β t < 0 .

23

ACCEPTED MANUSCRIPT Therefore we can obtain that if

s1 > 2 f + cm + 2b − s +

s − 2b u φ − − t vt β

, then

w*MD < w*M .

（iii）Since w*MD =

M1 M2 and w*MT = , 2 2 β + 2vt 2 β + 2vt 2

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where M1 = (2 f + 2cm + 2b − s − s1 )vt 2 + (s − 2b)vt − ut + β cm + φ ,

and M 2 = (2 f + 2cm + 2b − s − s2 )vt 2 + ( s − 2b)vt − ut + β cm + φ ,

∂w* MD ∂w*MT −vt 2 = = < 0 . So, we can get that if s1 > s2 , then ∂s1 ∂s2 2 β + 2vt 2

w* MD < w* MT . Since p =

φ + w / 2 , the proof of the relations of the retail price p is 2β

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then

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analogous.

Proof of Corollary 4. (i) To prove r * M D > r * M , we have to show that r *MD − r *M =

1 vs − u [( w − c m + s1 − b − f ) t + b − u / v ] − >0, 2 2v

2 where w = (2 f + 2 c m + 2b − s − s1 ) vt + ( s2− 2b ) vt − ut + β c m + φ . 2 β + 2 vt

After simplification, this reduces to showing that

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1 ( s1 − s ) vt 3 + ( s − 2 b ) vt 2 − ut 2 + (2 s1 − c m − 2 b − 2 f ) β t + φ t [ + b − s] > 0 , 2 2 β + 2 vt 2

namely ( s1 − s ) vt 3 + ( s − 2b ) vt 2 − ut 2 + (2 s1 − c m − 2 b − 2 f ) β t + φ t > ( s − b )(2 β + 2 vt 2 ) ,

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(vt 3 + 2 β t ) s1 > svt 3 + ( sv + u )t 2 + [(cm + 2b + 2 f ) β − φ ]t + 2 β ( s − b) . Based on the above, if s1 >

R , then r * MD > r * M , vt + 2 β t 3

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where R = svt 3 + ( sv + u )t 2 + [(cm + 2b + 2 f ) β − φ ]t + 2 β ( s − b) . The proof of G * MD > G * M is analogous. 1 1 （ii）Since r * MD = ( N1t + b − u / v) and r *MT = ( N 2t + b − u / v) , 2 2

where N1 = and N 2 =

M1 2 − cm + s1 − b − f , M1 = (2 f + 2cm + 2b − s − s1)vt + (s − 2b)vt −ut + βcm +φ , 2 β + 2vt 2

M2 2 − cm + s2 − b − f , M 2 = (2 f + 2cm + 2b − s − s2 )vt + ( s − 2b)vt − ut + β cm + φ , 2β + 2vt 2

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ACCEPTED MANUSCRIPT then

∂r *MD ∂r *MT 1 2 β + vt 2 = = t⋅ > 0 ∂ s1 ∂s2 2 2 β + 2 vt 2

. So, we can get that if s1 < s2 , then

r *MD < r * MT .

The proof of G * M D < G * M T is analogous.

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Proof of Corollary 5. (i) Since Π*DN = (φ -β cm )2 / (16β ) and Π *DM = (φ -β cm ) 2 / (16β ) , then we can get Π *DN = Π *DM .

Because Π*MN = (φ − β cm )2 / (8β ) and Π*MM = (φ − β cm )2 / (8β ) + (vs + u)2 / (4v) , we easily obtain that Π *MN < Π *MM .

and

φ2 φ M1 β M12 1 u − + + ( N1t + b + )(u + vN1t + vb) , 2 2 2 4 β 4( β + vt ) 16( β + vt ) 4 v

Π*DMT =

φ2 φM2 β M 22 , − + 2 4 β 4( β + vt ) 16( β + vt 2 ) 2

Π *TMT =

1 u ( N 2t + b+ )(u + vN 2t + vb) , 4 v

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then we get Π *DMD =Π *DMT + Π T*MT .

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Π*DMD =

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(ii) If s1 = s2 , then we can get M1 = M 2 and N1 = N2 . Since

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Highlights

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Propose remanufacturing models under technology licensing. Study OEMs and remanufacturers conducting remanufacturing simultaneously. Obtain the equilibrium strategies on chain members in a CLSC.

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Examine the impact of remanufacturing ability on channel performance and

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environment.