Decision for pricing, service, and recycling of closed-loop supply chains considering different remanufacturing roles and technology authorizations

Computers & Industrial Engineering 132 (2019) 59–73

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Decision for pricing, service, and recycling of closed-loop supply chains considering different remanufacturing roles and technology authorizations

T

Junjie Zhao, Chuanxu Wang , Lang Xu ⁎

School of Economics and Management, Shanghai Maritime University, Shanghai 201306, China

ARTICLE INFO

ABSTRACT

Keywords: Technology authorization Remanufacturing Supply chain management Third party recycling Pricing

In this paper, in the context of the manufacturer remanufacturing and remanufacturing commissioned by the manufacturers to the retailers under technology authorizations, we develop the decision models of closed-loop supply chains with third party recycling in three different remanufacturing roles and technology authorizations: manufacturer remanufacturing (MR), retailer remanufacturing after paying for the technology authorization fee per unit product (UR), and retailer remanufacturing after paying for fixed technology authorization fees (FR). By analyzing the pricing, service, recycling decisions, and the profit of the supply chain members in different remanufacturing modes, it is shown that the FR remanufacturing mode not only promotes the retailer to improve the product service level, but also enables the third-party to improve the recovery rate. When the consumer’s acceptance degree of remanufactured products reaches a certain level, relative to the MR and UR re-manufacturing modes, the FR remanufacturing model enables manufacturers, retailers, and third-party to simultaneously maximize profits. More managerial insights are provided from the numerical analysis.

1. Introduction Since the beginning of the 21st century, resources, energy and ecology have become core themes in world economy development, and it has increasingly drawn the public’s attention. Resource shortages and environmental pollution have been becoming increasingly acute, more and more the countries and international organizations are increasingly recognizing the importance of energy conservation and pollution emissions for sustainable manufacturing (Meng, Yao, Nie, Zhao, & Li, 2018; Wang, Wang, et al., 2017; Wang, Song, et al., 2017). Sustainable manufacturing plays an important role in saving energy consumption and reducing environment pollution. Many manufacturers have proactively taken measures to meet the evolving environmental performance requirements (Savaskan, Bhattacharya, & Van Wassenhove, 2004). Remanufacturing of used products is helpful for conserving natural resources and energy as well as protecting environment. For example, if all used automotive engines can be fully remanufactured, China can, on average, reduce electricity consumption of 6–9.4 billion kWh and CO2 emissions of 6.67–9.69 million tons each year before 2020 years (Xia, Govindan, & Zhu, 2015). Xerox saved 40–65% manufacturing costs by means of green remanufacturing program (Savaskan et al., 2004). Manufacturers are increasingly implementing remanufacturing of used products in parallel with the manufacturing of

⁎

new units to achieve both cost reduction and environment improvement. Remanufacturing has become one of the important ways to develop circular economy and promote sustainable manufacturing. The cost of producing remanufactured products is usually only about 50% of the production of new products, conserving about 60% of the energy and 70% of the material. It is noted that remanufacturing can be both faster-growing and more profitable than traditional manufacturing. The research and application of closed-loop supply chains (CLSC) are playing obviously significant roles by taking advantage of used materials and preventing waste and hazardous material from entering the environment (Wang, He, & Jiang, 2018). Closed-loop supply chains with remanufacturing have received widespread attention from a large number of scholars. In the past decade, more and more third party collectors of used products are trying to undertake the whole process of remanufacturing (Wang et al., 2018). The manufacturer may choose to outsource the collecting and reselling business to the retailer and ask the retailer to recycle the used products instead (Wang et al., 2018). Since a manufacturer’s production of patented products is protected by patent law, retailer who wishes to remanufacture that product must get the technology authorization from the manufacturer and pay the manufacturer the fixed or variable technology authorization fees (Hong, Govindan, Xu, & Du, 2017). Remanufacturing with technology authorization has gained momentum in some developing countries in

Corresponding author. E-mail address: [email protected] (C. Wang).

https://doi.org/10.1016/j.cie.2019.04.019 Received 24 June 2018; Received in revised form 15 January 2019; Accepted 12 April 2019 Available online 13 April 2019 0360-8352/ © 2019 Elsevier Ltd. All rights reserved.

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recent years because there is increasing awareness of remanufacturing’s potential benefits (Zou, Wang, Deng, & Chen, 2016). In 2015, Apple signed an agreement with Foxconn in which the latter acquires the proprietary rights to remanufacture the end-of-life iPhone mobile phones and remarket them in the Chinese market (Zou et al., 2016). Thus, technology authorization consideration is crucial in the decisions of the closed-loop supply chain with remanufacturing. Our paper combines the remanufacturing and technology in a closed-loop supply chain, and considers the manufacturer remanufacturing and remanufacturing commissioned by the manufacturers to the retailers under technology authorizations, develops the decision models of closed-loop supply chains with third party recycling in three different remanufacturing roles and technology authorization modes: manufacturer remanufacturing (MR), retailer remanufacturing after paying for the technology authorization fee per unit product (UR), and retailer remanufacturing after paying for fixed technology authorization fees (FR). In this paper, we address the following questions: (1) Under which condition, should the manufacturer remanufacturing or remanufacturing commissioned by the manufacturers to the retailers be chosen in a closed-loop supply chain? (2) How to charge the retailer the patent fee if the manufacturer entrusts remanufacturing to a retailer due to the limited scope of production or brand factor? (3) Which remanufacturing mode is conducive to improving product recovery rate in a closed-loop supply chain? (4) Is a variable patent fee or a fixed patent fee beneficial to supply chain enterprises’ profits? The remainder of the paper is organized as follows: In the following section, the current literature is reviewed. Problem descriptions and assumptions are listed in Section 3. In Section 4, the decision models of closed-loop supply chain under three different remanufacturing roles and technology authorization modes are developed, and the analytical results for the models are presented. Section 5 performs comparison analysis for the results of proposed three models. Numerical examples and sensitivity analysis are posted in Section 6. We summarize the conclusions and outline the possible directions for future research in Section 7.

price competition model for waste electrical and electronic equipment recycling markets, and analyzed the recovery price and government subsidies for both recycling channels. Wang, Li, Yan, and Zhu (2016) considered product recycling channels under the name-your-own-price bidding mechanism, studied manufacturers’ pricing and production strategies under the conditions of manufacturers having limited capacity of producing new and remanufactured products. Yenipazarli (2016) utilized the Stackelberg model of a game between the rulemaker who maximizes social welfare and the manufacturer who maximizes the profit to analyze the optimal carbon tax policy of the rulemaker and the manufacturer’s price, production decisions, and remanufacturing strategy. Fang, Lai, and Huang (2017) studied production strategy in the context of simultaneous production of both new and remanufactured products by taking into account the costs of new and remanufactured products, the uncertainty of recycling, demand substitution, and competition between the new and remanufactured products. Feng, Govindan, and Li (2017) considered the two-level reverse supply chain with two channels of online recycling and traditional recycling, introduced the consumer's preference for online recycling channels, and investigated the reverse supply chain network design and coordination. Giri, Chakraborty, and Maiti (2017) studied supply chain pricing and product recycling decisions by considering manufacturers using traditional retail channels and electronic sale channels in the forward logistics and using third-party recycling and electronic recycling channels in reverse logistics. Considering profit maximization and the social responsibility of product recycling and acknowledging that socially responsible manufacturers recycle used products through retailers, Panda and Modak (2017) analyzed channel coordination issues in closed-loop supply chains consisting of manufacturers and retailers. However, these works only evaluated remanufacturing by the original manufacturer. Most of these studies have focused mainly on manufacturer remanufacturing without regard to technology authorization fees. In reality, the manufacturer may entrust remanufacturing to a third party or a retailer due to the limited scope of production or brand factor, while charging them a variable or fixed patent fee.

2. Literature review

2.2. Remanufacturing closed-loop supply chain with variable or fixed patent fee

The literature closely related to our work can be classified as three main categories: the closed-loop supply chain with remanufacturing, remanufacturing closed-loop supply chain with variable or fixed patent fee, service incentives in remanufacturing closed-loop supply chain. Therefore, the literature is reviewed from above-mentioned three aspects.

With the rapid development of new technologies, the popularity of technology authorization is increasing. Some enterprises can get the new technology from the technology holding enterprises by fixed fee or variable fee technology authorization. Wang (2002)studied and compared technology authorization by means of a fixed patent fee and technology authorization by means of a variable patent fee from the viewpoints of the patent-holding firm and consumers in a differentiated Cournot duopoly market. Zhao, Chen, Hong, and Liu (2014) studied the optimal technology authorization contract with network effects from the viewpoints of enterprise profit maximization, social welfare optimization and consumer surplus optimization. Zhang, Wang, Qing, and Hong (2016) established a three-stage Stackelberg game model in a differentiated duopolistic competition market to analyze the effects of product differentiation and technology spillover on the optimal authorization strategy for a stochastic R&D firm. Zhang and Ren (2016) studied the pricing strategy of the recycled product when the manufacturer authorizes the third party to remanufacture products and designed the cost-sharing and benefit-sharing contract as well as the twopart tariff contracts to coordinate the supply chains. Hong et al. (2017) evaluated the two remanufacturing technology authorization modes (fixed-fee pattern and variable pattern) provided by manufacturers, to study the production and recycling decisions of the two-stage closedloop supply chain. They concluded that, from the consumer and environment point of view, royalty licensing is dominated by fixed fee licensing. Huang and Wang (2017) considered the manufacturer’s authorization for the distributor and third-party to recycle and

2.1. Closed-loop supply chains with remanufacturing Currently, there are a large number of studies on closed-loop supply chains with remanufacturing. Savaskan et al. (2004) studied the optimal decision for each member within the supply chain under three different closed-loop supply chain structures: manufacturer recycling, retailer recycling, and third-party recycling. Considering that manufacturers produce new products during the first stage and simultaneously produce both new and remanufactured products during later stages, Ferrer and Swaminathan (2010) studied the optimal price and remanufacturing strategies for manufacturers in two stages, multiple stages, and infinite stages. Huang, Song, Lee, and Ching (2013) studied the optimal pricing and recycling strategy for the two-channel closedloop supply chain, where the manufacturers sell the product through the retailer and recover the used product through the dual channel of the retailer and the third party. He (2015) focused on the closed-loop supply chain for centralized recycling channels and decentralized recycling channels to determine the manufacturer’s recovery price and production decisions under the fixed demand and stochastic demand conditions. Liu, Lei, Deng, Leong, and Huang (2016) considered the formal and informal recycling channels, developed a quality-based 60

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remanufacture products in a closed-loop supply chain consisting of the manufacturer, the distributor, and the third-party, analyzed the impact of remanufacturing ability on supply chain members and environmental sustainability, and investigated the role of the unit remanufactured product cost savings in the remanufacturing process. Yan and Yang (2018) studied the authorization behavior in a differentiated Bertrand duopoly market and compared the authorization contract in terms of fixed fee and variable fee. Recently, some scholars introduced the technology authorization in the closed-loop supply chain with remanufacturing. Zhang and Ren (2016) studied the pricing strategy of the recycled product when the manufacturer authorizes the third party to remanufacture products and designed the cost-sharing and benefit-sharing contract as well as the two-part tariff contracts to coordinate the supply chains. Zou et al. (2016) considered original equipment manufacturers who permit the third-party to remanufacture product through outsourcing or licensing mode. They developed game decision models for these two modes and performed comparative analysis for production capacity, sale price, and profits. Hong et al. (2017) evaluated the two remanufacturing technology licensing modes (fixed-fee pattern and royalty pattern) provided by manufacturers, to study the production and recycling decisions of the two-stage closed-loop supply chain. They concluded that, from the consumer and environment point of view, royalty licensing is dominated by fixed fee licensing. Huang and Wang (2017) considered the manufacturer’s authorization for the distributor and third-party to recycle and remanufacture products in a closed-loop supply chain consisting of the manufacturer, the distributor, and the third-party, analyzed the impact of remanufacturing ability on supply chain members and environmental sustainability, and investigated the role of the unit remanufactured product cost savings in the remanufacturing process. Wang et al. (2018) considered a closed-loop supply chain with competitive recycling-market and product-market, three different competition scenarios chosen by the manufacturer are studied. Liu, Lei, Huang, and Leong (2018) developed Bertrand competition models between an OEM and a TPR to study refurbishing authorization strategies OEMs can used in the secondary market for electrical and electronic products. Giovanni (2018) investigated a joint maximization incentive problem on closed-loop supply chains with competing retailers in the battery sector. Above-mentioned studies on the remanufacturing closed-loop supply chains with a patent fee has focused mainly on manufacturer and third-party remanufacturing, and there has been very little attention paid to remanufacturing by the retailer. Furthermore, previous research doesn’t consider the service incentives in closed-loop supply chain with remanufacturing.

retailer’s demand, the retailer may choose to improve the service level by buying products from the open market at a price higher than the manufacturer’s wholesale price but lower than the retail price. A supply chain decision model was developed using the game method. Zhao and Wang (2015) studied product pricing and retail service decisions in a supply chain containing one manufacturer and two retailers under fuzzy customer demand, manufacturing cost, and service cost coefficient. For a dual-channel supply chain consisting of two manufacturers and a retailer, in which one of the manufacturers sells products through online direct sales channels and retail sales channels, the two manufacturers produce two complementary products, and the retailer provides sales services. In the context of manufacturers using a dual channel supply chain with direct sales channels, Li and Li (2016) considered the retailers' fair concern and value-added services, and developed the Stackelberg game model to study the manufacturer’s wholesale and direct sale price decisions, and retailer’s value-added service level and retail price decisions. Nematollahi, Hosseini-Motlagh, and Heydari (2017) studied the coordination decisions regarding the supplier’s supply interval and retailer’s service level under the stochastic demand, and analyzed the effects of these coordination decisions. Wang, Wang, et al. (2017) and Wang, Song. et al. (2017) studied the pricing and service decisions of the two complementary products in a dual channel supply chain consisting of two manufacturers and one retailer. Although existing literature in supply chain decision considers the service level of retailers, these studies rarely involve the decision of closed-loop supply chain with remanufacturing. This paper differs from existing research in the following three aspects: First, previous research on the remanufacturing closed-loop supply chains has focused mainly on manufacturer and third-party remanufacturing, and there has been very little attention paid to remanufacturing by the retailer. We here assume manufacturers authorizing the retailer to remanufacture, and studied the closed-loop supply chain decision-making. Second, the current studies on non-manufacturer remanufacturing rarely consider different modes of technology authorization. We here proposed two different technology authorization modes based on retailer remanufacturing, and performed a comparative analysis. Third, although existing research literature in supply chain decision-making considers the service level of retailers, these studies rarely involve closed-loop supply chain decision-making. Based on the three factors outlined above, we here constructed closed-loop supply chain pricing, service, and recycling decision-making models with the consideration of three different remanufacturing modes (i.e. manufacturer remanufacturing, retailer remanufacturing after paying for unit product technology authorization fee, and retailer remanufacturing after paying for a fixed technology authorization fee. We then compared and analyzed the optimal pricing, recovery, and service decision-making for the three remanufacturing modes, and proposed an optimal remanufacturing strategy from the perspective of maximizing the profits of supply chain members.

2.3. Service incentives in remanufacturing closed-loop supply chain Since consumers are less aware of remanufactured products, retailers tend to provide service incentives in order to improve consumer confidence in remanufactured products. In this way, services can affect the demand for remanufactured products, and service decisions become an issue of concern in the supply chain decisions. In the study of existing product service decision-making, Dan, Xu, and Liu (2012) considered that manufacturers sell products through both traditional retail channels and online direct sales channels, used the two-stage optimization techniques and Stackelberg game to analyze the retail services and pricing decisions in both decentralized and centralized supply chains, and the impact of retail services and customer loyalties to retail channel on the pricing behavior of manufacturers and retailers. Wu (2012) analyzed the optimal prices and service decisions in a supply chain consisting of two manufacturers and one retailer in which the two manufacturers produce both new and remanufactured products and sell those products through the retailer. Girib (2014) examined a supply chain consisting of a manufacturer and two competitive retailers, and assumed that the market demand and retail prices are dependent on the retailers' service levels. When the manufacturer cannot fully meet the

3. Problem descriptions and model assumptions 3.1. Problem descriptions Consider a closed-loop supply chain consisting of a single manufacturer, a single retailer, and a single third-party collector. The retailer sells new and remanufactured products to consumers at the retail prices pn andpr , respectively, and provides after-sales services to consumers for both products. The third-party collects the used products at the unit price A and sells them to the remanufacturer at price b. In this paper, we considered three remanufacturing modes: the manufacturer remanufacturing mode (hereinafter referred to as NR), the retailer remanufacturing mode with the retailer paying unit product technology authorization fees (hereinafter referred to as UR), and the retailer remanufacturing mode with the retailer paying fixed technology authorization fees (hereinafter referred to as GR), as shown in Fig. 1. 61

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Manufacturer (Remanufacturer)

Retailer

Manufacturer

Manufacturer

Third party

Customer (a) manufacturer remanufacturing mode

Third party

Retailer (Remanufacturer)

Retailer (Remanufacturer)

Third party

Customer

Customer (b) retailer remanufacturing with variable technology authorization fee

Forward logistics

(c) retailer remanufacturing with fixed technology authorization fee

Reverse logistics

Fig. 1. Structure of three remanufacturing modes.

In the manufacturer remanufacturing mode, the manufacturer acts as remanufacturer, producing both new and remanufactured products, and wholesaling them to retailers at wholesale priceswn and wr , respectively. Manufacturers can also choose to commission retailers to remanufacture their products, providing some technical support and collecting technology authorization fees. When the retailers act as the remanufacturers, they can be divided into two groups: those who paying per-unit product technology authorization fees (UR), and those who pay fixed technology authorization fees (FR). In the UR remanufacturing mode, the manufacturer collects patent licensing fees f for per unit remanufactured product. In the FR remanufacturing mode, the manufacturer charges the retailer a fixed royalty F . i represents the profits of supply chain member i , where i {M , R, T } , M is the manufacturer, R is the retailer, and T is the third-party. The superscripts N , U , andG represent the manufacturer’s remanufacturing mode, the remanufacturing mode with the retailer paying the unit technology authorization fees, and the remanufacturing mode with the retailer paying the fixed technology authorization fees, respectively.

commissions retailers as remanufacturers, they provide certain types of technical support, so it is assumed that the costs for both retailer and manufacturer to produce the unit remanufactured product are the same asc s . This assumption states that the reusable components and cheaper materials in the production process of remanufactured products can result in cost reduction and provide more profit for remanufacturer. Remanufacturing systems reduce production costs and place less of a burden on the environment because they require fewer raw materials and less expensive production processes. Assumption 4. Retailers adopt the same service policies for new products and remanufactured products. As described by Chiang, Chhajed, and Hess (2003) and Zou et al. (2016), is the consumer’s follows the uniform willingness to pay for the unit product. distribution on the interval [0,1]. is the consumer’s minimum willingness to purchase remanufactured products relative to the new (0, 1) . The consumer products (hereafter referred to as discounts), pn + e , and the surplus of purchasing new products is Un = consumer surplus of purchasing the remanufactured products is Ur = pr + e , where is the elastic coefficient of the service (0, 1) . When Un > Ur , consumers level to the consumer utility, and buy new products, and when Un < Ur , consumers buy remanufactured products. The consumer’s range of willingness to purchase new products is n = { : Un max(Ur , 0)},and the consumer’s range of willingness to purchase remanufactured products is max(Un, 0)} . The market demands for new and r = { : Ur remanufactured products can be calculated as shown in (1) and (2).

3.2. Model assumptions Assumption 1. As mentioned in Savaskan et al. (2004), in some industries (i.e. auto industry), independent third parties are handling used product collection for the manufacturers. In this paper, we assume that the third-party recycle used products and then transfer them to the remanufacturer for remanufacturing. Since the low research and development investments, more and more third party collectors are willing to undertake the process of remanufacturing. This assumption is consistent with the reality.

pn

qn = 1

Assumption 2. As in Xu and Wang (2018), in the three remanufacturing modes, the manufacturer is the Stackelberg leader in the closed-loop supply chain. When retailers engage in remanufacturing, retailers are the Stackelberg leaders of the thirdparty.

qr =

pr

(1)

1

pn

pr

(1

)

+

e (2)

Assumptions 2 states that the manufacturer firstly determines the wholesale prices for new and remanufactured products, and then the retailer sets the retail price and the service level for the new and remanufactured products, lastly, the third-party determines the recovery rate.

Assumption 4 states that the consumers will choose to purchase new products when the utility resulted from using new product is greater than that from remanufactured products. The consumers will choose to purchase remanufactured products when the utility resulted from using remanufactured product is greater than that from new products. The market demands for new and remanufactured products are affected by their prices and consumers’ recognition of remanufactured products.

Assumption 3. As described by Savaskan et al. (2004), the cost of the unit new product produced by the manufacturers is c and the cost of the unit remanufactured product is c s , wheres is the cost savings made by producing remanufactured products. When the manufacturer

Assumption 5. The retailer’s after-sale service level ise , the recovery rate of third-party is , and 0 < < 1. According to the hypothesis for service level and recovery rate in Zhao and Wang (2015) and Savaskan et al. (2004), e = IR /h , = IT /k , where IR andIT represent the cost of 62

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J. Zhao, et al.

the retailer’s after-sale service and the investment cost of recycling old products by the third-party, respectively, and handk represent the retailer’s service level and the investment scale coefficient of the thirdparty, respectively. To ensure that the optimal solutions simultaneously exist in the three remanufacturing modes, h is assumed to satisfy the 2 > 0.According to the total cost of recovery described condition 4h by Dekker and Fleischmann (2004), the total cost of the third-party is C( ) = A (qn + qr) + I( ).

qnMR = qrMR =

MR M

=

=

MR

max

pnMR , prMR , e MR

max MR

MR

c ) qn + (wrMR

= (pnMR

c + s ) qr

wnMR ) qn + (prMR

b

MR (q n

wrMR ) qr

+ qr )

MR T

= (b

A)

T

MR (q n

+ qr )

k

MR 2

wrMR = pnMR =

bh (b

2bh (b A) + k ( + c s )(4h 2 )] 2[bh (b A) + k (4h bh (b

+ 2c

s

max UR

=

e MR = MR

=

2bh (b

2[bh (b

k ( c + s) A) + k (4h

h (b 2[bh (b

A)( c + s) A) + k (4h

c 2)]

)[bh (b

2Abhk

k2 2 )]

2 )]2

)(2sc + 2 c c 2 ) 2)]2 A) + k (4h

s 2] (15) (16)

UR

= (wnUR

c ) qn + fqr

UR

UR

=

(pnUR

(17)

wnUR ) qn

+

(prUR

c+s

f ) qr

R

= (b

(18)

heUR 2

+ qr )

A)

T

UR (q n

+ qr )

k

UR 2

(19)

Proposition 2. In the remanufacturing mode with the retailer paying the unit product technology authorization fees, the optimal decisions for the manufacturer, retailer and collector can be summarized as follows:

(7)

wnUR =

)]

f UR =

2)]

2 ) + k (6h A) + k (c s )(2h 2)] 2[bh (b A) + k (4h

)(2sc + 2 c + 2)]

(6)

(8)

prMR

k 2] + 4hk [s 2 + (1 )[bh (b A) + k (4h

2)(2b2hk A)2 + (4h )[bh (b A) + k (4h

2 )[(1

M

UR (q n

b

2)]

2 (3

(13)

kh2 (b A) 2 ( c + s)2 2)]2 4[bh (b A) + k (4h

=

max

2 )]

A)(3 + s + ) + k [4h (3 + c ) 4[bh (b A) + k (4h

A) 8(1

)2 [b2h2 (b 16(1

s

pnUR , prUR , eUR

(5)

A)(1 + s + ) + k (1 + c )(4h 2)] 2[bh (b A) + k (4h

)2 [bh (b

s

(1

max

wnUR, f

Proposition 1. Under the condition of the manufacturer remanufacturing, the optimal decisions for the manufacturer, retailer and collector can be summarized as follows:

wnMR =

)]

In this case, the manufacturer authorizes the technology to the retailer and collects royalties on the per unit remanufactured product produced by the retailer. The retailer remanufactures all the used products recovered by the third party, and then sells the new products and the remanufactured products to the consumer. At this point, the manufacturer first sets the wholesale price of the new product and the technology authorization fee per unit product; then, the retailer decides the retail price and the service level for the new products and the remanufactured products, and finally the third-party determines the recovery rate. The profit functions of manufacturer, retailer and the third party are respectively represented by

(4)

R

c (1 2 )]

4.2. Closed-loop supply chain decision in the retailer remanufacturing with retailer paying unit product technology authorization fees (Model UR)

(3)

he MR 2

(1

4hk 2 (4h 16(1

In this case, the manufacturer remanufactures all the used products recovered by the third party, and then distributes the new products and remanufactured products to the retailers for sale. For example, Xerox company remanufactured copiers whose lease contracts expired and saved $200 million in costs (Berko-Boateng, Azar, & De Jong, 1993). Kodak company recycled and remanufactured used cameras, and got extra profits (Toktay, Wein, & Zenios, 2000). At this point, the manufacturer first sets wholesale prices for new and remanufactured products, then the retailer and the third-party make their decisions. The retailer sets the retail price and the service level for the new and remanufactured products, and the third-party determines the recovery rate. The profit functions of manufacturer, retailer and the third party are respectively defined by

= (wnMR

A)](1 s ) + 4hk [s )[bh (b A) + k (4h

MR R

4.1. Closed-loop supply chain decision in manufacturer remanufacturing (Model MR)

MR

bh (b 4(1

(14)

4. Model formulations

max

2

[k

(12)

)

The optimal profits of manufacturer, retailer and the third party are shown as

Assumption 5 states that the service cost of retailer increases with the service level, the cost of recycling used product of the third party increases with recycle rate. The retailer and the third party should make their decisions to minimize the service cost and recycle cost respectively.

wnMR, wrMR M

1 s 4(1

pnUR =

2)

1+c 2 c+s 2

2bh (b

(9)

2)]

(10)

2 )]

(11)

(20) (21)

A)(

c + s ) + k [4h (3 + c ) 4[2bh (b A) + k (4h

2 (3

+ 2c

s

)]

2 )]

(22)

prUR =

eUR = UR

The optimal demands of new product and remanufactured product are shown as

=

4bh (b

2[2bh (b

A) + k ( 2[2bh (b

2

2h )(c s ) + k (6h 2)] A) + k (4h

k ( c + s) A) + k (4h

(b A ) h ( c + s) 2[2bh (b A) + k (4h

2)

(23)

2 )]

(24)

2 )]

(25)

The optimal new product demand and remanufactured product 63

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J. Zhao, et al.

demand can be obtained as

1 s 4(1

qnUR =

(1

qrUR =

qrFR =

)[k 2 2bh (b A)] + 4kh [s 4(1 )[2bh (b A) + k (4h

s

c (1

(27)

FR M

The optimal profit s of manufacturer, retailer and the third party can be obtained as UR M

(1

=

)2 [2bh (b A) k 2] + 4kh [s 2 + (1 8(1 )[bh (b A) + k (4h

s

)( + c 2 2 )]

2sc

FR R

2 c )]

=

=

(28) UR R

(1

=

)2 [2bh (b A) 16(1

s

k 2] + 4kh [s 2 + (1 )[bh (b A) + k (4h

)( + c 2 2 )]

2sc

kh2 (b 4[2bh (b

A) 2 ( c + s)2 2 )]2 A) + k (4h

(1 s 8(1

(1

2 c )] FR T

=

s

)2 )

+F

(41)

) 2 [2bh (b 16(1

+

(29) UR T

s]

The optimal profits of manufacturer, retailer and the third party can be obtained as

)]

2)]

)[k 2 2bh (b A)] + 4kh [(1 s )( 2c + s ) 2 )] 4(1 )[2bh (b A) + k (4h

s

(40)

(26)

)

(1

4kh [(1 )(4 16(1 )[2bh (b

A) k )[2bh (b 2

2]

16khc (1 A) + k (4h

+ 9 s + ) + s 2] 2)] A) + k (4h

s )(2 + 2s 2 )] F

c)

(42)

kh2 (b A) 2 ( c + s)2 2 )]2 [2bh (b A) + k (4h

(43)

(30)

5. Decisions analysis in the three different remanufacturing roles and technology authorizations

4.3. Closed-loop supply chain decision in retailer remanufacturing with the retailer paying fixed technology authorization fees (Model FR)

2 ) = X , bh (b A) = Y , For analytical purposes, we let k (4h c + s = Z , and according to the hypothesis, X , Y , and Z are all positive.

=

In this case, the manufacturer licenses the patent to the retailer for a fixed royalty. The retailer remanufactures all the used products recovered by the third party, and then sells the new and remanufactured products to the consumer. At this point, the manufacturer first determines the wholesale price of the new product; then, the retailer determines the retail price of the new product, the remanufactured product, and the service level. Finally, the third-party determines the recovery rate. The profits of the manufacturer, retailer, and third-party are shown in (35), (36), and (37), respectively.

max FR wn

FR M

= (wnFR FR

max

pnFR , prFR , e FR

c ) qn + F

= (pnFR

FR

Theorem 2. When 0 < 2 < 2h , the optimal retail prices of remanufactured product face the following relationships. prFR < prMR < prUR ; when 2h < 2 < 4h , the optimal retail prices of remanufactured product face the following relationships. prUR < prMR < prFR . Theorem 1 and Theorem 2 indicate that consumers' acceptance to remanufactured products has a greater impact on retail prices of retailer's products under different remanufacturing roles and technology authorizations. When the consumer’s acceptance degree to remanufactured products is high, the retail price of product under FR remanufacturing mode is the lowest; when the consumer’s acceptance degree to remanufactured products is low, the retail price of product under UR remanufacturing mode is the lowest. The lower the retail price of the product, the greater the benefit consumers will get. Therefore, the remanufacturing role and technology authorization are determined based on the consumers' acceptance degree to remanufactured products.

(31)

wnFR ) qn + (prFR

c + s ) qr

b

FR (q n

+ qr )

R

he FR 2 max FR

Theorem 1. When 0 < 2 < 2h , the optimal retail prices of new product pnFR < pnMR < pnUR ;when face the following relationships. 2h < 2 < 4h , the optimal retail prices of new product face the following relationships. pnUR < pnMR < pnFR .

= (b

A)

T

FR (q n

(32)

F + qr )

k

FR 2

(33)

Proposition 3. In the remanufacturing mode with the retailer paying the fixed technology authorization fees, the optimal decisions for the manufacturer, retailer and collector can be summarized as follows:

wnFR =

1 + 2c

s

2bh (b pnFR = prFR = e FR =

FR

=

+2

2bh (b

2 )(3

A)(3 + s + ) + k [(4h

2(

Theorem 3. The optimal wholesale prices of new product face the following relationships. wnFR < wnUR < wnMR .

(34)

2

c + s )] 4[2bh (b

A) + k (4h

2 )(c A) + k (2h 2bh (b A) + k (4h

+ 2c

2 )]

s ) + 2kh 2)

s

For the manufacturers, the wholesale price of new products is the highest when they choose to remanufacture themselves, while the wholesale price of new products is the lowest when they choose authorized retailers to remanufacture used products with fixed technology authorization fees. Consumers' acceptance degree to remanufactured products will directly affect the retail price of remanufactured products. Because of the price competition between new products and remanufactured products, consumers' acceptance degree to remanufactured products will indirectly affect the retail price of new products and ultimately affect the wholesale price of new products. The manufacturers should adjust the wholesale price of their products according to different remanufacturing roles and technology authorizations.

) (35)

2

(36)

h (b A)( c + s) 2bh (b A) + k (4h

2)

(37)

h (b A)( c + s) 2bh (b A) + k (4h

2)

(38)

The optimal qn and qr can be obtained as

qnFR

1 s = 4(1

)

Theorem 4. The optimal service levels of retailer face the following relationships.eUR < e MR < e FR .

(39)

Retailer’s 64

service

strategies

are

different

under

different

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J. Zhao, et al.

6. Numerical analysis

Table 1 Comparison of optimal decision variables under three remanufacturing modes.

pn pr

wn e

Mode MR

Mode UR

Mode FR

0.9313

0.9313

0.9313

0.6250

0.6250

0.6250

0.7120

0.700

0.5375

0.6018 0.1204

0.5603 0.1121

In this section, we use the numerical calculation to analyze the pricing, service level, recycling decisions, and the profits of supply chain members across three remanufacturing modes. The parameters in the models are defined as A = 0.05, b = 0.1, c = 0.4 , k = 0.05, h = 0.05, s = 0.1, = 0.25, and = 0.625.

1.1207 0.2241

6.1. Comparison analysis In this section, the retail prices of new product and remanufactured product prices, the wholesale prices of new product, service level of retailer and recycle rate of the third party, as well as the profits of supply chain members under three remanufacturing modes are compared.

remanufacturing roles and technology authorizations. It is shown that consumers have the highest requirements for product service level under the FR remanufacturing mode. Therefore, when manufacturers choose to authorize retailers for remanufacturing with fixed technology authorization fees, retailers should focus on the improvement of the service level, and when manufacturers choose to authorize retailers for remanufacturing with variable technology authorization fees, retailer should focus on the reduction of the service cost.

6.1.1. Comparison of prices, service levels and recycle rates The optimal retail prices of new product and remanufactured product, the optimal wholesale prices of new product, the optimal service level of retailer and recycle rate of the third party under three remanufacturing modes are obtained as Table 1. 2 = 0 , the retail prices of new product and reSince 2h manufactured product under three remanufacturing modes are the same. It can be know from Table 1 that UR UR pnMR = pn = pnFR = 0.9313, prMR = pr = prFR = 0.6250 . Therefore Theorem 1 and Theorem 2 are confirmed. The wholesale prices of new product, service level of retailer and recycle rate of the third party face wnFR < wnUR < wnMR , eUR the following relationships. < e MR < e FR , UR < MR < FR . Therefore2, Theorem 3, Theorem 4 and Theorem 5 are confirmed.

Theorem 5. The optimal recycle rates face the following relationships. UR < MR < FR ; The optimal profits of the third party face the following relationMR < TFR . ships. TUR < T It can be shown from Theorem 5 that the FR remanufacturing mode is more conducive to the recycling and remanufacturing of the used products. The profit of the third party under the FR remanufacturing is also higher than those under the MR and UR remanufacturing modes. Therefore, the government should encourage upstream manufacturers to authorize downstream retailers to remanufacture the used products with a fixed technology authorization fee. Theorem 6. The optimal profits of the manufacturer face the following UR hkZ2 U N FR < M ;when relationships. When F < 2(X + 2Y ) , M < M . M

F>

hkZ2 , 2(X + Y )

MR M

<

FR M

;

hkZ2 2(X + 2Y )


hkZ2 , 2(X + Y )

UR M

<

FR M

<

MR M

6.1.2. Comparison of profits The optimal profit of supply chain members under three remanufacturing modes can be obtained as Table 2. The optimal range of fixed patient license fee F can be obtained as [0.0391, 0.0546]. When F = 0.05, the profits of supply chain members under three remanufacturing modes are shown as Table 2. It can be UR < MMR < MFR , RMR < RUR < RFR , TUR shown that M MR FR < T < T . This indicates that there exists an optimal range of F which makes supply chain members simultaneously choose the remanufacturing mode with the retailer paying the fixed technology authorization fee. This verifies the Theorem 9.

。

Theorem 7. The optimal profits of the retailer face the following 3hkZ2 relationships. RMR < RUR ; when F < 4(X + 2Y ) , RUR < RFR ; when

F> F<

hkZ2 (3X2 + 6XY + 4Y2) , 4(X + 2Y )(X + Y )2 hkZ2 (3X2 + 6XY + 4Y2) , 4(X + 2Y )(X + Y )2

FR R MR R

<

FR R

< <

MR R UR R

;

3hkZ2 < 4(X + 2Y )

when .

Theorem 8. When X > Y , there is an optimal fixed technology authorization fee F , which maximizes the profits of the manufacturer, the hkZ2

3hkZ2

retailer, and the third-party in the interval [ 2(X + Y ) , 4(X + 2Y ) ] in the remanufacturing mode with the retailer paying the fixed technology authorization fee.

6.2. Sensitivity analysis We mainly analyze the impact of the consumer’s willingness to pay for remanufactured products , the cost savings of unit remanufacturing product s, and retail service level coefficient on retailer’s pricing and service decision, recycling decisions of the third-party, the profits of the closed-loop supply chain members, and the value range of the fixed technology authorization fee of the optimal remanufacturing mode under the three different remanufacturing models.

It can be shown from Theorem 6, Theorem 7 and Theorem 8 that, due to the uncertainty of fixed technology authorization fee in the FR remanufacturing mode, the profits of manufacturer and retailer vary with the different remanufacturing roles and technology authorizations. Under the FR remanufacturing mode, both manufacturer and retailer negotiate with a specific technology authorization fee on the basis of maximizing their individual profits. When the fixed technology authorization fee meets certain conditions, the profits of both manufacturer and retailer under the FR remanufacturing mode can be maximized simultaneously and achieve a “win-win” situation. This shows that, for the manufacturer who holding the technology authorization, the fixed technology authorization fee is not the more the better in the technology authorization negotiation. When the fixed technology authorization fee exceeds the retailer's affordability, the retailer will refuse to adopt the FR remanufacturing mode. Therefore, both manufacturer and retailer should seek the reasonable fixed technology authorization fee which is beneficial to each other.

6.2.1. Impact of the consumer’s willingness to pay We set s = 0.1 and = 0.25. In order to ensure that all optimal decision variables would be positive, varied within the range of [0.3, Table 2 Comparison of optimal profit of supply chain members under three remanufacturing modes.

M R T

65

Mode MR

Mode UR

Mode FR

0.0643

0.0616

0.0752

0.0007

0.0006

0.0025

0.0307

0.0308

0.0354

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J. Zhao, et al.

Fig. 4. Effect of consumer WTP Fig. 2. Effect of consumer WTP

on retail price of both products.

0.9]. The results are shown in Figs. 2–8. As shown in Fig. 2, when the consumers’ acceptance degree to remanufactured products is high, the retail prices of the new and the remanufactured products in the FR remanufacturing mode are lower than those in the MR remanufacturing mode, and the retail prices of the new and remanufactured products in the MR remanufacturing mode are lower than those in the UR remanufacturing mode, and vice versa. Furthermore, the retail prices of remanufactured products in the three remanufacturing modes increase with the degree of consumer willingness to purchase a remanufactured product. Due to price competition between new and remanufactured products, the retail price of new products can also be affected by consumer’s willingness to purchase the remanufactured products. The retail price of the new product in the MR remanufacturing mode and UR remanufacturing mode also increases with consumer willingness to purchase remanufactured products. If the degree of consumer’s acceptance to the remanufactured products is very low, the retail price of new products in FR remanufacturing mode decreases with the degree of consumer’s acceptance to remanufactured products. This indicates that retailer considers not only the difference between the new product and remanufactured product but also the degree of consumer’s acceptance to remanufactured products when the retailer determines the prices of new product and remanufactured product. As shown in Fig. 3, the service level in the UR remanufacturing mode is lower than that in the MR remanufacturing mode; the service level in the MR remanufacturing mode is lower than that in the FR remanufacturing model. Moreover, the retailer’s service level in the three remanufacturing modes increases with the degree of consumer willingness to purchase remanufactured products, and the greater the degree of consumer willingness to purchase remanufactured products,

Fig. 3. Effect of consumer WTP

on recycling rate.

Fig. 5. Effect of consumer WTP

on the third-party profit.

Fig. 6. Effect of consumer WTP

on manufacturer profit.

the gentler the curve of the retailer’s service level. This indicates that retailer should consider the degree of consumer’s acceptance to remanufactured products when the retailer determines the service level. If the FR remanufacturing mode is adopted, retailer should try to improve service level to achieve the maximum profits. As shown in Fig. 4, the recovery rate in the UR remanufacturing mode is lower than the recovery rate in the MR remanufacturing mode; the recovery rate in the MR remanufacturing mode is lower than the recovery rate in the FR remanufacturing mode. Additionally, the thirdparty recovery rate in the three remanufacturing modes increases with the consumer's acceptance degree to the remanufactured product. As illustrated in Fig. 5, the third-party earns less profit in the UR remanufacturing mode than in the MR remanufacturing mode, and the third-party in the MR remanufacturing mode earns less profit than in

on service level of retailer. 66

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J. Zhao, et al.

Fig. 7. Effect of consumer WTP

Fig. 8. Effect of consumer WTP range.

Fig. 8, the upper and lower bounds of the range of the optimal fixed technology authorization fee increase as consumer willingness to purchase remanufactured products increases, and the range itself grows wider. This shows that the greater the degree of consumer willingness to purchase remanufactured products, the more room there is for the negotiation between manufacturers and retailers on fixed technology authorization fees in the FR remanufacturing mode. It is shown that, with the increase of the degree of consumer’s willingness to purchase remanufactured products, the range of the optimal fixed technology authorization fee is gradually enlarged. If the FR remanufacturing mode is not considered, manufacturer should not authorize the retailer to remanufacture products when the manufacturer’s production capacity is sufficient. The manufacturer should entrust the retailer with remanufacturing of used products and charge variable technology authorization fee when the manufacturer has limited production capacity or consider brand factor. If the FR remanufacturing mode is considered, manufacturer should authorize the retailer to remanufacture products.

on retailer profit.

6.2.2. Impacts of unit remanufactured product cost saving Let = 0.25 , = 0.7 , i.e., when consumers are more willing to pay for remanufactured products (same results for consumers who are less willing to pay for remanufactured products), in order to ensure that all optimal decision variables are positive, s varies in the interval of [0, 0.3]. The results of the calculation are shown in Figs. 9–15. As shown in Fig. 9, the retail price of new products and remanufactured products in the GR remanufacturing mode are lower than that in the MR remanufacturing mode. The retail prices of new and remanufactured products in the MR remanufacturing mode are lower than that in the UR remanufacturing mode. Additionally, the retail price of new products increases with the unit cost saving of remanufactured products, the retail price of remanufactured products decreases with the unit cost savings of remanufactured products, and the retail price of new products is greater than the retail price of remanufactured products. This indicates that the increase in the unit cost savings of remanufactured products can increase the difference in the retail price between new and remanufactured products. The increase of cost savings of remanufactured products will lead to an increase in the price gap between new products and remanufactured products, and price-sensitive consumers will be more inclined to purchase remanufactured products, thus lead to the increase of demand for remanufactured products. As shown in Fig. 10, the service level in the UR remanufacturing mode is lower than that in the MR remanufacturing mode; the service level in the NR remanufacturing mode is lower than that in the FR remanufacturing mode. The retailer service levels in the three remanufacturing modes all increase with the unit cost savings of the remanufactured products. Retailers should consider the cost savings of

on optimal fixed technology authorization fee

the FR remanufacturing mode. Furthermore, the profit of the thirdparty in the three remanufacturing modes increases with the degree of consumer willingness to purchase remanufactured products. The greater the degree of consumer willingness to purchase remanufactured products is, the gentler the curve of the third-party’s profit is. This indicates that the third party recycler should consider the consumer's acceptance degree to the remanufactured product when the third party recycler determines the recovery rate. If the consumer's acceptance degree to the remanufactured product increases, the third party recycler should try to increase the recovery rate of used product. It is shown that the FR remanufacturing mode is beneficial for the recycle and remanufacturing of the used products. As shown in Fig. 6, the manufacturer earns less profit in the UR remanufacturing mode than in the MR remanufacturing mode; in the FR remanufacturing model, the manufacturer earns more profit as fixed technology authorization fees increases. As shown in Fig. 7, the retailer earns more profit in the MR remanufacturing mode than in the UR remanufacturing mode; in the FR remanufacturing mode, the retailer’s profit decreases as the fixed technology authorization fee increases. Comparing Fig. 6 with Fig. 7, if we consider only the MR remanufacturing mode and UR remanufacturing mode, remanufacturing used products can increase corporate profits; when considering the FR remanufacturing mode, the selection of the optimal remanufacturing mode for the manufacturer or the retailer depends on the fixed technology authorization fees. In the FR remanufacturing mode, there are optimal fixed technology authorization fees so that the manufacturers and retailers both choose FR remanufacturing. Moreover, As shown in

Fig. 9. Effect of unit cost saving s on retail price of both products. 67

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J. Zhao, et al.

Fig. 10. Effect of unit cost saving s on service level of retailer.

Fig. 13. Effect of unit cost saving s on manufacturer profit.

Fig. 11. Effect of unit cost saving s on recycling rate. Fig. 14. Effect of unit cost saving s on retailer profit.

Fig. 12. Effect of unit cost saving s on the third-party profit.

remanufactured products when making service level decisions. With the continuous development of remanufacturing technology, the cost savings of remanufactured products are increasing, and the service level of retailers should also be improved. As illustrated in Fig. 11, the recovery rate in the UR remanufacturing mode is less than that in the MR remanufacturing mode; the recovery rate in the MR remanufacturing mode is less than that in the FR remanufacturing mode. Moreover, the third-party recovery rates in the three remanufacturing modes all increase with the unit cost savings of the remanufactured product. As shown in Fig. 12, the profit of the third-party in the UR remanufacturing mode is less than the profit in the NR remanufacturing mode, and the profit of the third-party in the MR remanufacturing mode is less than the profit in the FR remanufacturing mode. Additionally, the third-party profits in the three remanufacturing modes all increase with the unit cost savings of the

Fig. 15. Effect of unit cost saving s on optimal fixed technology authorization fee range.

remanufactured product. As can be seen from Fig. 13, the manufacturer earns less profit in the UR remanufacturing mode than in the MR remanufacturing mode; meanwhile, the manufacturer earns more profit in the FR remanufacturing mode as the fixed technology authorization increase. As shown in Fig. 14, the retailer earns less profit in the NR remanufacturing mode than in the UR remanufacturing model; the retailer earns less profit in the FR remanufacturing mode as the fixed technology authorization increase. Comparing Fig. 13 with Fig. 14, if only considering the NR re-manufacturing mode and UR 68

Computers & Industrial Engineering 132 (2019) 59–73

J. Zhao, et al.

Fig. 18. Effect of service intensity coefficient Fig. 16. Effect of service intensity coefficient

on retail price of both products.

remanufacturing mode, remanufacturing used products can increase corporate profits; when considering the FR remanufacturing mode, the selection of the optimal remanufacturing mode for the manufacturer or retailer depends on the fixed technology authorization fees, and there are ideal technology authorization fees for manufacturers and retailers under the FR remanufacturing mode. As shown in Fig. 15, the upper and lower bounds of the optimal fixed license fee range increase with the unit cost savings of remanufactured products, and this range increases with the unit cost savings of remanufactured products. This shows that the greater the unit cost savings of remanufactured products, the more room there is for negotiation for manufacturers and retailers with respect to fixed technology authorization fees in the FR remanufacturing mode. 6.2.3. Effects of service elasticity coefficient Let = 0.7 , s = 0.1. In order to ensure that all optimal decision variables are positive, varies within the range of [0, 0.3]. Calculation results are shown in Figs. 16–22. As shown in Figs. 16 and 17, when the service elasticity coefficient is low, the retail price of the new product and the retail price of the remanufactured product in the FR re-manufacturing mode are lower than those in the MR reproduction mode. The retail price of new products and the retail price of remanufactured products in the MR remanufacturing mode are lower than those in the UR remanufacturing mode. Fig. 16 shows that the retail price of new products and the retail price of remanufactured products in all three remanufacturing modes all increase with the service elasticity coefficient, and the retail price of the new product is greater than the retail price of remanufactured products. Fig. 17 shows that the service level in the UR remanufacturing mode

Fig. 19. Effect of service intensity coefficient

on the third-party profit.

Fig. 20. Effect of service intensity coefficient

on manufacturer profit.

Fig. 21. Effect of service intensity coefficient Fig. 17. Effect of service intensity coefficient

on recycling rate.

on service level of retailer. 69

on retailer profit.

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J. Zhao, et al.

addition, the FR remanufacturing mode not only decreases the price of new products and remanufactured products, but also increases recovery rate of used product, promote resource recycling and reduce environmental pollution. 7. Conclusions

Fig. 22. Effect of service intensity coefficient authorization fee range.

In this paper, we develop the decision models of pricing, service, and recycling of closed-loop supply chains with three different remanufacturing modes (MR, UR, and FR) in the context of manufacturer remanufacturing, remanufacturing commissioned by the manufacturer to the retailer under the technology authorization, and third-party recycling. The results show the following: (1) Remanufacturing by retailers paying fixed technology authorization fees is conducive to improving the recovery rate and profits of third-party. (2) When the consumer is less receptive to the remanufactured product, the remanufacturing mode in which retailers pay technology authorization fees of the unit product is conducive to reducing the retail price of the new product and the remanufactured product; when the consumer has a higher degree of willingness to purchase the remanufactured product, the FR remanufacturing mode helps reduce the retail price of new and remanufactured products. (3) The service level of the retailer increases with the degree of consumer’s acceptance of remanufactured products, and the retailer has the highest service level in the FR remanufacturing mode. This suggests that retailers may improve their service levels to meet consumer demand as the remanufacturing industry matures. (4) When the degree of consumer willingness to purchase remanufactured products exceeds a certain threshold, there is an optimal fixed technology authorization fee for manufacturers, retailers, and third-party that allows all three to maximize their profits. There are a number of limitations associated with our paper. Firstly, our research only considers the supply chain consisting of one manufacturer and one retailer. In reality, one manufacturer usually supplies products to multiple retailers. Future research can focus on the supply chain consisting of one manufacturer and multiple competing retailer, in which one retailer obtain the technology authorization to remanufacture the products while the other retailers have no the technology authorization to remanufacture the products. Secondly, our research is conducted under the assumptions that only the third-party recycles used products and then transfers them to the remanufacturer for remanufacturing. However, there exist other recycle channels in a closed-loop supply chain such as manufacturers recycle directly used product from the consumers and retailers recycle used product from the consumers. In this sense, it is worthwhile to investigate the closed-loop supply chain decision with the consideration of different recycle channels. Thirdly, we assume that the manufacturer is the Stackelberg leader in the closed-loop supply chain, and the retailers who engage in remanufacturing are the Stackelberg leaders of the third-party. This assumption does not always hold. In practice, the leadership in a closedloop supply chain is different. Future research will be carried out considering the different power structures in a closed-loop supply chain.

on optimal fixed technology

is lower than that in the MR remanufacturing mode; the service level in the MR remanufacturing mode is lower than that in the FR remanufacturing mode. Additionally, the service level of retailers in the three remanufacturing modes all increase with the service elasticity coefficient. Retailers should consider consumers' sensitivity to service level when making pricing and service level decisions. When consumers pay attention to service level, retailers should not only improve service level, but also increase product price to compensate for additional service costs. As shown in Fig. 18, the recovery rate in the UR remanufacturing mode is lower than the recovery rate in the MR remanufacturing mode; the recovery rate in the MR remanufacturing mode is lower than the recovery rate in the FR remanufacturing mode. Furthermore, the thirdparty recovery rates in the three remanufacturing modes all increase with the service elasticity coefficient. As shown in Fig. 19, the thirdparty earns less profit in the UR remanufacturing mode than in the NR remanufacturing mode, and the third-party earns less in the MR remanufacturing mode than in the FR re-manufacturing mode. Moreover, the profits earned by the third-party increase with the service elasticity coefficient in all three remanufacturing modes. As illustrated in Fig. 20, the manufacturer earns less profit in the UR remanufacturing mode than in the MR remanufacturing mode; the manufacturer earns more profit in the FR remanufacturing mode as the fixed technology authorization fees increase. Meanwhile, Fig. 21 shows that the retailer earns less profit in the MR remanufacturing mode than in the UR remanufacturing mode; the retailer earns less profit in the FR remanufacturing mode as the fixed technology authorization fee increases. Comparing Fig. 20 with Fig. 21, if only the MR re-manufacturing mode and UR remanufacturing mode are considered, the remanufacturing of used products can increase corporate profits; when considering the FR remanufacturing mode, the selection of the optimal remanufacturing mode for manufacturers or retailers depends on the fixed technology authorization fees, and there are ideal fixed technology authorization fees for the manufacturers and retailers. Lastly, Fig. 22 shows that the upper and lower bounds of the range of the optimal fixed technology authorization fee increase with the service elasticity coefficient. It can be shown that when the manufacturer has enough capacity to carry out remanufacturing activities, the manufacturer should authorize the retailer to remanufacture products and charge fixed technology authorization fee instead of variable technology authorization fee. Compared with the UR remanufacturing mode, the FR remanufacturing mode improves the profits of manufacturers, retailers and third-party recyclers simultaneously. In

Acknowledgements We would like to be grateful to the editors and anonymous referees for their constructive comments. This study is supported by the National Natural Science Foundation of China (No. 71373157) and Innovation Program of Shanghai Municipal Education Commission (No. 2017-01-07-00-10-E00016).

70

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J. Zhao, et al.

Appendix Proof of proposition 1. Substituting new product demand qn and remanufacturing product demand qr into the manufacturer’s profit function MMR , retailer’s profit function RMR and the third-party’s profit function TMR , the second order partial derivatives of RMR with respect to pnMR , prMR and e MR are obtained. The Hessian matrix of MMR is shown as the following: 2

2

1

H MR1

2

2

=

0

1 (1

1

)

0

2h

From the assumption 0 <

second

order

matrix|H3MR1|

=

primary

2)

2(4h

principal

2

of

the

matrix|H2MR1|

Hessian

is negative definite,

2 MR T remanufactured product and service level. Since MR 2 = MR MR MR 2( 2) w 1 + wn wr ) 2h 2 + (2h MR MR r MR pn = + 2(4h 2) , pr = ,e = 2 2 4h

Substituting of MMR is shown as the following:

pnMR ,

prMR ,

e MR,

MR

1

into

k < 0,

=

(1

> 0,

)

the

is concave on

MR

third

order

primary

principal

1

of

the

4bh2 (b

1

A)(1

=

h (b

A)( k (4h

the second order partial derivatives of

2)(4h

) + k (4h

k (1

From the assumption 0 <

MR M

MR .

It can be obtained from the first order condition that

wrMR ) . 2)

with respect to wnMR and wrMR can be obtained. The Hessian matrix

2)

2)2

)(4h

< 1 and 4h

2

> 0 , it can be shown that the first order primary principal of the Hessian matrix |H1MR2| =

second order primary principal of the Hessian matrix

|H2MR2|

=

4h [bh (b k (1

concave on wnMR , wrMR ande MR .

2)]

A) + k (4h 2) 2

)(4h

> 0 . Therefore, the Hessian matrix

H MR2

1 1

profit function

UR R

and third-party’s profit function

is concave on

UR T

the second order partial derivatives of

2

H UR1

(1

2

=

1

with respect to

A)(eUR +

(b

UR

can be obtained as

is

UR M ,

retailer’s

=

k < 0,

2 UR T UR2

prUR )

= It can be obtained from the first order condition that . Substituting UR into retailer’s profit function 2k UR UR UR UR p p e with respect to , and can be obtained. The Hessian matrix of RUR can be obtained as the following. R r n UR

UR.

2 1 )(b A) + 2k k 2 (1 )

[b (b

0

order

primary

|H3UR1|

4bh (b

=

k 2 (1

condition that

=

2)

) ( +s

c

A) b 2 + 2hk 2 k 2

the Hessian matrix

< 0 . Therefore, f )[2bh (b

2[2bh (b

manufacturer’s profit function following. 1

A) + k 2]

A) + k (4h UR M , the

H UR1

+

2 )]

|H2UR1|

is negative definite,

1 + wnUR , 2

prUR

2bh (b

1 (1

A) + k (4h

)[2bh (b

From the assumption 0 <

k < 0 , therefore

2

HFR =

2 1

0

> 0 , the third

is concave on

s + f ) + 2bh (b

2bh (b

A) + k (4h UR M with

A) + 2hk 2 2)

order primary

pnUR ,

respect to

,

prUR

eUR

wnUR

=

and

eUR

the Hessian

matrix

. It can be obtained from the first order

k ( +s 2bh (b

principal of c

A) + k (4h

f)

2) .

Substituting pnUR , prUR , eUR into

and f can beobtained. The Hessian matrix of

UR M

is as

2) 2)]

A) + k (4h

< 1 and b > A, it can be shown that the first order primary principal of the Hessian matrix |H1UR2| = |H2UR2|

=

(1

Proof of proposition 3. Proof Substituting qn and qr into

1

2 )(c

second order partial derivatives of

order primary principal of the Hessian matrix

profit function the following.

=

k (2h

UR R

< 0 , the second

1

1

=

=

2[b (b A) + 2k ] k 2 (1 )

2 1

1

1

=

(b

A) + k ] k 2

< 1 and b > A, it can be shown that the first order primary principal of the Hessian matrix |H1UR1| =

principal of A) + 2k (4h

pnUR

0 [b (b

A) + k ] k 2

From the assumption 0 <

2 FR T FR2

UR T

MR M

the second order partial derivatives of 1

H UR2

UR T ,

< 0 , the

is negative definite,

Proof of proposition 2. Substituting new product demand qn and remanufacturing product demand qr into the manufacturer’s profit function

UR R ,

Hessian

1

1

therefore

< 0 , the

is a concave function about retail price of new product, retail price of

MR R

MR T

( wrMR ) 2 , 4h

4

1

1

H MR2 =

MR M ,

2

> 0 , it can be shown that the First order primary principal of the Hessian matrix |H1MR1| =

H MR1

< 0 。Therefore,

) 2

(1

< 1 and 4h

FR R ,

FR T

FR .

is concave on

[b (b

FR R ,

FR T

and

FR M ,

2)]

the second order partial derivatives of

FR R

with respect to

pnFR ,

0 ) + 2k )

A) + k ] k 2

[b (b (b

> 0 . Therefore, H UR2 is negative definite,

It can be obtained from the first order condition that

the second order partial derivatives of 2 1 b (b A)(1 k 2 (1

4hk )[2bh (b A ) + k (4h

A) + k ] k 2

A) b 2 + 2hk 2 k 2

71

prFR

and

e FR

FR

=

(b

UR M

< 0 , the second

is concave on wnUR and f .

FR T with respect A)(e FR + prFR ) 2k

1 1

to

FR

can be obtained as

. Substituting

can be obtained. The Hessian matrix of

FR R

FR

into retailer’s

can be obtained as

Computers & Industrial Engineering 132 (2019) 59–73

J. Zhao, et al.

From the assumption 0 <

< 1 and b > A, it can be obtained that first order primary principal of the Hessian matrix |H1FR| =

2[b (b A) + 2k ] > 0 , the third order primary principal of the Hessian matrix|H3FR| primary principal of the Hessian matrix|H2FR| = k 2 (1 ) FR FR Therefore, H is negative definite, is concave on pnFR and prFR . It can be obtained from the R FR 2 + 2bh (b A)]( 2)(c s ) + h [2bh (b A) 2k ] 1 + w [ k c + s ) k (2 h k ( c + s) n pnFR = + 2[2bh (b A) + k (4h 2)] , prFR = , e FR = 2bh (b A) + k (4h 2) . Substituting pnFR , 2) 2 2bh (b A) + k (4h

order partial derivatives of

FR M

with respect to wnFR can be obtained as

Proof of Theorem 1. pnFR

2h <

2

Proof

2h <

< 4h , pnUR < pnMR < pnFR .

of 2

2 ) XZ k2 (2h , 2(X + 2Y )(X + Y )

pnMR =

Theorem

2.

prFR

prMR =

< 4h , prUR < prMR < prFR .

pnMR

2 ) XZ k2 (2h , 2(X + 2Y )(X + Y )

Proof of Theorem 5. Since Since

UR T

MR T

UR

UR M

MR M

< 0,

=

hkZ2 . 2(X + Y )

Proof 3hkZ2 < 4(X + 2Y ) ;

of FR R

Theorem MR R

=

Proof of Theorem 8. if

7.

hkZ2

4(X + 2Y )

2(X + Y )

hkZ2 , 2(X + Y )

khYZ2 2(X + 2Y )(X + Y )

F < 0 if F >

=

prUR =

2 )YZ k(2h . 2(X + 2Y )(X + Y )

FR

4b2 (X + 2Y )2 (X + Y )2

UR M

FR M

UR R

=

hkZ2 (3X2 + 6XY + 4Y2) . 4(X + 2Y )(X + Y )2

< 0,

=F

UR T

<

hkZ2 2(X + 2Y )

hkY 2Z2 4(X + 2Y )(X + Y )2

hk (X Y ) Z2 > 0 , then X > Y . When 4(X + 2Y )(X + Y ) 3hkZ2 FR MR < RUR < RFR . M ;if F < 4(X + 2Y ) , R

=

< 0.

order

prFR , e FR into

FR M ,

the second

condition

that

When

2

0<

< 2h , pnFR < pnMR < pnUR , when 2

< 2h , prFR < prMR < prUR ;when

wnMR < 0 . < 0, eUR < e MR < e FR .

XYZ 2b (X + 2Y )(X + Y )

=

k (3X + 4Y ) XY 2Z2

first

)

k 2 (1

is concave on wnFR .

FR M

Therefore, when 0 <

k XZ 2(X + 2Y )(X + Y )

e FR =

MR

< 0,

MR R

< 0 . Therefore,

wnUR < 0 and wnUR

< 0,

FR T

Since

hkZ2 (3X2 + 6XY + 4Y 2) 4(X + 2Y )(X + Y )2

3hkZ2

MR T

1

2 )YZ k(2h . 2(X + 2Y )(X + Y )

prMR

< 0 , e MR

Y 2Z 2b (X + 2Y )(X + Y )

=

4b2 (X + 2Y )2 (X + Y )2

Proof of Theorem 6. Since

F>

MR

k (2X + 3Y ) Y 3Z2

=

k YZ 2(X + 2Y )(X + Y )

e MR =

1

=

pnUR =

Proof of Theorem 3. It can be easily proved by calculating wnFR Proof of Theorem 4. Since eUR

2 FR M 2

wnFR

=

2 < 0 , the second order 1 2 )] 2[2bh (b A) + k (4h

< 0, MR T

UR

FR T

<

< 0 if F <

< 0,

X > Y,

<

3hkZ2 4(X + 2Y )

UR R

<

MR

<

FR

.

. hkZ2 , 2(X + 2Y )

FR R

hkZ2 , 2(X + Y )

MR M

=F

FR M

=

3hkZ2 4(X + 2Y )

F+

<0

hkZ2 2(X + Y )

< 0 if

if

F

It can be known from Theorem 7 and hkZ2

3hkZ2

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MR M

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