Recycling mechanisms and policy suggestions for spent electric vehicles' power battery -A case of Beijing

Accepted Manuscript Recycling Mechanisms and Policy Suggestions for Spent Electric Vehicles’ Power Battery -A Case of Beijing

Yanyan Tang, Qi Zhang, Yaoming Li, Ge Wang, Yan Li PII:

S0959-6526(18)30694-2

DOI:

10.1016/j.jclepro.2018.03.043

Reference:

JCLP 12301

To appear in:

Journal of Cleaner Production

Received Date:

30 September 2017

Revised Date:

04 February 2018

Accepted Date:

05 March 2018

Please cite this article as: Yanyan Tang, Qi Zhang, Yaoming Li, Ge Wang, Yan Li, Recycling Mechanisms and Policy Suggestions for Spent Electric Vehicles’ Power Battery -A Case of Beijing, Journal of Cleaner Production (2018), doi: 10.1016/j.jclepro.2018.03.043

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ACCEPTED MANUSCRIPT

Recycling Mechanisms and Policy Suggestions for Spent Electric Vehicles’ Power Battery -A Case of Beijing

YANYAN TANG Academy of Chinese Energy Strategy, China University of Petroleum-Beijing, Changping, Beijing 102249, China

QI ZHANG (CORRESPONDING AUTHOR) Academy of Chinese Energy Strategy, China University of Petroleum-Beijing, Changping, Beijing 102249, China Email: [email protected]; [email protected] YAOMING LI Academy of Chinese Energy Strategy, China University of Petroleum-Beijing, Changping, Beijing 102249, China GE WANG Academy of Chinese Energy Strategy, China University of Petroleum-Beijing, Changping, Beijing 102249, China YAN LI Academy of Chinese Energy Strategy, China University of Petroleum-Beijing, Changping, Beijing 102249, China

1

ACCEPTED MANUSCRIPT Abstract In recent years, electric vehicles have developed rapidly in China, and recycling a large number of their spent power batteries will become a substantial challenge in the near future. However, the specific mechanisms and policies for recycling spent power batteries have still not been established in China. Therefore, the purpose of this study is to propose reward-penalty mechanisms and policies, and test their impacts on power battery recycling by using a Staklberg game theory based model. In the model, three single recycling channel modes and three competitive dual recycling channel modes were considered respectively. Furthermore, the total social welfare is used as the indicator to select the optimal recycling modes, which includes participants’ profit, consumer surplus, government’s supervision cost, energy-saving and carbon emission reduction effect. The obtained analysis results show that: (i) the intensive rewardpenalty mechanism is more suitable for higher recycling rate modes, otherwise it may cause benefit losses, and thus, setting a reasonable minimum recycling rate as benchmark for reward-penalty mechanism is critically important; (ii) Environmental awareness has significant impacts on social benefits of power battery recycling; (iii) M&R (mode with competition between manufacturer and retailer in the recycling channels) has obvious advantages among these six recycling modes.

Key words: Spent power battery; Electric vehicle; Recycling mode; Reward-penalty mechanism; Environmental awareness

2

ACCEPTED MANUSCRIPT 1. Introduction Electric vehicles (EVs) have become one of the most increasingly attractive alternatives for sustainable transportation, as the adoption of EV could be a promising solution to address the challenges resulted from oil security (Volling and Spengler, 2014) and air pollution (Lin and Tan, 2017). With growing considerations of energy transitions and environmental protection, Chinese government has taken EV as one of the seven strategic emerging industries in China and spared comprehensive efforts in promoting its deployment. According to the statistics, the sales of EV approximately reached 0.507 million in 2016(China Association of Automobile Manufacturers, 2017). Furthermore, the accumulated sales of EV are projected to reach 5 million in 2020 (General Office of the State Council, 2012). Based on manufacturers’ warranties and related literature (Nissan USA, 2017; Ahmadi et al., 2014a; Heymans et al., 2014), the service life for a power battery in the EV is approximately 8 years due to degradation in capacity. Therefore, power batteries in EV must be replaced before the capacity decreases to 70-80% of their original level(Saxena et al., 2015), otherwise the unexpected driving malfunction and safety problems might happen in all likelihood. As EV market has undergone an explosive development since 2012, power batteries will intensively face the retirement. Based on the estimation from China Automotive Technology and Research Centre, the volume of spent EV power battery in China is expected to reach 120 thousand to 170 thousand tons by the year of 2020. Actually, recycling EV power battery is full of significance. Firstly, if they are not properly disposed of, power batteries might pose great threat to the environment as they contain toxic electrolytes, organic chemicals and plastics(Ordoñez et al., 2016; Zeng et al., 2015). Secondly, apart from lithium, cobalt resource is also scarce in China, and more than 90% of China’s cobalt depends on import. The large number of demand will lead to price rising of these resources, which is not conducive to the penetration of EVs (Neubauer and Pesaran, 2011). Therefore, recycling power battery can significantly reduce the virgin material requirements. Thirdly, in fact, the direct disposal of spent power batteries without extracting a second 3

ACCEPTED MANUSCRIPT use is a further waste (Wang and Wu, 2017). Although power batteries at their automotive end-of-life no longer meet the power requirements for a EV, they do retain lots of capacity which can be used in other applications, such as energy storage system (Heymans et al., 2014). Over the past few years, China has worked to develop and implement proper mechanisms for effective management of spent power batteries. A series of regulations based on the EPR (Extend Producer Responsibility) principle has been introduced. The key power battery recycling policies throughout the recent years are shown in Fig. 1. In terms of clarifying specific responsibility, Beijing Municipal Government proposed that the EV manufacturers should provide power battery recycling service and promise to recycle in accordance with the requirements(The People’s Government of Beijing Municipality, 2015). In terms of the constructing recycling system, the main incentive measurements are to provide subsidies currently. For instance, Shanghai Municipal Government stipulated that EV manufacturers would receive a subsidy of 1000 RMB per power battery recycled(National Energy Administration, 2014). In order to improve recycling system, government is striving efforts to establish power battery coding systems for the full life traceability, which makes it possible to calculate recycling rate. Although definite punitive provisions have not been made, a deputy of the National People's Congress has already suggested that the government should implement reward- penalty mechanism (Tian Neng Group, 2017). In other words, enterprises that fail to fulfill their obligations will be punished. Currently, there are some leading participants in the power battery recycling market under the government’s regulations, and their recycling modes can be mainly classified as the following 6 kinds shown in Table 1.

4

ACCEPTED MANUSCRIPT The technical policy for recycling and utilization of EV power battery

Policy of pollution prevention and control for spent battery

Guidance on speeding up the development of renewable resources industry

Encourage enterprises to cooperate with recycling enterprises and material reusing companies so as to share recycling network and improve the recycling efficiency.

Establish an information supervision system for the recycling, transportation, storage, utilization and disposal of spent EV power battery gradually.

Establish pilots to recycle spent EV power battery, improve the standardized system for resource utilization and promote second use.

2016.12.25

2017.1.16 2016.12.26

2016.1.25

2017.3.1 2017.1.26

Implementation plan of extended producer responsibility system

Entry Regulation for EV manufacturers and products

Action plan to promote the development of power battery industry

EV and power battery manufacturers shall be responsible for building spent battery recycling system and make good use of after-sales service network .

EV manufacturers should establish after-sale service system including the recycling of power battery.

Strengthen enterprises' responsibility in production, use, recycling and reuse of EV power battery, and gradually improve the management system of recycling.

Fig. 1 Power battery recycling polices in China.

In fact, although China has introduced a number of policies based on the EPR principle, the specific mechanisms for recycling spent power batteries have not been established. In European Union, Directive 2006/66/EC was adopted in 2006 and has been subject to a number of revisions, which establishes rules for collection, recycling, treatment and disposal of batteries. In addition, the mandatory minimum recycling rate is specified in the Directive and the reward-penalty mechanism is implemented (European Union, 2006; The European Commission, 2016).The purpose of this study is to propose reward-penalty mechanisms and policies, and test their impacts on power battery recycling in China by using Staklberg game theory. Three single recycling channel modes and three competitive dual recycling channel modes were considered respectively, and the total social welfare is used as the indicator to select the optimal recycling modes, including participants’ profit, consumer surplus, government’s supervision cost, energy-saving and carbon emission reduction effect. By using numerical analysis method, the proposed modes were verified, and the reward-penalty mechanism and resident’s environmental awareness were discussed. The main contributions of the study include (1) enriching the existing research about recycling systems of power batteries;(2) investigating the impact of rewardpenalty mechanism on the mentioned six modes within the same framework;(3) developing general Staklberg game models with consideration of residents’ environmental awareness and recycling convenience. Even though this work was 5

ACCEPTED MANUSCRIPT originally carried out with the intention to promote the social welfare brought by recycling power batteries in Beijing, the outcomes can also provide relevant insights and suggestions for other cities. Table 1 Power battery recycling modes. Mode

Modes with single recycling channel

Description of mode

Example

Company's type

Business in power battery recycling

M

Manufacturer recycles power batteries BAK Battery himself directly from the customers.

Power battery manufacturer

It plans to construct the "Spent New Energy Vehicle Dismantling and Recycling" project that use specialized processes for effective recovery, recycling and proper disposal of power batteries.

R

Manufacturer provides suitable incentives to an existing retailer to induce the recycling.

Retailer of Jianghuai Automobile Group

It provides sale, spare part, survey and power battery recycling service for Jianghuai Automobile.

TP

Manufacturer subcontracts the GEM Co., Ltd recycling activity to a third party

Third party

GEM and Dongfeng Motor, one of the four major automobile groups in China, have the cooperaiton in green supply chain of EV including power battery recycling.

Power battery manufacturer

Its business covers power battery reserch, manufacturing, recycling and second use.

Retailer of Soundon New Energy

It prodivides power battery recycling service for Soundon New Energy.

Power battery manufacturer

It specializes in reasearch development, recycling and second use of power batteries.

Jianghuai Automobile Group's 6S shop

Soundon New Manufacturer Energy competes with retailer M&R in the recycling Soundon New channels. Energy's internet 4s shop CATL Manufacturer Modes with competes with the competitive M&TP third party in the dual recycling channels. recycling channels

Hunan Brunp

Third party

BYD 4s shop

Retailer of Jianghuai Automobile Group

Retailer competes R&TP with the third party in the recycling channels. GEM Co., Ltd

Third party

It's the largest state-level high-tech enterprise engaged in recycling and processing of spent power batteries.And it provides power battery recycling service for CATL. It is responsible for removing spent power batteries from cars and transporting them to BYD Baolong factory for household energy storage systems and other uses. BYD also cooperates with GEM to promote construction of whole industry chain including recycling of power battery.

The remainder of the paper is organized as follows. The relevant literature review is introduced in Section 2. Section 3 describes the problems and lists the notations and assumptions. Section 4 formulates the Stackelberg game and explores the optimal 6

ACCEPTED MANUSCRIPT strategies under different modes. The numerical experiments are conducted and the results of sensitivity analysis are presented in Section 5, followed by Section 6 in which the main findings and policy implications for the future are summarized. All proofs are in the supplementary material.

2. Literature Review Due to the rapid development of the EV industry all over the world, EV power batteries have attracted increasing attentions. At present, most of these studies focus on battery technologies (Cordoba-Arenas et al., 2015; Han et al., 2014; Jaguemont et al., 2016; Zhang and Lee, 2011), as well as economic and environmental analysis of repurposing EV batteries in other applications (Ahmadi et al., 2014b; Parra and Patel, 2016; Peterson et al., 2010; Uddin et al., 2017). However, only a few authors have investigated the impact of reward-penalty mechanism on competitive dual recycling channels. Relevant literature will be reviewed under four categories: (1) reward-penalty mechanism, (2) residents’ willingness to take part in recycling activities, (3) competition in recycling channels and (4) the related literature about Stackelberg game. The recycling activities involve several stakeholders, among which government plays a significant role. Modeling government regulation and its impact is a fastgrowing research filed. Govindan et al.(2013) finds that the main reasons closed-loop supply chain(CLSC) members participate into reverse logistics are to recapture the value of the recycled materials and end-of-life products, and to properly dispose spent as directed by government’s regulations. Wang et al. (2014) explored the mixedsubsidy policies have better positive effects on improving the development of recycling and remanufacturing than single subsidy policies, but involve higher cost accordingly. The government should employ proper subsidy policies by balancing between costs and benefits. Under the self-financing condition, Zhou et al. (2016) showed that there may be a gap between the upper limit and the optimal subsidy that maximizes the social welfare, which means a larger subsidy does not necessarily render a larger welfare. Zhang et al. (2017) investigates the impact of government’s intervention and found penalty mechanism was one of the key determinants affecting biofuel companies' 7

ACCEPTED MANUSCRIPT performance. Wang et al. (2017) examines that reward-penalty mechanism can keep the market competitive order for protecting the wholesale price of the leader's leading status in a CLSC with two sequential competing manufacturers. Jia et al. (2017) proposed that penalty can effectively reduce the illegally dumped spent and improve the recycle ratio. Besides, the intensity of penalty does not always follow the rule “bigger means better”, which makes the determination of reasonable range significant. With the consideration of supervision cost, Fan et al. (2017) discussed optimal strategy for government to supervise low-carbon subsidy and also draw the similar conclusion about punishment intensity. Apart from the efforts made by the government and enterprises, many scholars also pointed out that the role of residents is also very important in the recycling. Viscusi et al. (2011) summarized that individual behaviors that benefit the environment are potentially influenced by personal values of environmental quality, social norms, and economic incentives like financial rewards for return. From the perspective of public awareness, Cao et al. (2016) conducted the survey about Chinese people’s cognitive level and their participation in e-waste recycling, highlighting the education of environmental knowledge especially for children. Beukering and Jeroen C.J.M. van den Bergh (2006) shared the view that consumers with high-income levels are more likely to participate voluntarily in recycling. However, this willingness would decline if such recycling was time-intensive. During the investigation of residents’ behavior towards electrical and electronic waste recycling in Beijing, Wang et al. (2011) used the recycling condition of recovery spot around residential areas to represent the convenience of recycling facilities and proved its vital impact on the preference of recycling style. Similarly, Zhang et al.(2016) indicate that enhanced accessibility of recycling facilities would lower behavioral costs and encourage people to take action. From the perspective of economic incentives, He et al.(2016) estimated that when the compensation amount is between 1.08% and 1.31% of household annual income, households are willing to participate in agricultural waste recycling. Shaw and Maynard (2008) showed that positive changes in householders’ recycling may also potentially be achieved through financial incentives, but preferably delivered either as rewards at community level or as household-specific tax rebates. 8

ACCEPTED MANUSCRIPT Actually, competition intensity is a bridge linking residents and recyclers, which has large impact on the determination of optimal reverse channel. Savaskan and Van Wassenhove(2006) concluded that channel profits were driven by the impact of scale of return on recycling efforts in the direct recycling system and competitive interaction between retailers in the indirect recycling system. Huang et al. (2013) researched the situation of retailer and the third party competitively recycling used products in the reverse supply chain and derived the parameter domain which is defined as the set of competing intensities. Li and Li (2016) studied the game model of two sustainable supply chains under competition in product sustainability and put forward that the vertical integration was only beneficial to a supply chain when the competition degree is relatively low. Similarly, Heese et al. (2005) found that customers were always better off under product take-back, but it depended on the degree of competition, whether firms would use the benefits of takeback to increase their margins or to pass them on to the customers by lowering their prices. Yi et al. (2016) proposed that the advantages of being close to the market and convenience for providing the after-sale service make the retailer have better performance in developing remanufacturing activities. Hong et al. (2013) investigated three reverse dual recycling channel structures in a manufactureroriented CLSC, and concluded that the manufacturer and the retailer dual recycling channel was the most effective one. Game theory is widely used in the literature to model interactions among different stakeholders with various objectives. The Stackelberg game, which is a type of noncooperative game dealing with hierarchical decision-making processes of multiple decision makers, has attracted great attentions. (Li et al., 2017) proposed a Stackelberg game model to study the impacts of government's subsidy towards environmentalfriendly products in a dual-channel supply chain. The interactions among manufacturer, retailer, recycler and consumers in the recycling market have been formulated into a Stackelberg game model in (Wang et al., 2015; Zhao et al., 2017; Feng et al., 2017). Therefore, the Staklberg game theory is adopted here to model the recycling of spent power batteries under reward-penalty mechanism. 9

ACCEPTED MANUSCRIPT 3. Problem Description

Power Battery Manufacturer

EV Manufacturer

EV Retailer

Power Battery Recycling Company

Consumer

Evaluation

Material Reusing

Spent Power Battery after Second Use

Forward Logistics

Second Use

Backward Logistics

Fig. 2 Framework of power battery recycling process.

The power battery manufacturers and EV manufacturers are the main agents to fulfil the producer responsibility extension system. In this paper, we uniformly use the "power battery manufacturers" to represent them hereafter. EV retailers, third-party enterprises and residents are related participants in the whole activities. Government is the maker of policies to promote the power battery recycling. The entire recycling processes are shown in Fig. 2. The power battery came to the residents with the sale of EV. Then, the power battery recycling company is responsible for bring the batteries back to realize the remaining value. The problem here is which single participant or two participants serving as the roles of power batteries recycling company can promote the total social welfare. In this paper, we make the comparison of six kinds of modes. As for the three single recycling channel modes, the situation of manufacturer directly recycling power batteries himself from the customers (Mode M), providing suitable incentives to an existing retailer to induce the recycling (Mode R), and subcontracting the recycling activity to a third party (Mode TP) are proposed respectively. As for the three competitive dual recycling channel modes, the situation of manufacturer 10

ACCEPTED MANUSCRIPT competing with retailer (Mode M&R), manufacturer competing with the third party (Mode M&TP), and retailer competing with the third party (Mode R&TP) are established respectively. 3.1 Related results from online survey We conduct an anonymous online survey about subject attitude and cognitive level so as to characterize their behaviors better considering fewer investigation about residents’ willingness in power battery recycling. It was released at the So Jump platform on April 24, 2016. The total number of validly returned questionnaires was 355, and only the related results are listed here. Completely unnecessary

1

Not necessary

0

Generally necessary

12

Kind of necessary

23

Very necessary

319 0

40

80

120

160

200

240

280

320

Fig. 3 Survey results for necessity level to recycle power battery

No idea

202

A little

76

Basically Know

37

Quiet Well

23

Vey Well

17 0

30

60

90

120

150

180

210

Fig. 4 Survey results of knowing level of power battery recycling

11

ACCEPTED MANUSCRIPT

Other

10

Recycling convenience

207

Recycling price

239

Whether treatment is environmentally friendly

146

Whether recycling channels are formal

78 0

30

60

90

120

150

180

210

240

Fig. 5 Survey results about factors considered in recycling activities

As shown in Fig. 3 and Fig. 4, although 89.86% of the respondents think it is very necessary to recycle power battery, 56.9% has no idea about the recycling process. In other words, the significance of recycling can be clearly captured by the public, but there are some lacks in popularization about concerning knowledge. As for the factors affecting the participation willingness, we can see residents care more about recycling price and recycling convenience followed by treatment way and whether the channels are formal shown in Fig. 5. 3.2 Notation The notations are defined and summarized in Table 2. The superscript represents the recycling mode. The subscript stands for the corresponding participant.

Table 2 The description of the symbols.

Symbol Definition

D( ps ) demand for new power battery in the market



potential market size



sensitivity of consumers to the retail price of power battery

ps

unit retail price

pw

unit wholesale price 12

ACCEPTED MANUSCRIPT pr  j

t

average recycling price per spent power battery set by the recycler j unit transfer price for returning spent power battery from the third party/retailer to the manufacturer

Cm

unit cost of producing a new power battery with the raw materials

Cn

unit cost of producing a remanufactured power battery from the recycling materials recycler j’s investment for each power battery in recycling activities,

Ij

including construction of recycling network, advertisement, transportation etc.

Qj A

quantities of power batteries recycled by recycler j the quantities of spent power batteries consumers are willing to return free of charge, which is regarded as a measurement of environmental awareness

k

consumers’ sensitivity for recycling price

h1

competition coefficient between manufacturer and retailer

h2

competition coefficient between manufacturer and third party

h3

competition coefficient between retailer and third party A follows the normal the remaining capacity for one spent power battery, L

A L

λ

2 distribution with mean of μ L and deviation of σ L

the net profit gained for every unit of the remaining capacity in the spent power batteries in second use unit benefit by recycling, including the net save cost in production and the



A net profit in second use   Cm  Cn  λL

ξ0

minimum recycling rate set by the government

ξ

actual recycling rate

S

reward-penalty intensity established by government

τ

government’s fixed cost coefficient in reward penalty mechanism

13

ACCEPTED MANUSCRIPT

m

the profit of the manufacturer

r

the profit of the retailer

 tp

the profit of the third party

E

energy saving brought by purchasing an EV during its service time

B

carbon emission reduction brought by purchasing an EV during its service time

3.3 Assumptions To handle the problems stated in the above subsection, we propose some key assumptions mainly based on the works of Savaskan et al.(2004). (1) For simplification, we assume the market consists of one manufacturer, one retailer and one third party (Huang et al., 2013; Jafari et al., 2017) . (2) We assume the power batteries sold and recycled are same type. (3) For power battery, the processes of manufacturing, sale, recycling, second use, and material reusing in remanufacturing are considered in one period. (4) The information is symmetric, and all the participants are risk-neutral. (5) The manufacturer has sufficient channel power over the retailer and the third party to act as a Stackelberg leader. (6) The participants are completely rational and make their own optimal decision based on their respective maximum expected profit. (7) Manufacturer can use new material and reuse materials in the spent power batteries to carry out the production activities. There is no difference between remanufactured power batteries and the new ones. (8) For an electric vehicle, the cost of power battery accounts for nearly 60% of the total. Therefore, we regard the demand for power batteries as the demand for electric vehicles approximately. The market demand is a linear function of the power battery retail price which is D( ps )      ps . 14

ACCEPTED MANUSCRIPT (9) Because the recycling situation of power batteries is not satisfactory in China now, the impact of scale of return on recycling efforts in the recycling system will be ignored in this paper. (10)On one hand, the recycler should invest I j ( j  M, R,TP) for each battery on average, including the construction of recycling network, advertisement, transportation etc. On the other hand, recycler should pay recycling price pr  j ( j  M, R, TP) on average to get each spent power battery from consumer.

(11)According to our investigation, we assume the amount of recycled power batteries is equal to Q j  A  k  pr  j  hx  pr  z (j,z=M,R,TP and j≠z; x=1 for M&R, x=2 for M&TP, x=3 for R&TP)(Gong et al., 2014; Fallah et al., 2015; Feng et al., 2017). The competition efficient h is decided by the degree of recycling convenience. Considering the numbers of recycling stations and the distances to consumers, we assume h1  h2  h3 . (12)We assume 0 is the target recycling rate set by the government, and  0     ps  is the target recycling amount. In addition, the reward-penalty intensity is set as S for each unit in the difference part. In a sum, the total reward or penalty is

S  [( A  k  pr  j  hz  pr  z )   0     ps ] . (13)The supervision cost is involved for government to implement the penalty and reward mechanism(Wang et al., 2015). The fixed cost coefficient is  . And the total supervision cost is τ  S  [( A  k  pr  j  hz  pr  z )   0     ps ] . 2

(14)The spent power batteries should be first applied into second use and then recycled to extract materials, so as to improve the utilization ratio of the resource(National Development and Reform Commission, 2016). (15)Considering the technology level and practical situation, the used power batteries are only applied into the storage system in this paper. We assume the remaining A which follows a normal distribution capacities of the recycled power batteries is L 2

with mean μ L and standard deviation σ L (Zhu et al., 2016). We assume there is a 15

ACCEPTED MANUSCRIPT positive relationship between every unit of the remaining capacity in the spent power batteries and the net profit gained by storage system in the life span of operation. The coefficient is  . (16)As is mentioned previously, the manufacturer has the dominating power in this field. Therefore, in the process of material reusing, it only refers to remanufacturing the valuable materials obtained from the spent power batteries to produce new ones. (17)For manufacturer, remanufacturing through spent power battery after second use is less costly than manufacturing new power batteries through raw materials, which can be represented as Cn  Cm . (18)For government, the objective function is to maximum the social benefit. The social benefit takes account of all participants’ profit and consumer surplus (Ma et al., 2016) and the supervision cost. Because the promotion in the sale of EV has a positive impact in the aspect of energy-saving and carbon emission reduction (Ma et al., 2017; Zhang et al., 2014) . Therefore, the benefit in terms of these 2 aspects will also be considered. In a sum, the total social welfare can be represented as  m   r   tp  D  ps    E  B   τ S [( A  kpr  j  hz pr  z )   0 D  ps ] . 2

4. Stackelberg Game Model Based on the problem formulation and assumptions, we suppose that all of the manufacturer, the retailer and the third party are independent decision makers. Each of them aims to maximize its own profit, but the decision-making results are mutually influential. Due to its sufficient channel dominance, the manufacturer behaves as the Stackelberg leader and can use the foresight about other followers’ action functions when making his own first move. The retailer and the third party are followers which will observe the leader’s strategy and react correspondingly. Using the backward induction method, the follower makes his best response functions for his decision variables which are expressed with leader’s decision variables. After replacing followers’ decision variables by the previously mentioned response 16

ACCEPTED MANUSCRIPT functions in leader’s profit function, then the leader can calculate optimum values for his decision variables(Madani and Rasti-Barzoki, 2017). In order to obtain the optimal decisions for all related players under different models, the concavity of the profit functions should first be proven. Then the joint concavity of each profit function on decision variables is also required to be demonstrated. Because of the space limit, we only list the proofs about dual recycling channels in Appendix. 4.1 Mode M—Manufacturer Recycling

Recycling Price Spent Power Battery

Power Battery Manufacturer

Power Battery

Retailer

Wholesale Price

Power Battery

Customer

Retail Price

Forward Logistics Backward Logistics Cash Flow

Government Fig. 6 Framework of Mode M

As shown in Fig. 6, manufacturer produces the new power batteries with raw materials or with spent power batteries and sells the new power batteries to the retailer. Then, the retailer sells them to customers. In the reverse channel, the manufacturer M

collects the spent power batteries directly from the customers at a recycling price pr  m per unit. The purpose of both the manufacturer and the retailer is the same that is to maximize their own profits. Besides, the game order is as follows: firstly, the manufacturer determines power batteries’ wholesale price pw and recycling price pr  m M

using the response function of the retailer; then the retailer reacts to determine the retail price ps . Because the manufacturer is the Stackelberg leader, we begin by characterizing the best-response function of the retailer. For a given pw , the retailer’s profit function is shown below. 17

ACCEPTED MANUSCRIPT  rM   ps  pw       ps 

(1)

With the deducing of the first derivative and the second derivative of ps , which is omitted here for brevity, the objective function  r

M

proves to be concave in ps .

Therefore, the retailer’s first-order condition characterizes the unique best response and we can get ps =

   pw . 2

Next the manufacturer’s profit can be stated as

 mM   pw  Cm   0 S       ps      prM m  I m  S    A  k  prM m  After putting the results of ps =

(2)

   pw into Eq. (2), we can obtain the first and 2

M M second partial derivative of pw and pr  m . Again, the objective function  m proves to M be jointly concave in pw and pr  m . Consequently, we set the first derivatives of pw and

prMm equal to zero to obtain the optimal wholesale price and the recycling price for the manufacturer.

pw* 

   Cm  0 S 2

prM m* 

(3)

k   kS  kI m  A 2k

(4)

According to the backward induction method, we substitute the pw in ps = * with pw 

ps * 

   pw 2

   Cm  0 S , and get the optimal retail price for the retailer. 2

   pw 3   Cm  0 S  2 4

(5)

Under the optimal prices, we can calculate the manufacturer’s profit  m , retailer’s M*

profit  r and the actual recycling rate ξ . M*

*

18

ACCEPTED MANUSCRIPT

 mM * 

(   Cm   0 S ) 2 (k   kS  kI m  A) 2  8 4k

(6)

 rM * 

(   Cm   0 S ) 2 16 

(7)

2(k   kS  kI m  A)    Cm   0 S

(8)

ξ* 

4.2 Mode R—Retailer Recycling

Power Battery Manufacturer

Transfer Price

Recycling Price

Spent Power Battery

Spent Power Battery

Power Battery

Retailer

Wholesale Price

Power Battery

Customer

Retail Price

Forward Logistics Backward Logistics Cash Flow

Government Fig. 7 Framework of Mode R

As shown in Fig. 7, the retailer not only engages in the sale activities but also the recycling of spent power batteries. Correspondingly, it determines on the retail price ps

R

and the recycling price pr  r . Because the ownership of spent power batteries initially

rests with the retailer after the recycling, manufacturer has to pays a transfer price

t per

battery to retailer to take the spent power batteries back. And the transfer price

t is

decided by the manufacturer. The profit functions of the manufacture and the retailer are as follows

 mR   pw  Cm   0 S       ps      t  S    A  k  prR r 

(9)

 rR   ps  pw       ps   (t  prR r )   A  k  prR r   I r   A  k  prR r 

(10)

The calculation is first conducted by characterizing the best response function of 𝑀

the retailer. Subsequently, by substituting the retailer 's best response 𝑝𝑠 and 𝑝𝑟 ‒ 𝑚 into the manufacture 's objective function, the optimal values can be calculated. 19

ACCEPTED MANUSCRIPT From Eqs. (9) and (10), we can derive the optimal values of the R mode.

   Cm  0 S 2

(11)

k   kS  kI r  A 2k

(12)

pw*  t* 

ps * 

   pw 3   Cm  0 S  2 4

prR r * 



ξ* 

kt  kI r  A k   kS  kI r  3 A  2k 4k

(14)

(   Cm   0 S ) 2 (k   kS  kI r  A) 2  8 8k

(15)

(   Cm   0 S ) 2 (k   kS  kI r  A) 2   16  16k

(16)

k   kS  kI r  A    Cm  0 S

(17)

 mR*  R* r

(13)

4.3 Mode TP—Third Party Recycling Transfer Price

Recycling Price

Third Party Spent Power Battery

Spent Power Battery

Power Battery Manufacturer

Power Battery

Retailer

Wholesale Price

Power Battery

Customer

Retail Price

Forward Logistics Backward Logistics Cash Flow

Government Fig. 8 Framework of Mode TP

As shown in Fig. 8 , the profit functions of the manufacture, the retailer and the third party are as follows

 mTP   pw  Cm   0 S       ps      t  S    A  k  prTPtp 

(18)

 rTP   ps  pw       ps 

(19)

20

ACCEPTED MANUSCRIPT  tpTP  (T  prTPtp )   A  k  prTPtp   I tp   A  k  prTPtp 

(20)

We first calculate the best-response function of the retailer and the third party. Then, we substitute their best response into the objective function of the manufacturer so that we can deduce the optimal value of pw and t . From Eqs. (18) - (20), we can derive the optimal values of the TP mode.

pw*  t* 

   Cm  0 S 2

(21)

k   kS  kI tp  A 2k

ps * 

(22)

   pw 3   Cm  0 S  2 4

prTPtp* 

kt  kI tp  A 2k



k   kS  kI tp  3 A 4k

 mTP* 

(   Cm   0 S ) 2 (k   kS  kI tp  A)  8 8k

 rTP* 

(   Cm   0 S ) 2 16 



TP * tp

ξ* 



(23)

(24) 2

(25)

(26)

(k   kS  kI tp  A) 2 16k

(27)

k   kS  kI tp  A

   Cm   0 S

(28)

4.4 Mode M&R—Manufacturer and Retailer Recycling As shown in Fig. 9, the manufacture not only directly collect spent power batteries from consumers but also provide a unite transfer price t to the retailer to introduce the M &R

recycling activities. In this mode, the manufacturer firstly sets pw , pr  m

and t to 21

ACCEPTED MANUSCRIPT M &R

maximize his own profit. Then the retailer determines ps and pr  r

to maximize his

profit. Recycling Price Spent Power Battery Power Battery

Power Battery Manufacturer

Wholesale Price Spent Power Battery

Power Battery

Retailer

Transfer Price

Retail Price Spent Power Battery

Customer

Recycling Price

Forward Logistics Backward Logistics Cash Flow

Government

Fig. 9 Framework of Mode M&R

The profit functions of the manufacturer and the retailer are as follows.  mM & R   pw  Cm   0 S       ps      t  S    A  k  prM r& R  h1  prM m& R  

  p

M &r r m

 I m  S    A  k  prM m& R  h1  prM r& R 

(29 )

 rM & R   ps  pw       ps   (t  prM r& R  I r )   A  k  prM r& R  h1  prM m& R 

(30 )

The backward induction method is still applied here. We first calculate the bestM &R

response function of the retailer for a given pw , pr  m and t . Then, we substitute the retailer's best response in to the objective function of the manufacturer. From Eqs. (29) and (30), we can derive the optimal values of the M&R mode. The proofs are shown in Appendix A. Proofs in Mode M&R.

pw* 

   Cm  0 S 2

prM m& R*  t* 

  S  Im A  2 2(k  h1 )

  S  Ir A  2 2(k  h1 )

ps * 

   pw 3   Cm  0 S  2 4

(31 )

(32) (33 ) (34 ) 22

ACCEPTED MANUSCRIPT

prM r& R* 

k

2

 h12     S    k  h1  kI r  h1 I m   3 Ak  Ah1

(35

4k  4h1k 2

)

(   Cm  0 S ) 2  8 (k   h1  kS  h1S  A  kI r  h1 I r )(k   h1  kS  h1S  A  kI r  h1 I m )  8(k  h)

 mM & R* 

 k  h1    S  I m   A  2k 2  h1k  h12     S   h1kI r  2k 2 I m  h12 I m  2 Ak  Ah1  8k (k  h1 ) (36 ) 2 (   Cm   0 S ) 2 [ k  h1    S   h1 I m  kI r  A]  16  16k

 rM & R* 

ξ

*

 3k 

2

(37 )

 2h1k  h12     S    h1k  k 2  I r   h12  h1k  2k 2  I m  3 Ak  Ah1 k (   Cm   0 S )

(38 )

4.5 Mode M&TP—Manufacturer and Third Party Recycling Recycling Price Spent Power Battery Transfer Price

Recycling Price

Third Party Spent Power Battery

Power Battery Manufacturer

Power Battery

Spent Power Battery

Retailer

Wholesale Price

Power Battery

Customer

Retail Price

Forward Logistics Backward Logistics Cash Flow

Government Fig. 10 Framework of Mode M&TP

As shown in Fig. 10, the manufacturer not only directly collect spent power batteries from consumers but also provide a unite transfer price t to the third party to introduce the recycling activities. In this mode, the manufacturer firstly sets pw , prM m&TP and t to maximize his own profit. Then the retailer determines 𝑝𝑠 and the third party

23

ACCEPTED MANUSCRIPT determine prMtp&TP to maximize their respective profit. The profit functions of the manufacturer and the retailer are as follows.

 mM &TP   pw  Cm   0 S       ps      t  S    A  k  prMtp&TP  h2  prM m&TP      prM m&TP  I m  S    A  k  prM m&TP  h2  prMtp&TP 

(39 )

 rM &TP   ps  pw       ps 

(40 )

 tpM &TP  ( t  prMtp&TP  I tp )   A  k  prM m&TP  h2  prMtp&TP 

(41 )

We first calculate the best-response function of the retailer for a given pw , and the best-response function of the third party for a given prM m& R and t. Then, we substitute their best response in to the objective function of the manufacturer. From Eqs. (39) (41), we can derive the optimal values of the M&TP mode. The proofs are shown in Appendix B. Proofs in Mode M&TP.

pw* 

   Cm   0 S 2

prM m&TP* 

t* 

2



A 2(k  h2 )

k 

2

(43)

(44)

   pw 3   Cm   0 S  2 4

M &TP * r tp

p

  S  Im A  2 2(k  h2 )

  S  I tp

ps * 

(42)

(45)

 h2 2     S    k  h2   kI tp  h2 I m   3 Ak  Ah2 4k 2  4hk

(46)

24

ACCEPTED MANUSCRIPT (   Cm  0 S )2  8 (k   h2   kS  h2 S  A  kI tp  h2 I m )(k   h2   kS  h2 S  A  kI tp  h2 I tp )

 mM &TP* 

8(k  h2 )



 k  h2    S  I m   A  2k 2  h2 k  h2 2     S   h2 kI tp  2k 2 I m  h2 2 I m  2 Ak  Ah2  8k (k  h2 )



M &TP * r



M &TP * tp

ξ

*

 3k 

(47)

(   Cm   0 S ) 2  16   2

(48)

[ k  h2    S   h2 I m  kI tp  A]2 16k

(49)

 2h2 k  h2 2     S    h2 k  k 2  I tp   h2 2  h2 k  2k 2  I m  3 Ak  Ah2 k (   Cm   0 S )

(50)

4.6 Mode R&TP—Retailer and Third Party Recycling

Transfer Price

Recycling Price

Third Party Spent Power Battery

Spent Power Battery Power Battery

Power Battery Manufacturer

Wholesale Price Spent Power Battery

Power Battery

Retailer

Transfer Price

Retail Price Spent Power Battery

Customer

Recycling Price

Forward Logistics Backward Logistics Cash Flow

Government

Fig. 11 Framework of Mode R&TP

As shown in Fig. 11, we suppose that the manufacturer subcontracts the recycling activities to the retailer and the third-party collector. In this case, the manufacturer is the Stackelberg leader who first chooses pw and t to maximize profit, based on which the retailer chooses ps and prR&r TP , and the third-party collector chooses prR&tpTP simultaneously to maximize their profits respectively. The profit functions of the manufacturer, the retailer and the third party are as follows

25

ACCEPTED MANUSCRIPT  mR &TP   pw  Cm   0 S       ps      t  S    2 A   k  h3   prTP r  prTPtp   (51 )

 rR &TP   ps  pw       ps    t  prR&r TP  I r    A  k  prR&r TP  h3  prR&tpTP 

(52 )

 tpR &TP   t  prR&tpTP  I tp    A  k  prR&tpTP  h3  prR&r TP 

(53 )

We first calculate the best-response function of the retailer and the third party. Then, we substitute their best response into the objective function of the manufacture so that we can deduce the optimal values of pw and t . The proofs are shown in Appendix C. Proofs in Mode R&TP.

pw* 

t* 

   Cm   0 S 2

2  2 S  I r  I tp 4

ps * 



(54)

A 2k  2h3

(55)

   pw 3   Cm   0 S  2 4

(56)

prR&rTP* 

 4k

3

 2h3 k 2  2kh32     S    6k 3  7 h3 k 2  kh32  I r   2k 3  5h3 k 2  3kh32  I tp  12 Ak 2  2 Ah3 k  4 Ah32 16k 3  16h3 k 2  4kh32  4h33

prR&tpTP* 

 4k

3

(57)

 2h3k 2  2kh32     S    6k 3  7 h3k 2  kh32  I tp   2k 3  5h3k 2  3kh32  I r  12 Ak 2  2 Ah3k  4 Ah32 16k 3  16h3k 2  4kh32  4h33



R &TP * m

2 (   Cm   0 S ) 2 k[ k  h3   2  2 S  I r  I tp   2 A]   8 8(k  h3 )(2k  h3 )



R &TP * r

(   Cm   0 S ) 2   16 

(58)

(59)

k  4k 2  2h3 k  2h32     S    6k 2  h3 k  3h32  I r   2k 2  3h3 k  h32  I tp  2 Ah3  4 Ak  16(2k  h3 ) 2 (2k  h3 ) 2

2

(60)

26

ACCEPTED MANUSCRIPT

 tpR &TP* 

ξ* 

8k

2

k[ 4k 2  2h3 k  2h32     S    6k 2  h3 k  3h32  I tp   2k 2  3h3 k  h32  I r  2 Ah3  4 Ak ]2 16(2k  h3 ) 2 (2k  h3 ) 2

(61)

 8h3 k   2  2 S  I r  I tp   8 Ak (   Cm   0 S )(4k  h3 )

(62)

All the optimal solution in these modes are shown in Table 3 and Table 4.

27

Table 3 Summary of optimal solutions in Mode M, Mode R and Mode TP

M

R

TP

pw*

   Cm   S  0 2

   Cm  0 S 2

   Cm  0 S 2

ps*

3   Cm   0 S 4

3   Cm   0 S 4

3   Cm   0 S 4

pr*

k   kS  kI m  A 2k

k   kS  kI r  3 A 4k

k   kS  kI tp  3 A

k   kS  kI r  A 2k

k   kS  kI tp  A

t*

4k

2k

ξ*

2(k   kS  kI m  A)    Cm  0 S

k   kS  kI r  A    Cm  0 S

k   kS  kI tp  A

π m*

(   Cm   0 S ) 2 (k   kS  kI m  A) 2  8 4k

(   Cm   0 S ) 2 (k   kS  kI r  A) 2  8 8k

2 (   Cm   0 S ) 2 (k   kS  kI tp  A)  8 8k

πr *

(   Cm   0 S ) 2 16

(   Cm   0 S ) 2 (k   kS  A  kI r ) 2  16 16k

(   Cm   0 S ) 2 16

πtp*

   Cm  0 S

(k   kS  A  kI tp ) 2 16k

28

Table 4 Summary of optimal solutions in Mode M&R, Mode M&TP and Mode R&TP

M&R

M&TP

R&TP

pw*

   Cm   0 S 2

   Cm   0 S 2

   Cm   0 S 2

ps*

3   Cm   0 S 4

3   Cm   0 S 4

3   Cm   0 S 4

  S  Im A  2 2(k  h1 )

M:

pr

*

 k 2  h12     S    k  h1  kI r  h1 I m  

 3k

ξ*

  S  I tp

2

 3k

 2h1 k  h12     S  

h k  k  I  h 2

1

2

r

2

1

 h1 k  2k

2

I

m



3 Ak  Ah1 k (   Cm   0 S )

 k   h1  kS  h1 S  A  kI r  h1 I m  (   Cm   0 S ) 2 (k   h1   kS  h1 S  A  kI r  h1 I r )   8 8(k  h1 )

π m*

 k  h1    S  I m   A

[ 2k 2  h1 k  h12     S   h1 kI r  2k 2 I m  h12 I m  2 Ak  Ah1 ] 8k (k  h1 )

πr

*

2 (   Cm   0 S ) 2 [ k  h1    S   h1 I m  kI r  A]  16 16k

2

h k  k  I

tp

TP :

3

 2h3 k 2  2kh32     S    6k 3  7 h3 k 2  kh32  I tp 

 2k

3

 5h3 k 2  3kh32  I r  12 Ak 2  2 Ah3 k  4 Ah32 16k 3  16h3 k 2  4kh32  4h33

2  2S  I r  I tp

A 2k  2h2

4

8k

  h2 2  h2 k  2k 2  I m 

 k   h   kS  h S  A  kI 2

tp

A 2k  2h3

 8h3 k   2  2S  I r  I tp   8 Ak

 h2 I m 

(   Cm   0 S ) 2  k   h2   kS  h2 S  A  kI tp  h2 I tp    8 8(k  h2 )

2 (   Cm   0 S ) 2 k[ k  h3   2  2S  I r  I tp   2 A]  8 8(k  h3 )(2k  h3 )

 k  h2    S  I m   A  2k 2  h2 k  h 2     S   h2 kI tp  2k 2 I m  h2 2 I m  2 Ak  Ah2    8k (k  h2 )

   Cm   0 S  (   Cm   0 S ) 2 16

2



(   Cm   0 S )(4k  h3 )

3 Ak  Ah2 k (   Cm   0 S )

2

 2k 3  5h3 k 2  3kh32  Itp  12 Ak 2  2 Ah3 k  4 Ah32 16k 3  16h3 k 2  4kh32  4h33

 2h2 k  h2 2     S  

2

2



 2h3 k 2  2kh32     S    6k 3  7 h3 k 2  kh32  I r 

3

 4k

3 Ak  Ah2 4k 2  4h2 k

TP :

  S  Ir A  2 2k  2h1

t*

R:

 k 2  h2 2     S    k  h2   kI tp  h2 I m  

3 Ak  Ah1 4k 2  4h1k

R:

 4k

  S  Im A  2 2(k  h2 )

M:

16 

2



k  4k 2  2h3 k  2h32     S    6k 2  h3 k  3h32  I r   2k 2  3h3 k  h32  I tp  2 Ah3  4 Ak  16(2k  h3 ) (2k  h3 ) 2

πtp*

[ k  h2    S   h2 I m  kI tp  A]2 16k

k  4k 2  2h3 k  2h3     S    6k 2  h3 k  3h32  I tp   2k 2  3h3 k  h32  I r  2 Ah3  4 Ak  16(2k  h3 ) (2k  h3 ) 2

2

2

2

2

29

ACCEPTED MANUSCRIPT

5. Result 5.1 Data Through questionnaire survey and literature review, this study obtained the relevant data of power battery recycling in Beijing shown in Table 5, providing a basis for numerical analysis.

Table 5 Summary of Parameters’ Value



300000

λ

24780



1.6



26920

Cm

82243

k

1.1

Cn

67713

h1

0.2

Im

900

h2

0.3

Ir

500

h3

0.5

I tp

300

ξ0

0

L

0.5

S

1500

A

0

E

38634

τ

0.00000001

B

618

(1) Considering the quota in EV license plate lottery system, number of lottery applicants and the EV’s promotion target proposed in “Plan on energy saving and reducing energy consumption during the 13th five-year plan of Beijing”(The People’s Government of Beijing Municipality, 2016), we assume  =300000 and

 =1.6 , (2) We take Beiqi EU400 as an example. The power battery capacity is 54.4 kWh. According to the analysis report in McKinsey, the average battery pack price in China is 227 $/ kWh (McKinsey&Company, 2017). With the exchange rate 30

ACCEPTED MANUSCRIPT 1$=6.66 RMB, Cm =54.4  227  6.66=82243RMB . (3) The energy density of power battery is 125 Wh/kg. We can get the weight

54.4  1000 / 125  435.2kg . Some researchers found that 1 ton of Li-ion batteries in EV can generate $5013 profit margin under developed recycling process(Gratz et al., 2014). After calculation, we can get

Cn =82243-5013  435.2 /1000  6.66  67713RMB . (4) Considering the difficulty in building recycling network, we assume I m  900 ,

I r =500 and I tp =300 . (5) According to results of the questionnaire, people care a lot about the recycling price. Therefore, we set A=0 , which indicates the voluntary recycling cannot work at least now. (6) As for the net profit gained through storage system in the second use, we refer the research result in(Madlener and Kirmas, 2017) with the economic viability equal to 73 €/kWh in the whole lifespan. Besides, it is assumed that the spent power battery retains 80% of its rated energy capacity through aging during their “first life” in the electric vehicle. With the exchange rate 1€=7.80 RMB,

λ=0.8  73  54.4  7.80=24780RMB A =82243-67713+24780  0.5= 26920 RMB . Therefore,  =Cm  Cn +λ  L (7) We set  L =0.5 and k=1.1 . Considering the rank of recyclers in terms of recycling convenience de, we set h1 =0.2 h2 =0.3 and h3 =0.5 . (8) Because there’s no requirement about recycling rate at least for now, we set ξ 0 =0 . In addition, we assume the reward-penalty intensity S=1500 , which is close to the 1000 RMB subsidy in Shanghai we mentioned before. We set the government’s fixed cost coefficient τ=0.00000001 (Wang et al., 2015). (9) In Beijing’s public transportation areas, some researchers have conducted a thorough evaluation research on battery electric vehicles performance with the consideration of electricity generation structure and fuel type(Tang and Ma, 2016). 31

ACCEPTED MANUSCRIPT Here, we assume the service life for a power battery in the electric vehicle is 6 years (Souhu Auto, 2017). Based on the data mentioned, the benefit brought by energy saving E=6439  6=38634RMB and the benefit brought by carbon emission reduction B=103  6=618RMB . 5.2 Numerical Analysis Firstly, we conduct the analysis of current situation ( A=0 and ξ 0 =0 ) as shown in Fig. 12. Actually, because there is no required minimum recycling rate, as long as one power battery is recycled, the manufacturer can get the corresponding subsidy. When the reward-penalty intensity falls in the range between 0 and 1950 RMB, the total social welfare firstly rises and then declines in all modes. The subsidy can indeed promote power battery recycling in some degree, and the modes which have stronger sensitivity towards subsidy will outperform in recycling rate. However, higher recycling cannot always cause higher social welfare. When the intensity is above some certain level, it will bring lots of supervision burden for the government and offset the positive benefit brought by recycling. This viewpoint is also demonstrated in (Zhou et al., 2016). Although the overall trend of social welfare is similar, the optimal reward-penalty intensity for different modes are different. For Mode M+R and mode M+TP the optimal level is 350 RMB, while for mode R+TP the optimal level is 700 RMB. In addition, we can find that the mode M+R has obvious good performance and mode M+TP ranks second. The advantage of mode M+R has been mentioned in (Ma et al., 2016). From the optimal solutions shown in Table 3, we can find the distinction between Mode R and Mode TP is very small which can also be reflected here.

32

ACCEPTED MANUSCRIPT

M

Total Social Weflare (Unit:Million RMB)

5820

R

TP

M+R

M+TP

R+TP

5800 5780 5760 5740 5720 5700 5680 5660 5640 0

150

300

450

600

750

900

1050

1200

1350

1500

1650

1800

1950

Reward-Penalty Intensity (Unit:RMB)

Fig. 12 Effects of reward-penalty intensity changes on total social welfare without reward-penalty mechanism

Secondly, we explore the influence of reward-penalty mechanism on total social welfare ( A=0 and ξ 0 =0.4 ) as shown in Fig. 13. When the mechanism is implemented, manufacturer can receive the subsidy only when its actual recycling rate is higher than the minimum target set by the government. It’s clear to capture that the trend becomes much flat compared to the previous one, especially in the high level of intensity. For instance, when the intensity reaches 1800 RMB, the total social welfare with minimum recycling rate is better than the current situation with a surplus of 1318753 RMB. For the Mode M+R, the effects are more obvious. When the intensity is 1150 RMB, the surplus will be 1358208 RMB. However, because the recycling rate in Mode R and Mode TP is less than target, their corresponding welfare suffers losses due to the penalty and the supervision cost. We can find the intensive reward-penalty mechanism is more suitable for the modes with high recycling rate. Under this situation, Mode M+R also performs better than others.

33

ACCEPTED MANUSCRIPT

M

Total Social Weflare (Unit:Million RMB)

5850

R

TP

M+R

M+TP

R+TP

5800

5750

5700

5650

5600

5550 0

150

300

450

600

750

900

1050

1200

1350

1500

1650

1800

1950

Reward-Penalty Intensity (Unit:RMB)

Fig. 13 Effects of reward-penalty intensity changes on total social welfare with reward-penalty mechanism

Moreover, we discuss the impact of environmental awareness ( S=1500 and

ξ 0 =0.4 ) as shown in Fig. 14. The number of voluntary returns represents environmental awareness. The promotion effect is significant in all modes especially in the Mode R&TP. When the number of voluntary returns reaches 800, the total social welfare in Mode R&TP begins surpassing that in Mode M. Although Mode R&TP is more sensitive, Mode M&R is still the optimal choice under this case. Moreover, the influences on Mode R and Mode TP are very close. Because the manufacturer has the dominating power over the supply chain and can distribute the subsidy, the selection of Mode R or Mode TP is actually a kind of allocation problem, which is also be verified in (Savaskan et al., 2004).

34

ACCEPTED MANUSCRIPT

M

Total Social Weflare (Unit:Million RMB)

6000

R

TP

M+R

M+TP

R+TP

5950 5900 5850 5800 5750 5700 5650 5600 0

600

1200

1800

2400

3000

3600

4200

4800

5400

6000

6600

7200

7800

Number of Waste Power Batteries Consumers are Voluntary to Return

Fig. 14 Effects of environmental awareness changes on total social welfare with reward-penalty mechanism

6. Conclusions Although China has introduced a number of policies based on the EPR principle, the specific mechanisms and policy for recycling spent power batteries have not been established. The purpose of this study is to propose reward-penalty mechanisms and policies, and test their impacts on recycling power batteries by using a developed game analysis model. In this paper, three single recycling channel modes and three competitive dual recycling channel modes were considered respectively. The total social welfare is used as the indicator to select the optimal recycling modes, which includes participants’ profit, consumer surplus, government’s supervision cost, energysaving and carbon emission reduction effect. The obtained results shown as followings. (i) The intensive reward penalty mechanism is more suitable for modes with higher recycling rate. For instance, the total social welfare in Mode M&R can be improved through the new mechanism. 35

ACCEPTED MANUSCRIPT (ii) However, the mechanism may cause benefit losses because of the punishment from unqualified recycling rate, and thus setting a reasonable minimum recycling rate is critically important. (iii) Environmental awareness has significant impact on social benefit in all modes, especially in R&TP. According to our investigation result, there is still enough room for improvement. Government should make full use of various media, such as advertising, newspapers, television, internet and apps to educate the negative impacts of spent power batteries. (iv) All the modes with dual recycling channels have better performance than those with single channel, and thus introducing competitions in recycling activities is expected. (v) The manufacturer owns the dominating power over the supply chain and plays as a leader, and the retailer has the advantage of existing sales network, which makes the recycling easier in reverse logistics. Therefore, mode M&R has obvious advantages among six modes here. This research can be further extended in several directions to achieve broader insights. (i). the uncertainties of stochastic demand can be taken into account; (ii). the asymmetry information can be considered, such as asymmetry in recycling cost information of spent power batteries; (iii) the models are also limited to a three-echelon dual-channel supply chain consisting of a single manufacturer, a single retailer and a single third party. We will further study the competition relationship and develop supply chain game models composed of multiple manufacturers, multiple retailers and multiple third parties in the future work.

36

ACCEPTED MANUSCRIPT Appendix A. Proofs in Mode M&R To build up the Hessian matrix of  rM & R , we carry out the following calculations to acquire the first and second order derivatives of  rM & R to ps and prM r& R .

H rM & R

  2 rM & R  p 2 s   2 M &R   r  M &R  pr  r ps

 2 rM & R  ps prM r& R   2    2 rM & R   0  prM r& R 2 

0  2k 

The principal minor sequences of the discrimination matrix are

H rM & R  2   0, 1

H rM & R  4  k  0 2

It implies that the  rM & R is a concave function to ( ps , prM r& R ) . By setting

 rM & R ps

 rM & R and to zero, we can get the response function of the retailer. prM r& R  rR    2  ps   pw  0, ps

ps * 

   pw 2

 rM & R  kt  kI r  A  h1 prM m& R  2kprM r& R , prM r& R

prM r& R* 

kt  h1 prM m& R  kI r  A 2k

Then, we substitute the ps* and prM r& R* into Eq. (29), which is the objective function of the manufacturer. For constructing the Hessian matrix of  mM & R , we carry out the following calculations to acquire the first and second order derivatives of  mM & R to pw , prM m& R and t.

H mM & R

  2 mM & R  2  pw   2 M & R   M &mR  pr  m pw   2 M & R m   t pw

 2 mM & R pwprM m& R  p 2

M &R m M &R2 r m

 2 mM & R t prM m& R

 2 mM & R   pwt       2 mM & R    0 prM m& R t     2 mM & R   0 t 2 

0 h  2k k h1 2 1

2

0  h1   k 

The principal minor sequences of the discrimination matrix are 37

ACCEPTED MANUSCRIPT

H mM & R     0, 1

H mM & R    2

h12  2k 2  0( when h1  2k ), k

H mM & R  2  (k 2  h12 )  0 3

It implies that the  mM & R is a concave function to ( pw , prM m& R , t) .

 mM & R  mM & R  mM & R By setting , and to zero simultaneously, Eq. (31) -(33) pw prM m& R t can be obtained.

 mM & R   2  pw   Cm   0 S  0 pw 2 h  S  t    mM & R h12  M &R M &R M &R    A  kp  h p  k         pr  m  S  I m   0 r m 1 r r M &R pr  m 2 2k   M &R k    S  t  h1    S  pr  m  I m   mM & R M &R M &R    A  kpr  r  h1 pr  m    0 t 2 2

38

ACCEPTED MANUSCRIPT Appendix B. Proofs in Mode M&TP By Eq. (40), the first and second order derivatives of  rM &TP to ps can be calculate

 rM &TP  2 rM &TP    2  ps   pw，  2   0 ps ps2 It implies the concavity of  rM &TP . Setting

 rM &TP to zero, the optimal response ps

function of the retailer is ps * 

   pw 2  ps

By Eq. (41), the first and second order derivatives of  tpM &TP to prMtp&TP can be calculated

 tpM &TP prMtp&TP

 kt  kI tp  A  h2 p

M &TP r m

It implies the concavity of 

 2kp

M &TP tp

M &TP r tp

，

. Setting

response function of the third party is prMtp&TP* 

 2 tpM &TP prMtp&TP

 tpM &TP prMtp&TP

2

 2k  0

to zero, the optimal

kt  h2 prM m&TP  kI tp  A 2k

.

Then, we substitute the ps* and prMtp&TP* into Eq. (39), which is the objective function of the manufacturer. For constructing the Hessian matrix of  mM &TP , we carry out the following calculations to acquire the first and second order derivatives of  mM &TP to pw , prM m&TP and t.

H mM &TP

  2 mM &TP  2  pw   2 M &TP m   M &TP  pr  m pw  2 M &TP   m  t pw

 2 mM &TP pw prM m&TP  2

M &TP m M &TP 2 r m

p

 2 mM &TP t prM m&TP

 2 mM &TP   pwt       2 mM &TP     0 prM m&TP t      2 mM &TP   0 t 2 

0 h2  2k k h2 2

2

0  h2   k  39

ACCEPTED MANUSCRIPT The principal minor sequences of the discrimination matrix are

H mM &TP     0, 1

H mM &TP    2

h2 2  2k 2  0 when h2  2k , k





H mM &TP  2  (k 2  h2 2 )  0 3

It implies that the  mM &TP is a concave function to ( pw , prM m&TP , t) . By setting

 mM &TP  mM &TP  mM &TP , and to zero simultaneously, Eq. (42) -(44) can be pw prM m&TP t obtained.

 mM &TP   2  pw   Cm   0 S  0 pw 2 h2    S  t    mM &TP h2 2  M &TP M &TP M &TP    A  kp  h p  k         pr  m  S  I m  r m 2 r tp M &TP pr  m 2 2k   0 M &TP k    S  t  h2    S  pr  m  I m   mM &TP M &TP M &TP    A  kpr tp  h2 pr  m    0 t 2 2

40

ACCEPTED MANUSCRIPT Appendix C. Proofs in Mode R&TP To build up the Hessian matrix of  rR &TP , we carry out the following calculations to acquire the first and second order derivatives of  rR &TP to ps and prR&r TP .

H rR &TP

  2 rR &TP  ps2     2 rR &TP  R &TP  pr  r ps

 2 rR &TP   ps prR&r TP   2    2 rR &TP   0  2 prR&r TP 

0  2k 

The principal minor sequences of the discrimination matrix are

H rR &TP  2   0, 1

H rR &TP  4  k  0 2

It implies that the  rR &TP is a concave function to ( ps , prR&r TP ) . By setting

 rR &TP ps

 rR &TP and to zero, we can get the response function of the retailer. prR&r TP  rR &TP    2  ps   pw  0, ps

ps * 

   pw 2

 rR &TP  kt  kI r  A  hprR&tpTP  2kprR&r TP , prR&r TP

R &TP * r r

p



kt  h3 prR&tpTP  kI r  A 2k

By Eq. (53), the first and second order derivatives of  tpR &TP to prR&tpTP can be calculated.

 tpR &TP prR&tpTP

 kt  kI tp  A  h3 p

R &TP r r

 2kp

It implies the concavity of 

M &TP r tp

R &TP tp

,

 tpR &TP tprR&tpTP

. Setting

2

 2k  0

 tpR &TP prR&tpTP

to zero, the optimal response

function of the third party can be obtained.

 tpR &TP p

R &TP r tp

R &TP * r tp

p

 kt  kI tp  A  h3 prR&r TP  2kprMtp&TP  0,



kt  h3 prR&r TP  kI tp  A 2k 41

ACCEPTED MANUSCRIPT Furthermore, we can get the following equations. R &TP * r r

h3  kI tp  A   2k 2 I r  2kA kt   2k  h3 4k 2  h32

R &TP * r tp

h3  kI r  A   2k 2 I tp  2kA kt   2k  h3 4k 2  h32

p

p

prR&r TP*  prR&tpTP* 

2kt  2 A  k ( I r  I tp ) 2k  h3

Then, we substitute the ps* , prR&r TP* and prR&tpTP* into Eq. (51), which is the objective function of the manufacturer. To build up the Hessian matrix of  mR &TP , we carry out the following calculations to acquire the first and second order derivatives of

 mR &TP to pw and t .

H

R &TP m

  2 mR &TP  pw2   2 R &TP   m   t pw

 2 mR &TP    pwt     2 mR &TP   0   t 2 

0  4k(k  h3 )   2k  h3 

The principal minor sequences of the discrimination matrix are H mR &TP     0, H mR &TP  1

2

4  k(k  h3 )  0 (when h3  k ) 2k  h3

It implies that the  mR &TP is a concave function to ( pw , t) . By setting

 mR &TP and pw

 mR &TP to zero simultaneously, Eq. (54) and Eq. (55) can be obtained. t  mR &TP   2  pw   Cm   0 S  0 pw 2  2kt  2 A  k  I r  I tp    mR &TP 2k    2 A   k  h3  0      t  S  k  h3  t 2k  h3 2k  h3  

42

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