Optimal electric vehicle production strategy under subsidy and battery recycling

Energy Policy 109 (2017) 579–589

Contents lists available at ScienceDirect

Energy Policy journal homepage: www.elsevier.com/locate/enpol

Optimal electric vehicle production strategy under subsidy and battery recycling Huaying Gua, Zhixue Liua, Qiankai Qingb,c, a b c

MARK

⁎

School of Management, Huazhong University of Science and Technology, Wuhan 430074, China School of Automobile and Traffic Engineering, Wuhan University of Science and Technology, Wuhan 430081, China School of Automation, Huazhong University of Science and Technology, Wuhan 430074, China

A R T I C L E I N F O

A B S T R A C T

Keywords: Electric vehicle Production strategy Subsidy Battery recycling Loss aversion

Government subsidy and battery recycling are two common practical issues in the electric vehicle (EV) market. This study investigates a loss-averse EV manufacturer's optimal production strategy under uncertain market demand in the presence of both government subsidy and battery recycling. An analytical model is built and related optimal solution and numerical experiments are provided. Results indicate that increased subsidy promotes the manufacturer's optimal production quantity and expected utility. Increased battery recycling rate promotes the manufacturer's optimal production quantity. However, the manufacturer's expected utility decreases with the battery recycling rate if the optimal production quantity is sufficiently small. This result implies that the manufacturer may prefer a relatively small battery recycling rate when the market scale is small. Consequently, the government should establish regulations to promote battery recycling for environmental protection. We find that either subsidy or battery recycling can offset the negative effects of loss aversion on the optimal production quantity and expected utility. The majority of our results still hold if we consider multiple repurposing options for used batteries or an alternative subsidy mechanism. In particular, the manufacturer's optimal production quantity and expected utility are higher under cost subsidy mechanism than under consumer subsidy mechanism.

1. Introduction Electric vehicles (EVs), which primarily refer to plug-in hybrid EVs (PHEVs) and battery EVs (BEVs), are an increasingly attractive transportation option (Coffman et al., 2017). The adoption of EVs could be a promising solution to address the challenges resulted from climate change and crude oil scarcity in the 21st century (Kieckhäfer et al., 2014). If successfully and continuously introduced, EVs will result in a substantial reduction of greenhouse gas emissions and consequently contribute to environmental health to a certain degree. As noted by Casals et al. (2017), EV is one of the most promising alternatives for sustainable transportation. Because of its huge potential benefits, the EV market is undergoing an explosive development in recent years. According to statistics, the new registrations of EVs increased by 70% between the years of 2014 and 2015, with approximately 0.55 million EVs sold globally in 2015 (IEA, 2016). Furthermore, the International Energy Agency's electric vehicles initiative, which includes 16 member countries, aims to reach a global deployment of 20 million EVs by 2020. The rapid and sustainable development of EV market cannot occur ⁎

Corresponding author. E-mail address: [email protected] (Q. Qing).

http://dx.doi.org/10.1016/j.enpol.2017.07.043 Received 8 November 2016; Received in revised form 16 July 2017; Accepted 18 July 2017 0301-4215/ © 2017 Elsevier Ltd. All rights reserved.

without the effective participation of EV manufacturers. Although the EV market has attracted an increasing number of enterprises to invest on EV production, there still exist some challenges and barriers faced by both incumbent EV manufacturers and new market entrants. In particular, how to make decisions on reasonable production strategy is a primary challenge for an EV manufacturer. The reason is twofold. First, choosing appropriate production quantity is rather difficult for the EV manufacturer because the EV market is still at its early development stage and thus the market demand is highly uncertain. Second, and probably more important, the EV production strategy is affected by various external and internal factors. Together, these factors may significantly impact and complicate the EV manufacturer's production decision. Among these impact factors, government subsidy is considered as an important method to adjust the production strategy of EV manufacturers (Zhang, 2014; Zhang and Zhang, 2015). Many countries such as the United States and China have provided considerable subsidy and tax credits for the EV industry or consumer to promote the EV market. For example, as the largest EV market worldwide, China launched a strong incentive EV subsidy scheme in January 2009, followed by an

Energy Policy 109 (2017) 579–589

H. Gu et al.

of batteries, scare number of charging stations, and the EV's limited range have impeded EV development (Daziano and Chiew, 2012; Madina et al., 2016). In fact, many countries have implemented a number of policies to help overcome such obstacles. One of the most widely adopted measures is that the government to provide subsidy to promote broader use of EVs in the nascent stage, such as in the United States and China. Recently, Hao et al. (2014) present the rationale of China's two-phase EV subsidy scheme, which was launched in January 2009 and then updated in September 2013. Additionally, Luo et al. (2014) study EV supply chain under a government's price-discount incentive scheme. They find that the subsidy ceiling or discount rate is more effective in influencing the optimal wholesale pricing decision of the manufacturer when the unit production cost is relatively higher or lower, respectively. In addition to subsidy, the EV production strategy plays an essential role in the successful development of the EV market (Zhang, 2014). Prominent examples of this factor include Zhang (2014), who investigates the influence of subsidy, loss aversion and consumer tradeoffs on the EV manufacturer's optimal production strategy. Later on, Zhang and Zhang (2015) further discuss the optimal EV production decision under subsidy and shortage cost. However, they do not consider battery recycling despite its high importance to natural environment and EV development (Ahmadi et al., 2014; Neubauer and Pesaran, 2011). A number of studies on EV batteries emerge in recent years (Ahmadi et al., 2017; Assunção et al., 2016; Jaguemont et al., 2016; Jiao and Evans, 2016; Tagliaferri et al., 2016; Yano et al., 2016). However, most of these studies focus on battery technology (Samba et al., 2014) and the economic and environmental analysis of re-use EV batteries (Ahmadi et al., 2014, 2017; Heymans et al., 2014; Neubauer and Pesaran, 2011; Saxena et al., 2015). For example, Heymans et al. (2014) simulate a residential energy profile and regulated cost structure to analyze the feasibility and cost savings from repurposing an EV battery unit for peak shifting. Using a parameterized life cycle model, Ahmadi et al. (2014) analyze the environmental feasibility of reusing EV batteries. Then, Ahmadi et al. (2017) characterize the extended lifetime of Li-ion battery packs using a complex functional unit to cover both use and reuse phases over an 18-year lifetime. Based on the above research, the present study focuses on the impacts of battery recycling on the EV production strategy. As for the modeling framework, this study is closely related to the literature on the newsvendor model and closed-loop supply chain model. The newsvendor model is known as one of the most important method to study inventory problem. In a classic newsvendor problem, a risk-neutral newsboy needs to order a certain quantity at a regular price before a selling season. If the demand realized is less than the quantity ordered, then the demand gets satisfied and the leftover inventory has a salvage value that is lower than the selling price, otherwise the demand do not get satisfied. The newsvendor model, which was pioneered by Edgeworth (1888), has been extensively studied in the literature (Babich, 2010; Cohen et al., 2016; Krass et al., 2013; Qin et al., 2011). For example, Cohen et al. (2016) present a model to analyze the interaction between a government and a supplier when they design consumer subsidy mechanisms for green technologies, considering the response of the manufacturing industry. A common assumption in these studies is that the decision makers are risk-neutral rather than loss-averse. However, evidence suggests that enterprise managers’ decision-making behaviours deviate from expected profit maximization due to loss aversion (Feng et al., 2011; Fisher and Raman, 1996). As one of the key features in the prospect theory, loss aversion refers to the case in which a decision maker is more sensitive to losses than to an equivalent amount of gains (Kahneman and Tversky, 1979). Although the loss aversion behaviour has been observed decades ago, this concept has not been frequently considered in inventory models until recently (Ho et al., 2010; Hu et al., 2016; Liu et al., 2015; Schweitzer and Cachon, 2000; Wang and

update in September 2013. This scheme specifies the subsidy duration, scope, standard, phase-out mechanism and pilot cities for both public and private purchases and uses of EVs (Hao et al., 2014). The rationality of such government actions is directly supported by Zhang (2014) who first investigates the economic influence of government subsidy on the EV manufacturer's optimal production decision. Another impact factor that plays an important role in the EV manufacturer's production strategy is battery recycling, although it is generally overlooked by the existing literature. As predicted by the China Automotive Technology and Research Centre (CATRC), the volume of scrapped EV battery in China is expected to reach 120 thousand to 170 thousand tons by the year of 2020. It is widely acknowledged that battery recycling is essential for EV industry because used batteries that are not handled properly might do great harm to the environment. Because of this issue, battery recycling is usually mandatory for EV manufacturers in practice. For example, EV manufacturer Build Your Dreams (BYD) is required by the government of China to be responsible for recycling used batteries. The existing literature on battery recycling generally focuses on battery technology (Samba et al., 2014) and economic and environmental impacts of battery re-use (Ahmadi et al., 2014, 2017; Heymans et al., 2014; Neubauer and Pesaran, 2011). Hence, they ignore the impact of battery recycling on EV manufacturer's optimal production decision. This paper investigates an EV manufacturer's production strategy under government subsidy and battery recycling. The impacts of government subsidy and battery recycling on the EV manufacturer's optimal production decision are analyzed under the coexistence of these two factors. The analytical work is based on the classical newsvendor model (see Qin et al., 2011 for extensive reviews). In our base case, we consider that the EV manufacturer has a certain repurposing option for used batteries and adopt a subsidy mechanism under which customers are subsidized. We then extend our analysis to the case in which the EV manufacturer has multiple repurposing options, and the case in which the EV manufacturer's production is subsidized under an alternative subsidy mechanism. Our results suggest that under different subsidy mechanisms, government subsidy has an increasing effect on the EV manufacturer's optimal production quantity and expected utility. However, the battery recycling rate may have a decreasing effect on the EV manufacturer's expected utility. The remainder of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3 describes our model. Section 4 provides our main results. Section 5 extends the proposed models. Section 6 illustrates the results using numerical experiments. Section 7 discusses the results and limitations of this study. Section 8 summarizes the main findings and presents some useful policy implications. All proofs are in the supplementary material. 2. Literature review EV, which is propelled by one or more electric motors instead of an internal combustion engine, is considered to have the capability to reduce the transportation sector's carbon footprint and crude oil dependence as well as the ability to protect the natural environment Wu et al., 2015b). Due to the potential benefits of EVs, the development of EVs has attracted increasing attention from environmental advocates, governments, industry managers, and academics. The prominent body of the EV development literature covers a wide range of domains, including EV adoption (Lim et al., 2015; Matthews et al., 2017), charging and swapping infrastructure planning (Madina et al., 2016; Mak et al., 2013; Wu et al., 2015a), and government incentive policies for EV consumers or manufacturers (Hao et al., 2014; Huang et al., 2013; Langbroek et al., 2016; Li et al., 2016; Luo et al., 2014). For example, Lim et al. (2015) investigate the influences of both range anxiety and resale anxiety on the mass adoption of EVs. Although EV is beneficial to the environment compared with the internal combustion engine power vehicle (ICEV), the prohibitive cost 580

Energy Policy 109 (2017) 579–589

H. Gu et al.

Webster, 2009). Schweitzer and Cachon (2000) are the first to investigate the loss-averse newsvendor problem. Wang and Webster (2009) extend the model of Schweitzer and Cachon (2000) by considering the shortage cost. Our research is also closely linked to studies on closed-loop supply chain models. Thierry et al. (1995) establish a closed-loop supply chain system model, which is divided into repair, renovation, re-manufacturing, assembly and resource recovery. Souza (2013) systematically reviews the related literature on the closed-loop supply chain from the strategic, tactical and operational levels. Savaskan et al. (2004) are the first to investigate the manufacturer's choice of reverse channel structures for collecting used products from consumers. Atasu et al. (2013) study a manufacturer's choice of reverse channel structures based on two alterative collection cost structures, which include economies and diseconomies of scale. These studies focus on the closed-loop supply chain with deterministic demand. Chuang et al. (2014) extend the conventional newsvendor model to explore the reverse channel selection question for a high-tech product under different collection cost structures and uncertain demand. Differently, this paper focuses on the influences of loss aversion, subsidy and battery recycling on EV production quantity under uncertain demand.

Additionally, we suppose that the EV manufacturer is loss-averse, i.e., she is more sensitive to the losses than the equivalent gains within a certain reference point. Similar to Kahneman and Tversky (1979) and Tversky and Kahneman (1991), we use the following piecewise-linear form of the loss aversion utility function:

π − π0 , π ≥ π0 U (π ) = ⎧ λ (π − π0), π < π0 ⎨ ⎩

(1)

where π is the profit function, π0 is the reference point and λ is the loss aversion coefficient (λ ≥ 1). Before we proceed any further, we make the following assumptions. Assumption 1. The function F (x ) is differentiable, invertible, and strictly increasing for x ∈ [0, ∞) , and features an increasing generalized failure rate, named as function g (x ) , where g (x ) = xf (x )/[1 − F (x )]. Assumption 1 is commonly adopted in supply chain newsvendor models under wholesale price contracts (e.g. Lariviere and Porteus, 2001; Chuang et al., 2014). The increasing general failure rate function is satisfied under some common distributions such as uniform and normal distributions. Assumption 2. A < Δ < A + (c − s )/ τ We assume A < Δ, i.e., the unit collection cost is less than the unit revenue from recycling used batteries (Ahmadi et al., 2014; Savaskan et al., 2004; Chuang et al., 2014). Δ < A + (c − s )/ τ implies that recycling is not profitable enough to push the firms’ forward channel to supply unlimited products in the market (Chuang et al., 2014).

3. Model setting We consider a centralized closed loop supply chain in which an integrated EV manufacturer owns her retail channel, and battery recycling channel (e.g., BYD, Yinlong Energy). Before a selling season, the EV manufacturer needs to decide the EV production quantity Q . The EV market demand is stochastic and its market price is exogenous. Let F (x ) denote the cumulative distribution function (CDF) of the random market demand X , f (x ) denote the probability density function (PDF) of X ( x is the actual EV market demand), and c denote the EV unit production cost. If the production quantity exceeds the actual demand of the EVs, i.e., x < Q , then the remaining inventory after the selling season is sold at a clearance price or a discounted price s (s < c ). The government provides a subsidy y to a customer when the consumer buy one unit of the EV to reduce the purchase cost.1 In other words, the manufacturer's selling price equals the consumer's effective price p plus the unit subsidy y , where p + y > c . Suppose that the used EV batteries are collected and utilized by the EV manufacturer (e.g., BYD, Yinlong Energy). We assume that the EV manufacture has one repurposing option for used batteries. We extend our model to the case in which the EV manufacturer has multiple repurposing options for used batteries in Section 5.1, such as re-use in a vehicle, stationary energy storage, and metals extraction (see Ahmadi et al., 2014; Ahmadi et al., 2017; Richa et al., 2017 for more discussions on battery repurposing). Let Δ denote the unit revenue from recycling the used EV batteries. We use τ ∈ [0, 1] to denote the recycling rate of the used EV batteries. Following Chuang et al. (2014), we assume that τ is exogenous. And the recycled quantity of the used EV batteries equals τQ . Let CL (τ , Q) denote the total recycling cost of the used EV batteries and it consists of the following two parts. The first part is a collection cost, which equals the unit collection cost A of the unit used batteries multiplied by the recycled quantity τQ . The second part is the investment cost associated with the recycling rate and equals Bτ 2 , where B > 0 is a scaling parameter that measures the costliness of collecting. In order to ensure the EV manufacturer's incentive for recycling used batteries, we assume that the manufacturer can benefit from battery recycling, i.e., ΔτQ − AτQ − Bτ 2 ≥ 0 . This assumption is supported by Ahmadi et al. (2014) and Mao (2016), who note that EV battery recycling can reduce EV battery cost.

4. Model analysis The EV manufacturer's profit includes both her profit from the product sale in the forward channel and that from battery recycling in the reverse channel. The EV manufacturer's objective is to maximize her profit by choosing the optimal production quantity under subsidy, battery recycling and loss aversion. The EV manufacturer's profit function is written as follows:

π (Q, X = x ) (p + y ) x + s (Q − x ) − cQ + ΔτQ − AτQ − Bτ 2 if x ≤ Q =⎧ 2 ⎨ if x > Q ⎩ (p + y ) Q − cQ + ΔτQ − AτQ − Bτ (2) 2

Let qRY (Q) be the EV manufacturer's breakeven quantity for a given order quantity, satisfying π (Q, qRY (Q)) = 0 (Schweitzer and Cachon, 2000; Zhang, 2014). From Section 3 we can know that p + y > c and ΔτQ − AτQ − Bτ 2 ≥ 0 , then we infer π (Q, D = x ) > 0 if x > Q . Hence,

qRY (Q) =

cQ − sQ − ΔτQ + AτQ + Bτ 2 p+y−s

(3)

where the subscript RY indicates that the EV manufacturer makes production decision considering battery recycling and subsidy. We can 0 < qRY (Q) ≤ Q easily obtain from Assumption 2 and ΔτQ − AτQ − Bτ 2 ≥ 0 . Based on Eq. (3), we depict the influences of battery recycling and subsidy on the breakeven quantity in Lemma 1. Lemma 1. The breakeven quantity qRY (Q) decreases with the recycling 2Bτ 2Bτ rate τ if Q > Δ − A , and increases with the recycling rate τ if Q < Δ − A ; the breakeven quantity qRY (Q) decreases with the subsidy y . Lemma 1 demonstrates that the breakeven quantity of EV production quantity is negatively correlated with subsidy and battery recycling if the production quantity is sufficiently large. Hence, both subsidy and battery recycling may offset the negative effects of high EV production

1 This subsidy form is named consumer subsidy mechanism in this paper. We compared the optimal production quantity and expected utility under consumer subsidy and under cost subsidy mechanisms in Section 6.

2 The manufacturer's breakeven quantity is the point at which its sales exactly cover its expenses.

581

Energy Policy 109 (2017) 579–589

H. Gu et al.

cost, which are considered to be a main barrier in expanding the EV market (Argote and Epple, 1990; Daziano and Chiew, 2012; Zhang, 2014). In particular, such a result has significant implications on the EV industry. For example, higher subsidy and recycling rate may lower the market entry threshold at the early stage of the market because they can decrease the breakeven production quantity. We adopt the breakeven point π (Q, qRY (Q)) = 0 as the reference point under loss aversion. From Eq. (3) we can know that π (Q, X = x ) ≤ 0 if x > qRY (Q) , and otherwise π (Q, X = x ) > 0 . Then, the EV manufacturer's utility maximization problem based on Eq. (2) can be written as follows:

Max EULYR = (λ − 1)

∫0

qRY

Q

∫0

∞

∫Q

[(p + y )x + s (Q − x ) − cQ

(4)

Theorem 1. The EV manufacturer's expected utility EULYR is concave with respect to the production quantity Q . Then, there exists a unique * that maximizes EULYR , and QLYR * optimal production quantity QLYR satisfies the following first-order condition:

* ) F (QLYR * )) (p + y − c + Δτ − Aτ ) + (λ − 1)(s − c + Δτ − Aτ ) F (qRY (QLYR = p+y−s (5) From Eq. (5), we can obtain the optimal production quantities of different models in Table 1. They are as follows:

p + y − c + Δτ − Aτ p+y−s

*)= F (QLR

(7)

* )) (p − c + Δτ − Aτ ) + (λ − 1)(s − c + Δτ − Aτ ) F (qR (QLR p−s

p+y−c p+y−s

F (Q*) =

p−c p−s

(a) (b) (c) (d) (e)

(12) cQ − sQ − ΔτQ + AτQ + Bτ 2 p−s

cQ − sQ . p−s

* ≥ QLR *. * ≥ QLY * ; QLYR * ≤ QYR * ; QLYR QLYR * ≥ QR*. * ≥ QY*; QYR QYR * ≤ QR*. * ≥ QL*; QLR QLR * ≥ QL*. * ≤ QY*; QLY QLY Q* ≤ QY*; Q* ≥ QL*; QR* ≥ Q*.

The manufacturer produces more with battery recycling than without battery recycling, given the same conditions on loss aversion and subsidy. Similarly, the manufacturer produces more with subsidy than without subsidy, given the same conditions on loss aversion and battery recycling. However, a loss-averse EV manufacturer produces

(8)

F (QY*) =

(11)

Proposition 2. Comparative results of the optimal production quantity in Eqs. (5)–(12) are as follows:

(6)

* )) (p + y − c ) + (λ − 1)(s − c ) F (qY (QLY * )= F (QLY p+y−s

(p − c ) + (λ − 1)(s − c ) F (q (QL*)) p−s

From Proposition 1, whether the recycling rate has an increasing effect on the optimal production quantity depends on the magnitude of * . More specifically, QLYR * increases the optimal production quantity QLYR * is larger than a certain cut-off 2Bτ . with the recycling rate τ , if QLYR Δ−A Meanwhile, the EV production strategy also relates closely to subsidy and the loss aversion characteristic. Subsidy positively affects the optimal production quantity, and hence can promote the improvement of EV production. The degree of loss aversion, by contrast, has a negative effect on the optimal production quantity, and hence adversely affects the improvement of EV production. According to Proposition 1, the change of subsidy or the degree of loss aversion may alter the change tendency of the optimal production quantity with respect to battery recycling rate because both of them impact the production scale of EV. Therefore, the impacts of these three types of factors are interrelated. Proposition 2 further compares the manufacturer's decisions on the optimal production quantity under different cases with respect to subsidy, battery recycling and loss aversion.

where the subscripts L , Y and R represent the loss aversion characteristic, subsidy, and battery recycling respectively. Depending on the values of λ , y and τ , the newsvendor model proposed in Eq. (4) can be reduced to different models described in Table 1. The following theorem characterizes a loss-averse manufacturer's optimal production quantity decision considering subsidy and battery recycling.

*)= F (QYR

F (QL*) =

* increases with Proposition 1. The optimal production quantity QLYR * ≥ 2Bτ ; the optimal production quantity the recycling rate τ , if QLYR Δ−A * increases with the subsidy y and decreases with the degree of loss QLYR aversion λ .

((p + y )x + s (Q − x ) − cQ

((p + y )Q − cQ + ΔτQ − AτQ − Bτ 2)f (x )dx

(10)

qR = and q = where qY = Theorem 1 suggests the unique existence of the optimal production quantity. In particular, according to Eq. (5), the optimal production quantity depends on the parameters with respect to subsidy, battery recycling and loss aversion. The specific relationships are described in Proposition 1.

+ΔτQ − AτQ − Bτ 2)f (x )dx +

p − c + Δτ − Aτ p−s

cQ − sQ , p+y−s

+ΔτQ − AτQ − Bτ 2]f (x )dx +

F (QR*) =

(9)

Table 1 Models with different values of λ , y , and τ under consumer subsidy mechanism. Model

Value of different parameter sin Eq. (4)

Expected utility

Optimal production quantity

Standard subsidized newsvendor model considering battery recycling standard newsvendor model considering loss aversion and battery recycling standard newsvendor model considering loss aversion and subsidy

λ=1

EUYR

* QYR

y=0

EUλR

* QλR

qR

τ=0

EUλY

* QλY

qY

EUR EUY

standard newsvendor model considering loss aversion

λ = 1 and y = 0 λ = 1 and τ = 0 y = 0 and τ = 0

standard newsvendor model

λ = 1, y = 0 and τ = 0

EU

QR* QY* Qλ* Q*

standard newsvendor model considering battery recycling standard newsvendor model considering subsidy

EUλ

582

Breakeven quantity

q

Energy Policy 109 (2017) 579–589

H. Gu et al.

common battery repurposing options, re-use in a vehicle, stationary energy storage and metals extraction (Ahmadi et al., 2014, 2017; Richa et al., 2017; Yano et al., 2016). These repurposing options have a decreasing level of quality for used batteries. We next derive the optimal solutions under multiple repurposing options and discuss whether our results are impacted by incorporating multiple repurposing options. We use the symbol i = 1, 2, 3 to denote three decreasing levels of the quality of used batteries, which correspond to the repurposing options of re-use in a vehicle, stationary energy storage and metals extraction, respectively. Let αi be the possibility for an unit used batteries 3 to have the quality level i ; ∑i = 1 αi = 1. Let Δi denote the unit revenue from each unit used batteries and let Ai denote the fixed unit collection cost of an unit used batteries under quality level i . Then, the fixed unit value from the used battery θi equals Δi − Ai under quality level i . The model setting is the same as in Section 3 except for the multiple battery repurposing options. Applying a similar modeling and derivation process to that in Section 4 as basis, the EV manufacturer's breakeven quantity and expected utility to maximize are respectively as follows:

less than a risk-neutral EV manufacturer, given the same conditions on subsidy and battery recycling. From Proposition 2, either battery recycling or subsidy has a positive effect on the optimal EV production quantity unlike loss aversion. Furthermore, subsidy and battery recycling can offset the negative effect of loss aversion on the optimal production quantity. Proposition 3 describes the impacts of subsidy, battery recycling and loss aversion on the EV manufacturer's expected utility. Proposition 3.. The manufacturer's expected utility increases with the 2Bτ recycling rate τ if Q ≥ Δ − A , and otherwise it decreases with the recycling rate τ ; the manufacturer's expected utility increases with the subsidy y , and decreases with the degree of loss aversion coefficient λ. In general, battery recycling, subsidy, and loss aversion have an important effect on the manufacturer's expected utility. In particular, whether battery recycling has a positive effect on the EV manufacturers’ expected utility depends on the magnitude of Q . More specifically, battery recycling has a positive effect on the EV manufacturer's ex∂EU ∂EU 2Bτ pected utility, i.e., ∂τLYR ≥ 0 if Q ≥ Δ − A , and ∂τLYR < 0 otherwise. Subsidy positively impact the expected utility of the loss-averse man∂EU ufacturer, i.e. ∂yLYR > 0 , but loss aversion negatively impacts the EV

R qRY =

cQ − sQ − α1 θ1 τQ − α2 θ2 τQ − α3 θ3 τQ + Bτ 2 p+y−s

∂EU

manufacturer's expected utility, i.e. ∂λLYR < 0 . Proposition 4 further compares the EV manufacturer's maximum expected utility under different cases with respect to subsidy, battery recycling and loss aversion.

R Max EUλYR = (λ − 1)

∫0

R qRY

(13)

[(p + y )x + s (Q − x ) − cQ

+α1θ1τQ + α 2θ2τQ + α3θ3τQ − Bτ 2]f (x )dx

Proposition 4. Comparative results of the EV manufacturer's maximum expected utility in Eq. (4) and the models in Table 1 are as follows:

+

* ) < EUYR (QYR * ); * ) > EULR (QLR * ) ; EULYR (QLYR (a) EULYR (QλYR 2Bτ * ) ≥ EULY (QLY * ) EULYR (QLYR Q ≥ Δ − A, if and * ) < EULY (QLY * ). EULYR (QLYR * ) > EUR (QR*) ; (b) EUYR (QYR 2Bτ * ) ≥ EUY (QY*) EUYR (QYR Q ≥ Δ − A, if and * ) < EUY (QY*) . EUYR (QYR * ) < EUY (QY*) . * ) > EUL (QL*) ; EULY (QLY (c) EULY (QLY * ) < EUR (QR*) ; (d) EULR (QLR 2Bτ * ) ≥ EUL (QL*) EULR (QLR Q ≥ Δ − A, if and * ) < EUL (QL*) . EULR (QLR (e) EUY (QY*) > EU (Q *) ; EUL (QL*) < EU (Q*) ; 2Bτ EUR (QR*) ≥ EU (Q*) if Q ≥ Δ − A , and otherwise EUR (QR*)

+

Q

∫0

((p + y )x + s (Q − x ) − cQ + α1θ1τQ

+α 2θ2τQ + α3θ3τQ − Bτ 2)f (x )dx

otherwise

∞

∫Q

((p + y )Q − cQ + α1θ1τQ

+α 2θ2τQ + α3θ3τQ − Bτ 2)f (x )dx

(14)

Then, we can similarly obtain the optimal production quantity

otherwise

(p + y − c + α1 θ1 τ + α2 θ2 τ + α3 θ3 τ ) *R ) = F (QλYR

otherwise

R *R )) (QλYR + (λ − 1)(s − c + α1 θ1 τ + α2 θ2 τ + α3 θ3 τ ) F (qRY

p+y−s (15)

From Eqs. (13) and (15), the EV manufacturer's breakeven quantity R *R are decreasing in the fixed qRY and optimal production quantity QλYR unit value from each kind of repurposing option θi and the corresponding probability αi . Further, the EV manufacturer's breakeven quantity and optimal production quantity have similar forms to that in the case of a single repurposing option (refer to Eqs. (3) and (5) in Section 4). More specifically, we can obtain the EV manufacturer's breakeven quantity and optimal production quantity by replacing the fixed unit value θ = Δ − A in Eqs. (3) and (5) with the weighted fixed 3 value ∑i = 1 αi θi . Similarly, we can derive the EV manufacturer's max-

< EU (Q*) .

Proposition 4 demonstrates that the EV manufacturer's maximum expected utility considering battery recycling is more than that without considering battery recycling if the market scale is large enough, and otherwise it will have the opposite result. At the same time, the maximum expected utility of an EV manufacturer with subsidy is more than that without subsidy. However, a loss-averse EV manufacturer gains less than a risk-neutral EV manufacturer under the same conditions. Proposition 4 shows that either subsidy or battery recycling enhances their influences on the maximum expected utility. Moreover, either subsidy or battery recycling helps to offset the influence of loss aversion on the maximum expected utility.

3

imum expected utility by replacing θ with ∑i = 1 αi θi in her maximum expected utility in the case of a single repurposing option. It follows that our main results in the case of a single repurposing option (Propositions 1–4) continue to hold in this case. Similar inference holds true if there are more than three types of repurposing options for used batteries.

5. Model extensions In this section, we extend our base model to the case with multiple repurposing options for used batteries and an alternative subsidy mechanism.

5.2. Alternative subsidy mechanism

5.1. Multiple repurposing options for used batteries

In this subsection, we consider a different incentive policy where the manufacturer can receive a subsidy y for producing one unit of the EV. Similarly, the EV manufacturer's objective is to maximize her profit by choosing the optimal quantity under subsidy, battery recycling and loss aversion. Then, the EV manufacturer's profit function can be written as follows:

This subsection considers that the EV manufacturer has multiple repurposing options for used batteries, given that in practice used batteries may have different levels of quality and hence may be used for different specific purposes. In particular, we consider three types of 583

Energy Policy 109 (2017) 579–589

H. Gu et al.

*M ) F (QLYR

π M (Q, X = x ) px + s (Q − x ) − cQ + yQ + ΔτQ − AτQ − Bτ 2 if x ≤ Q =⎧ 2 ⎨ if x > Q ⎩ pQ − cQ + yQ + ΔτQ − AτQ − Bτ (16)

=

cQ − yQ − sQ − ΔτQ + AτQ + Bτ 2 p−s

(19)

(17)

Based on Eqs. (3) and (17), we compare the influences of these two different subsidy mechanisms on the breakeven quantity in Proposition 5.

6. Numerical experiments In order to illustrate our main results, we conduct three groups of numerical experiments to reveal the influences of subsidy, battery recycling and loss aversion on EV manufacturer's optimal production quantity and expected utility. In this section, we assume that the random demand X follows a standard normal distribution. Different expected utility functions under a normally distributed random demand are in the supplementary material. Due to limited space, the explanations of all the symbols and abbreviations in the figures are the same as Sections 4 and 5.

Proposition 5. The breakeven production quantity qRY (Q) under consumer subsidy mechanism is larger than the breakeven production M (Q) under consumer subsidy mechanism given the same quantity qRY subsidy and production quantity. We observe that more EVs are potentially subsidized under cost subsidy mechanism. In other words, the EV manufacturer's production quantity is higher under cost subsidy mechanism than that under customer subsidy mechanism. As a result, the consumers are better off in terms of available quantities. However, this phenomenon may cause excess EV production. Eq. (16) shows that the profit is negative if the order quantity is less M (Q) . We adopt the breakeven point than the breakeven quantity qRY M π0M (qRY ) = 0 as the reference point under loss aversion. Then, based on Eq. (16), the EV manufacturers’ utility maximization problem can be written as follows: M Max EUλYR = (λ − 1)

∫0

M qRY

6.1. Impact of subsidy on the EV manufacturer's optimal production quantity and expected utility Observation 1. Subsidy positively impacts the EV manufacturer's optimal production quantity and expected utility and such an effect is enhanced under an appropriate battery recycling rate. To study the effect of subsidy on the EV manufacturer's optimal production quantity and expected utility respectively based on consumer subsidy mechanism and cost subsidy mechanism, we use the following combinations of parameters for the numerical study:

[px + s (Q − x ) − cQ

+yQ + ΔτQ − AτQ − Bτ 2]f (x )dx +

Q

∫0

(px + s (Q − x ) − cQ

p = 1, c = 0.85, s = 0.60, Δ − A = 0.125, B = 1, μ = 500, σ = 380, λ = 1, τ = 0.8, y ∈ [0, 1].

+yQ + ΔτQ − AτQ − Bτ 2)f (x )dx +

∞

∫Q

p−s

From Eq. (19) we can easily obtain the optimal production quantity in Table 2. Based on Eqs. (18) and (19), we can obtain similar results to that characterized in Propositions 1–4 under customer subsidy mechanism. Therefore, we omit the related analysis process to avoid repetition and put them in the supplementary material.

By letting π M (Q, X = x ) = 0 in the profit function (16), the breakM for the EV production under Assumption 2 is: even quantity qRY M qRY =

M *M )) (p + y − c + Δτ − Aτ ) + (λ − 1)(s − c + y + Δτ − Aτ ) F (qRY (QLYR

(pQ − cQ + yQ + ΔτQ − AτQ − Bτ 2)f (x )dx

As is shown in the Figs. 1 and 2, subsidy has a positive impact on the EV manufacturer's optimal production quantity and expected utility; whereas, recycling rate can enhance the influence of subsidy on the EV manufacturer's optimal production quantity and expected utility. Either the EV manufacturer's optimal production quantity or expected utility under consumer subsidy mechanism is respectively lower than that under cost subsidy mechanism with the same per-unit subsidy. However, this result does not signify that consumer subsidy mechanism is better than the cost subsidy mechanism. The reason is that more EVs are potentially subsidized under cost subsidy mechanism. Besides, the consumers are better off in terms of available quantities but are worse off in terms of price. If the unit subsidy is more than 0.15, then the EV manufacturer's optimal production quantity or expected utility under

(18) Depending on the values of λ , y and τ , the newsvendor model in Eq. (16) can be reduced to different models described in Table 2. Theorem 2 characterizes the loss-averse manufacturer's production quantity decision. M Theorem 3.. The EV manufacturer's expected utility EUλYR is concave with respect to the production quantity Q . Then, there exists a unique M *M that maximizes EUλYR , and and finite optimal production quantity QLYR M * satisfying the following first-order condition: QLYR

Table 2 Models with different values of λ , y , and τ under cost subsidy mechanism. Model

Value of different parameter sin Eq. (4)

Expected utility

Optimal production quantity

Standard subsidized newsvendor model considering battery recycling standard newsvendor model considering loss aversion and battery recycling standard newsvendor model considering loss aversion and subsidy

λ=1

M EUYR

*M QYR

y=0

M EUλR = EUλR

* *M = QλR QλR

qRM = qR

τ=0

M EUλY

*M QλY

qYM

standard newsvendor model considering battery recycling

λ = 1 and y = 0

EURM = EUR

QR*M = QR*

standard newsvendor model considering subsidy

λ = 1 and τ = 0

EUYM

QY*M

standard newsvendor model considering loss aversion

y = 0 and τ = 0

EUλM = EUλ

Qλ*M = Qλ*

standard newsvendor model

λ = 1, y = 0 and τ = 0

EU M = EU

Q *M = Q*

584

Breakeven quantity

qM = q

Energy Policy 109 (2017) 579–589

H. Gu et al.

Fig. 1. Influence of subsidy on the optimal production quantity.

and expected utility, whereas subsidy can enhance the influence of battery recycling on the EV manufacturer's optimal production quantity and expected utility. In addition, we can observe that under cost subsidy mechanism, the combinational influence of subsidy and battery recycling on the optimal EV production quantity is more than the sum of their independent influence on the optimal EV production quantity.

cost subsidy mechanism becomes infinite. This result is because when the subsidy is more than 0.15, then battery recycling is adequately profitable to push the EV manufacturer's forward channel to supply unlimited EVs in the market. 6.2. Effect of battery recycling on the EV manufacturer's optimal production quantity and expected utility

6.3. Influence of loss aversion on the EV manufacturer's optimal production quantity and expected utility

Observation 2. The influences of battery recycling on the EV manufacturer's optimal production quantity and expected utility are positive and subsidy helps enhance the effects.

Observation 3. Either subsidy or battery recycling helps offset the negative influence of loss aversion on the EV manufacturer's optimal production quantity and expected utility.

To study the effect of battery recycling on the EV manufacturer's optimal production quantity and expected utility, we use the following combinations of parameters for the numerical study:

To investigate the impacts of loss aversion on the EV manufacturer's optimal production quantity and expected utility respectively based on consumer subsidy mechanism and cost subsidy mechanism, we use the following combinations of parameters for the numerical study:

p = 1, y = 0.10, c = 0.85, s = 0.60, Δ − A = 0.125, B = 1, μ = 500, σ = 380, λ = 1, τ ∈ [0, 1]. As is shown in Figs. 3 and 4, we observe that battery recycling exerts a positive impact on the EV manufacturer's optimal production quantity

Fig. 2. Influence of subsidy on the EV manufacturer's expected utility.

585

Energy Policy 109 (2017) 579–589

H. Gu et al.

Fig. 3. Influence of battery recycling on the optimal production quantity.

on EV production strategy, is generally overlooked by scholars. In fact, in many countries such as China, with growing EV ownership and usage time of EVs, there will be a lot of used EV batteries need to be recycled in the foreseeable future. Therefore, governments and manufacturers should consider how to reduce the adverse impacts of used batteries on environment and reuse them. In practice, it is quite common that EV manufacturers, such as BYD, construct specialized channel to recycle the used EV batteries. By considering government subsidy and battery recycling, this study focuses on how an EV manufacturer makes the optimal production decision under coexistence of the two factors. In particular, a newsvendor model is adopted to capture the uncertain market demand of EVs. It is found that, for a given battery recycling rate and degree of loss aversion, an increased subsidy has an increasing effect on the EV manufacturer's optimal production quantity and expected utility. This result demonstrates that the relationship between optimal production decision and subsidy specified by Zhang (2014) continues to hold if we incorporate battery recycling. The EV manufacturer's optimal production quantity increases with the battery recycling rate. However, the EV

p = 1, y = 0.1, c = 0.85, s = 0.60, Δ − A = 0.125, B = 1, μ = 500, σ = 380, τ = 0.8, λ ∈ [1, 8]. From Figs. 5 and 6, we can observe that loss aversion has a negative impact on the EV manufacturer's optimal production quantity and expected utility, whereas subsidy and battery recycling can offset the influence of loss aversion on the EV manufacturer's optimal production quantity and expected utility. We can also observe that cost subsidy mechanism has more advantage for the subsidy and battery recycling together to offset the impacts of loss aversion on the EV manufacturer's optimal production quantity and expected utility. 7. Discussion As a green and environmentally friendly transportation tool, EV has become increasingly popular in recent years. The benign and rapid development of the EV industry cannot do without a proper production strategy of the EV manufacturers. The decision-making on EV production strategy is often impacted by government subsidy (Zhang, 2014). However, battery recycling, which is another important impact factor

Fig. 4. Influence of battery recycling on the EV manufacturer's expected utility.

586

Energy Policy 109 (2017) 579–589

H. Gu et al.

Fig. 5. Influence of loss aversion on the optimal production quantity.

There exist some limitations to our research. We assume that the random customer demand of EVs is independent of market price. In practice, this assumption may not always hold because demand may be price-sensitive. Hence, a lack of the consideration of price-sensitive demand may cause an incomplete analysis with respect to the impact of the aforementioned factors on the EV manufacturer's production strategy. Meanwhile, we assume that the EV manufacturer is responsible for the recycling channel. This assumption is appropriate in the early stage of the EV market because battery recycling is mandatory for the manufacturer and the amount of used batteries is relatively small. However, with the rapid development of EV market, it might be necessary to introduce third-party provider to conduct the business on battery recycling in the near future. This could provide an interesting and promising research direction to our current study. Finally, we only consider a single manufacturer in the EV market. Introducing market competition of multiple manufacturers may enrich the understanding of EV production strategy, especially if competition exists between EV and ICEV manufacturers.

manufacturer's expected utility decreases with the battery recycling rate if the optimal production quantity is sufficiently small. This result suggests that EV manufacturers, such as BYD, may prefer a relatively small battery recycling rate. Further, given the subsidy and battery recycling rate, the degree of loss aversion has a decreasing effect on the EV manufacturer's optimal production quantity and expected utility. This result demonstrates that a high sensitivity to risk of the EV manufacturer adversely impacts the expansion of EV market and the manufacturer. By extending our study to the case in which the EV manufacturer has multiple repurposing options based on the quality of used batteries, we find that all the results can still hold. If the government provides subsidy for the EV manufacturer's production, then the manufacturer's optimal production quantity and expected utility will increase compared with the case when customers are subsidized. This result implies that compared with customer subsidy mechanism, cost subsidy mechanism is more desired by the EV manufacturer. However, the customers may not be better off under cost subsidy mechanism because they need to pay a higher price for the EV.

Fig. 6. Influence of loss aversion on the EV manufacturer's expected utility.

587

Energy Policy 109 (2017) 579–589

H. Gu et al.

8. Conclusions and policy implications

This work was partially supported by the National Natural Science Foundation of China (Grants 71320107001 and 71401129) and Research Center of Service Science and Engineering at Wuhan University of Science and Technology.

This study analyses a loss-averse EV manufacturer's optimal production strategy under government subsidy and battery recycling in the presence of uncertain market demand. We show that subsidy, battery recycling and risk preference are important factors that impact the manufacturer's optimal production decision and expected utility. Our main conclusions and related policy implications are summarized as follows. First, in a closed-loop supply chain with battery recycling, government subsidy is a positive impact factor on the EV manufacturer's production quantity and expected utility when the customers are subsidized for EV purchase. In particular, if the subsidy is sufficiently large, then the manufacturer's production quantity and expected utility will become infinite. Therefore, policy makers should provide certain subsidy to EV industry in order to promote its market size. Meanwhile, policy makers need to choose a proper subsidy to ensure a reasonable production quantity. If the subsidy is too high, then excessive production will arise, which subsequently causes considerable resource waste and a lower degree of social welfare for the customers. The manufacturer, on the other hand, may lose motivation to improve production technology and cost control. Second, battery recycling is a positive impact factor on the EV manufacturer's production quantity. This result suggests policy makers to establish regulations that require the manufacturer to recycle used batteries and to build a battery recovery system. In particular, such an action should be taken not only from perspective of environment protection, but also from perspective of promoting the EV market. Meanwhile, battery recycling may be a negative impact factor on the manufacturer's expected utility when the market scale is small. This result further shows that it is necessary for the policy makers to stipulate that the manufacturers are responsible for recycling batteries and building the battery recovery system, especially in the early stage of the EV market. The reason for this stipulation is simple: manufacturers may not be incentivized to recycle used batteries given a small market scale. If it is in this case, then the manufacturer's optimal production quantity may decrease and the development of the EV market is negatively impacted. Third, loss aversion is a negative impact factor on the EV manufacturer's optimal production quantity and expected utility and then the actual market scale. Meanwhile, subsidy and battery recycling can to some extent decrease such a negative impact. Therefore, policy makers need to learn about the manufacturer's risk preference characteristics, and then chooses appropriate subsidy and battery recycling rate to offset the negative effect of loss aversion. Fourth, the impacts of subsidy, battery recycling and loss aversion on the EV manufacturer's optimal production and expected utility remain unchanged under multiple repurposing options for used batteries, or under a subsidy mechanism with the manufacturer's production costs being subsidized. In particular, the manufacturer's optimal production quantity and expected utility are higher under cost subsidy mechanism than under consumer subsidy mechanism. This result bears significant implications for policy makers. For example, if the EV market is at its early stage and expanding the market scale is the primary objective, then the policy maker may need to directly provide subsidy to the EV manufacturer. Given this case, the customers may have to pay more for EV purchase and social welfare is negatively impacted. On the other hand, if EV market is in its mature stage and market scale is sufficiently high, then providing subsidy to customers directly may be a dominant choice because it ensures a higher customer satisfaction and social welfare.

Appendix A. Supporting information Supplementary material associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.enpol.2017.07.043. References Ahmadi, L., Yip, A., Fowler, M., Young, S.B., Fraser, R.A., 2014. Environmental feasibility of re-use of electric vehicle batteries. Sustain. Energy Technol. Assess. 6, 64–74. Ahmadi, L., Young, S.B., Fowler, M., Fraser, R.A., Achachlouei, M.A., 2017. A cascaded life cycle: reuse of electric vehicle lithium-ion battery packs in energy storage systems. Int. J. Life Cycle Assess. 22 (1), 111–124. Argote, L., Epple, D., 1990. Learning curves in manufacturing. Science 247 (4945), 920–924. Assunção, A., Moura, P.S., de Almeida, A.T., 2016. Technical and economic assessment of the secondary use of repurposed electric vehicle batteries in the residential sector to support solar energy. Appl. Energy 181, 120–131. Atasu, A., Toktay, L.B., Van Wassenhove, L.N., 2013. How collection cost structure drives a manufacturer's reverse channel choice. Prod. Oper. Manag. 22 (5), 1089–1102. Babich, V., 2010. Independence of capacity ordering and financial subsidies to risky suppliers. Manuf. Serv. Oper. Manag. 12 (4), 583–607. Casals, L.C., García, B.A., Aguesse, F., Iturrondobeitia, A., 2017. Second life of electric vehicle batteries: relation between materials degradation and environmental impact. Int. J. Life Cycle Assess. 22 (1), 82–93. Chuang, C.-H., Wang, C.X., Zhao, Y., 2014. Closed-loop supply chain models for a hightech product under alternative reverse channel and collection cost structures. Int. J. Prod. Econ. 156, 108–123. Coffman, M., Bernstein, P., Wee, S., 2017. Electric vehicles revisited: a review of factors that affect adoption. Transp. Rev. 37 (1), 79–93. Cohen, M.C., Lobel, R., Perakis, G., 2016. The impact of demand uncertainty on consumer subsidies for green technology adoption. Manag. Sci. 62 (5), 1235–1258. Daziano, R.A., Chiew, E., 2012. Electric vehicles rising from the dead: data needs for forecasting consumer response toward sustainable energy sources in personal transportation. Energy Policy 51, 876–894. Edgeworth, F.Y., 1888. The mathematical theory of banking. J. R. Stat. Soc. 51 (1), 113–127. Feng, T., Keller, L.R., Zheng, X., 2011. Decision making in the newsvendor problem: a cross-national laboratory study. Omega 39 (1), 41–50. Fisher, M., Raman, A., 1996. Reducing the cost of demand uncertainty through accurate response to early sales. Oper. Res. 44 (1), 87–99. Hao, H., Ou, X., Du, J., Wang, H., Ouyang, M., 2014. China's electric vehicle subsidy scheme: rationale and impacts. Energy Policy 73, 722–732. Heymans, C., Walker, S.B., Young, S.B., Fowler, M., 2014. Economic analysis of second use electric vehicle batteries for residential energy storage and load-levelling. Energy Policy 71, 22–30. Ho, T.-H., Lim, M.K., Cui, T.H., 2010. Reference dependence in multilocation newsvendor models: a structural analysis. Manag. Sci. 56 (11), 1891–1910. Hu, B., Meng, C., Xu, D., Son, Y.-J., 2016. Three-echelon supply chain coordination with a loss-averse retailer and revenue sharing contracts. Int. J. Prod. Econ. 179, 192–202. Huang, J., Leng, M., Liang, L., Liu, J., 2013. Promoting electric automobiles: supply chain analysis under a government's subsidy incentive scheme. IIE Trans. 45 (8), 826–844. IEA, 2016. Global EV Outlook 2016: Beyond One Million Electric Cars, 2016 ed. International Energy Agency, Paris. Jaguemont, J., Boulon, L., Dubé, Y., 2016. A comprehensive review of lithium-ion batteries used in hybrid and electric vehicles at cold temperatures. Appl. Energy 164, 99–114. Jiao, N., Evans, S., 2016. Secondary use of electric vehicle batteries and potential impacts on business models. J. Ind. Prod. Eng. 33 (5), 348–354. Kahneman, D., Tversky, A., 1979. Prospect Theory: An analysis of decision under risk. Econometrica 47 (2), 263–291. Kieckhäfer, K., Volling, T., Spengler, T.S., 2014. A hybrid simulation approach for estimating the market share evolution of electric vehicles. Transp. Sci. 48 (4), 651–670. Krass, D., Nedorezov, T., Ovchinnikov, A., 2013. Environmental taxes and the choice of green technology. Prod. Oper. Manag. 22 (5), 1035–1055. Langbroek, J.H.M., Franklin, J.P., Susilo, Y.O., 2016. The effect of policy incentives on electric vehicle adoption. Energy Policy 94, 94–103. Lariviere, M.A., Porteus, E.L., 2001. Selling to the newsvendor: an analysis of price-only contracts. Manuf. Serv. Oper. Manag. 3 (4), 293–305. Li, W., Long, R., Chen, H., 2016. Consumers' evaluation of national new energy vehicle policy in China: an analysis based on a four paradigm model. Energy Policy 99, 33–41. Lim, M.K., Mak, H.-Y., Rong, Y., 2015. Toward mass adoption of electric vehicles: impact of the range and resale anxieties. Manuf. Serv. Oper. Manag. 17 (1), 101–119. Liu, W., Song, S., Li, B., Wu, C., 2015. A periodic review inventory model with loss-averse retailer, random supply capacity and demand. Int. J. Prod. Res. 53 (12), 3623–3634. Luo, C., Leng, M., Huang, J., Liang, L., 2014. Supply chain analysis under a price-discount incentive scheme for electric vehicles. Eur. J. Oper. Res. 235 (1), 329–333.

Acknowledgments The authors thank the editor and three anonymous referees for their constructive suggestions that have significantly improved this paper. 588

Energy Policy 109 (2017) 579–589

H. Gu et al.

Schweitzer, M.E., Cachon, G.P., 2000. Decision bias in the newsvendor problem with a known demand distribution: experimental evidence. Manag. Sci. 46 (3), 404–420. Souza, G.C., 2013. Closed-loop supply chains: a critical review, and future research. Decis. Sci. 44 (1), 7–38. Tagliaferri, C., Evangelisti, S., Acconcia, F., Domenech, T., Ekins, P., Barletta, D., Lettieri, P., 2016. Life cycle assessment of future electric and hybrid vehicles: a cradle-tograve systems engineering approach. Chem. Eng. Res. Des. 112, 298–309. Thierry, M., Salomon, M., Van Nunen, J., Van Wassenhove, L., 1995. Strategie issues in product recovery management. Calif. Manag. Rev. 37 (2), 114–135. Tversky, A., Kahneman, D., 1991. Loss aversion in riskless choice: a reference-dependent model. Q. J. Econ. 106 (4), 1039–1061. Wang, C.X., Webster, S., 2009. The loss-averse newsvendor problem. Omega 37 (1), 93–105. Wu, T., Ma, L., Mao, Z., Ou, X., 2015a. Setting up charging electric stations within residential communities in current China: gaming of government agencies and property management companies. Energy Policy 77, 216–226. Wu, X., Freese, D., Cabrera, A., Kitch, W.A., 2015b. Electric vehicles' energy consumption measurement and estimation. Transp. Res. Part D. Transp. Environ. 34, 52–67. Yano, J., Muroi, T., Sakai, S., 2016. Rare earth element recovery potentials from end-oflife hybrid electric vehicle components in 2010–2030. J. Mater. Cycles Waste Manag. 18 (4), 655–664. Zhang, X., 2014. Reference-dependent electric vehicle production strategy considering subsidies and consumer trade-offs. Energy Policy 67, 422–430. Zhang, X., Zhang, C., 2015. Optimal new energy vehicle production strategy considering subsidy and shortage cost. Energy Procedia 75, 2981–2986.

Madina, C., Zamora, I., Zabala, E., 2016. Methodology for assessing electric vehicle charging infrastructure business models. Energy Policy 89, 284–293. Mak, H.Y., Rong, Y., Shen, Z.J.M., 2013. Infrastructure planning for electric vehicles with battery swapping. Manag. Sci. 59 (7), 1557–1575. Mao, Z., 2016. Fears for new energy vehicles batteries recycling over the next five years. Econ. Inf. Dly. 11 (in Chinese). Matthews, L., Lynes, J., Riemer, M., Del Matto, T., Cloet, N., 2017. Do we have a car for you? Encouraging the uptake of electric vehicles at point of sale. Energy Policy 100, 79–88. Neubauer, J., Pesaran, A., 2011. The ability of battery second use strategies to impact plug-in electric vehicle prices and serve utility energy storage applications. J. Power Sources 196 (23), 10351–10358. Qin, Y., Wang, R., Vakharia, A.J., Chen, Y., Seref, M.M.H., 2011. The newsvendor problem: review and directions for future research. Eur. J. Oper. Res. 213 (2), 361–374. Richa, K., Babbitt, C.W., Nenadic, N.G., Gaustad, G., 2017. Environmental trade-offs across cascading lithium-ion battery life cycles. Int. J. Life Cycle Assess. 22 (1), 66–81. Samba, A., Omar, N., Gualous, H., Firouz, Y., Van den Bossche, P., Van Mierlo, J., Boubekeur, T.I., 2014. Development of an advanced two-dimensional thermal model for large size lithium-ion pouch cells. Electrochim. Acta 117, 246–254. Savaskan, R.C., Bhattacharya, S., Van Wassenhove, L.N., 2004. Closed-loop supply chain models with product remanufacturing. Manag. Sci. 50 (2), 239–252. Saxena, S., Le Floch, C., MacDonald, J., Moura, S., 2015. Quantifying EV battery end-oflife through analysis of travel needs with vehicle powertrain models. J. Power Sources 282, 265–276.

589