Does Product Eco-design Promote Remanufacturing: Application of a Stylized Game-theoretic Model

Abstract

As an effective approach to reduce resource waste and production costs, remanufacturing has elicited extensive attention from the industry and academia. Many electronic original equipment manufacturers (OEMs) have increasingly begun to incorporate product eco-design (PED) into their remanufacturing processes since take-back regulations that hold OEMs responsible for handling their own end-of-life products have gradually become more stringent. The investment costs for the PED implementation vary across different PED effort levels (i.e., high, medium, and low) chosen by the OEM, and different PED effort levels may yield different remanufacturing strategies. In this paper, we develop a stylized game-theoretic model to investigate the impact of PED effort levels on the OEM’s equilibrium decisions (which include production quantities of new and remanufactured products) and supply chain performance in the context of take-back legislation. Our results demonstrate that high PED effort levels do not imply more remanufacturing and that the OEM’s choice of remanufacturing strategies depends on the trade-off between cost savings from remanufacturing and deterministic risks. Interestingly, we find that new products should have a certain level of profitability to ensure the validity of take-back legislation. Due to the substitution and complementary effects between new and remanufactured products, the optimal decisions exhibit different characteristics in remanufacturing strategies. Through a numerical study, we observe that the economic performance decreases with increases in the PED effort level under take-back legislation, but the change in the total environmental impact depends on the PED effort level and the production cost of new products.

1. Introduction

E-waste constitutes one of the fastest-growing streams of solid waste. The Global E-waste Monitor (2020) highlighted that a record 53.6 million tons of e-waste were generated in 2019, an increase of 21 percent in just five years. The report predicts that global e-waste will reach 74 million tons by 2030 (https://ewastemonitor.info/wpcontent/uploads/2021/11/REM_2021_CISGEORGIA_WEB_final_nov_11_spreads.pdf (accessed on 6 June 2022)). Furthermore, only 17 percent of e-waste is collected and recycled in an environmentally sound manner around the world, wasting valuable materials and causing damage to the environment (https://collections.unu.edu/view/UNU:7737 (accessed on 6 June 2022)). The causes of this phenomenon encompass rapid economic development, inefficient collection channels, and a lack of formal recycling infrastructure [1].

As an effective method to reduce resource waste and production costs, remanufacturing is increasingly being recognized as a more sustainable alternative for end-of-life products in the e-waste industry [2,3]. Remanufacturing recovers value from used products by replacing components or reprocessing used parts to bring the product to a like-new condition. Since it reduces both the natural resources needed and the waste produced, remanufacturing helps to reduce the environmental burden. Furthermore, commercial practices indicate that remanufacturing can generate significant profits for electronic producers. The United States International Trade Commission (USITC) estimated that the remanufacturing industry creates at least USD 43 billion in profits in the USA (https://www.usitc.gov/publications/industry_econ_analysis_332/2012/remanufactured_goods_overview_us_and_global.htm (accessed on 6 June 2022)). Due to the environmental and economic benefits of remanufacturing, an increasing number of electronic producers are taking it as a marketing strategy [4,5]. For example, many companies, such as Apple, Dell, Sony, and Fuji Xerox, have offered remanufactured (or refurbished) products in markets.

To divert as much e-waste as possible from landfills, many counties and states have implemented or are planning to enact take-back legislation, which holds producers responsible for collecting and treating end-of-life products they have sold. This type of legislation always requires mandatory collection targets and/or reuse targets for electronic producers who should collect a fraction of new products they have sold and/or remanufacture a fraction of cores they have collected from the market [6]. In recent years, these mandatory targets have increasingly become more stringent. For example, the collection target set by the European Union has been creeping up, from 45% before 2016 to 65% in 2019 (http://ec.europa.eu/environment/waste/weee/index_en.htm (accessed on 7 June 2022)). In the United States, 25 states have set various levels of the collection target (http://www.electronicstakeback.com/promote-good-laws/state-legislation-toolkit/ (accessed on 7 June 2022)).

Facing the stringent mandatory targets, many OEMs have increasingly begun to incorporate PED into their remanufacturing processes. The term PED has many similar expressions according to where it is used [7]. In Europe, it is primarily described as ecological design or life-cycle design. In addition, the PED can be extended to sustainable product design or design for sustainability by considering the social and economic issues. More details of the term PED can be found in Platcheck et al. [8] and Cerdan et al. [9]. In this paper, since many electronic producers implement PED and remanufacturing strategies simultaneously to fulfill their environmental responsibilities when they face stringent take-back legislation, the term PED means that OEMs improve the disassembly or accessibility of parts at the design stage and make products that are easier to remanufacture [10,11]. For example, Canon develops remanufacturing technologies and uses recyclable and reusable materials to enhance collection efficiencies during the production stage. End-of-life products are then remanufactured through the Product-to-Product Recycling Program (https://www.usa.canon.com/internet/portal/us/home/about/environment-sustainability-initiatives. (accessed on 7 June 2022)). Through strategic PED and by improving the remanufacturing technology, products are endowed with more environmental attributes and are easier to remanufacture.

Obviously, the implementation of PED is beneficial for remanufacturing since products with recyclable and reusable materials are easier to remanufacture [12]. Meanwhile, PED reduces production costs of new and remanufactured products because it reduces firms’ reliance on resources, and OEMs can produce the same quality or quantity of products with fewer resources [13,14]. For instance, Canon, Xerox, and HP have decreased their production costs of new and remanufactured products by conducting PED. Some auto manufacturers such as Toyota and BYD are making technological changes to the battery to achieve significant reductions in production costs [14]. With the increase in the PED effort level (i.e., high, medium, and low), the OEM will effectively reduce the production costs of new and remanufactured products as well as environmental impact, but the increased investment cost due to the enhancement of PED effort levels may be very high. Therefore, the OEM may choose different PED effort levels as the improvement of PED is costly through introducing remanufacturing technologies, purchasing advanced devices, and employing technical staff. Thus, a challenge of the PED implementation is the strategic balance between the reduction of production and remanufacturing costs and the huge investment cost. Additionally, although PED reduces the production costs of new and remanufactured products, it may reinforce the competition between the two products [14]. This means that some degree of cannibalization—a problem that the manufacturer fears—will eventually occur, which is a factor that has been considered a deterrent for companies to practice remanufacturing. Hence, the PED implementation affects not only the OEM’s remanufacturing decision but also its production quantity decision of new products. This motivates our research questions:

(1)

What are the OEM’s manufacturing and remanufacturing decisions when it implements the PED strategy to maximize its profits in the context of take-back legislation?

(2)

How do the key elements (such as production costs, PED factors, and mandatory targets) affect the OEM’s equilibrium decisions?

(3)

Does the implementation of PED improve economic and environmental performance under different levels of take-back legislation? If yes, under what conditions?

In this study, we focus on a monopoly OEM who enhances PED effort levels (i.e., design for remanufacturing) and produces new and remanufactured products. Using a stylized game-theoretic model, we consider three levels of take-back legislation: no legislation, take-back legislation with collection targets, and take-back legislation with collection and reuse targets. Employing KKT conditions to solve the optimization problem, we identify the optimal remanufacturing strategies under different PED effort levels and legislative scenarios and determine the occurrence condition per remanufacturing strategy. Furthermore, we examine the effects of production costs, PED activities, and legislative characteristics on the OEM’s equilibrium decisions. Finally, through a numerical study, we investigate the economic and environmental outcomes under different PED effort levels and legislative scenarios.

The contributions of our research are as follows:

(1)

We consider both PED (at the design level) and remanufacturing (at the recycling level) as the OEM’s operating strategies and investigate the interactive mechanism between them in the context of take-back legislation.

(2)

We consider different levels of take-back legislation (i.e., no legislation, take-back legislation with collection targets, and take-back legislation with collection and reuse targets) and study the OEM’s optimal collection and production quantity decisions under the three legislative scenarios.

(3)

We study the economic outcome and environmental impact under different PED effort levels and take-back regulations, yielding new insights in terms of how the policymaker should choose the take-back legislation to achieve economic and environmental benefits.

The rest of this paper is organized as follows. In the following section, we briefly discuss the related literature. Section 3 is devoted to the construction of the model. Following the development of the model, we solve the optimization problem by using KKT conditions and conduct a sensitivity analysis in Section 4. Section 5 investigates the economic and environmental outcomes. Section 6 concludes the research. All the proofs are relegated to the Appendix A.

2. Literature Review

There are a few streams of literature in operations management that relate to our work. One falls into the stream of product eco-design in closed-loop supply chains, and the other falls into the stream of operations management under take-back legislation.

2.1. Product Eco-Design in Closed-Loop Supply Chains

The topics of PED in closed-loop supply chains mostly pay attention to technology selection [15,16,17], PED implications of EPR programs [12,13,18], green product development [19,20,21], and product quality [22,23]. Krass et al. [16] explored how to use environmental tax to motivate green technology innovation. Huang et al. [18] studied the PED effects of an EPR program on durable goods by considering two design attributes, i.e., recyclability and durability. Raz et al. [20] examined how product costs, demands, and environmental impacts change when introducing environmental innovations in PED. Jackson et al. [23] studied the relationships of PED with economic and environmental performances. These papers used stylized economic models and uncovered the impact of technology innovation, environmental attributes, and policy tools on PED. However, the practice of PED around the globe has converged to remanufacturing [14].

To our best knowledge, the following two articles are most relevant to our study in the PED literature. Pazoki and Samarghandi [3] constructed four stylized models by considering a regulator and a manufacturer to investigate whether take-back legislation motivates PED or remanufacturing. Their results show that the more polluting products required take-back legislation, while the greener products did not if PED behaviors could effectively reduce the production cost, and the manufacturer would choose the remanufacturing strategy if the investment costs in PED are too high. They assumed that the manufacturer chooses either remanufacturing or PED under take-back legislation but did not integrate the two strategic choices simultaneously into the producer’s operating environments. Zheng et al. [14] developed a stylized model to explore an OEM’s production decisions and the implications of PED for remanufacturing in the monopolistic and competitive markets. They found that PED behaviors decrease the willingness of the OEM to choose the remanufacturing strategy in the monopolistic case, while the result was reversed in the competitive case. In addition, they also suggested that a high PED level may hurt the environment because it increases the total sales volume. They did not, however, capture the constraint of take-back legislation on the OEM’s production decisions, a gap our study addresses.

2.2. Operations Management under Take-back Legislation

In the last decade, there has been considerable interest within the academic community in product recovery issues. Within this literature, there is a more recent but fast-growing stream of research that investigates the impact of take-back legislation on operations management. Some studies were started based on EPR programs, which focused on new product introduction, PED, and cost efficiency. Plambeck and Wang [24] studied the impact of two types of e-waste legislation, i.e., fee-upon-sale and fee-upon-disposal, on new product introduction. Subramanian et al. [25] investigated the effect of EPR legislation on PED and coordination incentives by considering the product’s two attributes, i.e., performance and remanufacturability. Gui et al. [26] developed cost allocation models to maximize cost efficiency among different stakeholders.

Other papers in this domain, which are more closely related to our work, focus on the implementation details of product take-back legislation. Generally speaking, state-operated and manufacturer-operated constitute the two common collection systems of take-back legislation [4,27]. Under state-operated collection systems, the government undertakes collection tasks, and consumers or manufacturers finance relevant fees. Atasu et al. [4] studied the influence of take-back legislation on economic and environmental performances, and they suggested that the social planner make manufacturers responsible for their cores to avoid fairness concerns. Furthermore, Atasu et al. [5] compared the impact of a manufacturer-operated collection system and a state-operated collection system on different stakeholders (i.e., manufacturers, consumers, policymakers, and environmentalists). Under the manufactured-operated collection system, however, manufacturers are responsible for their waste, and the government set mandatory targets for them. Esenduran et al. [28] constructed a stylized economic model of take-back legislation that includes collection and reuse targets for the OEM from a social planner perspective and explored the economic and environmental outcomes. This model was extended in Esenduran et al. [6] to incorporate an independent remanufacturer (IR), where they observed that the remanufacturing level might decrease in the competitive market, but consumer surplus and the OEM’s profits might increase when OEM–IR competition exists in the market regulated by collection and reuse targets. Furthermore, Chen et al. [29] considered both take-back and carbon emission capacity regulations in stylized economic models. They found that the carbon emission capacity regulation reduces the total environmental impact and improves the remanufacturing level. However, the above literature did not introduce PED behaviors into the framework of take-back legislation. Guiding producers to implement PED is one of the primary goals of take-back legislation.

2.3. Research Gaps

In this subsection, we summarize the differences between this paper and the existing literature to show the gap that our study addresses in Table 1. We divide the above literature in Section 2.1 and Section 2.2 into five aspects, i.e., take-back legislation (which includes the collection target and reuse target), PED, product quantity decisions (which include the new product, collected product, and remanufactured product), supply constraint, and performance (which includes the economic outcome and environmental impact). The research background of our paper is based on the prevailing and common e-waste policy tool, i.e., take-back legislation. The primary goal of take-back legislation is to divert as much e-waste as possible from landfills, and hence we choose the product quantity decisions to reflect the change in the manufacturer’s quantity decisions under take-back legislation. Another important goal of take-back legislation is to provide PED incentives for electronic producers. Therefore, we also choose PED as a main aspect in the literature review. The supply constraint is a technical approach, and it represents more realistic scenarios. To be specific, in our paper, the quantity of collected products is less than the quantity of new products, and the quantity of remanufactured products is less than the quantity of collected products. Finally, the profitability and environmental impact are major concerns of the manufacturer and policymaker, respectively, in the context of take-back legislation. Thus, we also select the two performances to illustrate the research gap between the existing literature and this paper.

From Table 1, we can see that the PED studies (e.g., [16,18,20,23]) do not consider the remanufacturing strategy of the OEM. Although some articles combine PED and remanufacturing to study the impact of the two operating strategies on producers’ decisions (e.g., [3,14]), they do not consider the regulatory environment (because take-back legislation has been widely implemented in many countries and states such as Europe, Japan, China, and India). We contribute to this stream of literature by considering PED and remanufacturing simultaneously in the context of take-back legislation. We study an OEM’s collection and production quantity equilibrium decisions and explore the impact of key parameters (e.g., production costs, PED factors, and mandatory targets) on optimal solutions. In the literature of operations management under take-back legislation, some studies do not consider the specific mandatory targets (e.g., [4,24,25,26]). Although some articles consider different legislative scenarios and study the producer’s collection and production quantity decisions (e.g., [5,6,27,28,29]), they do not consider PED as the producer’s operating strategy. We contribute to this stream of literature by considering three levels of take-back legislation, i.e., no legislation, take-back legislation with collection targets, and take-back legislation with collection and reuse targets. Furthermore, based on the specific context in this paper, we also study the economic outcome and environmental impact and contribute to the operations management literature.

Table 1. Summary of literature review.

Sources	Take-Back Legislation		PED	Product Quantity Decisions			Supply Constraint	Performance
	Collection	Reuse		New	Collected	Remanufactured		Economy	Environment
[16]			√	√			√	√	√
[18]			√	√	√				√
[20]			√	√					√
[23]			√	√				√	√
[3]			√	√	√	√		√	√
[14]			√	√		√	√		√
[24]				√				√	√
[25]			√	√					√
[26]				√	√		√
[4]			√	√				√
[27]	√			√		√	√	√	√
[5]	√	√		√			√	√	√
[28]	√	√		√	√	√	√		√
[6]	√	√		√	√	√		√
[29]	√	√		√	√	√	√	√	√
This paper	√	√	√	√	√	√	√	√	√

Table 1. Summary of literature review.

Sources	Take-Back Legislation		PED	Product Quantity Decisions			Supply Constraint	Performance
	Collection	Reuse		New	Collected	Remanufactured		Economy	Environment
[16]			√	√			√	√	√
[18]			√	√	√				√
[20]			√	√					√
[23]			√	√				√	√
[3]			√	√	√	√		√	√
[14]			√	√		√	√		√
[24]				√				√	√
[25]			√	√					√
[26]				√	√		√
[4]			√	√				√
[27]	√			√		√	√	√	√
[5]	√	√		√			√	√	√
[28]	√	√		√	√	√	√		√
[6]	√	√		√	√	√		√
[29]	√	√		√	√	√	√	√	√
This paper	√	√	√	√	√	√	√	√	√

3. Problem Description and Notations

We use a stylized game-theoretic model to capture the salient characteristics of PED and remanufacturing when the market is regulated by take-back legislation. We focus on a monopoly OEM who sells new and remanufactured products simultaneously in the market and implements PED to make products that are easier to remanufacture and decrease the production costs of new and remanufactured products. In the remainder of this study, subscripts $n$, $r$, and $c$, respectively, are used to refer to new, remanufactured, and collected products. Parameters and decision variables are provided in

Table 2. Summary of notation.

Notations	Description
Decision variables
$q_n$	Quantity of the new product
$q_r$	Quantity of the remanufactured product
$q_c$	Quantity of the collected product
$p_n$	Price of the new product
$p_r$	Price of the remanufactured product
Parameters
$e$	PED effort level
$k$	Scale parameter of the investment function
${\theta }_1$	Marginal effect of PED on the new product’s production cost
${\theta }_2$	Marginal effect of PED on the remanufactured product’s production cost
$c_n$	Unit cost of the new product without PED
$c_r$	Unit cost of the remanufactured product without PED
${\tilde{c}}_n$	Unit cost of the new product with PED
${\tilde{c}}_r$	Unit cost of the remanufactured product with PED
$c_c$	Unit cost of the collected product
$\alpha$	Consumer valuation discount for remanufactured products
${\beta }_c$	Mandatory collection target
${\beta }_r$	Mandatory reuse target
${\chi }_n$	Per-unit environmental impacts of the new product without PED
${\chi }_r$	Per-unit environmental impacts of the remanufactured product without PED
${\tilde{\chi }}_n$	Per-unit environmental impacts of the new product with PED
${\tilde{\chi }}_r$	Per-unit environmental impacts of the remanufactured product with PED
${\phi }_1$	Marginal effect of PED on the new product’s environmental impact
${\phi }_2$	Marginal effect of PED on the remanufactured product’s environmental impact

.

We begin by introducing the demand model. In the remanufacturing market, consumers have three options, i.e., buying a new product, buying a remanufactured product, or being inactive, which depends on their utility. We normalize the market size to 1 without loss of generality, and each consumer buys, at most, one unit in each period. Consumers are heterogeneous, and their valuation, $v$, of the new product is uniformly distributed in the interval [0,1]. Given the sales price $p_n$ of new products, a consumer who purchases a new product can obtain utility $U_n(v)=v-p_n$. Following the common assumption in the remanufacturing literature [30,31,32], consumers are willing to pay only a fraction $\alpha$ of the full price for a remanufactured product because of loss aversion and fair price. The parameter $\alpha$ signifies the consumer valuation discount for remanufactured products. Thus, given the sales price $p_r$ of remanufactured products, a consumer who purchases a remanufactured product can obtain utility $U_r(v)=\alpha v-p_r$.

We confine ourselves to the context of a single-period model, which signifies that the remanufacturing market is in the maturity stage of the product life cycle, and the OEM’s manufacturing, collecting, and remanufacturing decisions are kept steady. Such single-period, steady-state settings have been widely used in the remanufacturing and take-back legislation literature [27,29]. The monopoly OEM decides how many new products to manufacture $q_n$, how many cores to collect $q_c$, and how many of those to remanufacture $q_r$. We assume that the service life of new and remanufactured products is one period. We also assume that the products ($q_c-q_r$) that are not remanufactured after collection are disposed of innocuously by the OEM and the cost of innocent treatment is normalized to 0, and the remaining products in the market ($q_n-q_c$) are disposed of by the consumer or the associated collection and recycling points. Therefore, consumers’ purchase decisions in each period are independent of each other. Given the OEM’s production decisions, consumers make their purchasing decisions, resulting in the following prices for new and remanufactured products: $p_n=1-q_n-\alpha q_r$ and $p_r=\alpha (1-q_n-q_r)$. For derivations, please refer to Ferguson and Toktay [33] and Yenipazarli [34].

In this study, the OEM’s cost structure is as follows: $c_n$ denotes the unit cost of manufacturing a new product, $c_r$ the unit cost of remanufacturing a core into a new one, and $c_c$ the unit collection cost. The OEM incorporates the PED strategy into its remanufacturing processes to make products easier to remanufacture and decrease the marginal costs of new and remanufactured products because take-back legislation becomes stringent, and its PED effort level is denoted by $e$. Following the same assumption in the remanufacturing and PED literature [14,19,20,35], the cost functions of new and remanufactured products are inversely proportional to the PED effort level $e$, resulting in the following cost functions when the OEM engages in PED activities: ${\tilde{c}}_n(e)=c_n(1-e{\theta }_1)$, ${\tilde{c}}_r(e)=c_r(1-e{\theta }_2)$, $0<{\theta }_1,{\theta }_2<1$, $0<e{\theta }_1,e{\theta }_2<1$, and ${\theta }_1\ne {\theta }_2$. ${\theta }_1$ signifies the marginal effect of PED behaviors on the new product’s production cost, and ${\theta }_2$ indicates the marginal effect of PED behaviors on the remanufactured product’s production cost. When the OEM makes efforts to improve the PED level, it will pay for additional expenditures by introducing green technologies and devices as well as technical staff. The investment $F(e)$ is quadratic and satisfies $dF(e)/de>0$, $d^{2}F(e)/d{e}^2>0$, and $F(0)=0$ [14,15]. Specifically, we assume that $F(e)=k{e}^2/2$, where $k$ is the scale coefficient. The function $F(e)$ captures the law of diminishing return to investment [20,35].

The primary goal of this paper is to understand the impact of PED on remanufacturing under take-back legislation. Hence, we consider the following three legislative scenarios: (1) Take-back legislation with collection targets. Under this type of legislation, the policymaker sets mandatory collection targets ${\beta }_c$ for the OEM. The parameter ${\beta }_c$ captures the minimum collection ratio of new products put on the market, and the OEM should collect at least ${\beta }_c{q}_n$ end-of-life products, i.e., $q_c\ge {\beta }_c{q}_n$. (2) Take-back legislation with collection and reuse targets. In this scenario, besides mandatory collection targets ${\beta }_c$, the policymaker imposes mandatory reuse targets ${\beta }_r$ on the OEM to enhance the remanufacturing level and resource recycling. The parameter ${\beta }_r$ signifies the minimum remanufacturing ratio of end-of-life products the OEM collects from the market, and it should remanufacture at least ${\beta }_r{q}_n$ products, i.e., $q_r\ge {\beta }_r{q}_n$. (3) No legislation. We also provide this scenario as a benchmark for comparison with the legislative situations.

While we separately solve the OEM’s problem under the three legislative scenarios, we present, here, only the problem formulation under take-back legislation with collection and reuse targets. One can obtain the OEM’s problems by setting ${\beta }_r$ to zero for the scenario of take-back legislation with collection targets and by setting both ${\beta }_c$ and ${\beta }_r$ to zero for the scenario of no legislation. We now formally state the problem the OEM faces. The OEM sells new and remanufactured products simultaneously in the monopolistic market regulated by take-back legislation. Facing collection and reuse targets, the OEM makes efforts to enhance the PED level and, thus, decreases manufacturing and remanufacturing costs and increases resource recycling. The OEM maximizes profits from selling new and remanufactured products, minus production and collection costs as well as investment costs in PED. Meanwhile, their remanufacturing activities are constrained by mandatory collection and reuse targets as well as market supply.

$$\begin{array}{ll}\underset{q_n,q_c,q_r\ge 0}{Max}\prod & =q_n(p_n-{\tilde{c}}_n)+q_r(p_r-{\tilde{c}}_r)-q_c{c}_c-k{e}^2/2\\ & =q_n(1-q_n-\alpha q_r-c_n(1-e{\theta }_1))+q_r(\alpha (1-q_n-q_r)-c_r(1-e{\theta }_2))-q_c{c}_c-k{e}^2/2\end{array}$$

$$\mathrm{s}.\mathrm{t}. {\beta }_c{q}_n\le q_c\le q_n$$

(1)

$${\beta }_r{q}_n\le q_r\le q_c$$

(2)

Constraint (1) ensures that the quantity of end-of-life products the OEM collects is more than the quantity of end-of-life products the collection target mandates but less than the quantity of new products it manufactures. Constraint (2) ensures that the quantity of remanufactured products is more than the quantity the reuse target mandates but does not exceed the quantity of end-of-life products the OEM collects from the market.

4. Problem Analysis

In this section, we first characterize the OEM’s optimal production and collection decisions in equilibrium under the three legislative scenarios. Then, we investigate the effect of cost parameters, PED activities, and legislative-level characteristics on the optimal strategies by conducting a sensitivity analysis. From now on, superscripts $NL$, $TC$, and $TD$, respectively, are used to refer to no legislation, take-back legislation with collection targets, and take-back legislation with collection and reuse targets. In this section, we regard the PED effort level $e$ as an exogenous variable to investigate the impact of the change in the PED effort level on the choice of the OEM’s optimal strategies, and we also calculate the optimal PED effort levels under different scenarios to better guide the firm’s operational practices in

Table A5. The OEM’s optimal PED levels.

Strategies	The PED Effort Level
$NL-N$	$\frac{c_n{\theta }_1(1-c_n)}{2k-c_n^2{\theta }_1^2}$
$NL-S$	$\frac{c_r{\theta }_2(c_c-\alpha c_n+c_r)-\alpha c_n{\theta }_1(1-\alpha +c_c-c_n+c_r)}{\alpha (c_n^2{\theta }_1^2-2k(1-\alpha )-2c_n{c}_r{\theta }_1{\theta }_2)+c_r^2{\theta }_2^2}$
$NL-A$	$\frac{(1+\alpha -c_c-c_n-c_r)(c_n{\theta }_1+c_r{\theta }_2)}{2k(1+3\alpha )-{(c_n{\theta }_1+c_r{\theta }_2)}^2}$
$TC-N$	$\frac{c_n{\theta }_1(1-c_n-c_c{\beta }_c)}{2k-c_n^2{\theta }_1^2}$
$TC-S$	$\frac{c_r{\theta }_2(c_r-\alpha (c_n+c_c{\beta }_c))-\alpha c_n{\theta }_1(1-\alpha +c_c{\beta }_c-c_n+c_r)}{\alpha (c_n^2{\theta }_1^2-2k(1-\alpha )-2c_n{c}_r{\theta }_1{\theta }_2)+c_r^2{\theta }_2^2}$
$TC-A$	$\frac{(1-c_n+{\beta }_c(\alpha -c_c-c_r))(c_n{\theta }_1+{\beta }_c{c}_r{\theta }_2)}{2k-c_n^2{\theta }_1^2-{\beta }_c(2c_n{c}_r{\theta }_1{\theta }_2+{\beta }_c{c}_r^2{\theta }_2^2-2k\alpha (2+{\beta }_c))}$
$TD-S$	$\frac{(1-c_n-c_c{\beta }_c+{\beta }_r(\alpha -c_r))(c_n{\theta }_1+{\beta }_r{c}_r{\theta }_2)}{2k-c_n^2{\theta }_1^2-{\beta }_r(2c_n{c}_r{\theta }_1{\theta }_2+{\beta }_r{c}_r^2{\theta }_2^2-2k\alpha (2+{\beta }_r))}$

of Appendix B.

4.1. No Legislation

We provide this scenario as a benchmark to identify the OEM’s remanufacturing strategies when it makes efforts to improve PED levels in the absence of legislation (recall that ${\beta }_c={\beta }_r=0$ in this scenario). We find that the OEM has three optimal strategies: in strategy $NL-N$, the OEM does not collect and remanufacture end-of-life products; in strategy $NL-S$, the OEM collects some end-of-life products and remanufactures all available end-of-life products; in strategy $NL-A$, the OEM collects all end-of-life products and remanufactures all available end-of-life products.

Proposition 1. 

Given the PED effort level$e$in the absence of take-back legislation, the OEM’s equilibrium solutions are as follows:

(i.) 

Strategy $NL-N$ ($e\ge {\eta }_1$). $q_n^{NLN}=\frac{1-c_n+e{c}_n{\theta }_1}{2}$, $q_c^{NLN}=q_r^{NLN}=0$;

(ii.) 

Strategy $NL-S$ (${\eta }_2<e<{\eta }_1$). $q_n^{NLS}=\frac{1-\alpha -c_n(1-e{\theta }_1)+c_r(1-e{\theta }_2)+c_c}{2(1-\alpha )}$, $q_c^{NLS}=q_r^{NLS}=\frac{\alpha c_n(1-e{\theta }_1)-c_r(1-e{\theta }_2)-c_c}{2\alpha (1-\alpha )}$;

(iii.) 

Strategy $NL-A$ ($e\le {\eta }_2$). $q_n^{NLA}=q_c^{NLA}=q_r^{NLA}=\frac{1+\alpha -c_n(1-e{\theta }_1)-c_r(1-e{\theta }_2)-c_c}{2(1+3\alpha )}$.

Proposition 1 shows that excessive PED effort levels hurt remanufacturing in the absence of legislation. Intuitively, the OEM will examine the trade-off between profits from remanufacturing and deterministic risks (including PED investment costs and cannibalization of new product sales). When the PED effort level is higher than the threshold ${\eta }_1$, the profit from remanufacturing cannot offset the negative implication of deterministic risks; therefore, the OEM forgoes the remanufacturing strategy and only sells new products in the market. On the contrary, remanufacturing is an attractive alternative for the OEM when the PED effort level is lower than ${\eta }_1$ because the profit from market segmentation outweighs the losses from deterministic risks.

The following table characterizes how the optimal production and collection decisions are shaped by the production cost ($c_n$ and $c_r$) and the PED activity (${\theta }_1$ and ${\theta }_2$) in the absence of legislation, where the signs $+$, $-$, and $\otimes$ denote an increase, a decrease, and no change in equilibrium, respectively. From

Table 3. Decision analysis in the absence of legislation.

Parameters	$q_n^{NLN}$	$q_n^{NLS}$	$q_n^{NLA}$	$q_r^{NLN}$	$q_r^{NLS}$	$q_r^{NLA}$	$q_c^{NLN}$	$q_c^{NLS}$	$q_c^{NLA}$
$c_n$	$-$	$-$	$-$	$\otimes$	$+$	$-$	$\otimes$	$+$	$-$
$c_r$	$\otimes$	$+$	$-$	$\otimes$	$-$	$-$	$\otimes$	$-$	$-$
${\theta }_1$	$+$	$+$	$+$	$\otimes$	$-$	$+$	$\otimes$	$-$	$+$
${\theta }_2$	$\otimes$	$-$	$+$	$\otimes$	$+$	$+$	$\otimes$	$+$	$+$

, we observe that the effects of model parameters on the optimal quantity of remanufactured products and collected cores are the same because the OEM collects and remanufactures cores only when remanufacturing is an attractive alternative (strategies $NL-S$ and $NL-A$). It is quite intuitive that the optimal quantity of new and remanufactured products is non-increasing in their own production cost and non-decreasing in their own marginal effect of PED. When the OEM’s optimal strategy is $NL-S$, new and remanufactured products are substitutes. Hence, the optimal quantity of new and remanufactured products is increasing in each other’s cost while decreasing in each other’s marginal effect of PED. When the OEM’s optimal strategy is $NL-A$, however, we observe that an increase in the remanufacturing (manufacturing) cost leads to a decrease in the optimal sales volume of the new (remanufactured) product, and an increase in the marginal effect of PED on the new (remanufactured) product’s production cost leads to an increase in the optimal quantity of remanufactured (new) products. In other words, the two products may exhibit the characteristics of complementary products, although they are substitutes [36].

4.2. Take-Back Legislation with Collection Targets

In this subsection, we assume that the policymaker imposes a mandatory collection target ${\beta }_c$ on the OEM and investigate the remanufacturing strategies when the OEM makes efforts to improve the PED level (recall that ${\beta }_r=0$ in this scenario). We find that the OEM has three optimal strategies under take-back legislation with collection targets: in strategy $TC-N$, the OEM achieves the mandatory collection target and does not remanufacture end-of-life products; in strategy $TC-S$, the OEM achieves the mandatory collection target and remanufactures some available end-of-life products; in strategy $TC-A$, the OEM achieves the mandatory collection target and remanufactures all available end-of-life products.

Proposition 2. 

Given the PED effort level$e$under take-back legislation with collection targets, the OEM’s equilibrium solutions are as follows:

(i.) 

Strategy $TC-N$ ($e\ge {\eta }_3$). $q_n^{TCN}=\frac{1-c_n(1-e{\theta }_1)-{\beta }_c{c}_c}{2}$, $q_c^{TCN}={\beta }_c{q}_n^{TCN}$, $q_r^{TCN}=0$;

(ii.) 

Strategy $TC-S$ ($\max \left\{{\eta }_4,{\eta }_5\right\}<e<{\eta }_3$). $q_n^{TCS}=\frac{1-\alpha -c_n(1-e{\theta }_1)+c_r(1-e{\theta }_2)+{\beta }_c{c}_c}{2(1-\alpha )}$, $q_c^{TCS}={\beta }_c{q}_n^{TCS}$, $q_r^{TCS}=\frac{\alpha c_n(1-e{\theta }_1)-c_r(1-e{\theta }_2)+\alpha {\beta }_c{c}_c}{2\alpha (1-\alpha )}$;

(iii.) 

Strategy $TC-A$ ($e\le \min \left\{{\eta }_4,{\eta }_6\right\}$). $q_n^{TCA}=\frac{1-c_n(1-e{\theta }_1)+{\beta }_c(\alpha -c_c-c_r(1-e{\theta }_2))}{2(1+2\alpha {\beta }_c+\alpha {\beta }_c^2)}$, $q_c^{TCA}=q_r^{TCA}={\beta }_c{q}_n^{TCA}$.

As with Proposition 1, Proposition 2 also shows that high PED effort levels reduce the OEM’s enthusiasm to adopt the remanufacturing strategy under take-back legislation with collection targets. In this scenario, the OEM always fulfills the mandatory collection target no matter whether the values of $e$ are high or low, resulting in a new deterministic risk, called the additional collection cost, compared to the no legislation scenario (strategies $TC-N$ and $TC-S$). When the PED effort level is high (i.e., $e\ge {\eta }_3$), the profit from remanufacturing is insufficient to overcome the ill effect of deterministic risks (including the investment costs of PED, cannibalization of new product sales, and the additional collection costs); therefore, the OEM collects end-of-life products only to fulfill the mandatory target and does not remanufacture. When the PED effort level is low (i.e., $e<{\eta }_3$), the cost savings from remanufacturing exceed the losses from deterministic risks; therefore, remanufacturing is a profitable strategy for the OEM.

The primary goal of take-back legislation is to divert as much e-waste as possible from landfills. Hence, in our paper, failure of the OEM to remanufacture leads to the take-back legislation being ineffective. The following corollary illustrates the effective condition of take-back legislation with collection targets.

Corollary 1. 

Under take-back legislation with collection targets,$\exists {\tilde{\theta }}_1=(\alpha (c_n+{\beta }_c{c}_c)-c_r(1-e{\theta }_2))/e\alpha c_n$and${\tilde{\theta }}_2=(c_r-\alpha {\beta }_c{c}_c-\alpha c_n(1-e{\theta }_1))/e{c}_r$, the legislation is effective if${\theta }_1\ge {\tilde{\theta }}_1$or${\theta }_2\le {\tilde{\theta }}_2$.

Corollary 1 shows that marginal effects of PED on the production cost have significant impacts on the OEM’s willingness to remanufacture under take-back legislation with collection targets. Specifically, when ${\theta }_1$ is high enough or ${\theta }_2$ is low enough, the OEM will adopt the remanufacturing strategy. It is quite intuitive that the increase in ${\theta }_1$ decreases the production cost of new products, and the decrease in ${\theta }_2$ increases the cost of remanufactured products, surprisingly, decreasing manufacturing costs or increasing remanufacturing costs and, in turn, enhancing the OEM’s willingness to remanufacture. In other words, the new product must have relative profitability to ensure the effectiveness of the legislation.

Table 4. Decision analysis under take-back legislation with collection targets (the symbol $\ast$ means an increase or a decrease under the certain condition).

Parameters	$$q_n^{TCN}$$	$$q_n^{TCS}$$	$$q_n^{TCA}$$	$$q_r^{TCN}$$	$$q_r^{TCS}$$	$$q_r^{TCA}$$	$$q_c^{TCN}$$	$$q_c^{TCS}$$	$$q_c^{TCA}$$
$c_n$	$-$	$-$	$-$	$\otimes$	$+$	$-$	$-$	$-$	$-$
$c_r$	$\otimes$	$+$	$-$	$\otimes$	$-$	$-$	$\otimes$	$+$	$-$
${\theta }_1$	$+$	$+$	$+$	$\otimes$	$-$	$+$	$+$	$+$	$+$
${\theta }_2$	$\otimes$	$-$	$+$	$\otimes$	$+$	$+$	$\otimes$	$-$	$+$
${\beta }_c$	$-$	$-$	${-}^{\ast }$	$\otimes$	$+$	${-}^{\ast }$	${+}^{\ast }$	${+}^{\ast }$	${+}^{\ast }$

characterizes how cost parameters ($c_n$ and $c_r$), the PED activity (${\theta }_1$ and ${\theta }_2$), and the mandatory collection target (${\beta }_c$) shape the optimal production and collection decisions under take-back legislation with collection targets. Consistent with Table 3, the effects of cost parameters and the PED activity on the optimal production decisions are kept steady under take-back legislation with collection targets. Differently, we observe that the effects of model parameters on the optimal quantity of new and collected products are the same in this scenario due to the constraint of collection targets ($q_c\ge {\beta }_c{q}_n$). Furthermore, we also observe that the OEM reduces the quantity of new products to fulfill relatively simple collection tasks under stringent collection targets. Due to the substitution effect, the quantity of remanufactured products increases with stringent collection targets in strategy $TC-S$. However, the result is reversed when the new and remanufactured products exhibit the characteristics of complementarity in strategy $TC-A$.

4.3. Take-Back Legislation with Collection and Reuse Targets

Next, we take both collection and reuse targets into account and explore the OEM’s production and collection decisions when it makes efforts to improve the PED level. We find that the OEM only has one optimal strategy in this scenario: in strategy $TD-S$, the OEM achieves mandatory collection and reuse targets.

Proposition 3. 

Given the PED effort level$e$under take-back legislation with collection and reuse targets, the OEM’s equilibrium solution is as follows:

$$Strategy TD-S (e\le {\eta }_7). q_n^{TDS}=\frac{1-c_n(1-e{\theta }_1)+{\beta }_r(\alpha -c_r(1-e{\theta }_2))-{\beta }_c{c}_c}{2(1+2\alpha {\beta }_r+\alpha {\beta }_r^2)},q_c^{TDS}={\beta }_c{q}_n^{TDS},q_r^{TDS}={\beta }_r{q}_n^{TDS}.$$

Proposition 3 shows that the OEM’s remanufacturing strategies are significantly restricted when the policymaker implements two mandatory targets simultaneously. In other words, only when the PED effort level $e$ does not exceed the threshold ${\eta }_7$, the OEM will produce new and remanufactured products simultaneously. Besides the deterministic risks in collection targets, the OEM may pay additional remanufacturing costs when facing dual targets. Under take-back legislation with collection and reuse targets, the profit from remanufacturing cannot overcome the ill effect of the deterministic risks even if the PED effort level is low enough; therefore, the OEM just collects and remanufactures mandated end-of-life products to fulfill the two targets.

The following corollary identifies the effective condition of take-back legislation with collection and reuse targets.

Corollary 2. 

Under take-back legislation with collection and reuse targets,$\exists {\overline{\theta }}_1=(-\alpha {\beta }_r(1-\alpha )+(\alpha c_n+\alpha {\beta }_c{c}_c)(1+{\beta }_r)-c_r(1+\alpha {\beta }_r)(1-e{\theta }_2))/e\alpha c_n(1+{\beta }_r)$and${\overline{\theta }}_2=(c_r+\alpha ({\beta }_r(1-\alpha +c_r)-{\beta }_c{c}_c(1+{\beta }_r)-c_n(1+{\beta }_r)(1-e{\theta }_1)))/e{c}_r(1+\alpha {\beta }_r)$, the legislation is effective if${\theta }_1\ge {\overline{\theta }}_1$or${\theta }_2\le {\overline{\theta }}_2$.

Consistent with Corollary 1, Corollary 2 shows that the dual targets are effective when the marginal effect of PED on the new product’s production cost is high enough or the marginal effect of PED on the remanufactured product’s production cost is low enough. Therefore, we conclude that take-back legislation is valid only if the new product is profitable relative to the remanufactured product, no matter whether the legislation includes collection targets or dual targets.

Table 5. Decision analysis under take-back legislation with collection and reuse targets (the symbol $\ast$ means an increase or a decrease under the certain condition).

Parameters	$$q_n^{TDS}$$	$$q_r^{TDS}$$	$$q_c^{TDS}$$
$c_n$	$-$	$-$	$-$
$c_r$	$-$	$-$	$-$
${\theta }_1$	$+$	$+$	$+$
${\theta }_2$	$+$	$+$	$+$
${\beta }_c$	$-$	$-$	${-}^{\ast }$
${\beta }_r$	${+}^{\ast }$	${+}^{\ast }$	${+}^{\ast }$

describes how cost parameters ($c_n$ and $c_r$), the PED activity (${\theta }_1$ and ${\theta }_2$), and the mandatory targets (${\beta }_c$ and ${\beta }_r$) shape the optimal production and collection decisions under take-back legislation with collection and reuse targets. Interestingly, the product market only has complementary effects due to the two mandatory targets. Overall, the effects of model parameters (except ${\beta }_r$) on the optimal decisions are similar to those in Table 4 when new and remanufactured products exhibit the characteristics of complementarity. Moreover, the quantity of remanufactured products increases with stringent reuse targets, and then, the quantities of new and collected products increase due to complementary effects.

5. Numerical Study

From the policymaker’s perspective, the OEM’s performance under take-back legislation is measured through a comprehensive set of economic and environmental criteria. Next, we investigate economic and environmental outcomes when the OEM incorporates the PED strategy into its remanufacturing processes in the context of take-back legislation.

We select cell phones covered by the most recent take-back legislation as a representative product category. We take Apple Inc’s iPhone, one of the most popular cell phones worldwide, as an example to illustrate the source of the data set used in this paper. A data report from STATISTA shows that the manufacturing costs of the iPhone 8 (64 GB), iPhone 8 Plus (64 GB), and iPhone X (64 GB) are USD 254.87, USD 295.44, and USD 370.25, respectively (https://www.statista.com/chart/5952/iphone-manufacturing-costs/ (accessed on 11 June 2022)). Atasu et al. [22] stated that the ratio of the manufacturing cost to the potential market size $Q$ is between 0.1 and 0.5, and we choose $Q=1000$. As $Q$ is normalized to 1 in this article, we normalize all cost parameter values accordingly. Hence, the manufacturing costs of the three iPhone models are 0.255, 0.295, and 0.370 after normalization. According to Savaskan et al. [37] and Guide Jr et al. [38], the remanufacturing cost accounts for 35–60% of the manufacturing cost. Based on the range of manufacturing costs, we find that the remanufacturing cost varies between 0.0875 and 0.222. Therefore, in this paper, the remanufacturing cost equals 0.1. Neira et al. [39] suggested that the collection cost of cell phones is in the range of USD 0.1 to USD 10, and we choose $c_c=$ USD 5. After normalization, $c_c=0.005$.

For the consumer valuation discount $\alpha$, the extant literature suggests that $\alpha$ varies from 0.45 to 0.85 [40,41], and these values have been used to carry out empirical and case studies [28,42]. In fact, Apple has been selling remanufactured iPhones (such as the iPhone SE series) through its online and offline channels, and its remanufacturing is a relatively mature industry. On Apple’s homepage, the sale prices of remanufactured iPhone XS MAX 64 GB-Space Gray (Unlocked) and remanufactured iPhone 11 Pro 64 GB-Silver (Unlocked) are USD 719 and USD 759, while the sale prices of new ones are USD 999 and USD 899 (https://www.apple.com/shop/refurbished (accessed on 6 June 2022)). Hence, the values of $\alpha$ in these two iPhone models are $719/999\approx 0.72$ and $759/899\approx 0.84$, respectively. Hence, we approximate $\alpha$ to be in the range between 0.72 and 0.84, and we choose $\alpha =0.8$ in this article.

For the marginal effect of PED activities on the production cost, we assume that ${\theta }_2>{\theta }_1$. Generally speaking, products with reusable and recyclable materials will significantly reduce the remanufacturing cost because producers only need to clean and reprocess used products, while the cost of manufacturing may increase (e.g., introducing advanced technology and purchasing equipment). To account for this, we assume that ${\theta }_2=0.9$ and ${\theta }_1=0.9$. Since we do not consider the implications of the industry scale, the scale parameter $k$ of the investment function equals 1. At present, the European Union sets the collection target as 65%, and this type of target is always between 50% and 60% in Japan. Furthermore, some environmental organizations such as RREUSE and the European Environmental Bureau strongly advocate an additional 5% reuse target. Therefore, we choose ${\beta }_c=0.6$ and ${\beta }_r=0.005$. Finally, we select $e\in \left\{0.3,0.6,0.9\right\}$ to represent low, medium, and high effort levels of PED.

5.1. The OEM Profit and Consumer Surplus

In the economic outcome, we consider the OEM profit and consumer surplus [5,20,27]. Bringing the equilibrium solutions back into the OEM’s optimization problem, we obtain its profits under different optimal strategies. Consumer surplus $S$ is the utility of consumers who buy new products, plus the utility of those who buy remanufactured products. The expression of $S$ can be written as follows:

$$S={\displaystyle \underset{\frac{p_n-p_r}{1-\alpha }}{\overset{1}{\int }}(v-p_n)dv+}{\displaystyle \underset{\frac{p_r}{\alpha }}{\overset{\frac{p_n-p_r}{1-\alpha }}{\int }}(\alpha v-p_r)dv}=\frac{q_n^2+\alpha q_r^2+2\alpha q_n{q}_r}{2}$$

(3)

The economic outcomes when the OEM makes efforts to improve the PED level under take-back legislation are shown in Figure 1. Figure 1 shows that the increases in the PED effort level are not beneficial for the economy under the two legislative structures. It is quite intuitive that the implementation of PED reduces the production costs of new and remanufactured products and then expands the product demand. Thus, consumer surplus increases with the enhancement of the PED effort level. However, the OEM profit is decreasing in the PED effort level because the profit from remanufacturing cannot overcome the ill effect of deterministic risks (see Propositions 2 and 3). Although the consumer surplus rises, it is not enough to offset the decrease in the OEM’s profits, and thus, the economic performance declines.

5.2. Environment

Next, we measure the environmental impact. The life cycle assessment (LCA) methodology is used to examine the total environmental impact of end-of-life products in the remanufacturing and take-back literature [28,43]. These studies did not, however, capture the impact of the PED effort level on the environment under take-back legislation. In this paper, we define that the total environmental impact relies on the quantity of new and remanufactured products, PED effort levels, and per-unit environmental impacts of manufacturing products. ${\chi }_n$ denotes the per-unit environmental impacts of new products, and ${\chi }_r$ denotes the per-unit environmental impacts of remanufactured products. Generally speaking, using end-of-life products to remanufacture a product rather than producing it from new parts and virgin materials results in approximately a 50–70% reduction in environmental impacts [34]. To account for this, we assume that ${\chi }_n=0.3$ and ${\chi }_r=0.15$. We use the marginal effect to capture the reduction degree of environmental impacts, where ${\phi }_1$ denotes the marginal effect of PED on new products’ environmental impact, and ${\phi }_2$ denotes the marginal effect of PED on remanufactured products’ environmental impact. Furthermore, we assume that ${\phi }_1>{\phi }_2$, ${\phi }_1=0.2$, and ${\phi }_2=0.12$. Compared to remanufactured products, manufacturing new products requires more complex technologies and processes, which means more environmental impacts during the production stage. However, when the OEM implements PED activities, remanufacturing is a relatively clean production process, and the role of the PED effort level is limited.

Following the common approach in the literature [43,44,45], we define the total environmental impact as

$$E={\tilde{\chi }}_n{q}_n+{\tilde{\chi }}_r{q}_r={\chi }_n(1-{\phi }_{1}e)q_n+{\chi }_r(1-{\phi }_{2}e)q_r$$

(4)

In take-back legislation, the total environmental impacts under various effort levels of PED are shown in Figure 2. From Figure 2a, we observe that the increase in the PED effort level is not always beneficial to the environment, depending on the cost of manufacturing new products. When the manufacturing cost is low (i.e., $c_n\le 0.213496$), the environment can benefit from a high effort level of PED. Moreover, when the cost of manufacturing new products is high (i.e., $c_n\ge 0.273593$), a low effort level of PED is beneficial to the environment. The reason is that high effort levels of PED just slightly reduce the production costs when the costs of manufacturing new and remanufactured products are low, consequently resulting in small increased sales of total products. However, when the costs of manufacturing new and remanufactured products are high, high PED effort levels will be detrimental to the environment and aggravate the environment due to the fast increased sales of new and remanufactured products (environmental externality). The result in Figure 2b is consistent with the case when $c_n\le 0.213496$ in Figure 2a.

6. Conclusions

Facing stringent take-back legislation, many OEMs have increasingly begun to incorporate the PED strategy into their remanufacturing processes. Most of the previous literature neglected the interactions between remanufacturing and PED practices in e-waste management, especially in the context of take-back legislation. To bridge this gap, we employ a stylized game-theoretic model to capture the major dynamics between remanufacturing and PED practices under three legislative structures, i.e., no legislation, take-back legislation with collection targets, and take-back legislation with collection and reuse targets. We first characterize the OEM’s optimal production and collection decisions by using KKT conditions. Then, we investigate how production costs, PED practices, and mandatory targets shape the optimal strategies. Finally, through a numerical study, we examine the economic and environmental outcomes under various effort levels of PED.

Our results demonstrate that different PED effort levels and mandatory targets lead to different remanufacturing strategies for the OEM. Overall, high PED effort levels do not imply more remanufacturing, while medium PED effort levels are conducive to the promotion of the remanufacturing industry. The stringent collection targets indeed reduce the quantity of new products, resulting in a lower remanufacturing performance. Our results also show that the stringent reuse targets may indeed be beneficial for remanufacturing. Through a numerical study, we observe that more efforts in the PED level cause a low performance in the economy, but this is not the case for the environmental impact. Specifically, if the production cost is relatively low, high PED effort levels are beneficial to the environment under take-back legislation; if the production cost is relatively high, low PED effort levels benefit the environment under take-back legislation with collection targets.

Furthermore, we put forward the following managerial implications. (1) PED activity increases the financial burden on electronic manufacturers, and the government needs to take measures, such as subsidies for producers with dismantling qualifications and/or removal of technical barriers, to promote the sustainable development of the remanufacturing industry. (2) Relatively high PED effort levels may promote remanufacturing under take-back legislation, but some potential unintended consequences such as cannibalization of new product sales and unreasonable cost structures should be focused on. (3) Electronic manufacturers should adopt different PED effort levels based on their goals. If they pursue economic performance, a low PED effort level is the best choice. If they are environmentalist, a high PED effort level should be set when the production cost is relatively low under take-back legislation with collection targets or when the market is regulated by dual targets. On the contrary, a low PED effort level should be adopted when the production cost is relatively high under take-back legislation with collection targets.

Finally, our research has some limitations. We did not consider the uncertainty in the quality of cores, which determines the OEM’s disposal methods and further influences the consumer demand for remanufactured products. In future research, we will incorporate PED and quality uncertainty into the model and examine the producer’s operating strategies. Although the type of legislation we model seems to be the predominant form worldwide, there exists other environmental legislation such as carbon emission capacity, carbon tax, and carbon cap-and-trade. Furthermore, we will explore the impact of PED on remanufacturing under different legislative combinations.