Does Product Ecodesign Promote Remanufacturing: Application of a Stylized Gametheoretic Model
Abstract
:1. Introduction
 (1)
 What are the OEM’s manufacturing and remanufacturing decisions when it implements the PED strategy to maximize its profits in the context of takeback 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 takeback legislation? If yes, under what conditions?
 (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 takeback legislation.
 (2)
 We consider different levels of takeback legislation (i.e., no legislation, takeback legislation with collection targets, and takeback 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 takeback regulations, yielding new insights in terms of how the policymaker should choose the takeback legislation to achieve economic and environmental benefits.
2. Literature Review
2.1. Product EcoDesign in ClosedLoop Supply Chains
2.2. Operations Management under Takeback Legislation
2.3. Research Gaps
Sources  TakeBack Legislation  PED  Product Quantity Decisions  Supply Constraint  Performance  

Collection  Reuse  New  Collected  Remanufactured  Economy  Environment  
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This paper  √  √  √  √  √  √  √  √  √ 
3. Problem Description and Notations
4. Problem Analysis
4.1. No Legislation
 (i.)
 Strategy $NLN$ ($e\ge {\eta}_{1}$). ${q}_{n}^{NLN}=\frac{1{c}_{n}+e{c}_{n}{\theta}_{1}}{2}$, ${q}_{c}^{NLN}={q}_{r}^{NLN}=0$;
 (ii.)
 Strategy $NLS$ (${\eta}_{2}<e<{\eta}_{1}$). ${q}_{n}^{NLS}=\frac{1\alpha {c}_{n}(1e{\theta}_{1})+{c}_{r}(1e{\theta}_{2})+{c}_{c}}{2(1\alpha )}$, ${q}_{c}^{NLS}={q}_{r}^{NLS}=\frac{\alpha {c}_{n}(1e{\theta}_{1}){c}_{r}(1e{\theta}_{2}){c}_{c}}{2\alpha (1\alpha )}$;
 (iii.)
 Strategy $NLA$ ($e\le {\eta}_{2}$). ${q}_{n}^{NLA}={q}_{c}^{NLA}={q}_{r}^{NLA}=\frac{1+\alpha {c}_{n}(1e{\theta}_{1}){c}_{r}(1e{\theta}_{2}){c}_{c}}{2(1+3\alpha )}$.
4.2. TakeBack Legislation with Collection Targets
 (i.)
 Strategy $TCN$ ($e\ge {\eta}_{3}$). ${q}_{n}^{TCN}=\frac{1{c}_{n}(1e{\theta}_{1}){\beta}_{c}{c}_{c}}{2}$, ${q}_{c}^{TCN}={\beta}_{c}{q}_{n}^{TCN}$, ${q}_{r}^{TCN}=0$;
 (ii.)
 Strategy $TCS$ ($\mathrm{max}\left\{{\eta}_{4},{\eta}_{5}\right\}<e<{\eta}_{3}$). ${q}_{n}^{TCS}=\frac{1\alpha {c}_{n}(1e{\theta}_{1})+{c}_{r}(1e{\theta}_{2})+{\beta}_{c}{c}_{c}}{2(1\alpha )}$, ${q}_{c}^{TCS}={\beta}_{c}{q}_{n}^{TCS}$, ${q}_{r}^{TCS}=\frac{\alpha {c}_{n}(1e{\theta}_{1}){c}_{r}(1e{\theta}_{2})+\alpha {\beta}_{c}{c}_{c}}{2\alpha (1\alpha )}$;
 (iii.)
 Strategy $TCA$ ($e\le \mathrm{min}\left\{{\eta}_{4},{\eta}_{6}\right\}$). ${q}_{n}^{TCA}=\frac{1{c}_{n}(1e{\theta}_{1})+{\beta}_{c}(\alpha {c}_{c}{c}_{r}(1e{\theta}_{2}))}{2(1+2\alpha {\beta}_{c}+\alpha {\beta}_{c}^{2})}$, ${q}_{c}^{TCA}={q}_{r}^{TCA}={\beta}_{c}{q}_{n}^{TCA}$.
4.3. TakeBack Legislation with Collection and Reuse Targets
5. Numerical Study
5.1. The OEM Profit and Consumer Surplus
5.2. Environment
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
Strategy  ${\lambda}_{10}$  ${\lambda}_{11}$  ${\lambda}_{12}$ 
$NLN$  $\ge 0$  $\ge 0$  $=0$ 
$NLS$  $=0$  $\ge 0$  $=0$ 
$NLA$  $=0$  $\ge 0$  $\ge 0$ 
$NLT1$  $=0$  $=0$  $=0$ 
$NLT2$  $\ge 0$  $=0$  $=0$ 
$NLZ1$  $=0$  $=0$  $\ge 0$ 
$NLZ2$  $\ge 0$  $=0$  $\ge 0$ 
$NLM$  $\ge 0$  $\ge 0$  $\ge 0$ 
Strategy  ${\lambda}_{20}$  ${\lambda}_{21}$  ${\lambda}_{22}$  ${\lambda}_{23}$  Strategy  ${\lambda}_{20}$  ${\lambda}_{21}$  ${\lambda}_{22}$  ${\lambda}_{23}$ 
$TCN$  $\ge 0$  $=0$  $=0$  $\ge 0$  $TCM2$  $=0$  $\ge 0$  $\ge 0$  $\ge 0$ 
$TCS$  $=0$  $=0$  $=0$  $\ge 0$  $TCM3$  $\ge 0$  $=0$  $\ge 0$  $\ge 0$ 
$TCA$  $=0$  $\ge 0$  $=0$  $\ge 0$  $TCM4$  $\ge 0$  $\ge 0$  $=0$  $\ge 0$ 
$TCT1$  $=0$  $=0$  $=0$  $=0$  $TCM5$  $\ge 0$  $\ge 0$  $\ge 0$  $=0$ 
$TCT2$  $\ge 0$  $=0$  $=0$  $=0$  $TCM6$  $\ge 0$  $\ge 0$  $\ge 0$  $\ge 0$ 
$TCZ1$  $=0$  $=0$  $\ge 0$  $=0$  $TCNLN$  $\ge 0$  $\ge 0$  $=0$  $=0$ 
$TCZ2$  $\ge 0$  $=0$  $\ge 0$  $=0$  $TCNLS$  $=0$  $\ge 0$  $=0$  $=0$ 
$TCM1$  $=0$  $=0$  $\ge 0$  $\ge 0$  $TCNLA$  $=0$  $\ge 0$  $\ge 0$  $=0$ 
Strategy  ${\lambda}_{30}$  ${\lambda}_{31}$  ${\lambda}_{32}$  ${\lambda}_{33}$  ${\lambda}_{34}$  Strategy  ${\lambda}_{30}$  ${\lambda}_{31}$  ${\lambda}_{32}$  ${\lambda}_{33}$  ${\lambda}_{34}$ 
$TDS$  $=0$  $=0$  $=0$  $\ge 0$  $\ge 0$  $TDM4$  $=0$  $\ge 0$  $\ge 0$  $=0$  $\ge 0$ 
$TDT1$  $=0$  $=0$  $=0$  $=0$  $=0$  $TDM5$  $=0$  $\ge 0$  $\ge 0$  $\ge 0$  $=0$ 
$TDT2$  $=0$  $=0$  $=0$  $=0$  $\ge 0$  $TDM6$  $=0$  $\ge 0$  $\ge 0$  $\ge 0$  $\ge 0$ 
$TDZ1$  $=0$  $=0$  $\ge 0$  $=0$  $=0$  $TDNLS$  $=0$  $\ge 0$  $=0$  $=0$  $=0$ 
$TDZ2$  $=0$  $=0$  $\ge 0$  $=0$  $\ge 0$  $TDNLA$  $=0$  $\ge 0$  $\ge 0$  $=0$  $=0$ 
$TDM1$  $=0$  $=0$  $\ge 0$  $\ge 0$  $=0$  $TDTCS$  $=0$  $=0$  $=0$  $\ge 0$  $=0$ 
$TDM2$  $=0$  $=0$  $\ge 0$  $\ge 0$  $\ge 0$  $TDTCA$  $=0$  $\ge 0$  $=0$  $\ge 0$  $=0$ 
$TDM3$  $=0$  $\ge 0$  $=0$  $\ge 0$  $\ge 0$  $TDA$  $=0$  $\ge 0$  $=0$  $=0$  $\ge 0$ 
Appendix B
Bound  Expression 

${\eta}_{1}$  $\frac{\alpha {c}_{n}{c}_{r}{c}_{c}}{\alpha {\theta}_{1}{c}_{n}{\theta}_{2}{c}_{r}}$ 
${\eta}_{2}$  $\frac{\alpha (\alpha +2{c}_{n}1)({c}_{r}+{c}_{c})(1+\alpha )}{2\alpha {\theta}_{1}{c}_{n}{\theta}_{2}{c}_{r}(1+\alpha )}$ 
${\eta}_{3}$  $\frac{\alpha {c}_{n}{c}_{r}+\alpha {\beta}_{c}{c}_{c}}{\alpha {\theta}_{1}{c}_{n}{\theta}_{2}{c}_{r}}$ 
${\eta}_{4}$  $\frac{\alpha {c}_{n}(1+{\beta}_{c}){c}_{r}(1+\alpha {\beta}_{c})\alpha {\beta}_{c}(1\alpha {c}_{c}(1+{\beta}_{c}))}{\alpha {\theta}_{1}{c}_{n}(1+{\beta}_{c}){\theta}_{2}{c}_{r}(1+\alpha {\beta}_{c})}$ 
${\eta}_{5}$  $\frac{\alpha +{c}_{n}+{\beta}_{c}{c}_{c}1{c}_{r}}{{c}_{n}{\theta}_{1}{c}_{r}{\theta}_{2}}$ 
${\eta}_{6}$  $\frac{\alpha {c}_{n}+{c}_{r}+{c}_{c}+\alpha {\beta}_{c}(1\alpha +{c}_{c}{c}_{n}+{c}_{r})}{{\theta}_{2}{c}_{r}(1+\alpha {\beta}_{c})\alpha {\theta}_{1}{c}_{n}(1+{\beta}_{c})}$ 
${\eta}_{7}$  $\frac{\alpha ({c}_{n}+{\beta}_{c}{c}_{c}{\beta}_{r}(1\alpha {c}_{n}+{c}_{r}{\beta}_{c}{c}_{c})){c}_{r}}{\alpha {\theta}_{1}{c}_{n}(1+{\beta}_{r}){\theta}_{2}{c}_{r}(1+\alpha {\beta}_{r})}$ 
Strategies  The PED Effort Level 

$NLN$  $\frac{{c}_{n}{\theta}_{1}(1{c}_{n})}{2k{c}_{n}^{2}{\theta}_{1}^{2}}$ 
$NLS$  $\frac{{c}_{r}{\theta}_{2}({c}_{c}\alpha {c}_{n}+{c}_{r})\alpha {c}_{n}{\theta}_{1}(1\alpha +{c}_{c}{c}_{n}+{c}_{r})}{\alpha ({c}_{n}^{2}{\theta}_{1}^{2}2k(1\alpha )2{c}_{n}{c}_{r}{\theta}_{1}{\theta}_{2})+{c}_{r}^{2}{\theta}_{2}^{2}}$ 
$NLA$  $\frac{(1+\alpha {c}_{c}{c}_{n}{c}_{r})({c}_{n}{\theta}_{1}+{c}_{r}{\theta}_{2})}{2k(1+3\alpha ){({c}_{n}{\theta}_{1}+{c}_{r}{\theta}_{2})}^{2}}$ 
$TCN$  $\frac{{c}_{n}{\theta}_{1}(1{c}_{n}{c}_{c}{\beta}_{c})}{2k{c}_{n}^{2}{\theta}_{1}^{2}}$ 
$TCS$  $\frac{{c}_{r}{\theta}_{2}({c}_{r}\alpha ({c}_{n}+{c}_{c}{\beta}_{c}))\alpha {c}_{n}{\theta}_{1}(1\alpha +{c}_{c}{\beta}_{c}{c}_{n}+{c}_{r})}{\alpha ({c}_{n}^{2}{\theta}_{1}^{2}2k(1\alpha )2{c}_{n}{c}_{r}{\theta}_{1}{\theta}_{2})+{c}_{r}^{2}{\theta}_{2}^{2}}$ 
$TCA$  $\frac{(1{c}_{n}+{\beta}_{c}(\alpha {c}_{c}{c}_{r}))({c}_{n}{\theta}_{1}+{\beta}_{c}{c}_{r}{\theta}_{2})}{2k{c}_{n}^{2}{\theta}_{1}^{2}{\beta}_{c}(2{c}_{n}{c}_{r}{\theta}_{1}{\theta}_{2}+{\beta}_{c}{c}_{r}^{2}{\theta}_{2}^{2}2k\alpha (2+{\beta}_{c}))}$ 
$TDS$  $\frac{(1{c}_{n}{c}_{c}{\beta}_{c}+{\beta}_{r}(\alpha {c}_{r}))({c}_{n}{\theta}_{1}+{\beta}_{r}{c}_{r}{\theta}_{2})}{2k{c}_{n}^{2}{\theta}_{1}^{2}{\beta}_{r}(2{c}_{n}{c}_{r}{\theta}_{1}{\theta}_{2}+{\beta}_{r}{c}_{r}^{2}{\theta}_{2}^{2}2k\alpha (2+{\beta}_{r}))}$ 
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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 
${\chi}_{n}$  Perunit environmental impacts of the new product without PED 
${\chi}_{r}$  Perunit environmental impacts of the remanufactured product without PED 
${\tilde{\chi}}_{n}$  Perunit environmental impacts of the new product with PED 
${\tilde{\chi}}_{r}$  Perunit 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 
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 $  $$  $+$  $\otimes $  $+$  $+$  $\otimes $  $+$  $+$ 
Parameters 
$${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 $  $+$  ${}^{\ast}$  ${+}^{\ast}$  ${+}^{\ast}$  ${+}^{\ast}$ 
Parameters 
$${q}_{n}^{TDS}$$

$${q}_{r}^{TDS}$$

$${q}_{c}^{TDS}$$

${c}_{n}$  $$  $$  $$ 
${c}_{r}$  $$  $$  $$ 
${\theta}_{1}$  $+$  $+$  $+$ 
${\theta}_{2}$  $+$  $+$  $+$ 
${\beta}_{c}$  $$  $$  ${}^{\ast}$ 
${\beta}_{r}$  ${+}^{\ast}$  ${+}^{\ast}$  ${+}^{\ast}$ 
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Wang, Q.; Wang, X. Does Product Ecodesign Promote Remanufacturing: Application of a Stylized Gametheoretic Model. Sustainability 2023, 15, 691. https://doi.org/10.3390/su15010691
Wang Q, Wang X. Does Product Ecodesign Promote Remanufacturing: Application of a Stylized Gametheoretic Model. Sustainability. 2023; 15(1):691. https://doi.org/10.3390/su15010691
Chicago/Turabian StyleWang, Qixiang, and Xiaobo Wang. 2023. "Does Product Ecodesign Promote Remanufacturing: Application of a Stylized Gametheoretic Model" Sustainability 15, no. 1: 691. https://doi.org/10.3390/su15010691