Building a demand-oriented optimal model for the recycling of used electronic products

Abstract

The recycling and remanufacturing of used electronic products are the great significance to environmental governance and resource management. From the demand perspective of remanufactured products, this paper proposes a demand-oriented recycling model of used electronic products based on the reverse supply chain and cooperative game theory. Taking cost–benefit analysis as the basis of the benefits model of the participants in the electronic waste product recycling system, a static multi-stage game model and a dynamic cooperative game model are established, there is an optimal strategy at each stage which may not be unique, depending on the decision model constructed. In the static multi-stage recycling mode, the strategic decisions at all stages are all based on the same demand for remanufactured products, the strategy decision at each stage of the recycling mode of waste electronic products is based on the multi-stage demand prediction of remanufactured products. The cost optimization of each link in the static multi-stage is to realize the optimal strategy combination of participants in each link. The study concluded that by setting demand as the main goal, both recycling and remanufacturing companies can improve their own benefits by realizing an optimal cost combination.

Appendix: Parameters setup.

Notation	Definitions
$C\left[ {{\text{Sale}}} \right]$	Total cost of sales of the remanufactured products
$C\left[ {{\text{Rem}}} \right]$	Total production cost of the remanufactured product
$C\left[ {{\text{Rec}}} \right]$	Total cost for recycling the waste electronics
$E\left[ {{\text{Rem}}\& {\text{Rec}}} \right]$	Cost of the recovery enterprise and remanufacturing enterprise in the dynamic situation
$E\left[ {{\text{Sale}}} \right]$	Expected sales benefits of the remanufactured products
$E\left[ {Cons} \right]$	Expected benefits for the consumer groups of the remanufactured products
$E\left[ {hol} \right]$	Expected benefits for the waste electronic product holders
$E\left[ {Rem\& Rec} \right]$	Expected benefits for the recycling and remanufacturing companies
$E\left[ {Sale\& Hol} \right]$	Expected benefits for the consumer groups of the remanufactured products and holders of waste electronic products
${\upalpha }_{i} \left( {i = 1,2,3} \right)$	Proportion of products sold through the direct sales channel during the remanufacturing sales process in constant market demand
$\beta_{i} \left( {i = 1,2} \right)$	Cost for a remanufactured product of different quality levels produced by remanufacturer when the remanufactured product demand is constant
${\upgamma }$	Proportion of the direct recycling channels adopted by the recycling companies when the demand for the waste electronic products is constant
$1 - {\upgamma }$	Proportion of the commissioned recycling channels adopted by the recycling companies
$C_{0} \left( {\sum Q_{i} } \right)$	Fixed costs for selling all the remanufactured products, including advertising and leasing
$C_{1} \left( {\sum Q_{i} } \right)$	Variable costs for selling all the remanufactured products, including discounts, cash and compensation, to promote sales
$C_{2} \left( {\alpha_{i} } \right)$	Cost to be paid to the retailer when taking commission sales; this cost is related to the proportion of commission
$P_{i} \left( {i = 1,2,3} \right)$	Sale price of the remanufactured product
$\mu_{i}$	Conversion rate of waste electronic products to remanufactured products
$\beta_{j} \in \left[ {0,1} \right]$	The quality level of different waste electronic products
$C_{0}^{^{\prime}} \left( {\sum Q_{i}^{^{\prime}} } \right)$	Fixed cost of remanufacturing; this cost is related to the scale of the waste products
$C_{1}^{^{\prime}} \left( {\sum Q_{i}^{^{\prime}} } \right)$	Variable costs in the remanufacturing process; this cost consists of the production costs of all the different processes $\mathrm{k}$ of the remanufacturing process
$Q_{i}^{^{\prime}}$	The quantity of waste electronic products required by remanufacturing enterprises $Q_{i}^{^{\prime}} \left( {i = 1,2,3} \right)$ ${Q}_{i}^{^{\prime}}\left(i=\mathrm{1,2},3\right)$ ${Q}_{i}^{^{\prime}}\left(i=\mathrm{1,2},3\right)$
$Q_{i}$	The demand forecast for different remanufactured products in the market ${\mathrm{Q}}_{\mathrm{i}}\left(\mathrm{i}=\mathrm{1,2},3\right)$ ${\mathrm{Q}}_{\mathrm{i}}\left(\mathrm{i}=\mathrm{1,2},3\right)$
$C_{0}^{^{\prime\prime}} \left( {\sum Q_{i}^{^{\prime}} } \right)$	Fixed cost of recycling
$\mathop \smallint \limits_{0}^{1} c^{\prime\prime}\left( {\beta_{j} } \right)q^{\prime}\left( {\beta_{j} } \right)$	Direct cost of recycling the product
$c^{\prime\prime}\left( {\beta_{j} } \right)$	Product recycling prices at different quality levels
$C_{1}^{^{\prime\prime}} \left( \gamma \right)$	Cost of adopting a commissioned recycling channel
$d_{n} \left[ {Q_{{i - }} \left( {t - n} \right)} \right]^{{r_{n} }} e^{{\theta _{n} }}$	Changes in the product demand in the current period caused by the product sales in the period $\left( {t - n} \right)$, where $d_{n}$, $r_{n}$ and $\theta_{n}$ denote the model parameters
$Q_{{i - }} \left( {t - n} \right)$	Number of products sold in $\left( {t - n} \right)$, $n \le t$
$n$	Number of data periods considered to generate the predictions
$F\left( {P_{i} ,Q_{i} } \right)$	Benefits such as satisfaction from the remanufactured consumer groups buying remanufactured products
$G\left( {\sum Q_{i}^{^{\prime}} ,P_{i}^{^{\prime\prime}} } \right)$	Cost effectiveness of the electronics products discarded by the product owners
$\alpha_{i}^{*} \left( {i = 1,2,3} \right)$	Strategies for the remanufacturing product sales phase
$\alpha_{i}^{*} Q_{i}$	Number of products sold through direct channels for different products
$\beta_{1}^{*} ,\beta_{2}^{*}$	Strategies in the remanufacturing phase
$\gamma^{*}$	Strategies for product recycling
$E\left[ {Rpv} \right]$	Cost constraints in the resale process
$a_{m} x_{m}^{{b_{m} }} e^{{\varepsilon_{m} }}$	Changes in the product demand caused by the factor $\left( {t - n} \right)$ affecting the demand for remanufactured products,where $a_{m}$, $b_{m}$ and $\varepsilon_{m}$ denote the model parameters
$x_{m}$	Value converted by qualitative or quantitative elements according to certain rules
$\varepsilon_{m}$	Number of variables that affect the demand forecast for the remanufactured products
$P_{i}$	Remanufactured product prices in the market
$q^{\prime}\left( {\beta_{j} } \right)$	Number of used electronic products at different quality levels
$Q_{{i - }} \left( {t + 2} \right)$	Forecast of the remanufacturing product demand in the period (t + 2)
$Q_{{i - }}^{'} \left( t \right)$	Number of waste electronic products to be recycled in the period t