# American Institute of Mathematical Sciences

May  2021, 17(3): 1505-1529. doi: 10.3934/jimo.2020032

## The comparison between selling and leasing for new and remanufactured products with quality level in the electric vehicle industry

 1 School of Management, Hefei University of Technology, Hefei, China 2 Key Laboratory of Process Optimization and Intelligent Decision-making, Ministry of Education, Hefei, China 3 Research Center of Industrial Transfer and Innovation Development, Hefei University of Technology, Hefei, China

* Corresponding author: Tao Zhou

Received  May 2019 Revised  September 2019 Published  May 2021 Early access  February 2020

Fund Project: The first author is supported by National Natural Science Foundation of China under grants 71871076, 71521001, 71531008, 71690235

Process uncertainty makes remanufacturing operations management sophisticated. To reduce the uncertainty of the timing, quality and quantity of product returns in remanufacturing, motivated by the selling and leasing of electric vehicle batteries, we consider a monopolist vendor who markets her products by adopting two models: (1) a single leasing model, and (2) a single selling model. We first investigate the firm's marketing model with remanufacturing and analyze the impact of the quality level of the returned products on the firm's marketing and remarketing models. Then we compare selling and leasing models. We first find that only when the quality level of returned sold products is relatively high will the vendor choose to remanufacture under the single selling model. Conversely, only when the quality level of returned leased products is relatively low will the vendor decide to remanufacture under the single leasing model. Secondly, we show that the space of remanufacturable quality level under the single selling model is bigger than the space under the single leasing model. Thirdly, selling is more profitable than leasing when the quality level of returned sold products is sufficiently high. These results are further demonstrated by a numerical study. Our study provides firms with guidance on how to optimally adopt remanufacturing and marketing strategies that take into account the quality level of the returned products.

Citation: Kai Li, Tao Zhou, Bohai Liu. The comparison between selling and leasing for new and remanufactured products with quality level in the electric vehicle industry. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1505-1529. doi: 10.3934/jimo.2020032
##### References:

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##### References:
Optimal quantity as a function of $v_{ir}$, given that $c$ and $\gamma$
Optimal price as a function of $v_{ir}$, given that $c$ and $\gamma$
Optimal profits as a function of $v_{ir}$, given that $c$ and $\gamma$
Optimal quantity as a function of $c$, given that $v_{ij}$ and $\gamma$
Optimal price as a function of $c$, given that $v_{ij}$ and $\gamma$
Optimal profits as a function of $c$, given that $v_{ij}$ and $\gamma$
Some Key Literature on Remanufacturing and Marketing Strategies
 Marketing strategy Selling Leasing Combination of selling and Leasing Remanufacturing strategy Remanufacturing Product performance (durability, depreciation, quality, etc.) Atasu and Souza [5] Mont et al. [21]Robotis et al. [25]Steeneck and Sarin [30] Product returns (reverse logistics, acquisition policy, inventory, etc.) Guide et al. [14] Mutha et al. [23]Östlin et al. [24]Wang et al. [37] Aras et al. [3]Loon et al. [19]Yalabik et al. [39] No remanufacturing Product performance Agrawal et al. [2] Desai and Purohit [11] Product returns (secondary market or discarding) Waldman [36]
 Marketing strategy Selling Leasing Combination of selling and Leasing Remanufacturing strategy Remanufacturing Product performance (durability, depreciation, quality, etc.) Atasu and Souza [5] Mont et al. [21]Robotis et al. [25]Steeneck and Sarin [30] Product returns (reverse logistics, acquisition policy, inventory, etc.) Guide et al. [14] Mutha et al. [23]Östlin et al. [24]Wang et al. [37] Aras et al. [3]Loon et al. [19]Yalabik et al. [39] No remanufacturing Product performance Agrawal et al. [2] Desai and Purohit [11] Product returns (secondary market or discarding) Waldman [36]
Summary of Notation
 Symbol Definition $\gamma$ A discount factor signifying the value of future cash flows $v_{ij}$ The quality level for product $j$ under decision $i$ $U^{m}_{kij}$ The utility of a customer for product $j$ of decision $i$ in period $k$ under market model $m$ $c(v_{ij})$ The marginal cost of product $j$ of decision $i$ $p^{m}_{kij}$ The one-period price for the product $j$ of decision $i$ in period $k$ under market model $m$ $q^{m}_{kij}$ The period $k$ demand for product $j$ of decision $i$ under market model $m$ $\pi^{m}_{k}$ The profits under market model $m$ in period $k$ $\pi^{m}$ The total profits under market model $m$
 Symbol Definition $\gamma$ A discount factor signifying the value of future cash flows $v_{ij}$ The quality level for product $j$ under decision $i$ $U^{m}_{kij}$ The utility of a customer for product $j$ of decision $i$ in period $k$ under market model $m$ $c(v_{ij})$ The marginal cost of product $j$ of decision $i$ $p^{m}_{kij}$ The one-period price for the product $j$ of decision $i$ in period $k$ under market model $m$ $q^{m}_{kij}$ The period $k$ demand for product $j$ of decision $i$ under market model $m$ $\pi^{m}_{k}$ The profits under market model $m$ in period $k$ $\pi^{m}$ The total profits under market model $m$
Optimal Solutions in Each Model
 Solutions of parties Model L Model S $q^{m\ast}_{1i n}$ $\frac{1-c}{2}$ $\frac{1-c}{2}+\frac{\gamma(v_{sr}+c(1-v^{2}_{sr}))}{4}$ $q^{m\ast}_{2i n}$ $\frac{1-v_{lr}-cv_{lr}-cv^{2}_{lr}}{2(1-v_{lr})}$ $\frac{1-v_{sr}-cv^{2}_{sr}}{2(1-v_{sr})}$ $q^{m\ast}_{2i r}$ $\frac{c(v^{2}_{lr}+2v_{lr}-1)}{2v_{lr}(1-v_{lr})}$ $\frac{c(v^{2}_{sr}+v_{sr}-1)}{2v_{sr}(1-v_{sr})}$ $p^{m\ast}_{1i n}$ $\frac{1+c}{2}$ $\frac{1+c}{2}+\frac{\gamma(v_{sr}+c(1-v^{2}_{sr}))}{4}$ $p^{m\ast}_{2i n}$ $\frac{1+c}{2}$ $\frac{1+c}{2}$ $p^{m\ast}_{2i r}$ $\frac{v+c(1-v_{lr}-v^{2}_{lr})}{2}$ $\frac{v_{sr}+c(1-v^{2}_{sr})}{2}$ $\pi^{m\ast}_{2}$ $\frac{1-2c-6c^2-5c^2v_{lr}-c^2v^{2}_{lr}}{4}+\frac{c^2(1+3v_{lr})}{4v_{lr}(1-v_{lr})}$ $\frac{1-2c-c^2-3c^2v_{sr}-c^2v^{2}_{sr}}{4}+\frac{c^2}{4v_{sr}(1-v_{sr})}$ $\pi^{m\ast}$ $\frac{(1-c)^2}{4}+\gamma(\frac{1-2c-6c^2-5c^2v_{lr}-c^2v^{2}_{lr}}{4}+\frac{c^2(1+3v_{lr})}{4v_{lr}(1-v_{lr})})$ $(\frac{1-c}{2}+\frac{r(v_{sr}+c(1-v^{2}_{sr}))}{4})^2+\gamma(\frac{1-2c-c^2-3c^2v_{sr}-c^2v^{2}_{sr}}{4}+\frac{c^2}{4v_{sr}(1-v_{sr})})$
 Solutions of parties Model L Model S $q^{m\ast}_{1i n}$ $\frac{1-c}{2}$ $\frac{1-c}{2}+\frac{\gamma(v_{sr}+c(1-v^{2}_{sr}))}{4}$ $q^{m\ast}_{2i n}$ $\frac{1-v_{lr}-cv_{lr}-cv^{2}_{lr}}{2(1-v_{lr})}$ $\frac{1-v_{sr}-cv^{2}_{sr}}{2(1-v_{sr})}$ $q^{m\ast}_{2i r}$ $\frac{c(v^{2}_{lr}+2v_{lr}-1)}{2v_{lr}(1-v_{lr})}$ $\frac{c(v^{2}_{sr}+v_{sr}-1)}{2v_{sr}(1-v_{sr})}$ $p^{m\ast}_{1i n}$ $\frac{1+c}{2}$ $\frac{1+c}{2}+\frac{\gamma(v_{sr}+c(1-v^{2}_{sr}))}{4}$ $p^{m\ast}_{2i n}$ $\frac{1+c}{2}$ $\frac{1+c}{2}$ $p^{m\ast}_{2i r}$ $\frac{v+c(1-v_{lr}-v^{2}_{lr})}{2}$ $\frac{v_{sr}+c(1-v^{2}_{sr})}{2}$ $\pi^{m\ast}_{2}$ $\frac{1-2c-6c^2-5c^2v_{lr}-c^2v^{2}_{lr}}{4}+\frac{c^2(1+3v_{lr})}{4v_{lr}(1-v_{lr})}$ $\frac{1-2c-c^2-3c^2v_{sr}-c^2v^{2}_{sr}}{4}+\frac{c^2}{4v_{sr}(1-v_{sr})}$ $\pi^{m\ast}$ $\frac{(1-c)^2}{4}+\gamma(\frac{1-2c-6c^2-5c^2v_{lr}-c^2v^{2}_{lr}}{4}+\frac{c^2(1+3v_{lr})}{4v_{lr}(1-v_{lr})})$ $(\frac{1-c}{2}+\frac{r(v_{sr}+c(1-v^{2}_{sr}))}{4})^2+\gamma(\frac{1-2c-c^2-3c^2v_{sr}-c^2v^{2}_{sr}}{4}+\frac{c^2}{4v_{sr}(1-v_{sr})})$

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