Refurbished products and supply chain incentives

Abstract

The emergence of online retail platforms and new retail technologies have enabled retailers to sell refurbished products to different markets, which exposes manufacturers to new challenges to control refurbished product market. This study investigates the incentives of supply chain members for refurbished products in a dual-channel supply chain. We examine the conditions under which the retailer is willing to sell refurbished products and the impact of refurbished products on manufacturer’s profits in three different cases, i.e., local market selling, across market selling, and dual market selling. Our results reveal that the manufacturer can effectively control the selling of refurbished products by a wholesale price contract when the retailer can only deliver refurbished products to her local market. However, when the retailer has the ability to deliver refurbished products into a cross-border market, supply chain members encounter different incentives for refurbished products.

Appendix: proof

Proof of Lemma 1

We use the backward induction method to solve the problem. First we analyze the retailer’s profit function $\pi _R^N=(p_n^N-w_n^N-c_{ns})(1-p_n^N)$, and get the optimal $p_n^{N}$ as a function of $w_n^N$. As two markets are independent, after solving the manufacturer’s problem $\pi _M^N=(w_n^N-c_n)(1-p_n^N)+(p_d^N-c_n-c_{ns})(1-p_d^N)$, we can get the optimal $p_d^{N}$ and $w_n^N$ respectively.

Proof of Lemma 2

We first show that $\pi _R^{L}$ is jointly concave in $p_n^L$ and $p_r^L$ by examining the Hessian matrix $H_1= \begin{bmatrix} \frac{2}{(\gamma -1)\lambda } &{} \frac{2}{(1-\gamma )\lambda } \\ \frac{2}{(1-\gamma )\lambda } &{} \frac{2}{(\gamma -1)\lambda \gamma } \end{bmatrix}$. It is straightforward to check that $H_1$ is negative definite. So the first order conditions (FOC) are necessary and sufficient to obtain the solutions. We find $p_n^{L*}=\frac{\lambda +c_{ns}+w_n}{2}$, $p_r^{L*}=\frac{\lambda \gamma +w_r}{2}$. Similarly, we solve the manufacturer’s problem. As two markets are independent, we can obtain the optimal retail price set by the manufacturer in his direct channel $p_d^{L*}=\frac{1+c_n+c_{ns}}{2}$ by FOC. Then, we show that $\pi _M^{L}$ is jointly concave in $w_n^L$ and $w_r^L$ by examining the Hessian matrix $H_2= \begin{bmatrix} \frac{1}{(\gamma -1)\lambda } &{} \frac{1}{(1-\gamma )\lambda } \\ \frac{1}{(1-\gamma )\lambda } &{} \frac{1}{(\gamma -1)\lambda \gamma } \end{bmatrix}$. It is straightforward to check that $H_2$ is negative definite. So the FOCs again are necessary and sufficient to find the solutions. We find $w_n^{L*}=\frac{\lambda +c_{n}-c_{ns}}{2}$, $w_r^{L*}=\frac{\lambda \gamma }{2}$. Finally, we can obtain the demands for the new and refurbished products in two markets, $D_{1n}^L=\frac{\lambda (1-\gamma )-(c_{n}+c_{ns})}{4\lambda (1-\gamma )}, D_{1r}=\frac{c_{n}+c_{ns}}{4\lambda (1-\gamma )}$. To make sure $D_{1n}^L\ge 0$, we need $c_{n}+c_{ns}\le \lambda (1-\gamma )$. Using the similar way, we can obtain the optimal decisions in Lemma 4 and Lemma 6, we’ve omitted the proofs.

All the propositions in this paper are based on the comparison of the manufacturer’s and retailer’s profits in different cases.