Optimal Pricing of the Dual-Channel Closed-Loop Supply Chain in Advance Selling Mode

Abstract

Nowadays, advance selling has become increasingly popular as one of the essential sales strategies. Due to the continuous development of e-commerce and remanufactured products, it is urgent for merchants to decide how to price the product properly. This paper establishes a two-stage pricing model for the dual-channel closed-loop supply chain in advance selling mode and analyzes the impact of market competition and consumers’ purchasing behavior on pricing strategies. Then we found that (1) The retailer’s optimal price is lower when the market competition is relatively significant. (2) When the recovery rate rises, the optimal price remains steady, but the profits of the retailer and the manufacturer both increase. (3) The advance selling price is generally higher than the regular selling price. However, the emergence of remanufactured products hugely increases the regular selling price.

Appendix

Derivation of $\tau ^*$

$$\begin{aligned} \tau ^*=\frac{-I+ap_e^2-ap_r^2-p_eq_0+p_rq_0-(a+b)p_ew_2+(a+b)p_rw_2}{S(A-b_r+\lambda p_e-\beta \lambda p_r-\lambda p_r-\delta w_2+2\delta \beta w_2)}. \end{aligned}$$

Derivation of $\tau _1$

$$\begin{aligned} \begin{aligned} \tau _1&=\{-ap_{2e}^2+(a-2b)p_{2r}w_2-6q_0w_2+p_{2e}[bp_{2r}+q_0+(2a-b)w_2]\\&+q_0x_2+3(a-b)w_2x_2-(a-b)x_2^2+c_m[(-a+b)(p_{2e}+p_{2r}+4q_0-(a-b)2x_2)]\}/\\&\{S[b_r+c_n-(1-\beta )\lambda p_{2e}-\beta \delta w_2]\} \end{aligned} \end{aligned}$$

Derivation of $\tau _2$

$$\begin{aligned} \begin{aligned} \tau _2&=\{-I-ap_{2r}^2+p_{2r}q_0+(2a-b)p_{2r}w_2-6q_0w_2+p_{2e}[bp_{2r}+(2a-b)w_2]\\&+q_0x_2+(3a-b)w_2x_2-(a-b)x_2^2+c_m[(-a+b)(p_{2e}+p_{2r})+4q_0-(a-b)2x_2]\}/\\&\{S[A+c_n-\beta \lambda p_{2r}-(1-\beta )\delta w_2]\} \end{aligned} \end{aligned}$$