Retailer's optimal pricing and replenishment policy for new product and optimal take-back quantity of used product

Abstract

In the world of limited resources, recovery of used products for reselling or recycling is a critical issue from the economic and environmental point of view. In this paper, we have assumed that a retailer sells the new product to customers as well as collects and sells the used products. We adopt a price dependent quadratic demand function, and the return of used product as a price and time-dependent linear function. The proposed problem is formulated as a profit maximization problem for the retailer. The objective is to find the optimal selling price, the optimal ordering quantity for the new product, and the optimal quantity of used product simultaneously such that the retailers total profit is maximized. The model is validated by a numerical example and sensitivity analysis is performed for the key parameters.