Optimal replenishment quantity for new products and return rate of used products for a retailer

Recently, due to increasing environmental concerns, the collection of used products for remanufacturing, reusing, or recycling in a closed-loop supply chain have attracted much attention from the academic and industrial communities. In this study, the decision maker is a retailer who follows the rule of the economic order quantity (EOQ) model. The EOQ decision-making retailer is assumed to sell the products to public consumers, as well as collect the used sold products from public consumers. The proposed problem for the retailer is formulated as a cost-minimization problem, where the replenishment quantity of new products and the return rate of used products are the decision variables. The optimal solution of the replenishment quantity and the return rate are obtained in closed-form under cost minimization. Furthermore, the cost-minimizing model is extended to consider the pricing decision so the total relevant profit for the retailer is maximized and an efficient iterative algorithm is provided to search for the solution. Several numerical examples are provided to illustrate the features of the proposed models and the iterative algorithm.