Optimal production and pricing policy for a closed loop system

A closed loop system is investigated, in which the manufacturer has two channels to satisfy the demand: manufacturing brand-new products and remanufacturing returns into as-new products. Remanufactured products have no difference from brand-new products and can be sold in the same market at the same price. The demand is uncertain and sensitive to the selling price, while the return is also stochastic and sensitive to the acquisition price of used products. A mathematical model is developed to maximize the overall profit of the system by simultaneously determining the selling price, the production quantities for brand-new products and remanufactured products, and the acquisition price of used products. Some properties of the problem are analyzed, based on which a solution procedure is presented. Through a numerical example, the impacts of the uncertainties of both demand and return on the production plan, selling price, and the acquisition price of used products are analyzed.