Optimal production planning for a multi-product closed loop system with uncertain demand and return

We study the production planning problem for a multi-product closed loop system, in which the manufacturer has two channels for supplying products: producing brand-new products and remanufacturing returns into as-new ones. In the remanufacturing process, used products are bought back and remanufactured into as-new products which are sold together with the brand-new ones. The demands for all the products are uncertain, and their returns are uncertain and price-sensitive. The problem is to maximize the manufacturer's expected profit by jointly determining the production quantities of brand-new products, the quantities of remanufactured products and the acquisition prices of the used products, subject to a capacity constraint. A mathematical model is presented to formulate the problem and a Lagrangian relaxation based approach is developed to solve the problem. Numerical examples are presented to illustrate the model and test the solution approach. Computational results show that the proposed approach is highly promising for solving the problems. The sensitivity analysis is also conducted to generate managerial insights.