Optimal decisions for a closed supply chain system

The return payment policy was considered when the firm collected used products. An inventory decision problem with two replenishment channels including the forward channel and the remanufacturing channel was proposed. Under the assumption that the return payment price influences the probability of product return, a stochastic inventory model with dependent return and demand was given. The optimal decision problem about the replenishment quantity of the forward channel and return payment price was studied in order to maximize the expectation profit of the system. For the joint decision problem, the property which the optimal decisions were obtained by optimizing two single variable problems was proved. And moreover, the search algorithm for the optimal decisions was given. Final, the numerical analysis was made.