Optimal Control Policy for Stochastic Inventory Systems with Multiple Types of Reverse Flows

We study a single-product periodic-review inventory system with multiple types of returns. The serviceable products used to fulfill stochastic customer demand can be either manufactured/ordered, or remanufactured from the returned products, and the objective is to minimize the expected total discounted cost over a finite planning horizon. We show that, under some circumstances but not all, the optimal policy has a simple form and can be completely characterized by a sequence of constant control parameters. However, in some other scenarios, the optimal policy can be quite complicated and control parameters are state-dependent. We present a partial characterization on the optimal control policy for the general case when there are only two types of returns.