A series system with returns: stationary analysis

This paper analyzes a series inventory system with stationary costs and stochastic demand over an infinite horizon. A distinctive feature is that demand can be negative, representing returns from customers, as well as zero or positive. We observe that, as in a system with nonnegative demand, a stationary echelon base-stock policy is optimal here. However, the steady-state behavior of the system under such a policy is different from that in systems with nonnegative demands. We present an exact procedure and several approximations for computing the operating characteristics and system costs for any stationary echelon base-stock policy, and also describe an algorithm for computing a good policy. As an alternative to the echelon base-stock policy, we discuss a policy that uses only local information. Finally, we describe how to extend the analysis to the case where returns occur at multiple stages instead of just at the stage closest to demand, and the case where returns require a recovery lead time.