Integration of shipment scheduling decisions for forward and reverse channels in a recoverable item system

In this paper, we consider the problem of finding the economic shipment quantities of failed and recovered items between a central depot and a collection center to coordinate the flow in both ways. Our model takes an explicit account for the transportation costs and capacities under the assumption of deterministic failure rate of items. The proposed solution provides the optimum shipment quantities, and the level of spare items to be held at the collection center with the objective of minimizing the long-run average total costs subject to a service level.