Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times

Managing perishable inventory systems with positive lead times and finite ordering capacities is important but notoriously difficult in both theory and computation. The optimal control policy is extremely complicated, and no effective heuristic policy has been proposed in the literature. In this paper, we develop an easy-to-compute approximation algorithm for this class of problems and prove that it admits a theoretical worst-case performance guarantee under independent and many commonly used positively correlated demand processes. Our worst-case analysis departs significantly from those in the previous studies, requiring several novel ideas. In particular, we introduce a transient unit-matching rule to dynamically match the supply and demand units, and the notion of associated demand processes that provides the right future demand information to establish the desired results. Our numerical study demonstrates the effectiveness of the proposed algorithm.