A simulation based heuristic for serial inventory systems under fill-rate constraints

We examine the problem of minimizing average inventory costs subject to a fill-rate constraint in a Clark and Scarf type serial inventory model with a normal demand process. We propose a simulation based heuristic procedure to solve this problem. Using a recent result by Sobel [1] that is an exact base-stock level for a single-stage model, the lower bounds of base-stock levels in each stage of the serial system are obtained. Then, through an effective approximate method, the given problem is decomposed into subproblems. Using the convexity of these subproblems, near optimal base-stock levels are determined sequentially from the most upstream stage to the downstream stage. Numerical tests have shown a highly accurate performance of the proposed heuristic.