Old and New Methods for Lost-Sales Inventory Systems

We present two results to aid the numerical solution of the notoriously di¢ cult discrete-time inventory model with stochastic demands, a constant leadtime, and lost sales. First, we show that the e¤ective state space is a relatively manageable compact set. Second, we show that the optimal cost is increasing in the leadtime, and we use this fact to construct a good lower bound on the optimal-cost function. Armed with these techniques, we test various plausible heuristics. We …nd that several perform reasonably well, though none is perfect. The standard base-stock policy, however, performs badly. (Inventory; Lost sales; Dynamic programming)