Projected Inventory-Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes

Inventory Projection and Asymptotic Optimality van Jaarsveld and Arts propose a new policy for the canonical periodic review lost sales inventory problem. Under this policy, orders are placed in each period such that the expected inventory level at the moment of replenishment order arrival is at a fixed level. This single-parameter policy is called the projected inventory-level (PIL) policy. The PIL inherits asymptotic optimality properties from the constant-order policy for long lead time and from the base-stock policy when the cost of losing a sale is large. The PIL policy has lower cost than competing heuristics in a numerical study. The PIL seems to be a promising approach for other inventory systems with a high-dimensional state space, such as the perishable item inventory management problem.