An Empirical Comparison of Two Approximately Optimal (s,S) Inventory Policies.

In this paper, we present an empirical comparison of two approximately optimal rules for computing s,S policies for single items under periodic review with a setup cost, linear holding and storage costs, fixed replenishment lead time, and backlogging of unfilled demand. The Naddor Approximation, originally designed for holding and shortage costs based on period-average inventory levels, is transformed for use in a system where these costs are based on period-end inventory. It is compared empirically with the Power Approximation and with exactly optimal policies in a system of independent inventory items having 576 distinct parameter settings. The Power Approximation yields lower expected total costs than the Naddor Approximation in 456 of the 576 cases. The cost differences tend to be rather small, however. When total costs are aggregated over the entire system, the Power Approximation is 1.65 above optimal, as compared with 2.34 for the Naddor Approximation. Significant differences appear only when components of total cost are examined. The robustness of the policies is examined by analyzing their performance when statistical estimates are used in place of the actual mean and variance of demand. We also discuss the sensitivity to parameter settings of the performance of the two rules. Author