The Power Approximation for Computing (s, S) Inventory Policies

Abstract

In this paper we present a new analytic approximation for computing (s, S) policies for single items under periodic review with a set-up cost, linear holding and shortage costs, fixed replenishment lead time, and backlogging of unfilled demand. The approximation formulae are derived by using existing results of asymptotic renewal theory to characterize the behavior of the optimal policy numbers as functions of the model parameters. These functions are then used to construct regressions with coefficients that are calibrated by using a grid of 288 known optimal policies as data. The resulting Power Approximation policies (formulae) are easy to compute and. require for demand information only the mean and variance of demand over lead time. Extensive computational results show that the approximations yield expected total costs that typically are well within one percent of optimal. The approximation's robustness is exemplified by analyzing its performance when statistical estimates are used in place of the actual mean and variance of demand.