The Optimal Review Period in a Dynamic Inventory Model

Abstract

Consider a single-item, periodic review, infinite-horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T periods, one observes the current stock level and orders deliveries for the next T periods, thus incurring a fixed setup cost. The goal is to find a review period T and an ordering policy that minimize the long run expected average cost per period. Flynn and Garstka (Flynn, J., S. Garstka. 1990. A dynamic inventory model with periodic auditing. Opns. Res. 38 1089–1103.) characterize an optimal ordering policy when T is fixed and study a myopic policy whose cost is often close to the optimal cost. This paper covers the problem of selecting T. We prove an optimal review period T* exists, characterize its properties, and present methods for its computation. We also study an approximation to T* based on the myopic policy of our earlier paper and a crude but simple approximation expressing T* in terms of the two-thirds power of the model parameters. Analytic results (where the coefficient of variation of demand is small) and computational experiments suggest both approximations perform well when demands are normal.