The optimal review period in a dynamic inventory model

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 characterize an optimal ordering policy when T if 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.