THE OPTIMAL REVIEW PERIOD IN A DYNAMIC INVENTORY MODEL

Consider a single-item, periodic review, infinite-horizon, undiscounte d, inventory model with stochastic demands, proportional holding and s hortage 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 deliv eries for the next T periods, thus incurring a fixed setup cost. The g oal is to find a review period T and an ordering policy that minimize the long run expected average cost per period. Flynn and Garstka (1990 ) characterize an optimal ordering policy when T is fixed and study a myopic policy whose cost is often close to the optimal cost. This pape r covers the problem of selecting T. We prove an optimal review period T, exists, characterize its properties, and present methods for its c omputation. We also study an approximation to T, based on the myopic p olicy of our earlier paper and a crude but simple approximation expres sing T, in terms of the two-thirds power of the model parameters. Anal ytic results (where the coefficient of variation of demand is small) a nd computational experiments suggest both approximations perform well when demands are normal.