The Optimal Review Period in a Dynamic Inventory Model

James Flynn and Stanley Garstka
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James Flynn: Cleveland State University, Cleveland, Ohio
Stanley Garstka: Yale University, New Haven, Connecticut

Operations Research, 1997, vol. 45, issue 5, 736-750

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.

Keywords: inventory/production; optimal review period; inventory/production; policies; periodic review; inventory/production; stochastic inventory model (search for similar items in EconPapers)
Date: 1997
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