Critical Number Policies for Inventory Models with Periodic Data

Paul H. Zipkin

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Supply Chain and Inventory Management Management and Optimization Techniques Optimization and Search Problems

Abstract

We consider an infinite-horizon in problem with stochastic demands where the data vary periodically. Karlin (Karlin, S. 1960a. Dynamic inventory policy with varying stochastic demands. Management Sci. 6 231–258; Karlin, S. 1960b. Optimal policy for dynamic inventory process with stochastic demands subject to seasonal variations. J. SIAM 8 611–629.) shows that a periodic critical-number policy is optimal and presents an algorithm for computing the critical numbers, assuming discounted costs. Here we develop an alternative, conceptually simpler approach to these problems. The results include a proof of the optimality of such policies for the average-cost case, and a qualitative description of the behavior of the optimal policy as “smoothing” fluctuations in the data.

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References

1960Forecasting Sales by Exponentially Weighted Moving Averages 1965Optimal Policy for a Multi-Product, Dynamic, Nonstationary Inventory Problem 1960Dynamic Inventory Policy with Varying Stochastic Demands

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