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The Optimality of (s, S) Policies for a Stochastic Inventory Problem with Proportional and Lump-Sum Penalty Cost

By Yash Aneja and A. Hamid Noori


In this paper we consider a single product multi-period inventory problem for which the penalty cost consists of two parts, a lump-sum portion which is independent of the size of the shortage and a portion which is linear in the size of the shortage. We show that for all nonincreasing demand density functions, the expected total cost function is K-convex and hence, there is an optimal policy for the n-period problem that is (s, S).inventory/production: stochastic models, inventory/production: planning horizons

DOI identifier: 10.1287/mnsc.33.6.750
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