Critical level policies in lost sales inventory systems with different demand classes

Authors:
Aleksander Wieczorek;Ana Bu$#353/i$#263/;Emmanuel Hyon
Affiliations:
INRIA and ENS, Paris, France;INRIA and ENS, Paris, France;Université/ Paris Ouest Nanterre, Nanterre, France
Venue:
EPEW'11 Proceedings of the 8th European conference on Computer Performance Engineering
Year:
2011

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Abstract

We consider a single-item lost sales inventory model with different classes of customers. Each customer class may have different lost sale penalty costs. We assume that the demands follow a Poisson process and we consider a single replenishment hypoexponential server. We give a Markov decision process associated with this optimal control problem and prove some structural properties of its dynamic programming operator. This allows us to show that the optimal policy is a critical level policy. We then discuss some possible extensions to other replenishment distributions and give some numerical results for the hyperexponential server case.