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

Aleksander Wieczorek 1 Ana Busic 1, * Emmanuel Hyon 2
* Auteur correspondant
1 TREC - Theory of networks and communications
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt
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.
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[Research Report] RR-7732, INRIA. 2011
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Aleksander Wieczorek, Ana Busic, Emmanuel Hyon. Critical level policies in lost sales inventory systems with different demand classes. [Research Report] RR-7732, INRIA. 2011. 〈inria-00620243〉

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