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

Aleksander Wieczorek (1) , Ana Bušić (1) , Emmanuel Hyon (2)

1 TREC - Theory of networks and communications
2 RO - Recherche Opérationnelle

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.

Mots clés: Markov decision process; Critical level policies; Inventory systems

Domaines: Performance et fiabilité [cs.PF]; Recherche opérationnelle [math.OC]

Aleksander Wieczorek, Ana Bušić, Emmanuel Hyon. Critical level policies in lost sales inventory systems with different demand classes. [Research Report] RR-7732, INRIA. 2011. ⟨inria-00620243⟩