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. © 2011 Springer-Verlag.
CITATION STYLE
Wieczorek, A., Bušić, A., & Hyon, E. (2011). Critical level policies in lost sales inventory systems with different demand classes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6977 LNCS, pp. 204–218). https://doi.org/10.1007/978-3-642-24749-1_16
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