Critical Level Policies in Lost Sales Inventory Systems with Different Demand Classes

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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Submitted on : Monday, March 14, 2016 - 11:54:44 AM
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Aleksander Wieczorek, Ana Bušic, Emmanuel Hyon. Critical Level Policies in Lost Sales Inventory Systems with Different Demand Classes. 8th European Performance Engineering Workshop EPEW 11, Oct 2011, Borrowdale, United Kingdom. pp.204-218, ⟨10.1007/978-3-642-24749-1_16⟩. ⟨hal-01287811⟩

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