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Average cost optimality in inventory models with Markovian demands. (English) Zbl 0873.90021
Summary: This paper is concerned with long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost. The states of the Markov chain represent different possible states of the environment. Using a vanishing discount approach, a dynamic programming equation and the corresponding verification theorem are established. Finally, the existence of an optimal state-dependent \((s,S)\) policy is proved.

MSC:
90B05 Inventory, storage, reservoirs
90C39 Dynamic programming
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