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Inventory models with Markovian demands and cost functions of polynomial growth. (English) Zbl 0908.90108
Summary: This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite-horizon problems, stationary and nonstationary discounted-cost infinite-horizon problems, and stationary long-run average-cost problems are addressed. Existence of optimal Markov or feedback policies is established. Furthermore, optimality of \((s,S)\)-type policies is proved when, in addition, the ordering cost consists of fixed and proportional cost components and the surplus cost is convex.

90B05 Inventory, storage, reservoirs
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