$ (s, S) $ Inventory policies for stochastic controlled system of Lindley-type with lost-sales

Abstract

<abstract><p>This paper presents a characterization of $ (s, S) $-inventory policies for Lindley systems with possibly unbounded costs, where the objective is to minimize the expected discounted total cost by ordering (production) strategies. Moreover, the existence of a subsequence of minimizers of the value iteration functions that converge to a $ (s, S) $ optimal inventory system policy is shown. A numerical example is given to illustrate the theory.</p></abstract>