(s, S) policy for uncertain single period inventory problem

The traditional single period inventory problem assumes that the market demand is a random variable. However, as an empirical or subjective estimation, market demand is better to be regarded as an uncertain variable. This paper is concerning with single period inventory problem under two main assumptions that (i) the market demand is an uncertain variable and (ii) a setup cost and an initial stock exist. Under the framework of uncertainty theory, the optimal inventory policy for uncertain single period inventory problem with an initial stock and a setup cost is derived, which is of (s,S) type. Also, some expansions are obtained.