Reliability classes in inventory models

Abstract In the present paper we study generalizations of some of the inventory models with non-linear costs considered in Rosling (2002). In particular we unify several models presented in the previous paper, by considering a random lead time and also by considering both discrete and continuous demands. In the unified model, we study conditions on the leadtime and the demand distribution guaranteeing the quasi-convexity of the cost function (and therefore the existence of optimal (s,S) policies), which will particularize to specific well-known models. Concretely, we study the case in which there is no cost per time period with backlogging, thus giving more general conditions than the existing in the literature for specific models. Moreover a random leadtime for the compound renewal model with periodic review is considered for first time. Our results rely mainly on reliability properties of the random variables under consideration. 2000 Mathematics subject classification: 62E10; 60E15