Inventory models with nonlinear costs and random lead times: a general framework and some generalizations using reliability techniques

Abstract In this paper, we generalize some of the inventory models with nonlinear costs presented in Rosling (Oper Res 50:1007–1017, 2002). In particular, we consider random lead times and study models with continuous and discrete demand. In the unified model, we study conditions on the lead time and the demand distribution that ensure the quasiconvexity of the cost function, thereby guaranteeing the existence of optimal ( s , S ) policies. These conditions are applied to specific well-known models. Particularly, we study the case where backlog costs per time equal to zero, thus providing more general conditions than those available in the literature for specific models. Moreover, we introduce a random lead time for the compound renewal model with periodic review. Our results are mainly based on the reliability properties of the random variables under consideration.