Optimization and optimality of (s, S) stochastic inventory systems with non-quasiconvex costs

This article considers the optimization and optimality of single-item/location, infinite-horizon, (s, S) inventory models. Departing from the conventional approach, we do not assume the loss function describing holding and shortage costs per period to be quasiconvex. As the existing optimization algorithms have been established on the condition of quasiconvexity, our goal in this article is to develop a computational procedure for obtaining optimal (s,S) policies for models with general loss functions. Our algorithm is based on the parametric method commonly used in fractional programming and is intuitive, exact, and efficient. Moreover, this method allows us to extend the optimality of (s, S) policies to a broader class of loss functions that can be non-quasiconvex.