Average Cost Models with Lost Sales

Abstract

This chapter is concerned with the long-run average cost minimization of a stochastic inventory problem with Markovian demand, fixed ordering cost, and convex surplus cost in the case of lost sales. The formulation of the problem is similar to that introduced in Chapter 4 except that we replace the discounted cost objective function by the long-run average cost objective function. To deal with this average cost problem, we apply the vanishing discount method to solve the dynamic programming equations defined for the problem, and establish the corresponding verification theorem.