Discount Cost Models with Polynomially Growing Surplus Cost

Abstract

This chapter studies stochastic inventory problems with unbounded Markovian demands and more general costs than those considered in Chapter 2. Finite horizon problems, as well as stationary and nonstationary discounted cost infinite horizon problems, are addressed. Existence of optimal Markov or feedback policies is established with Markovian demand: unbounded, ordering costs that are l.s.c., and surplus costs that are l.s.c. with polynomial growth. Furthermore, optimality of (s, S)-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost is convex.