INVENTORY MODELS WITH MARKOVIAN DEMANDS AND COST-FUNCTIONS OF POLYNOMIAL-GROWTH

This paper studies stochastic inventory problems with unbounded Markov ian demands, ordering costs that are lower semicontinuous, and invento ry/backlog (or surplus) costs that are lower semicontinuous with polyn omial growth. Finite-horizon problems, stationary and nonstationary di scounted-cost infinite-horizon problems, and stationary long-run avera ge-cost problems are addressed. Existence of optimal Markov or feedbac k policies is established. Furthermore, optimality of (s, S)-type poli cies is proved when, in addition, the ordering cost consists of fixed and proportional cost components and the surplus cost is convex.