Markov-modulated processes have been used in stochastic inventory models with setup costs for modeling demand under the innuence of uncertain environmental factors, such as uctuating economic and market conditions. The analyses of these models have been carried out in the literature only under the assumption that unsatissed demand is fully backlogged. The lost sales situation occurs in many ret...

We consider a single-location inventory system with periodic review and stochastic demand. It places replenishment orders to raise the inventory position—that is, inventory on hand plus inventory in transit—to exactly S at the beginning of every period. The lead time associated with each of these orders is random. However, the lead-time process is such that these orders do not cross. Demand tha...

We study a single-product single-location inventory system under periodic review, where excess demand is lost and the replenishment lead time is positive. The performance measure of interest is the long run average holding cost and lost sales penalty. For a large class of demand distributions, we show that when the lost sales penalty becomes large compared to the holding cost, the relative diff...