A continuous review inventory system with semi-Markovian demands

This paper analyzes a single item (s,S) inventory model with random lead times and a finite number of different types of customers in which the pooled demand epochs form a semi-Markov process. Demands that occur during stock-out periods are assumed to be lost. For the special case of renewal demands, the problem of minimizing the steady state expected cost rate is studied with numerical illustration of the results.