A lost sales inventory system with supply uncertainty

In this paper we analyze an environment dependent (s, S) inventory system with renewal demands and lost sales where the environment goes through available and unavailable periods according to a two state Markov chain. An order which is placed in an available period is replenished instantaneously and that placed in an unavailable period is replenished at the end of that period. The transform of the various operating characteristics are obtained explicitly. The problem of minimizing the long-run expected cost rate is discussed and an efficient algorithm to compute optimal s and S is developed. Numerical illustration of the results are also provided.