A single commodity inventory problem with maximum capacity S, zero lead time and unit demand is considered. The interarrival times of demands are independent and identically distributed random variables. The reordering levels constitute a Markov chain with state space (0,1,2,...,s) where s•S-1. The replenished quantity is always equal to M=S-s and no shortages are permitted. The distribution of the on hand inventory at arbitrary time point and the limiting distribution are obtained.
