This paper deals with the study of an (s,S) inventory model with zero lead time. The interarrival times of demands are independent and identically distributed random variables. Each arrival demands a random number of items, the maximum being a, a•s. The successive quantities demanded form a Markov chain. No shortage is permitted. The probability distribution of the stock level at arbitrary time points and also the steady state inventory level distribution are obtained. An optimization problem associated with the model is examined and numerical illustrations given.
