General analysis of an inventory system with Markov dependent reordering levels and unit demand

The authors consider a continuous review inventory problem in which the maximum capacity of the warehouse is fixed as S units. The demand process forms a renewal process. The reorder levels are governed by a Markov chain. Each order is to bring the inventory to its maximum level S. Lead time is zero and no shortage is permitted. Explicit expressions for the distribution of onhand inventory at arbitrary time point and also the limiting distribution are obtained. An optimization problem associated with the model is examined and some numerical illustrations given.