The use of phase-type distributions in inventory-control models

This article investigates the use of phase-type distributions to model the demand process and the replenishment leadtimes in the standard reorder-point/order-quantity model of inventory control. Our main result is that the marginal distribution of leadtime demand has a discrete phase-type distribution with the same number of phases as the leadtime distribution, regardless of the complexity of the inter-demand times. This result leads to relatively tractable formulas for several standard performance criteria.