Structural properties of the lost sales problem with fractional lead times

Abstract We consider an infinite horizon periodic review base-stock inventory system with discrete demand and lost sales. Every T periods the inventory is reviewed and an order, with arbitrary lead time L , is placed to bring the inventory position to R . Using a recursive Markovian representation, we develop the operating characteristics for any system with positive integer-valued base-stock R , review period T , and lead time L . Then, we develop an algorithm to find the optimal stationary R . Surprisingly, computational results yield the unintuitive findings that the optimal base-stock and cost are not monotone in L given T .