One-for-One Period Policy and its Optimal Solution

Abstract

In this paper we introduce the optimal solution for a simple and yet practical inventory policy with the important characteristic which eliminates the uncertainty in demand for suppliers. In this new policy which is different from the classical inventory policies, the time interval between any two consecutive orders is fixed and the quantity of each order is one. Assuming the fixed ordering costs are negligible, lead times are constant, and demand forms a Poisson process, we use queuing theory concepts to derive the long-run average total inventory costs, consisting of holding and shortage costs in terms of the average inventory. We show that the total cost rate has the important property of being entirely free of the lead time. We prove that the average total cost rate is a convex function and thus has a unique solution. We, then derive the relation for the optimal value of the time interval between any two consecutive orders. Finally we present a numerical example to compare the performance of this new policy with the classical one-for-one ordering policy. The provided example intends to re-examine the optimality of (s, S) policy in continuous review inventory models as well to establish the fact that even for the case where demand forms a Poisson process the optimality does not hold.