Optimal Policies for the Inventory Problem with Negotiable Leadtime

In this paper we study the dynamic inventory problem in which amounts of stock ordered at unit prices c k and c k+1 (c k > c k+1 ) are delivered, respectively, k and k + 1 periods later. It is demonstrated that under suitable cost conditions, the optimal policies are similar to those of the dynamic inventory problem with a delivery lag of k + 1 periods, except for an additional constant stock level up to which it is desired to order at unit price c K . If we assume that ordering decisions are made in every other period, it is demonstrated that analogous results are obtainable for the case in which amounts of stock ordered at unit prices c k , c k+1 , and c k+2 (c k > c k+1 > c k+2 ) are delivered, respectively, k, k + 1, and k + 2 periods later.