Optimal Inventory Location and Control in Production and Distribution Networks

The problem of finding optimal inventory control schemes has received considerable attention in the literature for the case of one inventory at a given location in a production process or distribution system. Almost no analytical work has been devoted to systems of interacting inventories at different locations, and to the problem of selecting optimal inventory locations from a number of possible ones. This is the subject of the present paper. The traditional cost-of-shortage concept is given up in favor of a functional relation between expected demand and average delivery time to the customer. The measure of system performance is sales revenue minus inventory carrying cost. A method employing a combination of dynamic programming and a one-dimensional maximization procedure, yields the optimal inventory locations as well as the corresponding order rules.