A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem

A one-warehouse N-retailer deterministic inventory system is examined. The objective is to determine the stocking policy which minimizes average system cost per unit time over the infinite time horizon. Necessary properties of an optimal policy are derived, and optimal solutions for the one-retailer and N identical retailer problems are given. Heuristic solutions for the general problem are suggested, tested against analytical lower bounds and, on the basis of these tests, found to be near optimal.