Asymptotically Optimal Lagrangian Policies for Multi-Warehouse, Multi-Store Systems with Lost Sales

Simple Algorithms for Complex Multiwarehouse, Multistore Inventory Control Problems Retailers (both brick-and-mortar and e-commerce) have always faced the problem of allocating inventories in their warehouses (or central distribution centers) to the stores (or smaller local warehouses) in order to minimize total costs. The problem is particularly challenging when the network structure is large and complex, the selling season is long, and the replenishment is frequent. For example, giant retail chains such as Macy’s typically have many warehouses and hundreds of stores across the United States, and online retailers such as Amazon have many distribution centers and over one hundred fulfillment centers. The authors develop algorithms to solve this multiwarehouse, multistore (MWMS) inventory control problem. Their algorithms are computationally efficient and asymptotically optimal as the problem becomes large and complex. This feature is very appealing to today’s fast-moving retail industry with rapidly expanding business scale.