Optimal Policies for a Multi-Echelon Inventory Problem with Periodic Ordering

Abstract

A central warehouse supplies two facilities with a product. The facilities are subject in each time period to stochastic demands. The warehouse can allocate stock to the facilities in each period, but can reorder from an exogenous source only after every T periods. Assuming convex holding and shortage costs, linear ordering and allocation costs, backlogging and no transshipment between facilities, the optimal ordering and allocation policies are characterized. It is also shown that after the last ordering instant, the optimal allocation policy reduces to a much simpler form when the cost-functions are separable in their variables, and that results on the zero time lag allocation problem apply to the fixed time lag case when the holding and shortage costs are functions only of the facility inventories and the total system inventory.