98%-Effective Lot-Sizing for One-Warehouse, Multi-Retailer Inventory Systems with Backlogging

Robin Roundy has analyzed a stationary, one-warehouse, N-retailer inventory system that permits no shortages or backlogging, that has a constant demand rate per unit time at each retailer, and that incurs setup and unit storage costs at each facility. By reducing the problem with backlogging to an equivalent problem with no backlogging, we extend Roundy's results to permit backlogging. This approach permits us to use Roundy's results to find a 98%-effective policy for the backlogging problem in O(N log N) time.