Single-Warehouse Multi-Retailer Inventory Systems with Full TruckLoad Shipments

We consider a multistage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Ordering costs are dominated by the shipping costs associated with full truckload transportation with cargo capacity constraints. All costs are stationary. Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system-wide cost without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T 2) algorithm for the single-stage dynamic lot sizing problem with stationary costs; (2) an O(T 3) algorithm for the case of a one-warehouse single-retailer system; and (3) a nested shortest-path algorithm for the one-warehouse multi-retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single-stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems.