Evaluation and control of inventory distribution systems with quantity based shipment consolidation

Joint consideration of inventory and shipment decisions is an important aspect of obtaining economically and environmentally sustainable distribution systems. We consider this issue in the context of a one-warehouse-multiple-retailer inventory system with quantity-based shipment consolidation to groups of nonidentical retailers facing Poisson demand. The system is centralized, with free information sharing and access to real-time point of sale data. Thus, demand information at the retailers is immediately conveyed upstream to the warehouse without any fixed ordering costs. However, fixed costs associated with handling and transporting goods from the warehouse to the retailers are reflected in the shipment consolidation policy. Stock replenishments at the warehouse are made from an outside supplier/manufacturer according to an (R, Q) policy. For this system, we derive an exact recursive method for determining the inventory level distributions at the retailers. This allows us to evaluate the expected inventory and shipment costs, fill-rates, and transport emissions for the entire system. We also show how to optimize the system by providing bounds on the optimal shipment quantities and the warehouse reorder level.