Exact analysis of One-Warehouse-Multiple-Retailer inventory systems with quantity restricted deliveries

Abstract

Joint consideration and coordination of inventory and shipment decisions is an important challenge in the quest for sustainable distribution systems. This paper addresses this issue by presenting a method for exact analysis of the inventory level distributions in a centralized One-Warehouse-Multiple-Retailer (OWMR) inventory system with quantity restricted deliveries from the warehouse. The system is characterized by continuous review (R,nQ) policies, complete backordering, and compound Poisson demand. The class of quantity restricted delivery policies we consider is motivated by a common desire in practice to ship full load carriers. It generalizes the assumption of unrestricted partial deliveries often used in the literature, and allows the warehouse to only ship retailer specific delivery batch quantities to the different retailers. The delivery batches typically represent package or pallet sizes, containers, or full truckloads. An attractive feature of our approach is that it does not add to the computational effort of analyzing the special case of unrestricted partial deliveries available in the existing literature. A numerical study shows that accounting for quantitative delivery restrictions used in transportation and handling operations when optimizing the reorder points in multi-echelon systems can be very important. Failure to do so can lead to high backorder costs and inadequate customer service.