Optimal base stock policies and truck capacity in a two-echelon system

Abstract

With the recent trend toward just-in-time deliveries and reduction of inventories, many firms are reexamining their inventory and logistics policies. Some firms have dramatically altered their inventory, production, and shipping policies with the goal of reducing costs and improving service. Part of this restructuring may involve a specific contract with a trucking company, or it may entail establishing in-house shipping capabilities. This restructuring, however, raises new questions regarding the choice of optimal trucking capacity, shipping frequency, and inventory levels. In this study, we examine a two-level distribution system composed of a warehouse and a retailer. We assume that demand at the retailer is random. Since the warehouse has no advance notice of the size of the retailer order, inventory must be held there as well as at the retailer. We examine inventory policies at both the warehouse and the retailer, and we explicitly consider the trucking capacity, and the frequency of deliveries from the warehouse to the retailer. Both linear and concave fixed transportation costs are examined. We find the optimal base stock policies at both locations, the optimal in-house or contracted regular truck capacity, and the optimal review period (or, equivalently, delivery frequency). For the case of normally distributed demand we provide analytical results and numerical examples that yield insight into systems of this type. Some of our results are counterintuitive. For instance, we find some cases in which the optimal truck capacity decreases as the variability of demand increases. In other cases the truck capacity increases with variability of demand. © 1993 John Wiley & Sons, Inc.