Stochastic models for the dispatch of consolidated shipments

Most studies on supply chain management have taken an "inventory" point of view: The chain, supplier-->manufacturer-->majormanufacturer, is thus analyzed as a series of production-inventory decisions. Although correct, that approach neglects issues on the transportation between nodes, thereby missing important opportunities for cost savings and optimization. Here we focus on the substantial economies of scale in transportation. These occur when merchandise is shipped in one's own truck (private carriage), or when transport is performed by a public, for-hire trucking company (common carriage). As a result, better inventory replenishment between successive echelons may have less impact than improved transportation decisions. This is especially true when the latter include a strategy for shipment consolidation, the policies whereby several small orders will be held as they accumulate, then dispatched as a single, combined load. In the present paper, we apply renewal theory to two strategies commonly utilized in practice. For the case of a quantity policy we obtain the optimal target weight before dispatch, while for a time policy, we calculate the optimal length of each consolidation cycle (maximum holding time for any order). These strategies are analyzed for private carriage and then for common carriage. Particular situations are studied graphically and numerically; general results are expressed in the form of propositions.