Markovian Decision Processes in Shipment Consolidation

Shipment consolidation is a logistics strategy that combines two or more orders or shipments so that a larger quantity can be dispatched on the same vehicle. This paper discusses a discrete-time Markovian decision process (MDP) approach for determining when to release consolidated loads. We assume that the shipper controls the timing of each load dispatch. Thus, whenever a customer places an order, a choice must be made between dispatching this order (plus all others waiting) immediately, or continuing to consolidate until at least the arrival of the next order. Our MDP models of shipment consolidation consider movement by for-hire transportation (common carriage) or by a firm's own vehicles (private fleet). Small but realistic numerical examples illustrate the application of these models and the data-aggregation issues that must be resolved. Two minimization criteria are considered: cost per unit time, or cost per hundredweight per unit time. For private carriage, the optimal policy is of the control-limit type; for common carriage, it may not be. These potential differences in form of the optimal policy are true for either objective function. The possibly contrasting optimal policies are interpreted in light of the costs encountered by an industrial firm's private fleet compared to the freight charges of a public trucking company.