Shipment Composition Enhancement at a Consolidation Center

When items of different shapes, sizes and weights are transported, some item combinations make most effective use of a vehicle's capacity. A consolidation center, receiving shipments of various items from different origins, can act as a point where those combinations can be formed. While sending shipments through the center invariably increases the total item-miles traveled, judicious shipping can reduce the vehicle-miles traveled. This paper examines ways in which loads should be made up to achieve as large a reduction in vehicle-miles as possible. The paper first considers a building block in which items are sent directly from one origin to one destination, and then analyzes a terminal serving many origins and one destination. The understanding developed from the building block leads to a linear programming formulation of the load make-up/routing problem that arises with many origins. The paper also presents a decomposition principle, and a matching algorithm that can be used to solve the problem in the important special case when vehicles can carry many items. The algorithm has a simple physical interpretation and does not require much data. It can be implemented by hand, or on an inexpensive computer.