A pickup and delivery problem using crossdocks and truckload lane rates

Abstract

This paper presents solution approaches for a shipper pickup and delivery planning problem to move freight from suppliers to distribution centers. Each shipment is moved either direct via a less-than-truckload (LTL) carrier, or possibly consolidated with other shipments and moved by one or two truckload (FTL) routes. When using a FTL carrier, the shipper takes advantage of contracted lane rates that establish prices per mile for a truck operated between two locations that are significantly less than the comparable LTL price for shipping a full truckload. The challenge for the shipper is to consolidate multiple shipments effectively to take advantage of this price differential. Consolidated FTL routes may each visit multiple shipment origins (supplier locations) and/or destinations (distribution center locations). Additionally, FTL routes may move shipments through a single crossdock facility en route. A path-based integer programming model for this planning problem is presented. The model can be solved directly with commercial integer programming software for smaller instances. For larger instances, a search scheme is developed in which restrictions to the integer program are solved sequentially. A computational study using data from a major US retailer demonstrates the effectiveness of the solution approaches. In each instance, substantial transportation cost savings are identified from baseline LTL costs.