Pickup and Delivery with Split Loads

Splitting loads such that the delivery of certain loads is completed in multiple trips rather than one trip results in opportunities for a reduction in cost and the number of vehicles used. Several studies have shown the benefit of split deliveries for the vehicle routing problem, in which a vehicle operating out of a depot makes a series of deliveries on each route. In this paper, we quantify the benefit of using split loads for the pickup and delivery problem. A heuristic to solve the pickup and delivery problem with split loads is developed and applied to a set of random large-scale problem instances, revealing the potential benefit of split loads. This benefit is reduced when the heuristic is applied to a real-world trucking industry problem because of several problem instance characteristics. The benefit of split loads is found to be most closely tied to three characteristics: load size, cost associated with a pickup or delivery, and the frequency with which loads have origins or destinations in common. Prior to a discussion of these results, we define the pickup and delivery problem with split loads and prove that for a set of given origins and destinations the most benefit can occur with load sizes just above one half of vehicle capacity.