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In this paper we formally introduce a generic real-time multivehicle truckload pickup and delivery problem. The problem includes the consideration of various costs associated with trucks' empty travel distances, jobs' delayed completion times, and job rejections. Although very simple, the problem captures most features of the operational problem of a real-world trucking fleet that dynamically moves truckloads between different sites according to customer requests that arrive continuously.

We propose a mixed-integer programming formulation for the offline version of the problem. We then consider and compare five rolling horizon strategies for the real-time version. Two of the policies are based on a repeated reoptimization of various instances of the offline problem, while the others use simpler local (heuristic) rules. One of the reoptimization strategies is new, while the other strategies have recently been tested for …