Making the most of fleets: A profit-maximizing multi-vehicle pickup and delivery selection problem

Road freight transportation is a pillar of the modern economy. Despite the increasing competition, over 20% of all vehicles run empty on European roads. As a remedy, freight exchanges have been established to bridge such supply-demand imbalances, with the largest markets trading over 200,000 daily offers. Carriers searching for profit-maximizing freights on such markets face a Profit-Maximizing Pickup and Delivery Selection Problem (PPDSP) that has not yet been addressed in previous research. In this paper, we develop a novel graph search that branches on feasible routes for an exact solution and, based on this, we develop a randomized search heuristic for the single vehicle case, a greedy heuristic for the multi-vehicle case, and a Maximum Set Packing formulation for the case of homogeneous and heterogeneous fleets. Computational experiments show that most instances of the various setups can be solved optimally and much faster than the solution offered by the Gurobi optimizer. Both heuristics are highly efficient and the problem of fleets can be solved almost as quickly as the single vehicle case.