A Multi-Vehicle Profitable pickup and Delivery Selection Problem with Time Windows

Today the transportation market is highly competitive yet asymmetric. Large carriers enjoy market power from economies of scale and better networking. Small carriers rely on horizontal cooperation between each other to compete with, usually by trading on freight exchanges. One major challenge for small carriers is how to select requests so that the total profit from the delivery can be maximized. Thus in this paper we model it as a Profitable Pickup and Delivery Selection Problem, which is a generalization of the classic Pickup and Delivery Problem, but with a goal of profit maximization and it does not require all requests to be delivered. For a solution, we propose a simple graph search that traverses through feasible routes to solve the problem optimally. Preliminary computer experiments show that random Euclidean instances with up to 500 requests can be solved optimally within seconds in a single-vehicle setup, and up to 50 requests and 4 vehicles in minutes for the multi-vehicle cases, both of which are faster than the solution by the GUROBI Optimizer. For multi-vehicle cases, we also devise a greedy heuristic that is able to find a 99% optimal solution in less than a second.