Practical and Effective Heuristics for the Backhaul Profit Maximization Problem

Given an empty delivery vehicle, the backhaul profit maximization problem (BPMP) is to select a profit-maximizing subset of available pick-up-and-delivery requests to accept considering the vehicle’s capacity and a time limit for the vehicle to reach a specified destination or, equivalently, a driving-distance limit. Implemented in our computing environment, the fastest known exact algorithm for BPMP requires approximately 11 hours and 44 minutes on average to solve the largest instances in the literature, which have 70 to 80 potential pick-up/drop-off locations. The fastest available heuristic from the literature is considerably faster, and finds high quality solutions, but requires a state-of-the-art mixed-integer programming solver. We present a heuristic framework for the BPMP based on greedy construction, iterative local search, and randomization. Algorithms developed with the framework are implemented in the freely and widely available C++ language and their effectiveness is demonstrated through an extensive computational experiment on both benchmark and randomly generated problem instances. We find that our approach is competitive with approaches from the literature in solution quality as well as running time.