Adaptive neighborhood simulated annealing for the heterogeneous fleet vehicle routing problem with multiple cross-docks

•We introduce the heterogeneous fleet vehicle routing problem with multiple cross-docks (HF-VRPMCD).•HF-VRPMCD can be used in a distribution system with multiple cross-docks and a heterogeneous fleet of vehicles.•We propose an adaptive neighborhood simulated annealing (ANSA) heuristic for solving HF-VRPMCD.•We perform analyses to provide insights into problem parameters and algorithmic performance.•Computational results show the excellent performance of ANSA in terms of solution quality and computational efficiency. This paper introduces the heterogeneous fleet vehicle routing problem with multiple cross-docks, a variant of the vehicle routing problem with cross-docking, which considers the use of multiple cross-docks and a heterogeneous fleet of vehicles in a distribution system. A mixed integer linear program and an adaptive neighborhood simulated annealing algorithm are developed for the problem. The proposed algorithm is a new variant of the simulated annealing algorithm that implements an adaptive mechanism for selecting neighborhood moves in order to improve the solution. Results of computational study show the excellent performance of the proposed algorithm in terms of solution quality and computational efficiency.