A hybrid local improvement algorithm for large-scale multi-depot vehicle routing problems with time windows

One of the major research topics in the supply chain management field is the multi-depot vehicle routing problem with time windows (m-VRPTW). It aims to designing a set of minimum-cost routes for a vehicle fleet servicing many customers with known demands and predefined time windows. This paper presents an m-VRPTW local search improvement algorithm that explores a large neighborhood of the current solution to discover a cheaper set of feasible routes. The neighborhood structure comprises all solutions that can be generated by iteratively performing node exchanges among nearby trips followed by a node reordering on every route. Manageable mixed-integer linear programming (MILP) formulations for both algorithmic steps were developed. To further reduce the problem size, a spatial decomposition scheme has also been applied. A significant number of large-scale benchmark problems, some of them including up to 200 customers, multiple depots and different vehicle-types, were solved in quite reasonable CPU times.