Issues for the Linehaul-Feeder Vehicle Routing Problem with Virtual Depots and Time Windows

The linehaul-feeder vehicle routing problem with virtual depots and time windows (LFVRPTW) is a new version of city logistics. Four important issues are explored and fifteen sample examples used for demonstration. First, the LFVRPTW always yields better results than the vehicle routing problem with time windows (VRPTW). Second, LFVRPTW is advantageous compared with VRPTW. Third, more virtual depot (VD) candidates would yield a bit better results than fewer VD candidates. Fourth, less restricted time window constraints can yield significant benefit to the LFVRPTW. We also test the combined effect of VD candidates and time window constraints. We conclude that: (1) The LFVRPTW problem generally performs better than the VRPTW; (2) The LFVRPTW algorithm embedding the modified sequential insertion heuristic I1 is more effective than that containing the minimum cost insertion method; (3) For LFVRPTW, a looser time window constraint is more critical than the addition of more VD candidates.