Column generation based matheuristics for a vehicle routing problem with time windows and variable start time

In this study, a vehicle routing problem with time windows is investigated, where the costs depend on the total duration of vehicle routes and the starting time from the depot for each vehicle is determined by a decision maker. In order to solve the problem, two column generation based mat-heuristics are developed, where the first one makes use of the iterated local search and the second one uses the variable neighbourhood search. In order to assess the accuracy of the mat-heuristics, they are first compared with an exact algorithm on small instances taken from the literature. Since their performance are quite satisfactory, they are further tested on 87 large instances by running each algorithm 3 times for each instance. The computational results prove that the mat-heuristic using the variable neighbourhood search outperforms the other one. Hence, this enables to obtain a good feasible solution in a very short time when it is not possible to solve large instances with an exact solution method in a reasonable CPU time.