A Branch-and-price Approach for a Multi-trip Vehicle Routing Problem with Time Windows and Driver Work Hours

This study considers a vehicle routing problem with time windows, accessibility restrictions on customers and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can perform multiple routes per day, all starting and ending at a single depot, and it is assigned to a single driver, whose total work hours are limited. A column generation algorithm embedded in a branch-and-bound framework is proposed. The column generation pricing subproblem required a specific elementary shortest path problem with resource constraints algorithm to deal with the possibility for each vehicle to perform multiple routes per day and to deal with the need to determine the workday beginning instant of time within the planning horizon. To make the algorithm efficient, a constructive heuristic and a metaheuristic based on tabu search were also developed.