A column generation algorithm for vehicle scheduling and routing problems

During natural or anthropogenic disasters, humanitarian organizations face a series of time-sensitive tasks. One of the tasks involves picking up critical resources (e.g., first aid kits, blankets, water) from warehouses and delivering them to the affected people. To successfully deliver these items to the people in need, the organization needs to make decisions that range from the quick acquisition of vehicles from the local market, to the preparation of pickup and delivery schedules and vehicle routes. During crises, the supply of vehicles is often limited, their acquisition cost is steep, and special rental periods are imposed. At the same time, the affected area needs the aid materials as fast as possible, and deliveries must be made within due time. Therefore, it is imperative that the decisions of acquiring, scheduling, and routing of vehicles are made optimally and quickly. In this paper, we consider a variant of a truckload open vehicle routing problem with time windows, which is suitable for modeling vehicle routing operations during a humanitarian crisis. We present two integer linear programming models to formulate the problem, with the first one being an arc-based mixed integer linear programming model. The second model is a path-based integer linear programming model, for which we design two fast path generation algorithms. The first model is solved exactly using the commercial solver, while we propose to solve the second model within a column generation framework. Finally, we perform numerical experiments and compare the results obtained from the two models. We show that the path-based model, when solved with our column generation algorithm, outperforms the arc-based model in terms of solution time without sacrificing the solution quality.