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. The first one is an arc-based mixed integer linear programming model that is solved using a general purpose solver. The second one, on the other hand, is based on a path-based formulation, for which we design a column generation framework so as to solve it. Finally, we perform numerical experiments and compare the performance of the two models. The comparison shows that the latter path-based formulation outperforms the former without sacrificing solution quality when employing our column generation framework.