A model for assigning vehicles to scheduled routes when there is a shortage of vehicles

The paper examines the problem of assigning available buses among bus lines under the conditions of a shortage of buses. This is frequently done by despatchers using experience and intuition, but because of the combinatorial nature of the problem, despatchers are often not able to discover the optimal solution. The authors use a dynamic programming approach to develop a model to minimize waiting time or to maximize the number of seats offered to passengers. The model offers a promising approach to help despatchers facing this problem.