A Bi-level Programming Model for Uncertain Regional Bus Scheduling Problems

Regional bus scheduling is the future trend in public transportation which deals with allocating trips belonged to several routes to buses located at different depots to reduce the size of bus fleets and their operating costs. Considering many emergency events which may affect on-time vehicle arrivals, a bi-level programming model is applied to address the relationship between bus scheduling and its procurement scheme from an overall perspective. The model takes into consideration several constraints such as depot capacities, fueling, and emissions of polluting gases. Solutions to different situations of the upper and lower model are obtained by using a genetic algorithm. Based on some established criteria for a satisfactory solution, a series of lower solutions meeting the established criteria are generated as inputs for the upper model. Thereby, the best lower and the corresponding upper solutions are generated by comparing them. Finally, an example is illustrated to prove the accuracy and effectiveness of our model and its algorithm.