A New Stochastic Model for Bus Rapid Transit Scheduling with Uncertainty

Nowadays, authorities of large cities in the world implement bus rapid transit (BRT) services to alleviate traffic problems caused by the significant development of urban areas. Therefore, a controller is required to control and dispatche buses in such BRT systems.. However, controllers are facing new challenges due to the inherent uncertainties of passenger parameters such as arrival times, demands, alighting fraction as well as running time of vehicles between stops. Such uncertainties may significantly increase the operational cost and the inefficiencies of BRT services. In this paper, we focus on the controller's perspective and propose a stochastic mixed-integer nonlinear programming (MINLP) model for BRT scheduling to find the optimal departure time of buses under uncertainty. The objective function of the model consists of passenger waiting and traveling time and aims to minimize total time related to passengers at any stop. From the modeling perspective, we propose a new method to generate scenarios for the proposed stochastic MINLP model. Furthermore, from the computational point of view, we implement an outer approximation algorithm to solve the proposed stochastic MINLP model and demonstrate the merits of the proposed solution method in the numerical results. This paper accurately reflect the complexity of BRT scheduling problem and is the first study, to the best of our knowledge, that presents and solves a mixed-integer nonlinear programming model for BRT scheduling.