Design of limited-stop bus service with capacity constraint and stochastic travel time

•Propose an integer nonlinear model for the limited-stop bus service.•Consider vehicle capacity and stochastic travel time.•Develop a hybrid artificial bee colony and Monte Carlo method.•Perform a sensitivity analysis on the passenger demand.

This paper develops a mathematical model for the optimal stopping design of limited-stop bus service, which allows each bus vehicle to skip some stops. To better reflect the reality, this paper considers the vehicle capacity and stochastic travel time. Also, vehicles are all allowed to skip stops whereas any stop is not allowed to be skipped by two consecutive vehicles. A hybrid artificial bee colony (ABC) and Monte Carlo method is developed to solve the optimal stopping strategy. Finally, the model and solution method are validated by a numerical example, and a sensitivity analysis is performed on the passenger demand.