Abstract: A single bus route schedule design (BRSD) problem with stochastic travel times was studied.The effect of the bus operators’ preference on the optimal schedule design was considered， and a stochastic programming model was established for the BRSD problem with the objective of minimizing the weighted sum of the expected value of random schedule deviation and the expected value of overtime for the bus running. The proposed model was transformed into a linear programming model by using Monte Carlo simulation and inequality constraints， and the model was solved by the optimization solvers CPLEX. Finally， a numerical example was given to analyze the sensitivity of the following characteristics. The first is the available bus route travel time， and the second is the weight coefficient for the schedule deviation when bus arrives late. The third is the weight coefficient of the overtime for the bus running and the last is the variances in the bus travel times.

Key words: bus route schedule design, stochastic travel time, timing control point, expected value model, Monte Carlo method