A minimum-cost model for bus timetabling problem

In urban traffic, a bus' running speed is greatly influenced by the
time-dependent road conditions. Based on historical GPS data, this paper for-
mulates a bus' running speed between each pair of adjacent stops as a step
function. A minimum-cost timetabling model is proposed, in which the total
operation cost consists of the cost for a xed setup and that for variable fuel
consumption. Furthermore, a genetic algorithm with self-crossover operation
is used to optimize the proposed integer nonlinear programming model. Finally, a real-world case study of Yuntong 128 bus line in Beijing is presented.
Comparisons among popular timetabling models are given, involving time-
dependent running speed, minimum running speed, maximum running speed,
and average running speed. The results demonstrate that the consideration of
time-dependent running speed is helpful to improve the prediction accuracy
of the fuel consumption cost by around 12.7%.