考虑随机行驶时间的单线路公交时刻表设计优化模型

研究了车辆随机行驶时间情况下的单线路公交时刻表设计问题.考虑了公交运营者主观偏好对最优时刻表设计的影响,建立了以车辆到站时刻偏差和车辆超时行驶时间的权重之和最小为优化目标的随机期望值模型.采用Monte Carlo仿真和不等式约束的方法将该期望值模型转化为线性规划模型,然后使用优化求解器CPLEX求解模型.最后通过一个算例,分别对模型中可用的线路行驶时间参数、晚于时刻表到站时刻偏差的惩罚系数、车辆超时行驶时间的惩罚系数及随机行驶时间的方差进行了灵敏度分析.

Optimization Model for Single Bus Route Schedule Design Problem with Stochastic Travel Time

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.