引入价格窗的定制公交线路优化研究

基于公共交通的公益性，综合考虑乘客与公交企业之间的权衡关系，以保证企业运营成本与服务更多乘客为目标，在浮动票价机制的框架下研究定制公交的线路优化问题。首先，引入价格窗概念，以描述乘客出行过程中的支付意愿，并定义基于时空窗与价格窗的出行需求特征；提 出超额均摊的票价支付假设规则，以在保证出行的基础上支付最少费用。其次，构建引入价格窗的整数线性规划模型，以乘客出行的时空窗和价格窗为输入，以企业运营成本最小化和服务乘客数最大化为目标，通过运营盈利约束来保证企业的运营成本，联合优化乘客-车辆匹配和车辆路径两个子问题。最后，采用GAMS软件进行建模和求解，在Sioux Falls网络开展算例分析。结果 表明，引入浮动票价机制可以服务更多的乘客，进而增加企业的运营收入，且在价格窗上界一定 的增幅内，所服务乘客数和企业的运营收入随价格窗上界增幅的扩大而增加。

Customized Bus Route Optimization with Price Window

Considering the welfare of public transportation and the trade-off between passengers and bus enterprises, the customized bus route optimization is studied under a floating pricing policy to ensure the operating cost of the enterprise and serve more passengers. Firstly, the concept of price window is introduced to describe passengers' willingness to pay, and the characteristics of travel demand based on temporal-spatial window and price window are defined. An assumption rule of over-equalized fare payment is proposed so that passengers pay the least cost on the basis of guaranteed travel. Secondly, an integer linear programming model is established with a price window, in which the temporal- spatial window and price window of passenger travels are set as input variables. The objectives are to minimize the operating cost and to maximize the number of passengers served. The operating cost of the enterprise is guaranteed by imposing the operating profit constraints. Two sub-problems are solved in an integrated manner, namely, passenger-to-vehicle assignment and vehicle routing. Finally, GAMS software is used for modeling and solving, and an example is analyzed on the Sioux Falls network. The results show that the introduction of the floating pricing policy can serve more passengers, and increase the operating income of the enterprise. The number of passengers served and the operating income will increase as the upper bound of the price window increases to a certain level.