The objective of designing timetables for public transportation is twofold: to ensure an efficient use of limited resources and to provide a comfortable ride for passengers. Two models for timetable optimization are investigated in this study. Model 1 uses a crisp constraint on the rate of vehicle capacity usage. Model 2 improves on model 1 by translating the crisp constraint into a fuzzy goal representing passenger satisfaction, and a fuzzy constraint, representing the extent of vehicle usage. Both, the fuzzy goal and the fuzzy constraint, are fuzzy sets on the number of on-board passengers. Heuristic methods together with linear programming are proposed for finding the optimal headway. Model 1 selects the largest time interval under the bound on vehicle size. The set of optimal time intervals in model 2 is decided by the simultaneous level cuts of the fuzzy goal and constraint. Experimental results show that fuzzy-set based model 2 is the most flexible and effective way to generate an optimal timetable.

中文翻译：

---

车辆容量模糊约束下的日程优化

设计公共交通时间表的目的是双重的：确保有效利用有限的资源，并为乘客提供舒适的乘车体验。本研究研究了两种时间表优化模型。模型1对车辆使用能力的比率使用了明确的约束。模型2通过将清晰约束转换为代表乘客满意度的模糊目标和代表车辆使用程度的模糊约束，对模型1进行了改进。模糊目标和模糊约束都是对机上乘客数量的模糊集合。提出了启发式方法和线性规划，以寻找最佳的前进方向。模型1在车辆尺寸范围内选择最大时间间隔。模型2中的最佳时间间隔集由模糊目标和约束的同时级别削减决定。实验结果表明，基于模糊集的模型2是生成最佳时间表的最灵活，最有效的方法。