Taxis are one of the most important urban transportation modes which provide prompt and comfortable service to customers. It is commonly known that demand for and supply of taxis fluctuate at different times of a day, leading to peak periods when customer waiting time for taxis is longer and the quality of taxi service is lower than that of the off-peak periods. There have been real-world practices to mitigate the demand-supply imbalance and improve the service quality of taxis during peak periods. For example, a peak-period surcharge is imposed on taxi passengers in Singapore; the city of Perth in Australia introduces a fleet of peak-period taxis (PTs) which are allowed to operate within specific hours as the additional supply to the market. However, there lacks theoretical evidence to tell which means (or both) should be implemented and it is also unclear which factor(s) is determinant to the optimal surcharge and the optimal fleet size and shift of PTs. Moreover, there is no methodology to design the optimal shifts (the permitted operating hours) and fleet size of PTs and the optimal peak-period surcharge. To tackle the above issues, this paper proposes a peak-period taxi scheme design problem (PTSDP) that aims to determine the optimal fleet size/shifts of PTs and a peak-period taxi surcharge. The problem is formulated as a bi-level optimization model in which the upper level is the regulator (government) problem and the lower level stands for the taxi driver problem. The model is solved by a brute force method combined with the Hooke-Jeeves pattern search and the Frank-Wolfe algorithm. Numerical examples are given to give policy implications and managerial insights into the regulation of taxi markets.

出租车是最重要的城市交通方式之一，可以为客户提供快捷舒适的服务。众所周知，出租车的需求和供应在一天的不同时间波动，从而导致高峰时段，此时客户的出租车等待时间更长，出租车服务的质量低于非高峰时段。在缓解高峰期期间，已经采取了现实的做法来减轻供需不平衡并提高出租车的服务质量。例如，在新加坡，出租车乘客将被征收高峰期附加费；澳大利亚的珀斯市引入了高峰时段出租车（PT）车队，这些出租车可以在特定时间内运行，作为向市场的额外供应。然而，缺乏理论证据来说明应采用哪种方法（或两种都采用），也不清楚哪种因素决定最优附加费，最优机队规模和PT换档。而且，没有方法来设计PT的最佳班次（允许的工作时间）和车队规模以及最佳的高峰期附加费。为了解决上述问题，本文提出了一种高峰期出租车计划设计问题（PTSDP），旨在确定最佳的PTT车队规模/班次和高峰期出租车附加费。该问题被表述为双层优化模型，其中上层是监管者（政府）问题，下层是出租车司机问题。该模型通过蛮力方法与Hooke-Jeeves模式搜索和Frank-Wolfe算法相结合来求解。