A peak-period taxi scheme design problem: Formulation and policy implications

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.