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The optimization of urban traffic efficiency and reduction of pollution through minimizing the number of taxis has become a topic of increasing interest. However, the problem of determining the minimum fleet that considers both time and distance efficiency has received limited attention. Furthermore, little research has been done on how this problem is influenced by factors such as city size and travel demand (i.e., the number of trips). This study extends the minimum fleet problem to the min-cost minimum fleet problem, and proposes a method to address the problem by constructing a "dispatch network" and finding the minimum weight and minimum path cover of it. A comparative analysis of the method is conducted with the taxi trajectory data of three cities, New York, Chengdu, and Chicago, and the results show a 60% reduction in the off-load travel time of vehicles compared to the previous method, while maintaining the same fleet size. With the introduction of an emissionsmodel and its combination with our methodology, emissions can also be minimized. Moreover, the relationship between min-cost minimum fleet and city size and travel demand (number of trips) is studied. Experimental results indicate that fleet size and idle time (distance) vary linearly with the number of trips. Meanwhile, city size also has an essential impact on the algorithm's performance. Furthermore, these results indicate that the min-cost minimum fleet will help small cities to achieve higher efficiency (smaller fleet and less connection time) than large cities. The acceleration of urbanization is driving changes in the transportation system.Our findings are expected to have significant implications for transport planning, resource conservation, and reducing pollution. [ABSTRACT FROM AUTHOR]