多時段計程車市場之最佳化研究

MULTIPLE PERIOD OPTIMIZATION OF A TAXI MARKET

計程車有便利、舒適、及門、私密等特性，為都市公共運輸重要一環。本研究建立最佳化數學模型以探討巡迴計程車市場空車率、費率、服務品質、車輛數等課題，首次引入閒置成本及多時段概念，能反映尖離峰市場之特性差異，合理分析非尖峰時段超額供給現象與單一費率制度下尖離峰旅次交叉補貼的問題。以臺北計程車市場為實際分析案例顯示，損益兩平限制下的次佳解為較佳營運模式，此情況下的尖峰、離峰及夜間最適費率分別為每車公里59、39.2、36元，最適空車率則分別為40.0%、33.3%、27.7%；研究結果亦顯示，實施尖離峰差別定價將使各時段空車率皆能維持最適水準，創造管理者、營運者與使用者多贏局面。

Featured with convenience, comfort, door-to-door and privacy, taxi has become an important mode in urban public transportation. Because taxi service is involved with public welfare, lots of issues should be planned and managed properly, such as vacancy rate, pricing scheme, market structure, and plate grant. Therefore, many researches had established optimization models to explore these important issues. Based on past studies, this study develops an optimization model with consideration of supply and demand in multiple periods and the concept of idle cost. With the multiple period optimization feature, we would be able to analyze the difference of market between peak and off-peak hours and the extra supply issue in off-peak hour. We can then find the optimal equilibrium in each time period in terms of fare, vacancy rate and service quality. In the study, taxi market in Taipei metropolis is used as a case study. The numerical results show that in order to maximize the social welfare and balance the revenue and cost, the optimal fare in peak, off peak and midnight will be 59.0, 39.2 and 36.0 NTD per kilometer, respectively while the optimal vacancy rate will be 40.0%, 33.3% and 27.7%, respectively. The fleet size of taxi market in Taipei metropolis should be 29,455 under the assumption that the daily average operation hour of taxi drivers is 9 hours. With the results of multi-period market optimization model, we can improve the social welfare by providing fewer fleet sizes of taxi while keeping the vacancy rate at optimal level in each time period. It is suggested that a differential pricing scheme applied in the taxi market will have a win-win situation for operator, customer, and public sector.