巡迴計程車市場多時段費率與空車率最佳化之研究

Multiple Period Optimization of Fare and Vacancy Rate for a Cruising Taxi Market

沈大維(Ta-Wei Shen)

指導教授 ： 張學孔

國立臺灣大學/工學院/土木工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.02614

摘要

計程車於都市公共運輸中被定義為「副大眾運輸系統」，相較於一般大眾運輸系統，具有方便、迅速、及門、私密、舒適等服務特性，在經濟活動頻繁的都會區中扮演著重要的角色。由於計程車服務涉及社會公眾利益，無論在費率訂定、產業結構、駕駛人資格或牌照發放等層面皆應有妥善的規劃與管理。國內外許多研究曾建立最佳化分析模型，以期作為相關主管機關對計程車管理之理論依據。然而過去研究普遍忽略計程車市場尖離峰差異之特性，最佳化結果僅能顯示一日平均的均衡狀態，無法反映非尖峰時段存在超額供給現象，且目前單一費率的制度下，將造成尖離峰旅次交叉補貼的問題。
本研究建立計程車市場尖離峰差異特性之最佳化模型，加入時間差別訂價以及離峰時段超額供給閒置的概念，分別以利潤最大、社會福利最大及損益平衡社會福利最大為系統目標，求取計程車市場最適供需均衡、最適費率與最適空車率。研究中以台北縣市地區計程車市場營運情形作為數值分析案例，並針對模式中各重要參數進行敏感度分析，瞭解各參數對決策變數與目標函數之影響程度。
數值分析結果顯示，基於兼顧社會福利及財務永續的考量，損益兩平限制下的次佳解應為較適合的營運模式。在設定尖峰、離峰、夜間價格彈性為：-1.33、-1.4、-1.47，且等候時間彈性為-0.22、-0.2、-0.18的假設下，台北縣市地區各時段之最適費率分別為53.78 $/km、33.84 $/km、31.09 $/km，最適空車率則分別為40.0%、33.3%、27.7%；在司機合理營業時數8小時的假設下，推估合理計程車數量為39,728輛，與2008年台北縣市掛牌登記的55,327輛減少了15,599輛。顯示目前台北地區計程車市場確實存在數量過多的問題，建議政府於計程車牌照減量的同時亦考慮實施尖離峰差別定價，以較少的車輛規模達到更大的社會福利，並使各時段空車率皆能維持於最適水準，創造營運者、使用者與管理者三贏的局面。

關鍵字

計程車 ； 多時段 ； 最佳化 ； 分析性模型 ； 閒置成本 ； 空車率

並列摘要

Taxi is defined as the paratransit in the urban public transit systems. Compared with conventional mass transit systems, taxi is featured with convenience, speediness, door-to-door, privacy and comfort; so it has become a popular mode in urban area. Because taxi service is involved with public welfare, there are lots of issues should be planned and managed properly, such as fare system, industry structure, driver qualification and plate grant. Therefore, many researches had established the optimization models to improve the taxi industry. However, most of those studies didn’t consider the difference of market between peak and off-peak hour, but the excess supply makes vacant taxis inefficiently cruise in off-peak hour. In other hand, the single fare system now might cause unfair subsidy between trips in peak and off-peak hour.
Cause of above problems, this study develops an optimization model involves multiple period fare and the concept of idle cost which can reduce the excess supply in off-peak hour. Through the model we can find the optimal equilibrium of taxi market, the optimal fare and vacancy rate at each time period. In the study, we use the operation data of taxi market in Taipei metropolis as a case. The numerical results show that in order to maximize the social welfare and balance the revenue and expenditure, the second-best solution should be the most appropriate operation mode. If the price elasticity in peak, off peak and midnight is -1.33, -1.4, -1.47 respectively, and the waiting time elasticity is -0.22, -0.2, -0.18, then the optimal fare will be 53.78 $/km、33.84 $/km、31.09 $/km respectively, the optimal vacancy rate will be 40.0%、33.3%、27.7%, and the fleet size of taxicabs in Taipei metropolis should be 39,728(reduced by 15,599 from now) under the assumption that the daily average operation hour of taxi drivers is 8 hours. It shows that there are truly too much taxis in Taipei metropolis now.
As the results of multi-period market optimization model, we can improve the social welfare by providing fewer taxicabs, and then keep the vacancy rate at the optimal level in each time period. Through the model, we can get a triple win solution between operator, customer, and government department.

並列關鍵字

taxicab, multiple period ； optimization ； analytic model ； idle cost ； vacancy rate

參考文獻

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