市區公車里程計費制之最佳費率結構與水準

Abstract

我國現行各縣市之市區公車，除過去公路客運改制之市區公車外，多採用單一費率與段次計費之費率結構；雖具有費率結構與收費方式單純等優點，但短程旅次交叉補貼長程旅次，以及分段緩衝區設置之問題，對於不同旅次長度與旅次起迄之使用者而言，並不公平。而現代科技之進步，複雜費率結構之實行困難度與成本已大幅降低，乃為費率結構之調整之適當時機。 基於此研究背景，本研究以公車運量最大化、區域公平性最大化、使用者付費公平性最大化，以及補貼額度最小化為目標，並以各別業者營收不變與政府補貼預算固定為限制式，研提一多目標費率最佳化模式，並以層級分析法(Analytic Hierarchy Process, AHP)求解各目標式之權重進行求解；其中區域公平性係計算各行政區每公車旅次之平均旅行成本之變異，而使用者付費公平性則以無起程里程與費率之「合理里程計費」或考慮業者基本服務成本與後勤營運成本之「基本費率」與「里程費率」為比較基礎，以最小平方法計算求解費率結構與前述費率之差異。此外，本研究之模式並可依決策變數與使用者付費公平性計算基礎之不同，進一步推展為四模式；其中，模式一與模式三皆以「合理里程計費」為比較基礎、模式二與模式四皆以「基本費率」與「里程費率」為比較基礎，前二模式將起程里程納入決策變數，後二模式則以起程費率與續程費率決定起程里程。 本研究並以臺北都會區市區公車為例，以邊際效應分析法進行運量變動之計算，並以遺傳演算法(Genetic Algorithm, GA)進行模式求解；求解結果顯示，模式一與模式二皆為短起程里程之費率結構，而模式三與模式四則皆為長起程里程之費率結構，而模式一與模式二求解結果較佳；四模式之運量與區域公平性皆可提升，且政府傾向不提供價差補貼，使用者付費公平性依模式不同而有不同結果，整體而言，模式二求解結果最佳。此外，本研究根據目標式與限制式不同，進行情境分析，包含考慮路網總營收、不考慮補貼額度最小化限制式、價差補貼方式調整，以及價差補貼預算敏感度分析等四情境，前三情境除考慮路網總營收之情境求得單一費率之費率結構外，其餘情境皆求得短起程里程之費率結構；而於敏感度分析中，補貼預算減少與不編列預算進行補貼之起程里程較長，其餘亦皆求得極短里程之費率結構。

City bus fare schemes in Taiwan are mostly flat-fare and stage fare. The cross-subsidization of short-haul trips and long-haul trips and the problem of segmentation points or buffer zones are the disadvantages of stage fare, though its fare scheme and fare collection is very simple and user-friendly. While the fast innovation of modern technologies, such as GPS and smart-cards, making complicated fare schemes more possible and low cost. Based on this background, this study proposed a multi-objective mathematical programming model to optimize the fare structure and level of distance-based fare. The objectives include maximization of bus trips, maximization of zonal equality, maximization of user equality, and minimization of subsidization, while the constraints include the revenue must be hold in different bus companies, and the subsidy budget is a finite amount. The zonal equality is defined as the variation of average travel cost per bus trip in every administrative districts, and the user equality is compared to reasonable fare rate or basic fare plus reasonable fare rate using ordinary least square. The Analytic Hierarchy Process was used to determine the weights in order to transform multi-objectives to a single objective. The model can be transformed into 4 models depending on its decision variables and the base of comparing user equality. Model 1 and 3 are based on the reasonable fare rate, and only the former model includes the basic-distance as a decision variable. Model 2 and 4 are based on the basic fare plus reasonable fare rate, and also only the former model includes the basic-distance. This study uses the city bus system in Taipei Metropolitan as an example, and marginal effect analysis was used to compute the changes of demand. The models are solved by the Genetic Algorithm, results show that model 1 and 2 have short basic-distances while model 3 and 4 have long basic-distances. The number of bus trips and the zonal equality could be enhanced, and government is prone to not subsidizing bus users in all models. However, the result of user equality is different depending on different models. In summary, model 2 has the best solving performance. Furthermore, this study conducted a scenario analysis by concerning different objectives and constraints, including overall revenue remaining the same in the network as a constraint, solving without subsidization minimization objective, different subsidization patterns, and sensitivity analysis of subsidization. In the first scenario, results show that the flat-fare is preferred while short basic-distance fare structures are preferred in the second and third scenarios. In the sensitivity analysis, results show that longer basic-distance is preferred only when the subsidy budget is zero and reduces 50%, otherwise, short basic-distance is preferred.