永續城際運輸之雙層規劃模式

Abstract

本研究以追求永續運輸為目標，構建兩個雙層規劃模式--營運型模式與規劃型模式。營運型模式之上層係決定最適營運費率，下層則決定運輸業者之最適發車班次及旅客數；規劃型模式上層係同時決定運輸系統的最適興建年期與最適費率，而下層則與營運型模式相同。主要之理論基礎係基於政府、運輸業者及旅客所追求的目標並不同，不能合併於同一層模型中。其中，政府以達到永續運輸為目標，考量了安全、能源消耗、空氣污染及旅行時間等因素；運輸業者則決定最適發車班次以達到利潤最大化；旅客則追求運具選擇的效用最大化。假設政府(領導者) 與運輸業者(跟隨者) 間存在Stackelberg均衡的關係，不同的運輸業者間存在Nash均衡的關係，旅客(跟隨者)與運輸業者(領導者)也隱含著Stackelberg均衡的關係。由於雙層規劃模式的解法複雜，本研究發展出遺傳演算法加以求解。 為檢驗雙層規劃模式及求解方法的可操作性，本研究以一個城際運輸走廊、四種運具（航空、鐵路、公路客運與小客車）可供選擇為例，假設總旅次需求已知，航空及鐵路的旅行時間固定，公路客運及小客車之旅行時間則依BPR公式計算。經分析測試於每日50,000旅次需求下，營運型模式求解結果顯示最適鐵路、航空、公路客運及小客車之費率（用）應分別為794元，1,508元，794元及3,000元，其搭乘比例分別為33％，23.09%，32.97%及10.94%。期初僅有一公路系統存在於此運輸走廊情況下，規劃型模式求解結果為第一年即應興建鐵路，第四年興建航空站及第七年再興建另一鐵路。

This study proposes two bi-level programming models -- operational model and planning model to achieve the goals for sustainable transportation along an intercity corridor. In the operational model, the upper level is to determine the optimal fare (toll) rates, while the lower level is to determine the optimal operating frequencies of transport carriers and patronage of passengers. In the planning model, the upper level is to simultaneously determine the optimal construction horizons and fare rates of transport systems, while the lower level is the same as that of the operational model. The underlying theories are basing on various objectives viewed by the government, transport carriers and passengers, which cannot be incorporated into a single-level programming model. The goal of government is to achieve sustainable transportation in terms of safety, energy consumption, air pollution, and travel time. The goal for transport carriers is to maximize their profits in determining the operating frequencies. The goal for passengers (road users) is to choose transport modes to maximize their utilities. It is assumed that Stackelberg equilibrium exists between the government (leader) and the transport carriers (followers); Nash equilibrium exists among the transport carriers in the lower level while competing the quantity (frequencies); and Stackelberg equilibrium also exists between transport carriers (leaders) and passengers (followers). Due to the complexity of the proposed bi-level programming models, this study develops a solution algorithm based on genetic algorithms (GAs). To investigate the operationability of the proposed models and solution algorithm, this study tests an exemplified case of intercity corridor with four modes including air, rail, bus and private vehicles. Assume that the annual travel demand and its growth rate are given, the travel times of air and rail are constant, and the travel times of buses and private vehicles follow a BPR function. Under the demand of 50,000 trips per day, the results of operational model show that the optimal regulated fares (tolls) are NT$ 794, 1,508, 794, and 3,000, respectively, for rail, air, bus and private vehicle in association with the corresponding market shares 33%, 23.09%, 32.97% and 10.94%. If only a freeway system exists in this corridor at the beginnig, the results of planning model show that the three transportation systems should be introduced on the horizon of first year (railway), fourth year (airports) and seventh year (another railway).