社會福利最大化之大眾運輸補貼雙層數學規劃模式－考量生態足跡限制

Abstract

為了達到永續運輸及社會福利最大化之目的，本研究試圖建構一雙層數學規劃模式針對預算的分配來訂定最適之永續政策。上層是在有限的預算、運輸系統的容量及生態足跡的限制下，求得每個旅次的社會福利最大化，並對於大眾運輸使用者進行票價補貼、大眾運輸班次的虧損補貼及可取得的綠能地來消化運輸所產生的生態足跡。下層則是經由運具選擇模式決定每個旅次發生所使用的運具，並針對使用私人運具進行使用者均衡模式來決定旅次路線。根據這些假設，本研究發展出單一世代雙層數學規劃模式模式(SG)及跨世代雙層數學規劃模式(AG)。單一世代模式僅考量現在所擁有的資源及預算來決定最適之政策；而跨世代模式則是兩個世代之間的資源及預算交易來求得最適之結果。

為驗證模式的實用性，本研究建構一模擬路網進行模擬分析，單一世代模式結果顯示，增加大眾運輸使用者的票價補貼及大眾運輸的班次，會吸引許多使用者使用大眾運輸，並達到相同的社會福利水準，然而，後者會伴隨著產生大量的生態足跡對於生態環境帶來莫大的傷害。而跨世代模式結果則顯示，現在這個世代可以藉由移轉部分的預算給未來的世代以增加整體總效益並達到對兩個世代最佳之決策。

To achieve transportation sustainability and social welfare, bi-level budget allocation models are proposed, in which the upper level is to maximize the social welfare of trip makers under the constraints of government budget, capacity of transport system, and ecological footprint by allocating budget to subsidize bus users for increasing public transportation patronage and reducing usage of private vehicles and/or to acquire additional green land for accommodating excess footprint. The lower level is to determine the mode choice decisions of all trip makers and the route choice decisions of those who use of private vehicles. Two models are developed and compared: the single generation (SG) model and the across generation (AG) model. The SG model assumes these decisions are made under the consideration of the contemporary generation alone, while the AG model compromises these decisions with the following generation. To investigate the applicability of the model, a case study on an exemplified network is conducted. Results of the SG model show that the measure of bus fare discount and the measure of bus frequency increase can both attract remarkable percentage of bus usage and achieve almost the same social welfare, however, the latter will generate much larger footprint than that of bus fare discount due to the high emission characteristic of buses. The results of the AG model show that the optimal decision of the contemporary generation will compromise its total utility with that of the next generation by intentionally leaving part of budget to the next generation.