應用多目標規劃法於低碳運輸計畫之預算分配

A MULTI-OBJECTIVE PROGRAMMING MODEL OF BUDGET ALLOCATION IN LOW CARBON TRANSPORTATION PROJECTS

運輸部門的溫室氣體排放量為全球產業最大宗排放源之一，發展低碳運輸計畫以減少碳排放量已成為近年來公共運輸系統建設之目標。以往決策者在公共建設規劃時多採用質性評選方式來決定預算分配比例，缺乏較客觀的量化因素。本研究建構一多目標數學規劃模式，以追求低碳運輸策略效益最大與減少區域間預算分配差距，同時導入「計畫可調整性」及「最低可執行預算規模比例」等因素，進行低碳運輸計畫預算分配。模式建構階段初始藉由典型背包問題（0-1 Knapsack Problem）發展整數規劃預算分配模型（即模式1）、考慮預算可調整性，將計畫分成連續型計畫及非連續型計畫之混合整數規劃預算分配模型（即模式2）、加入公平性目標式、區域預算配給比例等參數與考慮各計畫之最低可執行預算比例，構建一多目標混合整數非線性規劃預算分配模型（即模式3）。依據不同情境最佳化預算分配，並依據實例分析驗證模式之可行性。從我國行政院環保署之「低碳城市建構計畫」實例分析結果可以得知，當總預算額度偏低時，模式傾向將預算優先分配予減碳能力較佳之區域；當預算額度較為充足時，本研究發展之公平性目標式會有助於減少區域間預算配給之差異。由於分配結果會隨著權重目標調整而改變，本研究透過多目標權衡分析針對不同權重組合求取最佳解，可作為決策者未來執行模式之參考依據。

Reducing greenhouse gas emissions is one major issue and challenge in transportation sections. To achieve this mission, various administrative divisions under the central government were asked to propose some low-carbon transport projects for annual budget planning and allocation. Instead of arbitrarily evaluating the performance of those projects, this paper contributes a method for quantifying and jointly optimizing the results of project selections and budget allocations, while also considering the proportion and minimum required amount of each proposed budget. A basic model (Model 1) adapted from the typical 0-1 knapsack problem, an extended mixed integer programming model (Model 2), and a multi-objective mixed integer nonlinear programming model (Model 3) are developed in this study. Models 1 and 2 are maximizing the total reduction of emissions based on selected projects and approved budget. Model 3 is further pursuing the equality issue by minimizing the variance of allocation results among administrative divisions. Through a series of numerical examples and sensitivity analysis, the models demonstrate their ability to maximize emissions reduction through budget allocating decisions. Different weight combinations between two objective functions are also examined.