| 摘要: | 在公共投資中，公共工程投資為國家經濟建設之基礎，良好的公共工程建設將有助於提升生活品質與促進其他產業之發展，故無論國內外，公共工程建設一直是公共投資計畫中的重要環節。公共工程建設投資在社會福利最大化之考量下，需考量多個不同功能之效益，故計畫不但具多屬性，公部門之決策依據更具多目標，且基於預算及其他資源之限制，通常無法完全執行所有需求的建設計畫，故在公共工程建設計畫之規劃決策中，除需於眾多方案中選擇效益最大化的組合外，資源限制之考量亦不可避免，然而在過去之研究中，資源限制多僅以總資源需求與總資源限制作為決策之依據，對於一中長期計畫，不同時期之資源需求與資源限制可能不同，資源需求與資源限制應是具有時依性。此外，單一專案亦可能分成多個階段或多個次專案（作業項目）執行，不同階段間具先後順序之時間邏輯關係，且其效益亦可能隨其執行時間改變，故公共工程建設計畫除需考量選擇的問題外，應加入考量專案之時程規劃與資源排程問題。本文即針對此上述之特性，提出一考量多專案、多作業項目、時序性與資源限制之『公共工程建設計畫時序性組合規劃模式』，此模式不但可提供公部門決定效用較佳之計畫組合外，並可決定計畫之時程規劃。根據本問題特性建構之數學規劃模式，屬於0-1非線性整數規劃問題，於數學規劃上可歸類於背包問題（Knapsack Problem），其解法上具有NP-hard的特性，以傳統之數學規劃方法並不易求解其最佳解，有鑑於此，本研究以遺傳演算法整合多評準決策法，建立一具效率與效力之求解方法。 The decision on infrastructure investment is complex. It involves satisfying all constraints, in terms of time, activity precedence and resources, and maximizing the overall utility simultaneously. The decision itself is not about choosing the best among all potential alternatives identified, but to form a most favorable combinatorial plan of alternatives within the limitation of resources, in terms of money, time, and manpower. Since different alternatives are often in a competing position for an identical resource and such resource requirements vary from one period to another throughout the planning horizon, it is quite apparent that the determination of the combinatorial plan is a typical multi-objective resource scheduling problem. This work characterizes an infrastructure investment problem in four aspects: (1) multiple objectives, (2) multiple alternative projects with sub-projects, (3) definitive time-dependent resource constraints and resource demands, and (4) definitive time-logic constraints among sub-projects. This study proposes a time-series combinatorial planning model to represent the infrastructure investment problem. The model is formulated based on mathematical programming. It is observed that the model is a 0-1, non-linear, multi-objective knapsack problem, which exhibits the NP-hard nature. Since finding the optimal solution is computationally difficult, this work proposes an innovative approach, based on the concept of genetic algorithms, to tackle the non-linear optimization problem. Based on experimental results, the proposed approach is effective in producing quality solutions. The methodological significance of the proposed approach lies in the highly effective multi-point search mechanism afforded by the genetic algorithms. Another merit of the proposed approach is that it provides a bank of feasible solutions, rather than just the best solution found. This bank can serve as a good reference to the decision-maker. |
