軍事後勤補給、災變緊急避難，及重大活動之人員與車輛的集結與疏散，皆可利用「集結與疏散交通指派問題(Gathering and Evacuation Traffic Assignment Problems, GETAP)」來幫助決策者進行規劃與決策。由於GETAP問題往往具有時效的急迫性，因此考量以系統最佳化(System Optimization)的觀念來解決此類問題，亦即所有車輛均須依照指定路線來行駛。然若系統最佳化之結果無法滿足決策者，例如總旅行時間太長或最後一部車到達集節點(安全區域)的時間太晚，則顯示既有路網運輸容量不足或路網瓶頸容量太小。因此在處理GETAP呈現上述容量不足情況時，則可考慮藉由改善現有運輸網路中某些節線之容量，或新增某些節線來提高網路運輸的最大流量，並滿足集結或疏散所需的運輸能量。本研究旨在將上述問題轉換為「最大流量問題(Maximal Flow Problem, MFP)」後，並利用「最佳增量節線(Most Augmenting Arcs, MAA)」理論所提出求解最佳單一增量節線之演算法來找出路網瓶頸所在，並整合系統最佳化觀念提出一改善路網容量之啟發式演算法。最後以一範例示範其演算過程；此外，本文亦介紹如何將各類集結與疏散交通指派問題轉換為抽象數學網路問題，並依據各類GETAP問題特性的不同，提出注意事項。

In this research, the theory of the Most Augmenting Arcs (MAA) and system optimization with travel time constraint were applied to solve the Gathering and Evacuation Traffic Assignment Problems (GETAP). GETAP mostly occurred in an emergent or urgent situation. The Olympic games and emergency evacuations are good GETAP examples. For example, we need to plan how to transport audience from their origins to the stadium before Olympic games and transport audience from the stadium to their origins after the games. Since these emergent problems need to be solved in a short time, we might use network system optimization concept to solve these problems. An algorithm for the GETAP is also developed. First, the city street network is transferred as a s-t network. Secondly, the efficiency of the s-t network is evaluated by the maximum flow algorithm. If the current network is inefficient, i.e. the maximal flow is not large enough, the bottlenecks of the network will be found and improved by the most augmenting arc algorithm. The most augmenting arcs are those arcs which, when the capacities are augmented, can result in the greatest increase of the maximum flow of a given s-t network. In order to satisfy the system optimization, all vehicles have to drive according to the assigned paths. Finally, we used a simple example to show how to apply the proposed procedure to the considered transportation problems.