機隊排程與班次表規劃之優劣影響航空業者營運績效甚巨。機隊排程作業主要指 業者對其所擁有機隊中各飛行器之飛航時程與起迄場站之安排，其結果不但攸關設備之使用 效率、左右班次表之擬訂與人員之調度，更重要的，將直截影響業者之獲利、服務水準與市 場之競爭能力。本研究為能有效掌握需求與供給間之互動關係，茲以數學規劃方法構建一直 截整合旅次需求與航次供給之飛航排程模式。此模式係以時空網路來定式一包含人旅次流動 與飛機流動之多重貨物網路流動問題。本研究利用拉氏鬆弛法、次梯度法、網路單體法、最 短路徑法、流量分解法與最小成本流量推擠法等綜合發展一拉氏演算法，來求解此一在數學 上係屬於 NP-hard 性質之問題。經測試結果顯示此模式可供作為業者改善營運之參考。

　　　　　Fleet routing and flight scheduling are important in airline operations. In particular, they always affect the usage efficiency of facilities, the establishment of timetables and crew scheduling. As a result, they are essential to carriers' profitability, level of service and competitive capability in the market. This research attempts to develop an integrated model and a solution algorithm to help carriers simultaneously solve better fleet routes and proper timetables. In order to manage the interrelationships between trip demand and flight supply, we apply a time-space network model to formulate the movements of aircraft and passenger flows. Mathematically, the model is formulated as a special multiple commodity network flow problem. On the basis of Lagrangian relaxation, the subgradient method, the network simplex method, the shortest path algorithm, the flow decomposition algorithm and the least cost flow augmentation algorithm, we develop a Lagrangian-based algorithm to efficiently solve the problem. The results of a case study have shown the model to be useful for airlines to improve their operations.