本論文的主要目的是重新排序等待進離場的飛機，然後藉由新的進離場順序減少所有飛機完成起降的時間，以期能夠達到舒緩機場流量的目的。因此，此研究主要在探討如何利用排程演算法找出最佳化的近離場順序。在我們的排程演算法中，我們的首要目標是最小化所有飛機完成起降的時間。與現有的飛機起降排程演算法最大的不同是我們利用危險值分布流場的概念找出每種機型尾流的持續時間與抵抗能力，然後藉由這兩者的結合即可得到兩架飛機之間的隔離時間。因此，時間隔離的限制式可以用線性的方式來表示，而且限制式的數量也會隨著等待重新排序飛機數量呈現線性成長，而不是像其他排程演算法呈二次方的成長，可以大大的減少整個演算法的計算量。此外，我們同時最小化所有飛機的時間變動量，此變動量為預計抵達或出發時間與實際抵達或出發時間的差。因此，我們可以提供進場飛機的建議飛行速度。使用我們線性規劃排程演算法，結果會使飛機的近離場順序為最佳化排序，且為變動量最小的情況。最後，我們的模擬結果會與先到先服務(First-Come-First-Serve, FCFS)的模擬結果做比較，證明其方法的有效性。

This thesis studies the problem of sequencing aircraft take-off and landing operations at congested airports. The objective is to minimize the makespan for all the aircraft to land at or depart from the airport. Unlike the existing formulations of separation constraints, we consider the separation time as the combination of the turbulence generated by each type of aircraft and the ability to resist turbulence for each aircraft. Using this novel concept, the separation constraints are more flexible with aircraft types and are linear with the decision variables. The required number of separation constraints grows linearly with the number of aircraft instead of quadratic growth for existing formulations. Moreover, to minimize the deviation from scheduled arriving and departing time, we simultaneously solve for the speed change advisory for the arriving aircraft. Using our optimization process, the final result can meet both optimal sequence and minimal time variation requirements. Finally, several simulation results are used to demonstrate the effectiveness of our approach.

1. D'Ariano, A., D' Urgolo, P., Pacciarelli, D., and Pranzo, M. "Optimal sequencing of aircrafts take-off and landing at a busy airport," 13th International IEEE Conference on Intelligent Transportation Systems. Funchal, 2010, pp. 1569-1574.
2. "FAA Aerospace Forecast Fiscal Years 2013-2033." Federal Aviation Administration, 2012.
3. Zhang, X., Zhang, X., Zhang, J., and Liu, B. "Optimization of Sequencing for Aircraft Arrival Based on Approach Route," Intelligent Transportation Systems Conference IEEE Seattle, WA, 2007, pp. 592 - 596.
4. Beasley, J. E., Krishnamoorthy, M., Sharaiha, Y. M., and Abramson, D. "Scheduling aircraft landings- the static case," Transportation Science Vol. 34, No. 2, 2000, pp. 180-197.
5. Ding, Y., and Valasek, J. "Aircraft Landing Scheduling Optimization for Single Runway Noncontrolled Airports: Static Case," Journal of Guidance, Control, and Dynamics Vol. 30, No. 1, 2007, pp. 252-255.
6. Dear, R. G. "The Dynamic Scheduling of Aircraft in the Near Terminal Area," Report R76-9 Flight Transportation Laboratory, MIT, Cambridge, MA, , 1976.
7. Balakrishnan, H., and Chandran, B. "Scheduling aircraft landings under constrained position shifting," AIAA Guidance, Navigation and Control Conference and exhibit, Keystone. Colorado, 2006.
8. Hu, x. b., and Chen, W. H. "Receding Horizon Control for Aircraft Arrival," IEEE Transactions on Intelligent Transportation System Vol. 6, No. 2, 2005, pp. 189 - 197.
9. Amrahov, S. E., and Ibrahim Alsalihe, T. A. "Greedy algorithm for the scheduling aircrafts landings," 5th International Conference on Application of Information and Communication Technologies Baku, 2011, pp. 1-3.
10. Chen, S., and Xia, X. "Researches on Optimal Scheduling Model for Aircraft Landing Problem," International Conference on Information Engineering WASE Vol. 1, Taiyuan, Chanxi, 2009, pp. 418-421.
11. Meng, X., Zhang, P., and Li, C. "Aircraft category based genetic algorithm for aircraft arrival sequencing and scheduling," Chinese Control Conference. Beijing, 2010, pp. 5188-5192.
12. Bai, C., and Zhang, X. "Aircraft Landing Scheduling in the Small Aircraft Transportation System," International Conference on Computational and Information Sciences Chengdu, China, 2011, pp. 1019-1022.
13. Farah, I., Kansou, A., Yassine, A., and Galinho, T. "New Modelling and Exact Method for Aircraft Arrival Sequencing and Scheduling," 4th International Conference on Logistics (LOGISTIQUA). Hammamet, 2011, pp. 44-49.
14. Kupfer, M. "Scheduling Aircraft Landings to Closely Spaced Parallel Runways," Eighth USA/Europe Air Traffic Management Research and Development Seminar (ATM2009). 2009.
15. Bojanowski, L., Harikiopoulo, D., and Neogi, N. "Multi-Runway Aircraft Sequencing at Congested Airports," American Control Conference. San Francisco, CA, USA, 2011, pp. 2752 - 2758.
16. Wang, D., Peng, L., Tang, C., Li, s., and Sun, W. "Sequencing Optimization Model for Arrival and Departure Flights," International Conference on Information Science and Technology. Nanjing, Jiangsu, China, 2011, pp. 287 - 290.
17. Wang, T. C., and Li, Y. J. "Optimal Scheduling and Speed Adjustment in En Route Sector for Arriving Airplanes," Journal of Aircraft Vol. 48, No. 2, 2011, pp. 673-682.
18. Wang, T. C., and Tsao, C. H. "Time-Based Separation for Aircraft Landing Using Danger Value Distribution Flow Model," Mathematical Problems in Engineering Vol. 2012, 2012, pp. 1-16.
19. "Air Traffic Control." Order Jo 7110.65U ed., Federal Aviation Administration, 2012.
20. Ferguson, T. S. "Linear Programming: A Concise Introduction." http://www.math.ucla.edu/~tom/LP.pdf , 2012.
21. Taha, H. A. Operations Research: Pearson Education, 2008.
22. Freville, E., Nicolaon, J. P., Vidal, A., and Crick, P. "Potential Benefits of a Time-based Separation Procedure to maintain the Arrival Capacity of an Airport in strong head-wind conditions," ATM Seminar. Budapest,Hungary, 2003.