對於每間學校而言，排課作業都是每年必須面對的難題之一，如何排出有品質之課表，甚至同時讓學生或是老師滿意為一大學問。因此，許多專家學者對其進行研究，並發表許多關於時間表問題 (Timetabling Problem; TTP)中的學校排課問題(School Timetabling Problem; STP)之論文。隨著資訊科技之發達，排課作業已不像以往耗時又耗力，但現有市售軟體大多只能滿足排課的基本原則，並未將大多老師之考量因素納入系統，因此，雖能排出相關課表，許多老師仍會提出自己的修改建議，導致學校行政人員上的作業困難。本論文針對國民中學排課問題(High School Timetabling Problem; HSTP)中之國中排課問題(Junior High School Timetabling Problem; JHSTP)進行研究，根據國民中學排課之基本原則建構一整數線性規劃模型，同時實地走訪多間學校了解其排課時所注重之因素，作為數學模型之目標，建構一由老師角度出發之國中排課數學模型。本研究以某國民中學之資料建立題庫，並使用GUROBI及CPLEX分別對題庫進行求解。研究結果發現， GUROBI求解能力優於CPLEX。除此之外，本研究使用C#程式語言，開發一套簡易排課系統，將GUROBI求解器套用於其中，可實際用於求解國民中學排課問題。

Timetabling Problem (TTP) is one of the problems that must be annually faced in every academic institution. Creating high-quality timetables involving students and teachers’ satisfaction is an important consideration in School Timetabling Problems (STPs). Therefore, many scholars have conducted researches on variants of School Timetabling Problems (STPs). With the development of information technology, developing the school timetable is no longer time-consuming and labor-intensive. However, a new challenge appears in a way of how to use the information technology to establish the school timetables. Most of the existing commercially available software only meets the basic principles of class schedule, but they do not take into account more detailed factors considered by most teachers or students into the system. This research hence focuses on the Junior High School Timetabling Problem (JHSTP) of High School Timetabling Problem　(HSTP) of a Taiwan’s junior high school timetable problem and formulates a mathematical model based on not only the basic principles of the Junior High School Timetabling Problem (JHSTP) and most of the schools’ curriculum scheduling rules but also teachers’ perspective. The developed integer linear programming model was then applied to a real case of a junior high school involving real data instances. GUROBI and CPLEX were utilized to solve the instances. The experimental result shows that GUROBI performs better than CPLEX. Moreover, this research also develops a C#-based course scheduling software by including the GUROBI as the solver as a decision support system for creating the timetable.

Abramson, D., Krishnamoorthy, M., & Dang, H. (1999). Simulated annealing cooling schedules for the school timetabling problem. Asia Pacific Journal of Operational Research, 16, 1-22.
Ahmed, L. N., Özcan, E., & Kheiri, A. (2015). Solving high school timetabling problems worldwide using selection hyper-heuristics. Expert Systems with Applications, 42(13), 5463-5471.
Al-Yakoob, S. M., & Sherali, H. D. (2015). Mathematical models and algorithms for a high school timetabling problem. Computers & Operations Research, 61, 56-68.
Brito, S. S., Fonseca, G. H., Toffolo, T. A., Santos, H. G., & Souza, M. J. (2012). A SA-VNS approach for the high school timetabling problem. Electronic Notes in Discrete Mathematics, 39, 169-176.
Broder, S. (1964). Final examination scheduling. Communications of the ACM, 7(8), 494-498.
Carter, M. W., & Laporte, G. (1997, August). Recent developments in practical course timetabling. In International Conference on the Practice and Theory of Automated Timetabling (pp. 3-19). Springer, Berlin, Heidelberg.
Carter, M. W., & Tovey, C. A. (1992). When is the classroom assignment problem hard? Operations Research, 40(1-supplement-1), S28-S39.
Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111.
Demirović, E., & Musliu, N. (2017). MaxSAT-based large neighborhood search for high school timetabling. Computers & Operations Research, 78, 172-180.
Deris, S., Omatu, S., & Ohta, H. (2000). Timetable planning using the constraint-based reasoning. Computers & Operations Research, 27(9), 819-840.
Di Gaspero, L., McCollum, B., & Schaerf, A. (2007). The second International Timetabling Competition (ITC-2007): Curriculum-based course timetabling (track 3). Technical Report QUB/IEEE/Tech/ITC2007/CurriculumCTT/v1.0, Queen’s University, Belfast, United Kingdom.
Dorneles, Á. P., de Araújo, O. C., & Buriol, L. S. (2017). A column generation approach to high school timetabling modeled as a multicommodity flow problem. European Journal of Operational Research, 256(3), 685-695.
Drexl, A., & Salewski, F. (1997). Distribution requirements and compactness constraints in school timetabling. European Journal of Operational Research, 102(1), 193-214.
Even, S., Itai, A., & Shamir, A. (1975). On the complexity of time table and multi-commodity flow problems. In 16th Annual IEEE Symposium on Foundations of Computer Science (pp. 184-193).
Gotlieb, C. C. (1963). The construction of class-teacher timetables. In IFIP congress (Vol. 62, pp. 73-77).
Gunawan, A., Ng, K. M., & Poh, K. L. (2007). An improvement heuristic for the timetabling problem. International Journal Computational Science, 1(2), 162-178.
Kheiri, A., Özcan, E., & Parkes, A. J. (2016). A stochastic local search algorithm with adaptive acceptance for high-school timetabling. Annals of Operations Research, 239(1), 135-151.
Kristiansen, S., Sørensen, M., & Stidsen, T. R. (2015). Integer programming for the generalized high school timetabling problem. Journal of Scheduling, 18(4), 377-392.
Leite, N., Melício, F., & Rosa, A. C. (2019). A fast simulated annealing algorithm for the examination timetabling problem. Expert Systems with Applications, 122, 137-151.
Lewis, R. (2008). A survey of metaheuristic-based techniques for university timetabling problems. OR Spectrum, 30(1), 167-190.
McCollum, B. (2006). A perspective on bridging the gap between theory and practice in university timetabling. In International Conference on the Practice and Theory of Automated Timetabling (pp. 3-23). Springer, Berlin, Heidelberg.
Merlot, L. (2005). Techniques for academic timetabling. PhD thesis, Department of Mathematics and Statistics and Department of Computer Science and Software Engineering, The University of Melbourne.
Papoutsis, K., Valouxis, C., & Housos, E. (2003). A column generation approach for the timetabling problem of Greek high schools. Journal of the Operational Research Society, 54(3), 230-238.
Pillay, N. (2014). A survey of school timetabling research. Annals of Operations Research, 218(1), 261-293.
Qu, R., Burke, E. K., McCollum, B., Merlot, L. T., & Lee, S. Y. (2009). A survey of search methodologies and automated system development for examination timetabling. Journal of scheduling, 12(1), 55-89.
Saptarini, N. G. A. P. H., Suasnawa, I. W., & Ciptayani, P. I. (2018). Senior high school course scheduling using genetic algorithm. In Journal of Physics: Conference Series (Vol. 953, No. 1, p. 012067). IOP Publishing.
Saviniec, L., & Constantino, A. A. (2017). Effective local search algorithms for high school timetabling problems. Applied Soft Computing, 60, 363-373.
Saviniec, L., Santos, M. O., & Costa, A. M. (2018). Parallel local search algorithms for high school timetabling problems. European Journal of Operational Research, 265(1), 81-98.
Schaerf, A. (1999). A survey of automated timetabling. Artificial Intelligence Review, 13(2), 87-127.
Skoullis, V. I., Tassopoulos, I. X., & Beligiannis, G. N. (2017). Solving the high school timetabling problem using a hybrid cat swarm optimization based algorithm. Applied Soft Computing, 52, 277-289.
Tassopoulos, I. X., & Beligiannis, G. N. (2012a). Solving effectively the school timetabling problem using particle swarm optimization. Expert Systems with Applications, 39(5), 6029-6040.
Tassopoulos, I. X., & Beligiannis, G. N. (2012b). Using particle swarm optimization to solve effectively the school timetabling problem. Soft Computing, 16(7), 1229-1252.
Tassopoulos, I. X., Iliopoulou, C. A., & Beligiannis, G. N. (2020). Solving the Greek school timetabling problem by a mixed integer programming model. Journal of the Operational Research Society, 71(1), 117-132.
ten Eikelder, H. M., & Willemen, R. J. (2000, August). Some complexity aspects of secondary school timetabling problems. In International Conference on the Practice and Theory of Automated Timetabling (pp. 18-27). Springer, Berlin, Heidelberg.
Wood, J., & Whitaker, D. (1998). Student centred school timetabling. Journal of the Operational Research Society, 49(11), 1146-1152.
Yu, E., & Sung, K. S. (2002). A genetic algorithm for a university weekly courses timetabling problem. International Transactions in Operational Research, 9(6), 703-717.
Zhang, D., Liu, Y., M’Hallah, R., & Leung, S. C. (2010). A simulated annealing with a new neighborhood structure based algorithm for high school timetabling problems. European Journal of Operational Research, 203(3), 550-558.
王江山，「以多標規劃求解大學教師排課最佳化之研究」，國立成功大學工業與資訊管理學系碩士在職專班碩士論文，民國93年
李昆穎，「演化式策略在國民中學排課問題之最佳化研究」，中華大學資訊工程學系碩士在職專班碩士論文，民國102年。
林俐儀，「設計啟發式演化式策略最佳化國民中學排課問題」，中華大學資訊工程學系碩士論文，民國104年。
邱元泰，「遺傳演算法在排課問題之應用」，國立中正大學數學研究所碩士論文，民國91年。
邱炤幃，「基因演算法在國小排課問題之應用」，屏東科技大學資訊管理系所
碩士論文，民國100年。
侯兆昇，「運用基因演算法解決高等職業學校排課問題」，義守大學資訊工程學系碩士論文，民國107年。
唐學明，「軍事學校電腦排課問題之探討」，復興崗學報(59)，129-155，民國85年。
袁仲明，「混合圖形著色與限制條件為基礎之排課系統-以臺灣職業訓練中心為例」，元智大學資訊管理學系學位論文，民國102年。
康家豪，「國小自動排課系統之研究─粒子群最佳化演算法的應用」，臺北市立大學數學資訊教育學系數學資訊教育教學碩士學位班碩士論文，民國103年。
陳仲星，「國民中學排課問題最佳化研究─使用基因演算法」，樹德科技大學資訊管理系碩士論文, 民國106年。
陳奕憲，「基因演算法在國民中學排課問題之最佳化研究」，南華大學資訊管理學系碩士班碩士論文，民國100年。
陳熠，「以C語言撰寫排課系統-以逢甲應數系為例」，逢甲大學應用數學學系碩士論文，民國104年。
彭美玉，「演化式策略於國民小學排課問題之最佳化研究」，中華大學資訊工程學系碩士論文，民國104年。
賀羲之，「基於人工智慧之排課系統」，國立臺北教育大學資訊科學系碩士論文，民國105年。
廖聖揚，「應用限制規劃方法求解軍事院校排課問題」，國立高雄第一科技大學資訊管理所碩士論文，民國94年。