CLASSROOM SCHEDULING OPTIMIZATION USING LINEAR PROGRAMMING: A CRITICAL REVIEW OF MODELS, UTILIZATION MEASURES AND RESEARCH GAPS
AUTHORS:
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Prof. Tejaswini Angre
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B.Sc. Finance, Anil Surendra Modi School of Commerce, SVKM’s NMIMS, Mumbai, India
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Abstract
Every university routinely states that they are understaffed with classrooms, and that many classrooms are left half empty, leaving the Operations Research (OR) problem between these two assertions: that of the understaffed classroom, and that of the half empty classroom. In this paper, the use of linear programming (LP) and its integer extension for the assignment of classes to rooms and time slots is briefly reviewed. Two case applications, one in Landmark University, Nigeria (an aggregate LP) and the other in Uttara University, Bangladesh (two-stage binary integer programme) are presented, and a focused review of 25 studies is conducted between 1992 and 2026. The main room-assignment problem is computationally easy: It can be solved in minutes on real institutions with several hundred to "only" 1100 class meetings by solving the LP relaxation, which is naturally integral, one period at a time, and is an assignment problem in itself. The weakness is in the optimization. There has been a seat hour measure of utilisation since 2009, but each institutional case study maximises at least six different fit measures, which can favour different rooms, report gains based on different baselines and plan against a single enrolment number. Re-running this case with its own data reveals that the case's headline figure of 3,544 seats is higher than the number of seats actually available (2,861). It is illustrated in a five-class example that a tight-fit objective results in 15 students being unseated when there is a heavy load of students, and 2 when there is not. Finally, the paper suggests that the next step in this research is the development of an LP-solvable seat-fit model that is enrolment-robust and a common reporting protocol.
The keywords are operations research, linear programming, integer programming, classroom assignment, university course timetabling, space utilisation and robustness.
Keywords—operations research; linear programming; integer programming; classroom assignment; university course timetabling; space utilisation; robustness
The keywords are operations research, linear programming, integer programming, classroom assignment, university course timetabling, space utilisation and robustness.
Keywords—operations research; linear programming; integer programming; classroom assignment; university course timetabling; space utilisation; robustness
Keywords
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Double-Blind Peer Review
License:
CC BY-NC 4.0
Volume/Issue:
Volume 02, Issue 10
Review Rounds:
2
Article Type:
Research Article
Publication Date:
Oct 09 2026
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Ramina, I., Jain, K., Sanghavi, K., Bamboli, K. & Kedia, K. (2026). Classroom Scheduling Optimization Using Linear Programming: A Critical Review of Models, Utilization Measures and Research Gaps. International Journal of Science, Strategic Management and Technology, 02(10). https://doi.org/10.55041/ijsmt.v2i10.027
Ramina, Ishwar, et al.. "Classroom Scheduling Optimization Using Linear Programming: A Critical Review of Models, Utilization Measures and Research Gaps." International Journal of Science, Strategic Management and Technology, vol. 02, no. 10, 2026, pp. . doi:https://doi.org/10.55041/ijsmt.v2i10.027.
Ramina, Ishwar,Kaashvi Jain,Kavish Sanghavi,Kabir Bamboli, and Kanav Kedia. "Classroom Scheduling Optimization Using Linear Programming: A Critical Review of Models, Utilization Measures and Research Gaps." International Journal of Science, Strategic Management and Technology 02, no. 10 (2026). https://doi.org/https://doi.org/10.55041/ijsmt.v2i10.027.
References
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[2] N. M. Arratia-Martinez, C. Maya-Padron, and P. A. Avila-Torres, “University course timetabling problem with professor assignment,” Mathematical Problems in Engineering, vol. 2021, art. no. 6617177, 2021, doi: 10.1155/2021/6617177.
[3] C. Beyrouthy, E. K. Burke, D. Landa-Silva, B. McCollum, P. McMullan, and A. J. Parkes, “Towards improving the utilization of university teaching space,” Journal of the Operational Research Society, vol. 60, no. 1, pp. 130–143, 2009, doi: 10.1057/palgrave.jors.2602523.
[4] M. W. Carter and C. A. Tovey, “When is the classroom assignment problem hard?,” Operations Research, vol. 40, suppl. 1, pp. S28–S39, 1992, doi: 10.1287/opre.40.1.S28.
[5] M. C. Chen, S. N. Sze, S. L. Goh, N. R. Sabar, and G. Kendall, “A survey of university course timetabling problem: Perspectives, trends and opportunities,” IEEE Access, vol. 9, pp. 106515–106529, 2021, doi: 10.1109/ACCESS.2021.3100613.
[6] Y. Chen, M. Bayanati, M. Ebrahimi, and S. Khalijian, “A novel optimization approach for educational class scheduling with considering the students and teachers’ preferences,” Discrete Dynamics in Nature and Society, vol. 2022, art. no. 5505631, 2022, doi: 10.1155/2022/5505631.
[7] M. A. Cruz-Chávez, M. Flores-Pichardo, A. Martínez-Oropeza, P. Moreno-Bernal, and M. H. Cruz-Rosales, “Solving a real constraint satisfaction model for the university course timetabling problem: A case study,” Mathematical Problems in Engineering, vol. 2016, art. no. 7194864, 2016, doi: 10.1155/2016/7194864.
[8] S. Daskalaki, T. Birbas, and E. Housos, “An integer programming formulation for a case study in university timetabling,” European Journal of Operational Research, vol. 153, no. 1, pp. 117–135, 2004, doi: 10.1016/S0377-2217(03)00103-6.
[9] X. Han and D. Wang, “Gradual optimization of university course scheduling problem using genetic algorithm and dynamic programming,” Algorithms, vol. 18, no. 3, art. no. 158, 2025, doi: 10.3390/a18030158.
[10] A. Lemos, F. S. Melo, P. T. Monteiro, and I. Lynce, “Room usage optimization in timetabling: A case study at Universidade de Lisboa,” Operations Research Perspectives, vol. 6, art. no. 100092, 2019, doi: 10.1016/j.orp.2018.100092.
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