Presenting an Integer Programming Model for Course Timetabling in Military Universities Considering Operational Constraints and Educational Requirements

Articles in Press

Document Type : Research Article

Authors

Mohammad Abbasian ¹

Sayed Alireza Ghazi Mirsaeed ²

ali absiraei ³

¹ [e-mail]

² Researcher

³ Assistant Prof. Faculty of Engineering and Aviation, Imam Ali Officers’ University, Tehran, Iran.

10.22067/jstinp.2026.95837.1182

Abstract

University course timetabling requires the coordination of educational requirements, instructor assignments, and institutional availability restrictions. This coordination is particularly important in military higher education, where protected periods may be required for organizational and operational activities. This study develops a strengthened mixed-integer linear programming formulation for course timetabling in an Iranian military university. The model completely schedules all required course-class meetings and partially assigns the instructors whose requests for morning teaching are represented in the objective. Standard hard constraints concerning course coverage, student-class and instructor non-overlap, instructor eligibility, teaching-load limits, and prescribed meeting frequencies are integrated with alternate-week meeting patterns and expert-defined protected periods. The objective maximizes the number of morning teaching-assignment occurrences allocated to the modeled instructors. The initial nonlinear relationship was reformulated through exact linearization, and a strengthened sparse formulation was implemented in Optimization Programming Language within IBM ILOG CPLEX Optimization Studio. The model was evaluated using real data from Imam Ali (AS) Officers’ University, comprising 23 courses, 62 student classes, 33 modeled instructors, and 15 weekly time slots. The optimal solution scheduled all 806 required course-class-time occurrences, assigned 317 course-class combinations to the modeled instructors, and achieved 339 morning teaching-assignment occurrences. CPLEX proved optimality at the root node in 6.30 seconds with a 0.00% optimality gap. Sensitivity and scalability experiments further showed that the strengthened formulation solved all tested instances, including synthetic extensions of up to 124 student classes, to proven optimality within 8.89 seconds. These results indicate that the strengthened exact formulation is computationally suitable for the investigated decision scope while providing an auditable scheduling tool for the institution.

Keywords

University Course Timetabling

Scheduling

Military Universities

Integer Programming

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