Date: 20/10/2021 ## Summary - Define date and time classes are given - Can be political - Reykjavik University - *Term Time* software - Teachers have lots of independence - Optimize room usage, - COVID considerations - \# of people constraint - Teacher-centric problem -> NP complete - Student considerations added -> "NP insane" ### Formulation - Hard constraints - class has one teacher, teach one class at a time - Soft constraints - preferences from time, room location - Two common objective functions - sum of hard + soft constraint violations - weighted sum of hard + soft constraint violations - has used: - branch and bound - integer linear programming - mixed integer linear programming ### Implementation Reykjavik Engineering MSc. - 7 programs - 17 courses - 125 students - randomly assigned - 4 time slots - 5 rooms in each time slot - binary variables for teacher and student - maximize sum product of student preference and enrollment Achieved 100% enrollment in core courses, 93% enrollment in elective courses #### Pros - less errors - more efficient - avoids resentment between teachers ## Discussion Difficulty in expanding? - article uses a different method for larger problem, finds near-optimal solution