I have been searching for a solution to my below problem but without luck. I am wondering if there could be a solution that is perhaps a branch of graph theory but I haven't been able to find anything - so my first question should really be:
"Is there an approach to maximizing the number of series' (eg class schedules) that can fit into a finite number of resources (eg classrooms)?
My problem:
Assuming/hoping it is possible, here is an example scenario with the following assumptions: - Classrooms are available from 9am until 4pm, Monday to Friday - All classes are 1 hour in length - Classrooms for a specific lesson type have to occur in one of the corresponding rooms
I have 10 classrooms:
- 4 general-purpose (for registration, history, languages, technology - and of course Maths!
- 2 Science
- 2 Art
- 1 Music
- 1 Library
I have a ranked list of schedules I need to fit (as many as possible) in - and each class should begin a day with a registration class and then the other classes can be in any order:
- Class01: 2 days/week of 4 hours: Maths/science/technology
- Class02: 4 days/week of 3 hours: Art/Music/Library
- Class03: 1 day/week of 6 hours: Art/Music/Library
- Class04: 4 days/week of 3 hours: Art/Music/Library
- ...etc...