We are planning the course schedule for a class of students and we have one day that is particularly straining. In mods 1 to 6, we have to teach mathematics, physical education, philosophy, theatre, social studies and creative writing. These subjects strain the kids resources in different ways. Math and philosophy are hard mental work, theatre and social studies drain the kids' social batteries, and gym and theatre are physically demanding.
The engagement of the children in each course is affected by their resources. For each category (mental, physical, and social), the kids start with a "charge" of 20 points before Mod 1 each morning. Charges for all three "batteries" never go below 0 or above 20. Per mod, the kids recharge each battery with 4 points. The different subjects consume charges according to the matrix 'R' below.
Now, the engagement in a subject depends on the kids' resources in each category at the end of each mod. If the incoming charges for category 'c' are 'C_c,' then the charges at the end of teaching subject 's' are computed by the following formula:
Then, the engagement in the subject 's' is computed as
There are some additional constraints:
- In Mod 1, the gym and the stage are occupied, so we cannot schedule theatre or physical education then.
- The math teacher is only available in mods 1 and 2.
- The day has to end with either creative writing or drama (we had mistakenly put physical education here in a previous version).
The school has asked to design the schedule in such a way that the students are well engaged. Can you do it?
Do you care more about the minimum engagement or the average engagement?
With its proprietary multi-objective optimizer, Seeker suggests this roster:
- Mod 1: Social Studies - Engagement 80
- Mod 2: Math - Engagement 60
- Mod 3: Gym - Engagement 75
- Mod 4: Creative Writing - Engagement 65
- Mod 5: Philosophy - Engagement 45
- Mod 6: Drama/Theatre - Engagement 35
Total Engagement: 360 - Minimum Engagement: 35
The maximum total engagement we could achieve is 370, but with a minimum of 30. Maximizing the minimum engagement yields also 35.