MIP: Private tutoring scheduling

A private tutor wants to schedule students. We have some necessary, and some desired properties of the solution:

• All 10 students must get a time
• Each student is only available at certain times
• The teacher can max teach 3 students at a time
• The teacher wants to fit in the students in as few days as possible
• The teacher wants to minimize the total on-site time, including time waiting between classes

This can be modeled as an integer program and solved efficiently with a MIP solver. I use CBC, which is open source. 

Assuming that students are available randomly at 5% of the time, we get:

Coloring: Dark blue is active. Light blue is available student. Red is teacher waiting time.