0. Simulcast Students are not considered as part of this optimization problem. They will be assigned to AM/PM cohorts as a second optimization problem.

1. Students will be divided into AM and PM cohorts. Siblings must be assigned to the same cohort.

2. Each Student has an initial Teacher assignment. Assignments MAY be changed, but such moves should be minimized.

3. Each classroom has a maximum capacity.

4. Each teacher has an initial Classroom assignment. We do not attempt to move teachers.

5. Maintaining Gender balance is desirable.

We load the rooms, teachers, and students data. Then we group siblings together by home address. Once siblings have been linked together, we assign each set of siblings to an AM or PM cohort in pseudo-random order ensuring AM and PM have roughly equal distribution. Note that we DO NOT assign these students to a teacher in this phase.

Next, group all students based on their affinity to their current teacher. There are 4 tiers of affinity (0-3), 0 being minimal affinity, and 3 being maximal affinity.

For each tier, starting with maximal affinity, we shuffle the list of students. We assign all sibling students, and then all non-sibling students. We prefer the student's current teacher, and fall back to other teachers within that grade level if their current teacher is full. Non-sibling students are placed in whichever AM/PM cohort has the least students assigned so that the AM and PM sessions remain balanced.