I've been tasked to optimize the assignment of reviewers for a group assignment.
The problem follows as such, we have $x_i$ student teams $i \in 1 ... n_1$ and $y_j$ reviewers $j \in 1 ... n_2$. Some of these reviewers are senior reviewers.
Over the course of a single day every team needs to have 3 meetings, 2 with normal reviewers and one with a senior reviewer. These meetings need to be between 1 team and 1 reviewer.
This feels like it's constrained linear optimization, though I suspect there's an enormous number of solutions, and we don't really have a target function to optimize here, just constraints. There's too many reviewers and teams to go through all permutations with a computer, so I'm not exactly sure where to begin here.
Thanks!
It's hard for me to see what the problem is, so I suspect there is some additional complication you haven't mentioned.
Say we have reviewers A,B,C, of whom A is the only senior reviewer. In period 1, team a meets with A, team b with B, team c with C. In period 2, team a meets with B, b with C, c with A. In period 3, a meets with C, b meets A, c meets B. In periods 4,5,6 teams d, e, and f go through the same cycle. In another 3 rooms, reviewers D (senior),E, and F go through the same procedures with other teams.
Once the reviewers have had their quota of meetings, they are replaced by other reviewers. The only reason this will fail to work, (if the problem is soluble at all) is if fewer than one-third of the reviewers are senior. Is this the case?