First of all, I am not a mathematician. I'm mainly asking the question to see if what I want to do is even possible via math -- and whether I then could computerize this math.
So you may throw this question out. If so, I understand.
But here is the question:
100 musicians participate in a chamber music workshop.
A musician may play one of the following: Violin, viola, cello, contrabass, oboe, clarinet or flute. (There are lots more violins, violas and cellos than there are other instruments.)
Each musician practices in four different groups at the workshop.
A group may be anything from an octet (rare) down to a quartet (most common).
These groups have been pre-assigned. In other words, the composition of the groups is set when the workshop begins.
Each group plays its piece in a concert at the end of the workshop.
There are three separate concerts so that this large number of groups don't all have to play in one concert (which would take hours and hours).
So it's possible that each musician would end up playing in all three concerts. Or it might end up being two, or (rarely) even one.
The question is: How can you take these groups and assign them to concerts such that each individual musician plays in the fewest possible number of concerts?
(Assume it's desirable to reduce as much as possible the number of concerts each musician must participate in.)
I've looked up things like employee scheduling software, classroom scheduling software, manufacturing software and everything else I can think of. I can't find any software that can handle the problem as I have stated it above.
Can anyone help point me to an answer or technique or (ideally) know of existing software that will let me tackle this problem?