Generalized assignment

I have a problem like this: there are Y people that need to be assigned to no more than X sessions at different times according to their availability, ensuring that no session contains more or less than a given amount of people (Y/X +/- 20% for example).

The specific problem in which the number of people and the number of sessions are the same seems to be the same as an assigmnent problem.

However, does anyone have an idea on how to solve this more genral case?

I'm ok with both pseudo-algorithms or with suggestions on how to use the GLPK. I could code this in perl or javascript.

Solution

I think you are referring to Generalized assignment problem. which fits into your case. The generalized assignment problem is NP-hard

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