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How to solve assignment problem with additional constraints?

You can create additional "group agents" that represent combinations of actual agents (for instance, $P_{17}$ might be the pairing of $P_1$ and $P_2$) and/or additional "combo tasks&...
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How to solve assignment problem with additional constraints?

This sounds like a special case of the parallel assignment problem in which the preemption (this is a standard notation in the scheduling theory) would be allowed. I am not aware of how this problem ...
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