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A variant of the Assignment Problem
(Not a comp.scientist, but have the basic research. Please excuse me if I've overlooked anything obvious.)
In my variant of the problem I have a set $A$ of agents and a set (of possibly different cardinality) $T$ of tasks. Each agent needs to be assigned exactly $n$ or $n+1$ tasks, and each task needs to be assigned to exactly $m$ or $m+1$ agents.
It is guaranteed that this is possible: the segment $[ |A|n, |A|(n+1) ]$ intersects the segment $[ |B|m, |B|(m+1) ]$.
Each agent-task combination yields a profit, and I want to maximize the profit.
Is this a special case of one of the known problems? How can this be solved? If not practical for $n=100000$, what are good approximations and what is their complexity?
Cheers!
