In my variant of the assignment 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 this this is possible: the segment $\left[ |A|n, |A|(n+1) \right]$ intersects the segment $\left[ |B|m, |B|(m+1) \right]$.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=100,000, what are good approximations and what is their complexity? Not a comp.scientist, but have done the basic research. Please excuse me if I've overlooked anything obvious. 
A variant of the Assignment Problem
optimization;linear programming;assignment problem