Recently I've learned hungarian algorithm for solving the assignment problem, Now I'm curious about how to solve more general problem: for given n × m table select several numbers, maximizing their sum with following constraints: in each row the number of selected numbers is not less than Rmin and not more than Rmax, and for each column the number of selected numbers is not less than Cmin and not more than Cmax.
If Rmin = Rmax = 1 and Cmin = Cmax = 1 this is the standard assignment problem. But what can we say about more general case? Any ideas about this (maybe, at least in case Rmin = Rmax = R, Cmin = Cmax = C)? Any thoughts would be greatly appreciated.