# A more general case of assignment problem

Recently I've learned hungarian algorithm for solving the assignment problem, Now I'm curious about how to solve more general problem: for given $n \times m$ table select several numbers, maximizing their sum with following constraints: in each row the number of selected numbers is not less than $R_{min}$ and not more than $R_{max}$, and for each column the number of selected numbers is not less than $C_{min}$ and not more than $C_{max}$.

If $R_{min} = R_{max} = 1$ and $C_{min} = C_{max} = 1$ this is the standard assignment problem. But what can we say about more general case? Any ideas about this (maybe, at least in case $R_{min} = R_{max} = R$, $C_{min} = C_{max} = C$)? Any thoughts would be greatly appreciated.

The general case can be modeled as a flow problem in a bipartite graph $G=(V_1\cup V_2,E)$, with $|V_1|=n$ and $|V_2|=m$.
To take into account your constraints, add a source $s$ and link to all vertices of $V_1$, and a sink $t$, linked to all vertices of $V_2$. Impose that the entering flow in each node of $V_1$ is at least $R_{min}$ and at most $R_{max}$, and that the exiting flow from each node of $V_2$ is at least $C_{min}$ and at most $C_{max}$, and you are done.