Consider having two sets $L$ (left) and $R$ (right). $R$ nodes have a capacity limit. Each edge $e$ has a cost $w(e)$.
I want to map each of the $L$ vertices to one node from $R$ (one-to-many matching), with minimum total edge-costs.
Each vertex in $L$ must be mapped to one vertex in $R$ (but each node in $R$ can be assigned to multiple $L$-nodes).
Examples: Consider the capacity of $R$ nodes is $2$.
1) This is NOT correct, since one node from $L$ has not assigned to a node in $R$.
2) This is NOT correct, since the capacity of a node in $R$ is violated.
3) This IS correct. All $L$ nodes are assigned to a node in $R$, and the capacity of $R$ nodes is not violated.
Any idea how can I solve this?