The problem I'm attempting to solve is formulated like this:
A department consists of n groups such as for each group i in $\overline{1,n}$ contains $p_i$ members.
A change in the organization is wanted so that:
- the new organizing schema contains q groups of members
- each group in $\overline{1,q}$ will contain $k_i$ members
- the new groups may not contain more than c members which were part of the same old group (c $\geq$ 2 , c $\in \mathbb{N}$)
How to find a model based on a flow network to build this new organizing schema?
I've tried building a network flow graph but I had trouble in representing the member groups and the restriction that no more than c members which were part of an old group can be present in a new group. Thank you for reading the question, any hint or solution is greatly appreciated.
I'll repeat my answer from this deleted question from another user earlier today:
Define a complete bipartite graph with $n$ supply nodes and $q$ demand nodes. The flow from node $i$ to node $j$ indicates the number of students that move from old group $i$ to new group $j$. Each flow variable has an upper bound of $c$.