Create a graph network flow model for the Computer Science Department

Question

I need to create a network flow model for building (if possible) the new organizing schema for the following problem:

At the Computer Science Department at the beginning of the first semester there are p freshmen (study) groups: group i contains n(i) students, for all i = 1, p. For the second semester the Department wants to reorganize these groups in such a way that:

->the new organizing schema has r groups;

->the new group j contains m(j) students, for any j = 1, r;

->any new group cannot contain more than c students which were classmates in a same old group from the former organizing schema (c ∈ NN∗ \ {1}).

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My idea would be to use a network that contains a bipartite graph but don't know how to organise students and grups inside it and how to describe this bipartition.

Answer 1

Define a complete bipartite graph with $p$ supply nodes and $r$ 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 $c$.