# graph theory – Creating a network flow model for building a new organizing schema for a departament

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.