Consider the classic network flow problem where the constraint is that the inflow to a vertex is equal to the sum of its outflows. Consider having a more specific constraint where the flow cannot be split between edges. The constraint is that the inflow
a to a vertex
v is equal to
b (the amount that
v has acquired from
c (the outflow carried by only one of the non-visited edges of
The figure below demonstrates this in 3 mutually exclusive cases. The green directed edge carries an inflow of value
b takes some value of
a, then only one of the edges (disregarding the inflow edge) carries the outflow of value
c=a-b (illustrated in 3 cases - the red edge represents the edge carrying the outflow, the rest of the edges should have zero outflow).
Is this constraint possible to formulate under the linear/integer programming setting ?
Thanks in advance!