What is a flow balance constraint How is it implemented at e

What is a flow balance constraint? How is it implemented at each node in a network?

Solution

Flow balance constraint states that (flow out of node) - (flow into a node) = (net supply at a node).

There is one balance equation for each node in the network.

For example,

x₁₂ + x₂₃ = 20 for node 1

x₂₃ + x₂₄ + x₂₅ - x₁₂ = 0 for node 2

The flow variables x_ij only have 0, +1 and -1 as coefficients.

Further, each variable appears in exactly two balance equations, once with a +1 coefficient,
corresponding to the node from which the arc emanates; and once with a 1 coefficient, corresponding to the node upon which the arc is incident.