Flow is associated with the network, entering and leaving at the nodes and passing through the arcs. Flows entering or leaving a node from external sources are called external flows and are shown adjacent to the nodes in the square brackets. A positive external flow is a supply, flow that enters the network, and a negative external flow is a demand, flow that leaves the network. Flow is conserved at each node, implying that the total flow entering a node, either from arcs or external supplies, must equal the total flow leaving the node, either to arcs or to external demands. The arc flows are the decision variables for the network flow programming model.
Flow is limited in an arc by the lower and upper bounds on flow.
In this example we specify 0 as the lower bound for all arcs and 200 as the upper bound. Sometimes the term capacity refers to the upper bound on flow. The problem is to find a feasible flow, if one exists, and an optimal flow from the set of feasible flows. The criterion for optimality is cost. If a flow x passes through the arc with unit cost c , a cost cx is incurred.