Network Simplex - Evaluating a Nonbasic Arc Previous Next
Suppose arc AD with flow  is added to the feasible spanning tree. Adding a nonbasic arc to a spanning tree always creates a unique undirected cycle. In this case, that cycle is AD-DE-EC-CA. If the flow  is added to arc AD, then the other arcs in the cycle will need to be adjusted to retain the required net flow at each node. The effect of adding the flow  to arc AD on each of the other flows in the cycle is shown in the network above.