Network Simplex - Evaluating a Nonbasic Arc Previous Next
Suppose arc AD with flow is added to the feasible spanning tree. The unique undirected cycle in this case is AD-DB-BC-CA. The above network shows next to each arc the resulting incremental flow (in parentheses) and the cost per unit flow (to the left of the parentheses).
When , the resulting overall increment in total cost () is
  = 5(1) + 3(-1) + 2(1) + 4(-1) = 0.
Hence, the rate of change of  as  is increased is 0.