
Construct a subgraph graph G consisting of the "best cost edge" Find a maximal flow in subgraph G repeat until all supplies are exhausted { Add the "next best cost edge" to G; // Notice the quotes: it's more complex that just // looking at the cost of an edge Find a maximal flow in (modified) subgraph G; } 
This shipment is equivalent to commidity flow


Example:

Note:



(We just apply the definition of the flow augmenting path to the Transportation bipartite graph:
backward edges always run from Y → X)
Cost Matrix:  b1 b2 b3 + A1  3 5 7 A2  6 4 3 



Transportation graph  Cost Matrix 

 b1 b2 b3 b4 + a1  5 4 7 6 a2  2 5 3 2 a3  6 3 4 4 

Value of objective function: 54.00 Actual values of the variables: x11 2 x12 3 x13 0 x14 0 x21 3 x22 0 x23 0 x24 1 x31 0 x32 0 x33 5 x34 1 
Side by side comparison:
LP solution  Solution by Hungarian Algorithm 

Note:
