Maximal Flow Problem Algorithm

Step1

Determine a path from source to sink that can hold a positive flow of material. If no such path exists then go to step 5

Step2

Find out the highest flow that can be shipped from this path and indicate by 'k' units.

Step3

Reduce the direct capacity of each branch of this path 'k' and amplify the reverse capacity k₁. Add 'k' units to the amount distributed to sink.

Step4

Go on step1

Step5

The maximal flow is the quantity of material delivered to the sink. The optimal shipping schedule is recognized through comparing the original network with the final network. Any deduction in capacity indicates shipment.

Sample Assignment

Take the following network and find the amount of flow among the networks.

Answer

Iteration 1: 1 - 3 - 5

Iteration 2: 1 - 2 - 3 - 4 - 5

Iteration 3: 1 - 4 - 5

Iteration 4: 1 - 2 - 5

Iteration 5: 1 - 3 - 2 - 5

Maximum flow = 60 units. Thus the network can be written as

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