Maximal Flow Problem Algorithm
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
Find out the highest flow that can be shipped from this path and indicate by 'k' units.
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.
Go on step1
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.
Take the following network and find the amount of flow among the networks.
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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