The document discusses the maximal flow problem and its technique. The maximal flow problem aims to compute the maximum possible flow that can leave the source and enter the sink. The maximal flow technique involves 5 steps: 1) choosing a path from source to sink, 2) finding the path with the lowest flow capacity, 3) subtracting the lowest capacity in the source to sink direction and adding it in the reverse direction, 4) completing the addition and subtraction for the first iteration, and 5) repeating steps 1-4 until all paths have a zero flow capacity from source to sink.

1. THE MAXIMAL FLOW
PROBLEM
GIEJAN C. SECRETARIA

2. OBJECTIVE
• To compute a maximum flow-a flow with the maximum-possible value, meaning the total
amount of flow that leaves source. This is the same as the total amount of flow that enters
sink.
e.g.
Shopee delivery, trucking services and public transportation.
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4. Maximal –flow Technique
• Five steps of the Maximal-flow Technique
1. Choose any path from the start to end of the network flow
2. Find the arch with the lowest flow capacity that is available going from
a source of a sink.
3. This lowest flow capacity is subtracted from the direction of source to
sink while in reverse direction, it is added.
4. Complete the addition and subtraction to find the first iteration.
5. Repeat steps 1-4 to find the next iteration until all paths have at least
one zero flow capacity from a source to a sink
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15. REFERENCES
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https://www.slideshare.net/AbdulMujeebDalal/max-flow-problem-70859649?qid=76ea0b4a-
531e-461f-986a-4f37d9f57bfa&v=&b=&from_search=2
https://www.slideshare.net/agneskpuspita/quantitative-management-ch-11-network-
models?qid=76ea0b4a-531e-461f-986a-4f37d9f57bfa&v=&b=&from_search=7
https://www.slideshare.net/ahmedjubayer3/shortest-route-minimal-spanning-
tree?qid=76ea0b4a-531e-461f-986a-4f37d9f57bfa&v=&b=&from_search=15
https://www.slideserve.com/Ava/chapter-2-fundamentals-of-decision-theory
https://www.slideshare.net/FreeNews4All/chp12networksmodel-121128084640phpapp01

16. Thank you for
listening and
have a nice trip
everyone.
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