AUTHOR AND 
GEORGE MATHEW 
KEYWORDS: 
Network, flow, feasible flow, flow value, st cut, augmenting path, leeway, maximum flow, Subject classification: 05C21 
Issue Date: 
October, 2017 
Pages: 
440447 
ISSN: 
23198044 (Online) – 2231346X (Print) 
Source: 
Vol.29 – No.10 
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DOI: 
http://dx.doi.org/10.22147/juspsA/291004 
ABSTRACT:
The maximum flow problem was first formulated in 1954 by T.E. Harris and F.S. Ross as a simplified model of soviet Railway traffic flow1. In 1955, Lester R. Ford, Jr. and Delbert R. Fulkerson created the first known algorithm for calculating the maximum flow, the FordFulkerson algorithm2. It was in 1951 when the American mathematician, George Dantzig put forward the network simplex algorithm to solve mininimum cost flow problem. We take a typical example and find the maximum flow and minimum cost. Finally we generalise The Producer’s Problem based on some assumptions and find the maximum flow and minimum cost in it. We observe that the minimum unit cost in The Producer’s Problem increases with the number of items produced increases, in contrast to natural expectation.
Copy the following to cite this Article:
G. Mathew; M. M. Abraham, “Network Flow in Graph Theory – The Producer’s Problem”, Journal of Ultra Scientist of Physical Sciences, Volume 29, Issue 10, Page Number 440447, 2017
Copy the following to cite this URL:
G. Mathew; M. M. Abraham, “Network Flow in Graph Theory – The Producer’s Problem”, Journal of Ultra Scientist of Physical Sciences, Volume 29, Issue 10, Page Number 440447, 2017
Available from: http://www.ultrascientist.org/paper/852/networkflowingraphtheorytheproducersproblem
The maximum flow problem was first formulated in 1954 by T.E. Harris and F.S. Ross as a simplified model of soviet Railway traffic flow1. In 1955, Lester R. Ford, Jr. and Delbert R. Fulkerson created the first known algorithm for calculating the maximum flow, the FordFulkerson algorithm2. It was in 1951 when the American mathematician, George Dantzig put forward the network simplex algorithm to solve mininimum cost flow problem. We take a typical example and find the maximum flow and minimum cost. Finally we generalise The Producer’s Problem based on some assumptions and find the maximum flow and minimum cost in it. We observe that the minimum unit cost in The Producer’s Problem increases with the number of items produced increases, in contrast to natural expectation.