Linear Programming pp 225-252 | Cite as

# Network Flow Problems

Chapter

## Abstract

Many linear programming problems can be viewed as a problem of minimizing the “transportation” cost of moving materials through a network to meet demands for material at various locations given sources of material at other locations. Such problems are called *network flow problems*. They form the most important special class of linear programming problems. Transportation, electric, and communication networks provide obvious examples of application areas. Less obvious, but just as important, are applications in facilities location, resource management, financial planning, and others.

## Keywords

Span Tree Tree Solution Linear Programming Problem Simplex Method Dual Variable
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## References

- Ford, L. & Fulkerson, D. (1962),
*Flows in Networks*, Princeton University Press, Princeton, Princeton.MATHGoogle Scholar - Christofides, N. (1975),
*Graph Theory: An Algorithmic Approach*, Academic Press, New York.MATHGoogle Scholar - Lawler, E. (1976),
*Combinatorial Optimization: Networks and Matroids*, Holt, Rinehart and Winston, New York.MATHGoogle Scholar - Bazaraa, M., Jarvis, J. & Sherali, H. (1977),
*Linear Programming and Network Flows*, 2 edn, Wiley, New York.MATHGoogle Scholar - Kennington, J. & Helgason, R. (1980),
*Algorithms for Network Programming*, John Wiley and Sons, New York.MATHGoogle Scholar - Jensen, P. & Barnes, J. (1980),
*Network Flow Programming*, John Wiley and Sons, New York.MATHGoogle Scholar - Bertsekas, D. (1991),
*Linear Network Optimization*, The MIT Press, Cambridge, Cambridge.MATHGoogle Scholar - Ahuja, R., Magnanti, T. & Orlin, J. (1993),
*Network Flows: Theory, Algorithms, and Applications*, Prentice Hall, Englewood Cliffs, NJ.Google Scholar - Dantzig, G. (1951a), Application of the simplex method to a transportation problem,
*in*T. Koopmans, ed., ‘Activity Analysis of Production and Allocation’, John Wiley and Sons, New York, pp. 359–373.Google Scholar - Ford, L. & Fulkerson, D. (1958), ‘Constructing maximal dynamic flows from static flows’,
*Operations Research***6**, 419–433.CrossRefMathSciNetGoogle Scholar

## Copyright information

© Robert J.Vanderbei 2008