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2014 | OriginalPaper | Chapter

7. Sensitivity and Parametric Analyses

Author : Robert J. Vanderbei

Published in: Linear Programming

Publisher: Springer US

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Abstract

In this chapter, we consider two related subjects. The first, called sensitivity analysis (or postoptimality analysis) addresses the following question: having found an optimal solution to a given linear programming problem, how much can we change the data and have the current partition into basic and nonbasic variables remain optimal? The second subject addresses situations in which one wishes to solve not just one linear program, but a whole family of problems parametrized by a single real variable.

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Footnotes
1
In the first edition, this method was called the primal–dual simplex method.
 
Literature
Borgwardt, K. -H. (1982). The average number of pivot steps required by the simplex-method is polynomial. Zeitschrift für Operations Research, 26, 157–177.
Dantzig, G. (1963). Linear programming and extensions. Princeton: Princeton University Press.CrossRef
Gass, S., and Saaty, T. (1955). The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly, 2, 39–45.
Lemke, C. (1965). Bimatrix equilibrium points and mathematical programming. Management Science, 11, 681–689.CrossRef
Nazareth, J. (1986). Homotopy techniques in linear programming. Algorithmica, 1, 529–535.CrossRef
Nazareth, J. (1987). Computer solutions of linear programs. Oxford: Oxford University Press.
Smale, S. (1983). On the average number of steps of the simplex method of linear programming. Mathematical Programming, 27, 241–262.CrossRef
Metadata
Title
Sensitivity and Parametric Analyses
Author
Robert J. Vanderbei
Copyright Year
2014
Publisher
Springer US
Book
Linear Programming

Print ISBN: 978-1-4614-7629-0

Electronic ISBN: 978-1-4614-7630-6

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-1-4614-7630-6_7