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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In the first edition, this method was called the primal–dual simplex method.
Bibliography
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.
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.
Nazareth, J. (1986). Homotopy techniques in linear programming. Algorithmica, 1, 529–535.
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.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this chapter
Cite this chapter
Vanderbei, R.J. (2014). Sensitivity and Parametric Analyses. In: Linear Programming. International Series in Operations Research & Management Science, vol 196. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-7630-6_7
Download citation
DOI: https://doi.org/10.1007/978-1-4614-7630-6_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4614-7629-0
Online ISBN: 978-1-4614-7630-6
eBook Packages: Business and EconomicsBusiness and Management (R0)