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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Notes
Parametric analysis has its roots in Gass & Saaty (1955). G.B. Dantzig’s classic book (Dantzig 1963) describes the self-dual simplex method under the name of the self-dual parametric simplex method. It is a special case of “Lemke’s algorithm” for the linear complementarity problem (Lemke 1965) (see Exercise 17.7). Smale (1983) and Borgwardt (1982) were first to realize that the parametric self-dual simplex method is amenable to probabilistic analysis. For a more recent discussion of homotopy methods and the parametric self-dual simplex method, see Nazareth (1986) and Nazareth (1987).
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© 2001 Robert J. Vanderbei
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Vanderbei, R.J. (2001). Sensitivity and Parametric Analyses. In: Linear Programming. International Series in Operations Research & Management Science, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5662-3_7
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DOI: https://doi.org/10.1007/978-1-4757-5662-3_7
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-5664-7
Online ISBN: 978-1-4757-5662-3
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