March 2014
Intermediate to advanced
412 pages
11h 16m
English
Content preview from Numerical Methods and Optimization
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Chapter 11
The Simplex Method for Linear
Programming
In this chapter, we discuss one of the first and most popular methods for
solving LPs, the simplex method originally proposed by George Dantzig in
1940s for solving problems arising in military operations. In order to apply
this method, an LP is first converted to its standard form, as discussed in the
following section.
11.1 The Standard Form of LP
LP in the standard form has only equality and nonnegativity constraints.
An inequality constraint can easily be converted into an equality constraint by
introducing a new variable in the left-hand side as follows. If the i
th
constraint
is of “≤” type, we add ...
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