Titlebook: Linear Programming; Foundations and Exte Robert J. Vanderbei Textbook 20144th edition Springer Science+Business Media New York 2014 Linear

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Efficiency of the Simplex MethodIn the previous chapter, we saw that the simplex method (with appropriate pivoting rules to guarantee no cycling) will solve any linear programming problem for which an optimal solution exists. In this chapter, we investigate just how fast it will solve a problem of a given size.

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The Simplex Method in Matrix NotationSo far, we have avoided using matrix notation to present linear programming problems and the simplex method. In this chapter, we shall recast everything into matrix notation. At the same time, we will emphasize the close relations between the primal and the dual problems.

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Implementation IssuesIn the previous chapter, we rewrote the simplex method using matrix notation. This is the first step toward our aim of describing the simplex method as one would implement it as a computer program. In this chapter, we shall continue in this direction by addressing some important implementation issues.

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Problems in General FormUp until now, we have always considered our problems to be given in standard form. However, for real-world problems it is often convenient to formulate problems in the following form: In this chapter, we shall show how to modify the simplex method to handle problems presented in this form.