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Zbl 1162.65355
Nabli, Hédi
An overview on the simplex algorithm. (English)
[J] Appl. Math. Comput. 210, No. 2, 479-489 (2009). ISSN 0096-3003

Summary: The simplex algorithm and its variants are investigated. First, we define a new concept called formal tableau, which leads to derive easily the dual solution from the latest primal table; without any distinction between the original variables and the slack ones. Second, we propose a new method for initializing the simplex algorithm. Unlike the two-phase and the big-M methods, our technique does not involve artificial variables. The computational results reveal that this new method is very favorable especially when the number of artificial variables is significant. Finally, this method will be combined with the notion of formal tableau leading naturally to a second new approach.

MSC 2000:: *65K05 Mathematical programming (numerical methods)
90C05 Linear programming

Keywords: linear programming; simplex algorithm; dual-simplex algorithm; big-M method; two-phase method

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Zentralblatt MATH Berlin [Germany]