Lecture 7 - Simplex 2 Phase

# Lecture 7 - Simplex 2 Phase - 540:311DETERMINISTICMODELSIN...

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540:311 DETERMINISTIC MODELS IN OPERATIONS RESEARCH Lecture 7: Chapter 4.13 Class MeeBng: Thu Feb 10 th 10:20‐11:40am Prof. W. Art Chaovalitwongse

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4.13 The Two‐Phase Simplex Method When a basic feasible soluGon is not readily available, the two‐phase simplex method may be used as an alternaGve to the Big M method. In this method, arGFcial variables are added to the same constraints, then a bfs to the original LP is found by solving Phase I LP. In Phase I LP, the objecGve funcGon is to minimize the sum of all ar0Fcial variables . At compleGon, reintroduce the original LP’s objec0ve func0on and determine the opGmal soluGon to the original LP.
Because each a i ≥ 0 , solving the Phase I LP will result in one of the following three cases: The opGmal value of w’ is greater than zero. The opGmal value of w’ is equal to zero, and no arGFcial variables are in the opGmal Phase I basis. In this case, drop all columns in the opGmal Phase I tableau that correspond to the arGFcial variables.

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## This note was uploaded on 09/20/2011 for the course ENG 300 taught by Professor Albin during the Fall '11 term at Rutgers.

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Lecture 7 - Simplex 2 Phase - 540:311DETERMINISTICMODELSIN...

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