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Unformatted text preview: Advanced Operations Research Techniques IE316 Lecture 9 Dr. Ted Ralphs IE316 Lecture 9 1 Reading for This Lecture Bertsimas 3.53.9 IE316 Lecture 9 2 Finding an Initial Basic Feasible Solution Recall that we need an initial BFS to start the simplex methods. Ideally, the initial basis matrix would also be the identity matrix (easy to invert). In some cases, this is easy to achieve. If the formulation contains only inequalities and the origin is feasible, then there is no problem. The initial BFS is simply x = 0 ,s = b and the initial basis matrix is the identity matrix (easy to invert). For problems with equalities or where the origin is not feasible, things are more difficult. To deal with this, we need the concept of an artificial variable . Artificial variables are used in the equality rows like slack variables, but then forced to zero. IE316 Lecture 9 3 Obtaining a Feasible Solution Suppose we are given an LP min { c T x  Ax = b,x } already in standard form....
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 Fall '08
 Ralphs
 Operations Research

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