Lecture9

# Lecture9 - Advanced Operations Research Techniques IE316...

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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 3.5-3.9 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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Lecture9 - Advanced Operations Research Techniques IE316...

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