Lecture8 - Introduction to Mathematical Programming IE406...

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Unformatted text preview: Introduction to Mathematical Programming IE406 Lecture 8 Dr. Ted Ralphs IE406 Lecture 8 1 Reading for This Lecture • Bertsimas 3.3, 3.5-3.7 IE406 Lecture 8 2 The Tableau Method • This is the standard method for solving LPs “by hand.” • We update the matrix B- 1 [ b | A ] instead of just B- 1 . • In addition, we keep track of the reduced costs in row “zero.” • This method is more expensive then revised simplex and is really just used for illustration. • The method for updating the matrix is the same as in revised simplex. IE406 Lecture 8 3 What the Tableau Looks Like • The tableau looks like this- c B B- 1 b c- c B B- 1 A B- 1 b B- 1 A • In more detail, this is- c B x B ¯ c 1 ··· ¯ c n x B (1) . . . B- 1 A 1 ··· B- 1 A n x B ( m ) IE406 Lecture 8 4 Parts of the Tableau • Row zero contains the reduced costs. • Column zero contains the values of the current basic variables. • The upper left-hand corner entry is the opposite of the current objective function value. • Each nonbasic column contains the feasible direction corresponding to increasing the given nonbasic variable. • The basic columns are the columns of B- 1 B = I , i.e., they are the unit vectors. • All the information needed to perform an iteration of the simplex method is readily available. • If variable j is to enter the basis, perform elementary row operations to turn column j of the tableau into the i th unit vector, where i is the variable leaving the basis. IE406 Lecture 8 5 Implementing the Tableau Method 1. Start with the tableau associated with a specified BFS and associated1....
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This note was uploaded on 08/06/2008 for the course IE 406 taught by Professor Ralphs during the Fall '08 term at Lehigh University .

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Lecture8 - Introduction to Mathematical Programming IE406...

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