# lect8 - ISE 536Fall03: Linear Programming and Extensions...

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September 24, 2003 Lecture 8: Simplex Method, Optimality Conditions Lecturer: Fernando Ord´o˜nez 1 The Tableau 1.1 Reminder A BFS: x B = B - 1 b 0 , x N = 0. Find a basic direction d : ( d N ) j = 1, ( d N ) i = 0 , i 6 = j , and d B = - B - 1 A j . Reduced cost: ¯ c j := ( c N ) j - c t B B - 1 A j < 0 Can move until x + θd 0, which is: θ = min i : u ij > 0 ( x B ) i u ij , where u j = B - 1 A j = - d B . 1.2 Tableau The tableau is a simple way of being organized, we represent all coeﬃcients of interest in a table, with the goal of keeping I as the matrix for the basic variables, with operations Multiply a row by a scalar Multiply a row by a scalar and add to another row For example 0 c t B c t N b B N simple operations - c t B B - 1 b 0 c t N - c t B B - 1 N B - 1 b I B - 1 N Recall the example min c 1 x 1 + c 2 x 2 + c 3 x 3 + c 4 x 4 + c 5 x 5 s . t . x 1 + x 2 + x 3 + x 4 = 5 x 2 - x 3 + x 5 = 3 2 x 1 + x 2 = 4

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## This note was uploaded on 02/13/2012 for the course ISE 536 taught by Professor Yy during the Spring '05 term at South Carolina.

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lect8 - ISE 536Fall03: Linear Programming and Extensions...

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