simplex_lecture_3-1

simplex_lecture_3-1 - FLOW CHART - SIMPLEX ALGORITHM start...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
FLOW CHART - SIMPLEX ALGORITHM start with a bfs is it optimum ? stop yes no is there a leaving variable? stop no yes find new bfs unbounded solution optimum solution Saigal (U of M) IOE 310 1 / 14
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
DEGENERACY AND CONVERGENCE I DEFINITION : If an LP has a bfs with at least one basic variable with value 0, then this LP is called degenerate . 1 If the value of entering variable in new bfs is > 0, then the new z-value is > the current z-value, for the maximization problem. 2 If the value of the entering variable is zero, then the z-value of the new bfs is equal to the current z-value. maximize z = 5 x 1 + 2 x 2 x 1 + x 2 6 x 1 - x 2 0 x 1 0 x 2 0 Saigal (U of M) IOE 310 2 / 14
Background image of page 2
DEGENERACY AND CONVERGENCE II Adding slack variables we get the standard form: max z = 5 x 1 + 2 x 2 x 1 + x 2 + s 1 = 6 x 1 - x 2 + s 2 = 0 x 1 0 x 2 0 s 1 0 s 2 o Consider BV = { s 1 , s 2 } and NBV = { x 1 , x 2 } . This is a bfs with s 2 = 0, and thus this LP is degenerate. Saigal (U of M) IOE 310 3 / 14
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
3D OBJECTS Saigal (U of M) IOE 310 4 / 14
Background image of page 4
SIMPLEX AND DEGENERATE LP I TABLEAU I: Basic Var. z x 1 x 2 s 1 s 2 rhs Ratio z 1 -5 -2 0 0 0 none s 1 0 1 1 1 0 6 6 s 2 0 1 -1 0 1 0 0 TABLEAU II: basic var. z x 1 x 2 s 1
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/02/2008 for the course IOE 310 taught by Professor Saigal during the Spring '08 term at University of Michigan.

Page1 / 15

simplex_lecture_3-1 - FLOW CHART - SIMPLEX ALGORITHM start...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online