{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

simplex_lecture_3-1

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

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

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

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

View Full Document
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
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

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

View Full Document
3D OBJECTS Saigal (U of M) IOE 310 4 / 14
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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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
Ask a homework question - tutors are online