L20 - CO350 Linear Programming Chapter 7: The Two-Phase...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: CO350 Linear Programming Chapter 7: The Two-Phase Method 17th June 2005 Chapter 7: The Two-Phase Method 1 Recap ( P ) max ( z =) x 1 s.t. 3 x 1 + 5 x 2 + 2 x 3- x 4 = 7 2 x 1 + 5 x 2 + 3 x 3 + x 4 = 3 x 1 , x 2 , x 3 , x 4 So far this week, we learned to construct the auxiliary problem ( A ) , to detect infeasibility by solving ( A ) , to obtain a feasible basis of ( P ) from optimal tableau for ( A ) , two observations that may simplify the construction and solution of ( A ) . Chapter 7: The Two-Phase Method 2 An Exceptional Case ( 7.4) It may happen that ( A ) has optimal value , and yet the optimal tableau has basic artificial variables . BUT we want a feasible basis for ( P ) ! I.e., no artificial variables should be basic . Good news: Optimal value is 0 = all artificial variables = 0 . So, every basic artificial variable has value . (This, by definition, means that the bfs is degenerate.) To force the artificial variable out of basis, we pivot! Chapter 7: The Two-Phase Method 3 Example (Pg 96) Suppose that only x 5 is artificial . w + 2 x 4 = 0 x 2 + 4 x 3 + 3 x 4 = 2- 2 x 3- 2 x 4 + x 5 = 0 x 1 + 3 x 3 + 2 x 4 = 1 We want x 5 to leave. We choose either x 3 or x 4 to enter. BUT this violates the rules of the simplex method . Neither c 3 nor c 4 are positive. Neither a 53 nor a 54 are positive. HOWEVER, b 5 = 0 = r.h.s. values will not change . i.e., obj. value remains , and tableau remains feasible....
View Full Document

Page1 / 12

L20 - CO350 Linear Programming Chapter 7: The Two-Phase...

This preview shows document pages 1 - 5. Sign up to view the full document.

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