Download presentation

Presentation is loading. Please wait.

Published byJessie Hone Modified over 3 years ago

1
Linear Programming – Simplex Method: Computational Problems Breaking Ties in Selection of Non-Basic Variable – if tie for non-basic variable with largest relative profit ( ), arbitrarily select incoming variable. Ties in Minimum Ratio Rule (Degeneracy) – if more than one basic variable have same minimum ratio, select either variable to leave the basis. This will result in a basic variable taking on a value of 0. When this occurs, the solution is referred to as a degenerate basic feasible solution. When this occurs, you may transition through more than one simplex tableau with the same objective (Z) value.

2
Linear Programming – Simplex Method: Computational Problems Unbounded Solutions – if when performing the minimum ratio rule, none of the ratios are positive, then the solution is unbounded (e.g Max Z = or Min = - ). See pages 44-46 for good examples.

3
Simplex Method – Finding an Initial Basic Feasible Solution Min Z = -3x1 + x2 + x3 s.t. x1 – 2x2 + x3 <= 11 -4x1 + x2 +2x3 >= 3 2x1 - x3 = -1 x1, x2, x3 >= 0 Standard Form: (-) Max Z = 3x1 - x2 - x3 s.t. x1 – 2x2 + x3 + x4 = 11 -4x1 + x2 +2x3 -x5 = 3 -2x1 + x3 = 1 x1, x2, x3, x4, x5 >= 0

4
Simplex Method – Finding an Initial Basic Feasible Solution (-) Max Z = 3x1 - x2 - x3 s.t. x1 – 2x2 + x3 + x4 = 11 -4x1 + x2 +2x3 -x5 = 3 -2x1 + x3 = 1 x1, x2, x3, x4, x5 >= 0 Only x4 is basic. Introduce artificial variables. s.t. x1 – 2x2 + x3 + x4 = 11 -4x1 + x2 +2x3 -x5 + x6 = 3 -2x1 + x3 + x7 = 1 x1, x2, x3, x4, x5, x6, x7 >= 0

5
Simplex Method – Solve Using Big-M Method Let M be an arbitrarily large number, then: (-) Max Z = 3x1 - x2 - x3 + 0x4 + 0x5 – Mx6 – Mx7 s.t. x1 – 2x2 + x3 + x4 = 11 -4x1 + x2 +2x3 -x5 + x6 = 3 -2x1 + x3 + x7 = 1 x1, x2, x3, x4, x5, x6, x7 >= 0 Note: If the simplex algorithm terminates with one of the artificial variables as a basic variable, then the original problem has no feasible solution.

Similar presentations

Presentation is loading. Please wait....

OK

Multiplication Facts Practice

Multiplication Facts Practice

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on water cycle for class 9 Ppt on power grid control through pc Ppt on teaching reading skills Ppt on organised crime in india Ppt on google chrome web browser Genetics for kids ppt on batteries Ppt on do's and don'ts of group discussion images Ppt on remote operated spy robot controller Ppt on layers of soil Ppt on video conferencing basics