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THE TWO-POHASE METHOD & THE BIG-M METHOD

THE TWO-POHASE METHOD & THE BIG-M METHOD. IENG511 Optimization Theory. Introduction. THE TWO-POHASE METHOD. SUMMARY OF THE TWO-POHASE METHOD & THE BIG-M METHOD. THE TWO-POHASE METHOD & THE BIG-M METHOD Phase 1: (to find the extreme point) 1-change to standard format.

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THE TWO-POHASE METHOD & THE BIG-M METHOD

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  1. THE TWO-POHASE METHOD&THE BIG-M METHOD IENG511 Optimization Theory

  2. Introduction

  3. THE TWO-POHASE METHOD

  4. SUMMARY OF THE TWO-POHASE METHOD & THE BIG-M METHOD THE TWO-POHASE METHOD & THE BIG-M METHOD Phase 1: (to find the extreme point) 1-change to standard format. 2-Add numbers to table and add the Artificial values if necessary. 3-Try to do the row operation in order to change the artificial values to zero. • 4-Change all number in the “ x0 “ row to non-positive by using the row operation. • Phase 2: (takes us from feasible region to the optimal point) • 5-Remove artificial values from the table and rewrite the table with using the C=(C1 , C2 , …) but with reverse sign. • 6-Change all number in the “ z “row to non-positive by using the row operation. THE BIG-M METHOD The Big-M Method steps are exactly like the Tow-phase method: 1-change to standard format. 2-Add numbers to table and add the Artificial values if necessary. 3-Try to do the row operation in order to change the artificial values to zero. 4-Change all number in the “ z “ row to non-positive by using the row operation. Note: No feasible region (Empty feasible region): Artificial >0

  5. Example ofTHE TWO-POHASE METHOD

  6. Example of THE TWO-POHASE METHOD

  7. Example of THE TWO-POHASE METHOD

  8. Example of THE TWO-POHASE METHOD

  9. Example of THE TWO-POHASE METHOD .

  10. Example of THE TWO-POHASE METHOD

  11. Example of THE TWO-POHASE METHOD

  12. Example of THE TWO-POHASE METHOD

  13. Example of THE TWO-POHASE METHOD 5 Phase II 4 3 Feasible point 2 Phase I 1

  14. Example of THE BIG-M METHOD

  15. Example of THE BIG-M METHOD

  16. Example of THE BIG-M METHOD

  17. Example of THE BIG-M METHOD

  18. Example of THE BIG-M METHOD

  19. Example of THE BIG-M METHOD

  20. Example of THE BIG-M METHOD 5 4 3 2 1

  21. Thanks for your attention

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