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

  x0 XB XN Xa RHS

x0 1 0 0 -1 0

XB 0 I B -1N B-1 B-1b  x0 XB XN Xa RHS

x0 1 0 0 -M 0

XB 0 I B -1N B-1 B-1b

THE BIG-M METHODThe 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.

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.

Example of THE TWO-POHASE METHOD

Example of THE TWO-POHASE METHOD

Example of THE TWO-POHASE METHOD

Example of THE TWO-POHASE METHOD

Example of THE TWO-POHASE METHOD

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Example of THE TWO-POHASE METHOD

Example of THE TWO-POHASE METHOD

Example of THE TWO-POHASE METHOD

Example of THE TWO-POHASE METHOD

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Feasible point

Phase

IPhase

II

Example of THE BIG-M METHOD

Example of THE BIG-M METHOD

Example of THE BIG-M METHOD

Example of THE BIG-M METHOD

Example of THE BIG-M METHOD

Example of THE BIG-M METHOD

Example of THE BIG-M METHOD

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2

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5

Thanks for your attention