the two-pohase method & the big-m method
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
.
Example of THE TWO-POHASE METHOD
Example of THE TWO-POHASE METHOD
Example of THE TWO-POHASE METHOD
Example of THE TWO-POHASE METHOD
1
2
34
5
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
1
2
34
5
Thanks for your attention