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 x0x0 XBXB XNXN XaXa RHS x0x XBXB 0IB­ -1 NB -1 B -1 b x0x0 XBXB XNXN XaXa RHS x0x0 100-M0 XBXB 0IB­ -1 NB -1 B -1 b Note: No feasible region (Empty feasible region): Artificial >0 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. 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 “ x 0 “ 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=(C 1, C 2, …) 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

.

Feasible point Phase I Phase II

Example of THE BIG-M METHOD

Thanks for your attention