Lecture_10_The Revised Simplex Method

10.1 The Revised Simplex Method

While solving linear programming problem on a digital computer by regular simplex method, it requires storing the entire simplex table in the memory of the computer table, which may not be feasible for very large problem. But it is necessary to calculate each table during each iteration. The revised simplex method which is a modification of the original method is more economical
on the computer, as it computes and stores only the relevant information needed currently for testing and / or improving the current solution. i.e. it needs only

• The net evaluation row ?j to determine the non-basic variable that enters the basis.
• The pivot column
• The current basis variables and their values (XB column) to determine the minimum positive ratio and then identify the basis variable to leave the basis.

The above information is directly obtained from the original equations by making use of the inverse of the current basis matrix at any iteration.

There are two standard forms for revised simplex method
• Standard form-I – In this form, it is assumed that an identity matrix is obtained after introducing slack variables only.

• Standard form-II – If artificial variables are needed for an identity matrix, then two- phase method of ordinary simplex method is used in a slightly different way to handle artificial variables.



10.2 Steps for solving Revised Simplex Method in Standard Form-I

Solve by Revised simplex method Max Z = 2x1 + x2
Subject to
3 x1 + 4 x2 ? 6
6 x1 + x2 ? 3
and x1, x2 ? 0



SLPP
Max Z = 2x1 + x2+ 0s1+ 0s2 Subject to
3 x1 + 4 x2 + s1 = 6
6 x1 + x2 + s2 = 3
and x1, x2, s1, s2 ? 0

Step 1 – Express the given problem in standard form – I
• Ensure all bi ? 0
• The objective function should be of maximization
• Use of non-negative slack variables to convert inequalities to equations The objective function is also treated as first constraint equation

Z - 2x1 - x2 + 0s1 + 0s2 = 0
3 x1 + 4 x2 + s1 + 0s2= 6 -- (1)
6 x1 + x2 + 0s1 + s2= 3
and x1, x2, s1, s2 ? 0



Step 2 – Construct the starting table in the revised simplex form Express (1) in the matrix form with suitable notation