BigM

.

%Big-M

clc;

clear all;

close all;

cost= [3 2 0 0 -1000 0];

a = [1 1 ; 1 3 ;1 -1];

b = [2;3;1];

[m,n] = size(a);

s = eye(m);

A = [a s b];

bv = n+1:1:n+m;

zjcj = cost(bv)*A - cost;

zcj = [zjcj; A];

simplexTable=array2table(zcj);

simplexTable.Properties.VariableNames(1:size(zcj,2))={'x1','x2','s1','s2','a1','Sol'}

flag=true;

while flag

if any(zjcj<0)

fprintf("The Current BFS is not Optimal \n");

zc = zjcj(1:end-1);

[Enter_val, pvt_col] = min(zc);

if all (A(:,pvt_col)<=0)

error("LPP is Unbounded all entries are <=0 in column %d",pvt_col);

else

sol = A(:,end)

column = A(:,pvt_col)

for i = 1:m

if column(i) > 0

ratio(i) = sol(i)./column(i);

else

ratio(i) = inf;

end

end

[leaving_val, pvt_row] = min(ratio);

end

bv(pvt_row) = pvt_col;

pvt_key = A(pvt_row, pvt_col);

A(pvt_row,:) = A(pvt_row,:)./pvt_key;

for i = 1:m

if (i~=pvt_row)

A(i,:) = A(i,:) - A(i, pvt_col).*A(pvt_row,:);

end

end

zjcj = zjcj - zjcj(pvt_col).*A(pvt_row,:);

zcj = [zjcj;A];

table = array2table(zcj);

table.Properties.VariableNames(1:n+m+1) = {'x1','x2','s1','s2','a1','Sol'}

else

flag = false;

fprintf("The Current BFS is Optimal \n")

end

end