ot-lab-dualsimplex

code

%input

clc;

close all;

variables={'x1','x2','x3','s1','s2','Sol'};

cost=[-2 0 -1 0 0 0];

info=[-1 -1 1;-1 2 -4];

b=[-5;-8];

%creating identity for slack variables

s=eye(size(info,1));

%making combined matrix

A=[info s b];

[m n]=size(info);

%finding basic variable column number

bv=n+1:n+m;

%calculating zj-cj row

zjcj=cost(bv)*A-cost;

%attaching zj0cj row to combined matrix

zcj=[zjcj;A];

%creating simplex table

simptable=array2table(zcj);

simptable.Properties.VariableNames(1:size(zcj,2))=variables;

flag=true;

while flag

sol=A(:,end);

if any(sol<0)

fprintf("Current bfs is not feasible");

%finding leaving variable

[leavingVar,pvt_row]=min(sol)

% finding entering variable

row=A(pvt_row,1:end-1);

Zj=zjcj(:,1:end-1);

for i=1:size(row,2)

if row(i)<0

ratio(i)=abs(Zj(i)./row(i));

else

ratio(i)=inf;

end

end

[minval,pvt_col]=min(ratio)

%update the bv

bv(pvt_row)=pvt_col;

%dividing pvt_row by pvt_key

pvt_key=A(pvt_row,pvt_col);

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

%updating other rows

for i=1:size(A,1)

if i~=pvt_row

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

end

end

%updating zj-cj

zjcj=cost(bv)*A-cost

zcj=[zjcj;A]

%creating simplex table again

simptable=array2table(zcj);

simptable.Properties.VariableNames(1:size(zcj,2))=variables;

else

flag=false;

fprintf("Current bfs is feasible");

end

end