TwoPhase

.

%Two-Phase

clc;

clear all;

close all;

Variables={'x_1','x_2','x_3','s_1','s_2','A_1','A_2','Sol'};

OptVariables={'x_1','x_2','x_3','s_1','s_2','Sol'};

C=[-7.5 3 0 0 0 -1 -1 0];

A=[3 -1 -1 -1 0 1 0 3; 1 -1 1 0 -1 0 1 2];

BV=[6 7];

D=[0 0 0 0 0 -1 -1 0];

StartBV=find(D<0);

fprintf('Phase 1\n');

[BFS,A]=simp(A,BV,D,Variables);

fprintf('Phase 2\n');

A(:,StartBV)=[];

C(:,StartBV)=[];

[OptBFS,OptA]=simp(A,BFS,C,OptVariables);

FINAL_BFS=zeros(1,size(A,2));

FINAL_BFS(OptBFS)=OptA(:,end);

FINAL_BFS(end)=sum(FINAL_BFS.*C);

OptimalBFS=array2table(FINAL_BFS);

OptimalBFS.Properties.VariableNames(1:size(OptimalBFS,2))=OptVariables

function [BFS,A]=simp(A,BV,D,Variables)

ZjCj=D(BV)*A-D;

RUN=true;

while RUN

ZC=ZjCj(1:end-1);

if any(ZC<0)

fprintf(' The Current BFS is NOT Optimal \n\n')

[entcol, pvt_col]=min(ZC);

fprintf('Entering Col=%d \n',pvt_col) ;

sol=A(:,end);

Column=A(:,pvt_col);

if Column<0

fprintf('Unbounded Solution\n');

else

for i=1:size(A,1)

if Column(i)>0

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

else

ratio(i)=inf;

end

end

[MinRatio, pvt_row]=min(ratio);

fprintf('Leaving Row =%d \n',pvt_row)

end

BV(pvt_row)=pvt_col;

pvt_key=A(pvt_row,pvt_col);

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

for i=1:size(A,1)

if i~=pvt_row

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

end

end

ZjCj=ZjCj-ZjCj(1,pvt_col).*A(pvt_row,:);

ZCj=[ZjCj;A];

TABLE=array2table(ZCj);

TABLE.Properties.VariableNames(1:size(ZCj,2))=Variables;

display(table);

BFS(BV)=A(:,end);

else RUN=false;

fprintf('Current BFS is Optimal\n');

fprintf('Phase 1 END\n\n\n');

BFS=BV;

end

end

end