ot-lab-lcm_transportation

code

clc

clear all

format short

% Matlab Code of Least Cost Method (LCM)

% Input Information

%% Input Phase

Cost=[11 20 7 8; 21 16 10 12; 8 12 18 9];

A=[50 40 70];

B=[30 25 35 40];

%% To check unbalanced/balanced Problem

if sum(A)==sum(B)

fprintf('Given Transportation Problem is Balanced \n');

else

fprintf('Given Transportation Problem is Unbalanced \n');

if sum(A)<sum(B)

Cost(end+1,:)=zeros(1,size(A,2));

A(end+1)=sum(B)-sum(A);

elseif sum(B)<sum(A)

Cost(:,end+1)=zeros(1,size(A,2));

B(end+1)=sum(A)-sum(B) ;

end

end

ICost=Cost; %copying the cost in another var

X=zeros(size(Cost)); % Initialize allocation

[m,n]=size(Cost) ; % Finding No. of rows and columns

BFS=m+n-1 ; % Total No. of BFS

%% Finding the cell(with minimum cost) for the allocations

for i=1:size(Cost,1)

for j=1:size(Cost,2)

hh=min(Cost(:)); % Finding minimum cost value

[Row_index, Col_index]=find(hh==Cost); % Finding position of minimum cost cell

x11=min(A(Row_index),B(Col_index));

[Value,index]=max(x11); % Find maximum allocation

ii=Row_index(index) ; % Identify Row Position

jj=Col_index(index) ; % Identify Column Position

y11=min(A(ii),B(jj)) ; % Find the value

X(ii,jj)=y11;

A(ii)=A(ii)-y11;

B(jj)=B(jj)-y11;

Cost(ii,jj)=Inf;

end

end

%% Print the initial BFS

fprintf('Initial BFS =\n');

IBFS=array2table(X);

disp(IBFS);

%% Check for Degenerate and Non Degenerate

TotalBFS=length(nonzeros(X));

if TotalBFS==BFS

fprintf('Initial BFS is Non-Degenerate \n');

else

fprintf('Initial BFS is Degenerate \n');

end

%% Compute the Initial Transportation cost

InitialCost=sum(sum(ICost.*X));

fprintf('Initial BFS Cost is = %d \n',InitialCost);