Hi everyone! I need to get a script for transportation problem (balanced).

I need to write a program

function [x,cost]=transport(s,d,c);
% [x,cost]=transport(s,d,c)
% Input:
% s = supplies (m*1)
% d = demands (n*1)
% c = costs (m*n)
% Output
% x = optimal solution (m*n)
% cost = minimal transport cost
....

I already have this part:

function [x,b]=northwest(s,d)
% [x,b]=northwest(s,d)
% x: shipments using nw-rule (m*n)
% b: 1 for each basic variables 0 for nonbasic (m*n)
% s: supplies (m*1)
% d: demands (n*1)
if (sum(s)~=sum(d)),
disp('ERROR: The total supply is not equal to the total demand.');
return;
end
m=length(s);
n=length(d);
i=1;
j=1;
x=zeros(m,n);
b=zeros(m,n);
while ((i<=m) & (j<=n))
if s(i)<d(j)
x(i,j)=s(i);
b(i,j)=1;
d(j)=d(j)-s(i);
i=i+1;
else
x(i,j)=d(j);
b(i,j)=1;
s(i)=s(i)-d(j);
j=j+1;
end
end

function [u,v]=multipliers(x,c,b)
% [u,v]=multipliers(x,c,b)
% x: current solution (m*n)
% b: 1 for each basic variables 0 for nonbasic (m*n)
% c: costs (m*n)
% u: lagrange multipliers for rows (m*1)
% v: lagrange multipliers for columns (n*1)
[m,n]=size(x);
if sum(sum(b))< m+n-1
disp('Error in multipliers')
break
else
u=Inf*ones(m,1);
v=Inf*ones(n,1);
u(1)=0; % choose an arbitrary multiplier = 0
nr=1;
while nr<m+n % until all multipliers are assigned
for row=1:m
for col=1:n
if b(row,col)>0
if (u(row)~=Inf) & (v(col)==Inf)
v(col)=c(row,col)-u(row);
nr=nr+1;
elseif (u(row)==Inf) & (v(col)~=Inf)
u(row)=c(row,col)-v(col);
nr=nr+1;
end
end
end
end
end
end

function [y,bout]=cycle(x,row,col,b)
% [y,bout]=cycle(x,row,col)
% x: current solution (m*n)
% b: entering basic variables (m*n)
% row,col: index for element entering basis
% y: solution after cycle of change (m*n)
% bout: new basic variables after cycle of change (m*n)
bout=b;
y=x;
[m,n]=size(x);
loop=[row col]; % describes the cycle of change
x(row,col)=Inf; % do not include (row,col) in the search
b(row,col)=Inf;
rowsearch=1; % start searching in the same row
while (loop(1,1)~=row | loop(1,2)~=col | length(loop)==2),
if rowsearch, % search in row
j=1;
while rowsearch
if (b(loop(1,1),j)~=0) & (j~=loop(1,2))
loop=[loop(1,1) j ;loop]; % add indices of found element to loop
rowsearch=0; % start searching in columns
elseif j==n, % no interesting element in this row
b(loop(1,1),loop(1,2))=0;
loop=loop(2:length(loop),:); % backtrack
rowsearch=0;
else
j=j+1;
end
end
else % column search
i=1;
while ~rowsearch
if (b(i,loop(1,2))~=0) & (i~=loop(1,1))
loop=[i loop(1,2) ; loop];
rowsearch=1;
elseif i==m
b(loop(1,1),loop(1,2))=0;
loop=loop(2:length(loop),:);
rowsearch=1;
else
i=i+1;
end
end
end
end
% compute maximal loop shipment
l=length(loop);
theta=Inf;
minindex=Inf;
for i=2:2:l
if x(loop(i,1),loop(i,2))<theta,
theta=x(loop(i,1),loop(i,2));
minindex=i;
end;
end
% compute new transport matrix
y(row,col)=theta;
for i=2:l-1
y(loop(i,1),loop(i,2))=y(loop(i,1),loop(i,2))+(-1)^(i-1)*theta;
end
bout(row,col)=1;
bout(loop(minindex,1),loop(minindex,2))=0;

Thank you!

[Walter Roberson]

It is not clear how your problem relates to the functions you have already created?