Code matlab giải bài toán vận tải (transportation)

SOURCE CODE GIẢI BÀI TOÁN VẬN TẢI BẰNG MATLAB
CostMin.m

clc;
c = input('Nhap ma tran chi phi:\n');
s = input('Nhap ma tran cung cap (dang cot):\n');
d = input('Nhap ma tran nhu cau (dang dong):\n');
[m,n] = size(c);
r = 0.01;
x = zeros(m+1,n+1);
s1 = zeros(m,1);
d1 = zeros(1,n);
sumd = 0;
sumd1 = 0;
for j = 1 : n
sumd = sumd + d(j);
d1(j) = d(j);
sumd1 = sumd1 + d1(j);
end
sums = 0;
sums1 = 0;
for i = 1 : m
sums = sums + s(i);
s1(i) = s(i);
sums1 = sums1 + s1(i);
end
if sums ~= sumd
disp('Bai toan cung khac cau!');
return
end
for j = 1 : n

while d1(j) > 0
for i = 1 : m
if s1(i) > 0 && d1(j) > 0
t = i;
k = j;
break
end
end
if d1(k) > s1(t)
d1(k) = d1(k) - s1(t);
x(t,k) = s1(t);
s1(t) = 0;
elseif d1(k) < s1(t)
s1(t) = s1(t) - d1(k);
x(t,k) = d1(k);
d1(k) = 0;


end

elseif d1(k) == s1(t)
x(t,k) = d1(k);
d1(k) = 0;
s1(t) = 0;
end

end
disp('Loi giai ban dau:');
disp(x);
cost = 0;

for i = 1 : m
for j = 1 : n
if x(i,j) > 0
cost = cost + x(i,j)*c(i,j);
end
end
end
NonBasic = 0;
for i = 1 : m
for j = 1 : n
if x(i,j) > 0
NonBasic = NonBasic + 1;
end
end
end
Check = m + n - 1;
if NonBasic >= Check
disp('Tong Chi Phi:');
disp(cost);
degen = 0;
else
disp('Tong Chi Phi:');
disp(cost);
degen = 1;
end

if degen == 1
NumDegen = Check - NonBasic;
CountDegen = 0;
for A = 1 : NumDegen

CountDegen = CountDegen + 1;
for j = 1 : n
CountCol = 0;
for i = 1 : m
if x(i,j) > 0
CountCol = CountCol + 1;
end
end
x(m+1,j) = CountCol;
end


for i = 1 : m
CountRow = 0;
for j = 1 : n
if x(i,j) > 0
CountRow = CountRow + 1;
end
end
x(i,n+1) = CountRow;
end
for j = 1 : n - 1
if x(m+1,j) == 1
jEnter = j;
for i = 1 : m - 1
if x(i,n+1) == 1
iEnter = i;
break
end
end

end
end
if x(iEnter,jEnter) == 0
x(iEnter,jEnter) = r;
break
end

end

end
for j = 1 : n
for i = 1 : m
if x(i,j) == r
d(j) = d(j) + r;
end
end
end
for i = 1 : m
for j = 1 : n
if x(i,j) == r
s(i) = s(i) + r;
end
end
end

countxdegen=0;
for i = 1 : m
for j = 1 : n
if x(i,j) > 0
countxdegen = countxdegen + 1;

end
end
end
if countxdegen >= Check;
else
disp('Do not correct Degeneracy VAM');
end
CountStep = 0;
for A = 1 : m*n


CountStep = CountStep + 1;
nonx = zeros(m,n);
for j = 1 : n
for i = 1 : m
if x(i,j) == 0
nonx(i,j) = 1;
end
end
end
CostLoop = zeros(m,n);
for j = 1 : n
for i =1 : m
if x(i,j) > 0
CostLoop(i,j) = inf;
end
end
end
for k = 1 : (m*n)
countnon=0;

for j=1:n
for i=1:m
if nonx(i,j)==1
ibas=i;
jbas=j;
countnon=1;
end
if countnon==1
nonx(ibas,jbas)=inf;
break
end
end
if countnon==1
end

break

end
% Construct the equivalent basic cell matrix
x11=zeros(m+1,n+1);
x22=zeros(m+1,n+1);
for j=1:n
for i=1:m
if x(i,j)>0
x11(i,j)=x(i,j);
x22(i,j)=x(i,j);
end

end
end

%% Construct stepping stone path for searching the improvement index
for j=1:n
for i=1:m
x11(ibas,jbas)=inf;
x22(ibas,jbas)=inf;


end
end
% Count the number of the basic cell on each row and column

for j=1:n
countcol=0;
for i=1:m
if x11(i,j)>0
countcol=countcol+1;
end
end;
x11(m+1,j)=countcol;
x22(m+1,j)=countcol;
end
for i=1:m
countrow=0;
for j=1:n
if x11(i,j)>0
countrow=countrow+1;
end
end
x11(i,n+1)=countrow;
x22(i,n+1)=countrow;

end
%% Eliminate the basic variables that has only one on each row
iterationloop=0;
for i=1:m
iterationloop=iterationloop+1;
for i=1:m
if x22(i,n+1)==1
ieliminate=i;
for j=1:n
if x22(ieliminate,j)x22(ieliminate,j)>0
jeliminate=j;
x22(ieliminate,jeliminate)=0;% Eliminate the basic variable on
row
x22(ieliminate,n+1)=x22(ieliminate,n+1)-1; % decrease the
number of the basic variable on row one unit
x22(m+1,jeliminate)=x22(m+1,jeliminate)-1; % decrease the
number of the basic variable on column one unit
end

end

end
end
%% Eliminate the basic variables that has only one on each column
for j=1:n
if x22(m+1,j)==1
jeliminate1=j;
for i=1:m
if x22(i,jeliminate1)<inf && x22(i,jeliminate1)>0

ieliminate1=i;
x22(ieliminate1,jeliminate1)=0;% Eliminate the basic
variable on row


x22(m+1,jeliminate1)=x22(m+1,jeliminate1)-1; % decrease the
number of the basic variable on column one unit
x22(ieliminate1,n+1)=x22(ieliminate1,n+1)-1;% decrease the
number of the basic variable on row one unit
end
end
end
end
%% Control the constructing loop path
for j=1:n
for i=1:m
if (x22(i,n+1)==0 || x22(i,n+1)==2) && (x22(m+1,j)==0 ||
x22(m+1,j)==2)
break
else

end
end
end
end
%% Make +/-sign on basic variables in the loop path (x2)
%1. Add - sign on basic variable on row(imax) and on basic variable on
%column (jmax)
for j=1:n
if

(x22(ibas,j)~=0 && x22(ibas,j)jneg=j;
x22(ibas,jneg)=(-1)*x22(ibas,jneg);
x22(m+1,jneg)=1;
x22(ibas,n+1)=1;
for i=1:m
if (x22(i,jneg)>0 && x22(m+1,jneg)==1)
ineg=i;
end

end

end
end
for p=1:n
for j=1:n
if (j~=jneg && x22(ineg,j)>0 && x22(ineg,n+1)==2)
jneg1=j;
x22(ineg,jneg1)=(-1)*x22(ineg,jneg1);
x22(ineg,n+1)=1;
x22(m+1,jneg1)=1;
for i=1:m
if (x22(i,jneg1)>0 && x22(m+1,jneg1)==1)
ineg1=i;
ineg=ineg1;


jneg=jneg1;
end

end

end
end
% Control loop
if jneg1==jbas
%break

end

end
%% Compute the improvement index (based on the unit cost of each basic
cell)
sumloop=0;
for i=1:m
for j=1:n
if x22(i,j)~=0
icost=i;
jcost=j;
if x22(icost,jcost)>0
sumloop=sumloop+c(icost,jcost);
elseif x22(icost,jcost)<0
sumloop=sumloop+(-1)*c(icost,jcost);
end

end
end

end
CostLoop(ibas,jbas)=sumloop;

end
%% Loop controller
countcontrol=0;
for j=1:n
for i=1:m
if CostLoop(i,j)>=0
countcontrol=countcontrol+1;
end
end
end
if countcontrol==m*n
return
end
%% Searching the absolute smallest improvement index
minindex=0;
for j=1:n
for i=1:m
if CostLoop(i,j)<=0
if CostLoop(i,j)<=minindex
minindex=CostLoop(i,j);
ismall=i;
jsmall=j;
end
end


end
end
%% Construct a new stepping stone loop using add the new basic variable to
change in x matrix

% Construct the equivalent basic cell matrix
x33=zeros(m+1,n+1);
x44=zeros(m+1,n+1);
for j=1:n
for i=1:m
if x(i,j)>0
x33(i,j)=x(i,j);
x44(i,j)=x(i,j);
end
end
end
%% Construct stepping stone path for searching the improvement index
for j=1:n
for i=1:m
x33(ismall,jsmall)=inf;
x44(ismall,jsmall)=inf;
end
end
% Count the number of the basic cell on each row and column

for j=1:n
countcol1=0;
for i=1:m
if x33(i,j)>0
countcol1=countcol1+1;
end
end
x33(m+1,j)=countcol1;
x44(m+1,j)=countcol1;
end

for i=1:m
countrow1=0;
for j=1:n
if x33(i,j)>0
countrow1=countrow1+1;
end
end
x33(i,n+1)=countrow1;
x44(i,n+1)=countrow1;
end
% Eliminate the basic variables that has only one on each row
iterationloop1=0;
for i=1:m
iterationloop1=iterationloop1+1;
for i=1:m
if x44(i,n+1)==1
ieliminate3=i;
for j=1:n
if x44(ieliminate3,j)x44(ieliminate3,j)>0
jeliminate3=j;


x44(ieliminate3,jeliminate3)=0;% Eliminate the basic variable

on row

x44(ieliminate3,n+1)=x44(ieliminate3,n+1)-1; % decrease the
number of the basic variable on row one unit
x44(m+1,jeliminate3)=x44(m+1,jeliminate3)-1; % decrease the

number of the basic variable on column one unit
end
end
end
end
%% Eliminate the basic variables that has only one on each column
for j=1:n
if x44(m+1,j)==1
jeliminate4=j;
for i=1:m
if x44(i,jeliminate4)<inf && x44(i,jeliminate4)>0
ieliminate4=i;
x44(ieliminate4,jeliminate4)=0;% Eliminate the basic
variable on row
x44(m+1,jeliminate4)=x44(m+1,jeliminate4)-1; % decrease the
number of the basic variable on column one unit
x44(ieliminate4,n+1)=x44(ieliminate4,n+1)-1;% decrease the
number of the basic variable on row one unit
end
end
end
end

%% Control the constructing loop path
for j=1:n
for i=1:m
if (x44(i,n+1)==0 || x44(i,n+1)==2) && (x44(m+1,j)==0 ||
x44(m+1,j)==2)
break
end

end
end

end

%% Make +/-sign on basic variables in the loop path (x2)
%1. Add - sign on basic variable on row(imax) and on basic variable on
%column (jmax)
for j=1:n
if

(x44(ismall,j)~=0 && x44(ismall,j)jneg=j;
x44(ismall,jneg)=(-1)*x44(ismall,jneg);


x44(m+1,jneg)=1;
x44(ismall,n+1)=1;
for i=1:m
if (x44(i,jneg)>0 && x44(m+1,jneg)==1)
ineg=i;
end

end

end
end
for p=1:n
for j=1:n
if (j~=jneg && x44(ineg,j)>0 && x44(ineg,n+1)==2)

jneg1=j;
x44(ineg,jneg1)=(-1)*x44(ineg,jneg1);
x44(ineg,n+1)=1;
x44(m+1,jneg1)=1;
for i=1:m
if (x44(i,jneg1)>0 && x44(m+1,jneg1)==1)
ineg1=i;
ineg=ineg1;
jneg=jneg1;
end
end
end
end
% Control loop
if jneg1==jsmall
% return
end

end
% Eliminate column j that has the number of basic variables =2
for j=1:n
if x44(m+1,j)==2
for i=1:m
if x44(i,j)>0
x44(i,j)=0;
end
end
x44(m+1,j)=0;
end
end

%Eliminate row i that has the number of basic variables =2
for i=1:m
if x44(i,n+1)>=2
for j=1:n
if x44(i,j)>0
x44(i,j)=0;
end


end
x44(i,n+1)=0;
end
end
%% Searching the absolute smallest path and add this path to
(ismall,jsmall) cell
minpath=inf;
for j=1:n
for i=1:m
if x44(i,j)<0
if abs(x44(i,j))<=minpath
minpath=abs(x44(i,j));
end

end

end
end
%% Add the new path to x matrix
for j=1:n
for i=1:m

if x44(i,j)~=0
x44(i,j)=abs(x44(i,j)+minpath);
if x44(i,j)==0
x44(i,j)=inf;
end
end

end

end
% Add a entering (ismall,jsmall)cell to x matrix
for j=1:n
for i=1:m
x44(ismall,jsmall)=minpath;
end

end
%% Combine the new path and the non-degeneracy path
for j=1:n
for i=1:m
if x44(i,j)>0
x(i,j)=x44(i,j);
end

end

end
for j=1:n
for i=1:m
if x(i,j)==inf

x(i,j)=0;
end


end

end

countstepdegen=0;

for i=1:m
for j=1:n
if x(i,j)>0 && x(i,j)~=inf
countstepdegen=countstepdegen+1;
end

end

end
sumdemand=zeros(1,n);
for j=1:n
demandsum=0;
for i=1:m
if round(x(i,j))>0
demandsum=demandsum+round(x(i,j));
end
end
sumdemand(j)=demandsum;
end
for j=1:n

if sumdemand(j)~=round(d(j))
disp('Unbalanced demand');
break
end
end
% Check supply
sumsupply=zeros(m,1);
for i=1:m
supplysum=0;
for j=1:n
if round(x(i,j))>0
supplysum=supplysum+round(x(i,j));
end
end
sumsupply(i)=supplysum;
end
for i=1:m
if sumsupply(i)~=round(s(i))
disp('Unbalanced supply');
break
end
end

if countstepdegen >= Check
else
% How to correct the degeneracy problem


%% How to correct degeneracy matrix
numstepdegen=reducetant-countstepdegen;

iterationstepDegen=0;
for A=1:numstepdegen
iterationstepDegen=iterationstepDegen+1;
%% Construct the u-v variables
%% Construct the u-v variables
udual=zeros(m,1);
vdual=zeros(1,n);
for i=1:m
udual(i)=inf;
end
for j=1:n
vdual(j)=inf;
end
udual(1)=0;
for i=1:1
for j=1:n
if x(i,j)>0
vdual(j)=c(i,j)-udual(i);
end
end
end
for j=1:1
for i=1:m
if x(i,j)>0
iu=i;
if udual(iu)vdual(j)=c(i,j)-udual(iu);
else
if vdual(j)udual(iu)=c(i,j)-vdual(j);

end
end
end
end
end
for k=1:m*n
for i=1:m
if udual(i)iu=i;
for j=1:n
if x(iu,j)>0
vdual(j)=c(iu,j)-udual(iu);
end
end
end
end
for j=1:n
if vdual(j)jv=j;
for i=1:m
if x(i,jv)>0
udual(i)=c(i,jv)-vdual(jv);


end

end

end
end

countu=0;
countv=0;
for i=1:m
if udual(i)countu=countu+1;
end
end
for j=1:n
if vdual(j)countv=countv+1;
end
end
if (countu==m & countv==n)
return
end
end
unx=zeros(m,n);
for j=1:n
for i=1:m
if x(i,j)==0
unx(i,j)=udual(i)+vdual(j)-c(i,j);
end
end
end
%% Search maximum positive of udual+vdual-c(i,j) to reach a new basic
variable
maxunx=0;
for j=1:n
for i=1:m
if unx(i,j)>=maxunx

maxunx=unx(i,j);
imax=i;
jmax=j;
end
end
end
%% Count the number of basic variable on each and row
for j=1:n
sumcol=0;
for i=1:m
if x(i,j)>0
sumcol=sumcol+1;
end
end
x(m+1,j)=sumcol;
end
for i=1:m
sumrow=0;
for j=1:n
if x(i,j)>0


sumrow=sumrow+1;

end
end

x(i,n+1)=sumrow;
end
%% Construct the equipvalent x matrix

for j=1:n+1
for i=1:m+1
x1(i,j)=x(i,j);
end
end
%% Eliminate an entering variable for adding a new one
for j=1:n
for i=1:m
if (x(i,j)==r || x1(i,j)==r)
end

x1(i,j)=0;

end
end
% Add a new entering variable to x1 matrix
for j=1:n
for i=1:m
end

x1(imax,jmax)=r;

end
% Seaching and adding the entering point for corrective action
for i=1:m
if i~=imax
if x1(i,jmax)>0
ienter1=i;
for j=1:n
if j~=jmax

if x1(ienter1,j)>0
jenter1=j;
end
end
end
end
end
end
x1(imax,jenter1)=r;
x(imax,jenter1)=r;
% Add demand and supply
for j=1:n
d(jenter1)=d(jenter1)+r;
end
for i=1:m
s(imax)=s(imax)+r;
end
end
end
%The number of basic variable
countopt=0;


for j=1:n
for i=1:m
if x(i,j)>0
countopt=countopt+1;
end
end
end

% Convert x matrix
xpath=zeros(m,n);
for j=1:n
for i=1:m
if x(i,j)>0
xpath(i,j)=round(x(i,j));
end
end
end
% Total cost
Zopt=0;
for j=1:n
for i=1:m
if xpath(i,j)>0
end

Zopt=Zopt+(xpath(i,j)*c(i,j));

end
end
disp('Ma tran ket qua:');
disp(xpath);
disp('Tong chi phi:');
disp(Zopt);
end