## how do i create a binary [0,1]?

Asked by sharifah shuthairah syed abdullah

### sharifah shuthairah syed abdullah (view profile)

on 15 May 2018
Latest activity Edited by semi legend

### semi legend (view profile)

on 11 Nov 2018
how can i write to declare that x will be variable for binary 0,1
if x(i,j)=1 ;
else (x(k,q)= 0;
end;
i want to put it in my coding below
clc;
clear;
%sum sum sum sum(fik*djq*xij*xkq)
%i,k= facilities
%j,q= location
%f(i,k)= flow between facilities i and k
%d(j,q)= distance between locations j and q
%xij = 1 if facility i is assigned to location j and if otherwise, xij = 0
% Flow matrix: flow assigning facility i (column) to facility k (row)
f = [0 5 7 9;
5 0 4 6;
7 4 0 3;
9 6 3 0];
%Distance matrix: distance assigning location j (column) to location q (row)
d = [0 6 8 9;
6 0 5 1;
8 5 0 2;
9 1 2 0];
z= 0;
nf= 4;
nd= 4;
for i=1:nf
for j=1:nf
for k=1:nd
for q=1:nd
z = min('z','f(i,k)*d(j,q)*x(i,j)*x(k,q)');
end
end
end
end
%Constraints
%The first set of constraints requires that each facility gets exactly one
%location, that is for each facility, the sum of the location values
%corresponding to that facility is exactly one
Constraints.constr1 = sum(x,2) == 1;
%The second set of constraints are inequalities. These constraints specify
%that each office has no more than one facility in it.
Constraints.constr2 = sum(x,1) == 1;
disp (z);

### Image Analyst (view profile)

on 16 May 2018

Do you mean like this???
% x(i, j) = 1 if facility i is assigned to location j and if otherwise, xij = 0
% Flow matrix: flow assigning facility i (column) to facility k (row)
f = [0 5 7 9;
5 0 4 6;
7 4 0 3;
9 6 3 0];
x = zeros(size(f));
[rows, columns] = size(f)
for row = 1 : rows
for col = 1 : columns
facility_i = col;
facility_k = row;
if f(row, col) == facility_k
x(row, col) = 1;
end
end
end
x
Not exactly what i, j, and k mean. How are they related to row and column. If you say xij, then i=row and j=column, but then in your flow matrix explanation you say i is column, not row and you don't even mention j - you mention k which is row, but i was row. I'm confused (or you are).

#### 1 Comment

sharifah shuthairah syed abdullah

### sharifah shuthairah syed abdullah (view profile)

on 16 May 2018
im sorry...
i and k represent facilities in flow matrix, j and q represent location in distance matrix ..
x(i,j) mean that x will be equal to 1 if i (facility) is assign in j (location) ..
x(i, j) = 1 if facility i is assigned to location j and if otherwise, xij = 0,
so otherwise mean that if x(k,q) =1 , x(i,J) will be 0...
for example
Min =(f i1,k1 * d j1,q1 * x i1,j1 * x k1,q1) + (f i1,k1 * d j1,q2 * x i1,j1 * x k1,q2) + (f i1,k1 * d j1,q3 * x i1,j1 * x k1,q3)..
( 0*0* 1*1 ) + ( 0* 6* 1*0 ) + ( 0*8 * 1 *0 )...
I want to *xi1,j1 * xk1,q1 to be 0 or 1.. if i choose i1, j1=1 the other will bw 0.. for example i2,j1 will be equal to 9

### semi legend (view profile)

on 11 Nov 2018
Edited by semi legend

### semi legend (view profile)

on 11 Nov 2018

imagine if you have 5 virables , and you want to set the last 2 either on of them 0 or 1
you could do it, but that depends in what you want for that problem "to be or not to be"
[Inf;Inf;Inf;1;1]; to be % it will force (4) and (5) to be binary by 1 or 0 or [Inf;Inf;Inf;0;0]; or not to be
inf ; means array of infinite ( integers)
hope that at least helps