how do i write a constraint and the sum of the z value?

i have the code and i try to make x as constraint but when i run i always get an error said that Undefined function or variable 'x'. below is the code and how can i get the sum of the z value?

    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;%no of facilities
     nd= 4;%no of locations 

     for i=1:nf 
         for j=1:nf 
             for k=1:nd 
                 for q=1:nd 
                      z = min('z','sum(sum(f(i,k)*d(j,q)*x(i,j)*x(k,q)))');
                     %if x(i,j)==1;
                     %else x(k,q)==0;
                     end
                 end
             end
         end

%Constraints %x as binary 0 1, %x(i,j) = 1 if facility i is assigned to location j 0r otherwise, x(i,j) = 0

    Constraints.constr1 = (x(i,j))==1;

%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.constr2 = 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.constr3 = sum(x,1) == 1;

     disp (z);

are the constraint i code is wrong? and how can i get the sum of z value?

[Image Analyst]

Why do you think that x should be anything when you never assigned anything to it before you tried to use it? It doesn't just magically have some value.

[John D'Errico]

Are you hoping that somehow, MATLAB will know that you are apparently wanting to do some sort of optimization here? MATLAB cannot read your mind.

I would guess that you want to do some optimization, but for that to happen, you would need to use an optimization tool, perhaps linprog might be right. You would also need to define an objective.

And, no matter what, this has NO chance of doing what you think it will do:

min('z','sum(sum(f(i,k)*d(j,q)*x(i,j)*x(k,q)))')

So it looks like you need to first learn MATLAB, then learn how to formulate this as an optimization for a proper solver.

[sharifah shuthairah syed abdullah]

can u give me an example please? i have been searching and learning and trying but i cannot get the right answer...

[Walter Roberson]

Constraints are inputs, not outputs. If you want your x matrix to be a constraint, then you need to know it ahead of time, or at least randomly generate it before you do your optimization.

[sharifah shuthairah syed abdullah]

if i put it like this

   x = [0 1 0 0;
     1 0 1 0;
     0 1 0 1;
     0 0 1 0];

    Constraints.constr1 = (x(i,j))==1;

then error came out and said Index in position 1 is invalid. Array indices must be positive integers or logical values.

[Walter Roberson]

If you tried to do that before your for i loop, then i would not have been defined, and would have the default value of sqrt(-1)