How can I define a constraint to my optimization problem?

Hi,

I am trying to write my optimization model by following the way of Factory, Warehouse, Sales Allocation Model: Solver-Based example. Unfortunately, I have this error:

% Unable to perform assignment because the size of the left side is 90-by-1 and the size of the right side is 5-by-3.
% 
% Error in Constraint (line 28)
%     xtemp(:,:,ii) = d_ik;

The optimization model:

This is the code I tried to write:

i = 5; k = 3; t = 6;
d_ik = [1,5,6; 3,6,3; 5,7,0; 6,3,9; 2,8,8];
TR_t = [1000, 1000, 1000, 1000, 1000, 1000];

X_ikt = zeros(i,k,t); % Allocate arrays

for ii = 1:i
    for jj = 1:k
        for kk = 1:t
            obj(ii,jj,kk) = 1;
        end
    end
end

obj = X_ikt(:);

matwid = length(obj);
Aineq = spalloc(t,matwid,i*k*t);
bineq = zeros(t,1);

clearer1 = zeros(size(obj));
clearer12 = clearer1(:);

counter = 1;
for ii = 1:t
    xtemp = clearer1;
    xtemp(:,:,ii) = d_ik;
    xtemp = sparse(xtemp(:)); % Convert to sparse
    Aineq(counter,:) = xtemp'; % Fill in the row
    bineq(counter) = TR(ii)';
    counter = counter + 1;
end

intcon = t+1:length(obj);
lb = zeros(length(obj),1);
ub = Inf(length(obj),1);

opts = optimoptions('intlinprog','Display','off','PlotFcn',@optimplotmilp);
[solution,fval,exitflag,output] = intlinprog(obj,intcon,Aineq,bineq,lb,ub,opts);

PS: I am intended to write my model like Factory, Warehouse, Sales Allocation Model: Solver-Based example to obtain computational efficiency for large scale models and to solve using different techniques such as Genetic Algorithm.

[Matt J]

OK, well you need to tell us which information in the error message contradicts what you intended to happen? If you didn't intend the left hand side xtemp(:,:,ii) at line 22 to be 90x1 then what did you intend? Similarly if you didn't intend the right hand side d_ik to be 5x3 what did you intend for that?

[Alperen BAL]

I want to obtain Aineq matrix corretly to run intlinprog function. It must be (t, i*k*t) sized matrix. I am not very familiar with coding using Matlab but please let me demonstrate it with an example below:

Aineq = [2 3 1 6 7 5 0 --------------------------------------------------- 0 % for t = 1
         0 --------- 0 3 5 1 5 6 8 0 ------------------------------------- 0 % for t = 2
         0 ------------------------0 3 6 8 4 2 4 0 ----------------------- 0 % for t = 3
         0 --------------------------------------0 1 4 3 2 5 5 0 --------- 0 % for t = 4
         0 --------------------------------------------------- 0 2 4 5 6 2 5] 

Row size must be t = 6, column size equal to i*k*t = 90 and each coefficient size (non-zero elements in a row) is i*k = 15. Coefficients are coming from d_ik. For instance the coefficient for d_ik(1,2)*X(1,2,5) = 5*X(1,2,5).

I was following Factory, Warehouse, Sales Allocation Model: Solver-Based example. I just couldn't figure out what part I am missing.

Thank you.

Answer 1

[Matt J]

Aineq=kron(speye(t),d_ik(:).');
bineq=TR;

Note also that your call to intlinprog is the wrong syntax. You haven't specified the equality constraints (or indicated that there are none),

intlinprog(-obj,intcon,Aineq,bineq,[],[],lb,ub,opts)

[Alperen BAL]

Yes, it works! I appreciate your help. Here is the code I run:

P.S: Inf ub resulted with an unbounded solution and I defined 500 as ub.

i = 5; k = 3; t = 6;
d_ik = [1,5,6; 3,6,3; 5,7,0; 6,3,9; 2,8,8];
TR_t = [1000, 1000, 1000, 1000, 1000, 1000];

obj = zeros(i,k,t); % X_ikt

for ii = 1:i
    for jj = 1:k
        for kk = 1:t
            obj(ii,jj,kk) = 1;
        end
    end
end

obj = obj(:);

matwid = length(obj);

Aineq=kron(speye(t),d_ik(:).');
bineq=TR_t;

intcon = t+1:length(obj);
lb = zeros(length(obj),1);
ub = repmat(500,length(obj),1);

opts = optimoptions('intlinprog','Display','off','PlotFcn',@optimplotmilp);
[solution,fval,exitflag,output] = intlinprog(-obj,intcon,Aineq,bineq,[],[],lb,ub,opts)

[Matt J]

Note that instead of this part

obj = zeros(i,k,t); % X_ikt
for ii = 1:i
    for jj = 1:k
        for kk = 1:t
            obj(ii,jj,kk) = 1;
        end
    end
end
obj = obj(:);

you could just do,

obj=ones(i,t,k);

[Alperen BAL]

Good simplification! Thank you.

Answer 2

[Alan Weiss]

Perhaps you would find it easier to follow the problem-based version of the example. It is indeed difficult to get the constraint matrices straight using the solver-based approach.

If you eventually have to convert the problem to a solver-based approach, you can first write the model in the problem-based approach and then convert it using prob2struct.

Alan Weiss

MATLAB mathematical toolbox documentation

[Alperen BAL]

Thank you Alan, I will consider it.