i want to declare that x will be variable for binary 0,1
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...
example of the manual calculation
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 be 0.. for example i2,j1 will be equal to 0
below is the coding
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);
Choosing 1 value in a row of a matrix of binary variables is simple: just create a sum of elements of the row and make it equal to one.
PS. Could you specify what is the meaning of your objective function? It looks to me as it is a flow multiplied by the corresponding distance and by binary(indicator) variables. What does it mean?
yes..
i,k= facilities
j,q= location
matrix flow f(i,k) multiply by matrix distance d(j,q) multiply by x(i,j)*x(k,q)..
x( i,j) means that if facility i (fi) is assigned to location j (dj) the binary value will be 1,
and vice versa which is x(k,q) will be value 0..
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