formulate max and min in the same linear programing in matlab - matlab

Question

I am programing a "customer satisfaction" model which I should use max and min in one linear programing. How can I do that? I have this Idea to use max term as a "subtraction" so it's get minimize in the code line; am I doing right?
I have another question too, how can I formulate a sigma such as picture in matlab whithout getting error?
as you seem we have Qst and Xst but three sigma (s, r and t), I wonder if my model has problem and I don't know how program this.
can you help me please?

Answer 1

I don't quite understand what you are describing in your first question, but you can calculate your MinZ1 using nested loops:
s = randi(5);
r = randi(5);
t = randi(5);
Q = rand([s,r]);
X = rand([s,t]);
L = rand([r,s,t]);
M = rand([r,s,t]);
C = rand([s,r]);
S = rand(1);
P = rand(1);
R = rand(1);
MinZ1 = 0;
for si = 1:s
for ri = 1:r
for ti = 1:t
MinZ1 = MinZ1 + Q(si,ri)*X(si,ti);
end
end
end
for si = 1:s
for ri = 1:r
for ti = 1:t
MinZ1 = MinZ1 + S*L(ri,si,ti)*(P*M(ri,si,ti)+R*C(si,ri));
end
end
end
end
disp(MinZ1)
If you don't like nested loops, you can achieve the same result by generating all indices combinations and passing the result to the sum function.
[si,ri,ti] = ndgrid(1:s,1:r,1:t);
MinZ1 = sum(Q(sub2ind(size(Q),si,ri)).*X(sub2ind(size(X),si,ti)),'all') + sum(S.*L(sub2ind(size(L),ri,si,ti)).*(P.*M(sub2ind(size(M),ri,si,ti))+R.*C(sub2ind(size(C),si,ri))),'all');