Linear optimization with sums in the objective function

Hello everybody,

I am trying currently to solve a linear problem in Matlab. For the solution I am taking the cplex solver.

My problem is how to hand sums in the objective function as well as in the constraints. All examples are for straight linear problems like:

obj function: 2x+3y (min)

4x + 2 y >= 10

Therefore I would write in matlab:

f = [2; 3];

A = [4 2];

b=10;

[x,z,exitflag,output,lambda] = linprog(f,A,b,Aeq,beq,lb,ub);

Pls keep in mind, that the example isn´t complete.

How I have to change f for sums.

For example the objective function is: sum(i)(sum(j)(pi*xij))

So this means I am having a double sum where p only changes for the different i and x changes for i and j.

But how can I bring the xij into the objective function f?

p=[ 10 13 14]

f=[p(i) ] is that correct? How does Matlab know that I need for x a consideration for xi and xj?

Any help would be very appreciated

Answer 1

[Torsten]

Do you know how to define f if the objective is

min: x11*p1 + x12*p1 + x13*p1 + x21*p2 + x22*p2 + x23*p2

?

Define

(y1,y2,y3,y4,y5,y6)=(x11,x12,x13,x21,x22,x23)

and write the objective as

min:[p1 p1 p1 p2 p2 p2]*[y1;y2;y3;y4;y5;y6]

Best wishes

Torsten.

[Martin Polz]

Hello everybody and Torsten thanks for the reply.

I tried a model but so far it s not working. My model and the instruction is at the attachement.

Maybe somebody can tell me what I made wrong?

I would appreciate it a lot.

Answer 2

[Martin Polz]

Dear Thorsten,

could you maybe show the conversion of x in y in a small example? I have tried it in matlab, but I still can t solve it.

Coz I don t know how to take the sums with y. So is y also noted in Aieq or not?

(y1,y2,y3,y4,y5,y6)=(x11,x12,x13,x21,x22,x23)

I have to define an x matrix? Or is the solution giving me x11, x12 and so on? As I said a small Matlab example would help me so much.

I can t find any linear optimization where y is used instead of x