# Sum(sum()) with optimization variable

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I want to write the following equation as a constraint

and x is an optimization variable.

I managed to get to following formulation

Constraint2 = sum(sum(x,3),1) <= ones(1,nRess)

Now the problem is, that I do not know how to change the running boundries of the inner sum, to the above given form (so not all the elements of the dimension 3, but only starting from l=t-pt_jr to t, and also while l>0).

pt_jr is a 2D matrix.

I tried to write it with sum(sum()) as I read about vectorization and didn't want to generate too long working times wir for loops.

Thanks ahead for any ideas.

##### 1 Comment

Walter Roberson
on 15 Aug 2022

### Answers (2)

Jan
on 15 Aug 2022

Edited: Jan
on 15 Aug 2022

Constraint2 = sum(x(:, :, (t - pt(j, r)):t), [1, 3]) <= 1;

##### 6 Comments

Jan
on 18 Aug 2022

nTasks = 3;

nRess = 2;

maxPT = 50;

x = optimvar('x',nTasks,nRess,maxPT,'Type', 'integer','LowerBound',0,'UpperBound',1);

x is not an array we can sum over. While I was talking about an array, the introduction of optimvar() was out of my view. I have no idea, what the realtion between the question and this code is.

Bruno Luong
on 15 Aug 2022

What about this:

L = reshape(1:size(x,3),1,1,[])

b = L >= t-pt_rj & L <= t;

Constraint2 = sum(sum(b.*x,3),1) <= ones(1,size(x,2))

##### 4 Comments

Bruno Luong
on 18 Aug 2022

I'm lost, it sounds like you are stuck with how to transforming whatever the scheduling problem you want to solve in math formulation, and not transforming math into matlab.

If that is the case I won't be able to help you, for the simple reason is that I don't understand what you wrote in the description.

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