Why do you need this Q vector? Can you tell us how you plan to use it in your model?

Maybe it's not necessary after all :)

Charlie Vanaret Basically, I am solving a Mixed Integer Linear Programming Optimization problem.

1. Here, vector P is fixed. It shows a time value of a quantity ( fouling in heat exchanger).

2. y(i) is a binary variable (which indicates if heat exchanger is cleaned at ith instant).

Thus, if exchanger is cleaned , the fouling will become zero and will restart it again.

So, if the exchanger is cleaned on 5th time interval (y(5) = 1). So fouling profile will be : [1 2 3 4 0 1 2 3 4...............].

Above, we can see, due to cleaning, fouling has become 0 on fifth interval.

Lets say cleaning is on 3rd and 8th interval, then profile will be :

[1 2 0 1 2 3 4 0 1 2 3 4...........].

Therefore, the variable Q is required in my case. Pl. note that P is a just a parametric vector and y is decision variable.

Thank you.

Thanks for the details. You didn't mention what the next steps are, that is, how the fouling profile is used in the objective or in the constraints. I think that's the important part.

Charlie Vanaret , I think that the objective function and constraints etc. are not important to fix the posed question. Thank you.

Indeed no. But I'd like to understand what you're trying to do, because Q is a (difficult) construct that, in the end, might not be necessary for the definition of the objective and constraints if we approach it from a different angle.

If all you need is the definition of Q, I'll let other people answer.

It is probably possible to reindex the variables so that P(n)=[1,2,3,4,5,...,n]...

In this case, try something like this:

1) q(i) >= 0 for all i

2) q(1) = 1 - y(1)

3) q(i+1) >= q(i) + 1 - (n+1)*y(i), i < n

4) q(i)

Leonardo D. Secchin Thank you for your answer . But, P(n) can also be any random vector. P(n) can also be [1,2,4,60,10] etc. P(n)=[1,2,3,4,5,...,n]... is just an example.

So basically, your formulation works for P(n)=[1,2,3,4,5,...,n], but not for any other P(n).

I wanted to have it where P(n) can be anything , which is defined previously.

In case of MATLAB you can try this:

CLC; clear;

P=[1:10]; %can work for any size or elements of P

Y=[1 1 0 1 1 1 0 1 1 1];

Q=P;

for i=1:length(p)

If y(i) ==0

Q(i)=0;

Q(i+1:end)=P(1:end-i)

end

end