summation over an index subset

[ursula challita]

Hello,

I have the following scenario:

I have a set of users:k, and a set of base stations:i. each user k is served by a specific base station i.

In one of my constraints, i want to do the summation over the users served by a given base station and for all the base stations.

How can I index my summation? shall I create a new set and make it a subset of users? 

Thank you.

Regards,

Ursula

[Guido Diepen]

Hi Ursula,

you could create additional indexed subsets. However, it might be easier to have a binary parameter UserLinkedToBaseStation(k,i), which gets the value 1 if the user k is linked to base station i and 0 otherwise.

Then in some constraint that is indexed over all basestations i, you can do the summation in the definition as follows:

sum(k | UserLinkedToBaseStation(k,i) ,   theVariable(k) ) <= someValue

Guido Diepen

AIMMS Specialist

[ursula challita]

Hello Guido,

I created the binary variable and called it s(i,k).

The definition of my constraint is: sum(k | k in s(i,k,t), w(m,k,t)) = 1

However, I am getting the following error: The variable "s" is not a set which is required for the RHS of the IN operator.

Thank you.

[ursula challita]

Hi Guido,

I corrected the constraint to :sum(k | s(i,k,t), w(m,k,t)) = 1

I still get the error: The condition "s(i,k,t) $ s.index domain(k,t)" in sum cannot contain variables.

note that s(i,k,t) is a variable in my problem and not a parameter.

Thanks again.

Ursula

[Guido Diepen]

Hi Ursula,

good to hear that you found the problem with the error about the in operator.

Regarding your new question, there is no way around this: you cannot use a variable as a domain condition. Is this s(i,k,t) something that your model decides? Does the value change during a solve?

If so, and you want to achieve such a thing, you will have to formulate this with additional (linear) constraints and variables.

If not, you can make the variable s(i,k,t) a parameter and ensure it gets the correct values before the solve and the error should disappear :)

Guido Diepen

AIMMS Specialist

[ursula challita]

Hi Guido,

Unfortunately, s(i,k,t) something that the model decides. However, I did not understand what u mean by "formulate this with additional (linear) constraints and variables".

Thanks for the help:)

Ursula

[Guido Diepen]

Hi Ursula,

what I meant with that is that you will have to do some additional modeling to achieve this. 

In a nonlinear way, you could write down something like:

 sum(k , s(i,k,t) *  w(m,k,t) ) = 1

If you want to stick with a linear problem, you will have to reformulate your problem in such a way that you achieve the above, but without the multiplication of the two variables.  To do this, typically you will need some additional variables and constraints.

Guido Diepen

AIMMS Specialist

[ursula challita]

Hello Guido,

I have added a new constraint! The problem is running correctly.

Thanks:)

Ursula