Dear staff,

I need your help with an objective function where I have the product of two variables.

I have the following variables and parameters:

y(i,j,c,a) binary variable

x(a) continuous variable

P(c) parameter

How can I linearise the following objective function:

MIN:

sum((i,j,c,a), P(c) * y(i,j,c,a) - P(c) * y(i,j,c,a) * x(a))

Thank you

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A similar question was answered in https://community.aimms.com/developers-math-or-programming-39/modelling-question-241. The trick can be used here as well.

Thank you Deanne, you are right!

So basically I just need to create another variable U(a) and then impose that:

if Y(i,j,c,a) = 1 then U(a) = P(c)*x(a)

if Y(i,j,c,a)=0 then U(a) = 0

And then use U(a) in the objective function instead of P(c) * y(i,j,c,a) * x(a)

Therefore yes, this becomes the same type of constraint that you linked.

I will try that!

So basically I just need to create another variable U(a) and then impose that:

if Y(i,j,c,a) = 1 then U(a) = P(c)*x(a)

if Y(i,j,c,a)=0 then U(a) = 0

And then use U(a) in the objective function instead of P(c) * y(i,j,c,a) * x(a)

Therefore yes, this becomes the same type of constraint that you linked.

I will try that!

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