I have an Equation which is similar to the equation below:
Sum((i,j) , xij * Aij) = C
then this can be implemented by two constraints in GAMS syntax:
constr1.. B + flag * M =G= C;
* if flag=0 this constraint is equivalent to B >= C
*flag= 1 this constraint is always true which is equivalent to be removed from the model
constr2.. A + B + (1-flag)*M =G=C;
*when flag=1 this constraint is equivalent to A+B >=C
*when flag=0 this constraint is always true which is equivalent to be removed from the model
Debopam Ghosh
hi
I tried it the math adds up but it is still considered as a MINLP because the coefficients of the constraint are still 0 or 1 variables and we are multiplying them to another variable.
My apologies Mehrab, I missed the condition that A(i,j) terms are also decision variables in the problem, in which case we have a bilinear form satisfying an upper bound constraint, which is indeed a nonlinear constraint.
Deeply apologising to you once again, i will reply back to you once i think of a possible solution.
D.Ghosh
Hello,
To replace this non-linear product, I advise you to use another variable which will take the same value Aij when xij=1 and will be null when xij=0.
The variables are linked using four constraints (view attached file)
with Z is a "large" number which exceeds all possible values of Aij :
Nassim Mrabti , it's necessary to mention that such linearization as presented by you works if Aij >=0 (and the non-negativity condition for Aij wasn't stated explicitly in the original problem)
Details can be found in https://documentation.aimms.com/_downloads/AIMMS_modeling.pdf page 84.
Przemysław Kowalik, thank you for your intervention and your precision.
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