Model Linearization

[paulacabrales]

Hello,

I have non-linear constraints in an LRP model and I want to make a linearization and solve it with CPLEX. This is the constraint:

R(t).. sum[(w,m), (q(w,t) * trat(w,m) * (1-alpha(w,m)) * (beta(w,m)) ]=E= sum(r, Tr(t,r) )

q(w,t) = Continuous variable
trat(w,m)= Binary variable

alpha and beta have no problems because they are parameters. So, ¿How can I make linearization of [q(w,t) * trat(w,m)]?

Thanks,

[Fred]

Assuming that the continuous variable is non-negative, a product of binary variable b and continuous variable x can be linearized as follows.

We want to model z = b*x via linear constraints, where z is a nonnegative continuous variable:

Code: Select all

z <= b *x.up
z <= x
z >= x - (1-b)*x.up

Maybe you can adopt this for your case.

I hope this helps!

Fred

[paulacabrales]

Thanks for your answer Fred. I did it and it's ok.