Originally posted by: devos1

Dears, 

I am wondering how can I write this constraint using cplex in my ILP:  |x1-x2|-x3<=0

In fact, all variables are binaries and I want that x3 is set to 0 when x1 and x2 are equal to 1.

thanks in advance.

Best regards.

Hi,

in OPL CPLEX you could write

dvar boolean x1;
dvar boolean x2;
dvar boolean x3;

subject to
{
abs(x1-x2)-x3<=0;
((x1==1) && (x2==1)) => (x3==0);
}

which gives

x1 = 0;
x2 = 0;
x3 = 1;

regards

Originally posted by: devos1

Sorry, I forget to precise that I am coding in java.

I think that ((x1==1) && (x2==1)) => (x3==0) is not equivalent to |x1-x2|-x3<=0.

I miss express my need.

Tell me please,  how can I exress/write my constraint ((x1==1) && (x2==1)) => (x3==0) using cplex in a java based-code ?

Your help is very appreciated.

kind regards.

Hi,

have you tried to use

public final IloConstraint ifThen(IloConstraint con1, IloConstraint con2) throws IloException

?

regards

You can just add the constraint x1 + x2 + x3 <= 2. If x1 and x2 are both 1, this forces x3 to be 0. For any other combination of values of x1 and x2, x3 can be either 0 or 1.

Originally posted by: devos1

Thanks for your great help.

I will try this tomorrow because the source code and build environment is in my professional machine.

Best regards.

Originally posted by: devos1

Thank you for your help and support.

The solution is to add the constraint suggested by PaulRobin: x1 + x2 + x3 <= 2

It works fine.

Best regards.