Originally posted by: zab.a

Hi there

I am working on modeling a problem where I have a binary variable which is dependent on the values of integer variables of the model 

I need to define a binary variable in cplex  y[i][j]=1 if x[i]>x[j] , 0 otherwise . where x[i] and x[j] are decision variables

how to do this?

Hi,

let me share a tiny example in OPL:

range R=1..4;
dvar int x[R];
dvar boolean y[R][R];

subject to
{
forall(ordered i,j in R) y[i][j]==(x[i]>=x[j]);
}

regards

Originally posted by: zab.a

Thank you AlexFleischer for your answer,

for the constraint :

I have two issues 

1-  y[i][j]=1 if (x[i]>x[j]) , "> instesd >=" . but using > gives me error .

2- i want to exptess the following  in this constarint

y[i][j]=1 if x[i]>x[j] , where i in range R=1..n,  j=i+1..n 

i am attaching the code text file

Thanks in Advance 

Hi,

then you could use an epsilon to use >= for >

int P[ i in cont]=i;
int Amax=10;

//variables

dvar int+ x[cont];
dvar boolean y[cont][cont];  

// model

    // objective function
    
minimize  sum (i,j in cont) y[i][j];

    // constaints
subject to {

forall (i in cont) abs(x[i]-P[i])<=Amax;
forall ( ordered i,j in cont) y[i][j]==(x[i]>=x[j]+epsilon);

}

works fine

regards

Originally posted by: EdKlotz

Just a quick note on Alex's last response.   If the x variables are integer, which appears to be the case, you should just use epsilon = 1.0.   If they are continuous, then you need to use something smaller, and you need to think carefully about the proper choice given the other coefficients in your model and the feasibility tolerance used (CPLEX's default is 1e-6).