Originally posted by: whitegreen

Suppose, a, b, and c are binary variables in an integer program. How to add a "c = a AND b" logical constraint via Java API?

Otherwise I have to use  0<=a+b-2c<=1  instead. 

I am not sure I understand you correctly. If you want to have "c = a AND b" then just add constraints "c == a" and "b == 1". That gives what you wrote but I think that is probably not what do meant. Did you mean "IF c == a THEN b == 1"? That would be modeled using the ifThen() function. If that was not what you meant, could you try to rephrase your question?

Originally posted by: whitegreen

Thank you Daneil, I mean c=(a && b ) where && is the logical AND operator, or: c must be 1 if and only if both a==1 and b==1.   

I am family with ifthen function, but it is not applicable for such constraint. 

The IloCplex class has a function called and() (there are several overloads for this, see here). This allows you to create the logical AND of two constraints. There are also functions to create OR constraints. Together with ifThen() you should be able to state your constraint.

However, for all binary variables it is probably more efficient to just state the constraint yourself, unless you are worried about readability or maintainability of your code.

Originally posted by: whitegreen

Thank you again for the answer!

However, I am still confused about the syntax of using and() after reading the doc saying

IloAnd and(
IloConstraint con1,  
IloConstraint con2)

Given three binary variables: IloNumVar a, b, c, Could you please give me a few lines of codes to implement the "c= (a && b)" constraint using and()?

Have you tried something like this (untested code):

IloAnd and = cplex.and(cplex.eq(a, 1.0), cplex.eq(b, 1.0)); // a == 1 && b == 1
cplex.add(cplex.ifThen(and, cplex.eq(c, 1.0)));             // if a == 1 && b == 1 then c == 1

The reverse direction is simpler and does not even require a logical AND:

cplex.add(cplex.ifThen(cplex.eq(c, 1.0), cplex.eq(a, 1.0)));
cplex.add(cplex.ifThen(cplex.eq(c, 1.0), cplex.eq(b, 1.0)));

Originally posted by: whitegreen

The following codes

IloAnd and = cplex.and(cplex.eq(a, 1.0), cplex.eq(b, 1.0)); // a == 1 && b == 1
cplex.add(cplex.ifThen(and, cplex.eq(c, 1.0)));             // if a == 1 && b == 1 then c == 1

can run, however, it does Not impose the " if a == 1 && b == 1 then c == 1" logic.

I get the results: a=0,b=0, and c=1. Something is wrong.

The values a=0, b=0, c=1 do in fact satisfy the constraint "if a == 1 and b == 1 then c == 1". Perhaps you are misstating what you want. Are you actually looking for "c == 1 if and only if a == 1 and  b == 1"?

The thing Paul suspects you are missing is the "reverse direction" I mentioned in my post.