Hi,

at

https://www.ibm.com/developerworks/community/forums/html/topic?id=aa9aa3db-4fbc-4209-a767-5b5e54902cbd&ps=25

I explained how to multiply a decision variable with a binary decision variable but I may have not been explicit enough for when we multiply two binary decision variables:

1) With CPO we can write

using CP;

dvar boolean x;
dvar boolean y;
 
 dvar boolean xy; // x times y
 
 subject to
 {
  xy==x * y; // We can write that with CPO but not with CPLEX
 
 }

2) We can linearize

dvar boolean x;
 dvar boolean y;
 
 dvar boolean xy; // x times y
 
 subject to
 {
 // xy==x * y; // We can write that with CPO but not with CPLEX
 xy<=x;
 xy<=y;
 xy>=x+y-1;
 }

3) We can rely on logical constraints:

dvar boolean x;
 dvar boolean y;
 
 dvar boolean xy; // x times y
 
 subject to
 {
 // xy==x * y; // We can write that with CPO but not with CPLEX
 xy==(x==1)&&(y==1);
 }

regards

PS:

Many how to with OPL at https://www.linkedin.com/pulse/how-opl-alex-fleischer/