3.7.209. Reified constraint

The reified version 𝐢𝑅 of a given constraint C, where 𝐢𝑅 has as arguments all arguments of C plus one extra 0-1 variable. This 0-1 variable is set to 1 when constraint C holds, and 0 otherwise. Note that constraint 𝐢𝑅 inherits from all restrictions of constraint C (i.e., incorrect parameters for constraint C are also incorrect for constraint 𝐢𝑅). Within the context of linear programming the extra 0-1 variable is often called an indicator variable.

It was shown in Β [BeldiceanuCarlssonFlenerPearson12] how to reify a global constraint by reformulating it as a conjunction of pure functional dependency constraints together with a constraint that can be easily reified (e.g., an automaton with or without counter, or a Boolean combination of linear arithmetic equalities and inequalities and 0-1 variables).