Reification: OnlyEnforceIf

Use the OnlyEnforceIf method to conditionally activate constraints via a Boolean indicator, build full reifications by combining two half-reifications, and encode logical implications between constraints.

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Tutorial

Half-Reification with OnlyEnforceIf

Many CP solvers (e.g., OR-Tools CP-SAT) let us conditionally activate a constraint via a Boolean indicator. Given a constraint $C$ and a Boolean variable $b$ , attaching \texttt{OnlyEnforceIf(b)} to $C$ imposes the rule

b = 1 \implies C \text{ holds.}

When $b = 0$ , the constraint $C$ is deactivated — it places no restriction on the model. This is called half-reification: the implication runs in one direction only. Even if $C$ happens to be satisfied, $b$ is not forced to $1$ .

For example, with $x \in \{0,1,2,3\}$ and Boolean $b$ , the statement

\texttt{model.Add(x >= 2).OnlyEnforceIf(b)}

admits the following assignments:

$(x,b) = (3,1)$ : feasible — $b=1$ forces $x \geq 2$ , and $x=3$ satisfies it.
$(x,b) = (0,0)$ : feasible — $b=0$ deactivates the constraint.
$(x,b) = (3,0)$ : feasible — $b=0$ deactivates the constraint, even though $x \geq 2$ happens to hold.
$(x,b) = (0,1)$ : infeasible — $b=1$ requires $x \geq 2$ , but $x=0$ violates it.

Notice that nothing in the model forces $b$ to be $1$ when $x \geq 2$ . Half-reification is strictly one-way.