Consider adding semi-integer constrained decision variable

[fastbodin]

Would act like an IntegerNode but 0 would be in the domain irregardless of the lower and upper bounds.

[mhramani]

More details: We like to define an implicit integer variable that can take either the value $0$ or any integer value in a prescribed interval:

$$ x_{ij} \in {0} \cup {\underline{X}_{ij}, \ldots, \overline{X}_{ij}}, \qquad 1 \le \underline{X}_{ij} \le \overline{X}_{ij}. $$

The corresponding implicit constraint is

$$ \underline{C}_{j} \le \sum_i x_{ij} \le \overline{C}_{j}, \qquad \forall j, \qquad \underline{C}_{j}, \overline{C}_{j} \in \mathbb{Z}. $$

Currently, this can only be modeled using auxiliary variables with explicit constraint as follows:

$$ x_{ij} \in {\underline{X}_{ij}, \ldots, \overline{X}_{ij}}, $$

$$ y_{ij} \in Binary , $$

and

$$ \underline{C}_{j} \le \sum_i x_{ij} y_{ij} \le \overline{C}_{j}, \qquad \forall j. $$

Goal is to introduce a new decision variable that is semi-integer and implicitly apply the sum constraint.