Indicator Constraints
An indicator constraint is a new way of expressing relationships among variables by specifying a binary variable to control whether or not a linear constraint takes effect. For example, indicator constraints are useful in problems where there are fixed charges to express only if a given variable comes into play.
So-called Big M formulations often exhibit trickle flow, and at times, they behave unstably. The main purpose of indicator constraints is to avoid the unwanted side-effects of Big M formulations. Generally, the use of indicator constraints is not warranted when the unwanted side-effects of Big M formulations are not present.
For example, instead of the following Big M formulation, which relies on the x values summing to less than one billion (a formulation that can cause numeric instability or undesirable solutions in some situations):
constr01: x1 + x2 + x3 - 1e+9 y <= 0
you can enter the following formulation, where y is a binary variable, using an indicator constraint, like this:
constr01: y = 0 ® x1 + x2 + x3 = 0
A model with an indicator constraint introduces no new assumptions about upper bounds.
Note
The constraint must be linear; a quadratic constraint is not allowed to be an indicator constraint.
Only Big M constraints that are not eliminated by preprocessing should possibly be reformulated as an indicator constraint. The option Print Presolve Status can be used to find out which (Big M) constraints are eliminated by preprocessing.
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