ILOG CPLEX 11.0 User's Manual

What Are Indicator Variables?The binary variable introduced in an indicator constraint is known as an indicator variable.Usually, an indicator variable will also appear in the objective function or in otherconstraints. For example, in fixnet.c, the indicator variables f appear in the objectivefunction to represent the cost of building an arc. In fact, an indicator variable introduced inone indicator constraint may appear again in another, subsequent indicator constraint.Restrictions on Indicator ConstraintsThere are a few restrictions regarding indicator constraints:◆◆◆The constraint must be linear; a quadratic constraint is not allowed to have an indicatorconstraint.A lazy constraint cannot have an indicator constraint.A user-defined cut cannot have an indicator constraint.◆ Only z= 0 (zero) or z=1 (one) are allowed for the indicator variable because the indicatorconstraint implies that the indicator variable is binary.ILOG CPLEX does not impose any arbitrary limit on the number of indicator constraints orindicator variables that you introduce, but there may be practical limits due to resourcesavailable on your platform.Best Practices with Indicator ConstraintsThe following points summarize best practices with indicator constraints in Callable Libraryapplications:◆◆◆◆Use indicator constraints when Big M values in the formulation cannot be reduced.Do not use indicator constraints if Big M can be avoided.Do not use indicator constraints if Big M is eliminated by preprocessing. Check thepresolved model for Big M.If valid upper bounds on continuous variables are available, use them. Bounds strengthenLP relaxations. Bounds are used in a MIP for fixing and so forth.ILOG CPLEX 11.0 — USER’ S MANUAL 357