An interval variable is a decision variable whose value is an interval of integers. Thus, the value of an interval variable is characterized by two integers, one for the start of the interval and the other for the end of the interval. An important additional feature of interval variables is the fact that they can be optional: that is, one can decide not to consider them in the solution. When considered in the solution, the interval is said to be present, otherwise it is absent. When an interval is absent attributes like start and end are meaningless. Each constraint and expression on interval variables specifies how it handles absent intervals.

The length of an interval variable is defined as its end value minus its start value. The size of an interval variable is a non-negative integer characteristic of an interval variable, and related to the start and end of the interval variable through an intensity function. When an intensity function is specified, the size is equal to the integral of the intensity function between the start and the end of the interval. By default, when no intensity function is specified, the intensity is assumed to be the constant unit function and thus, the size and length of of the interval are equivalent.