CPLEX Optimization Studio provides a set of modeling features for applications dealing with scheduling over time. Although time points in OPL and CP Optimizer are represented as integers, the possible very wide range of time points means that time is effectively continuous.

A consequence of scheduling over effectively continuous time is that the evolution of some known quantities over time (for instance the instantaneous efficiency/speed of a resource or the earliness/tardiness cost for finishing an activity at a given date t) needs to be compactly represented in the model. To that end, CP Optimizer provides the notion of piecewise linear and stepwise functions (see Piecewise linear and stepwise functions in CP Optimizer).

Most of the scheduling applications consist of scheduling in time activities, tasks, or operations that have a start and an end time. In CP Optimizer, this type of decision variable is represented by an interval variable (see Interval variables in CP Optimizer). Several types of constraints are expressed on and between interval variables, including constraints:

• to limit the possible positions of an interval variable (forbidden start/end or "extent" values) (see Intensity and size and forbidden values),
• to specify precedence relations between two interval variables (see Precedence constraints) and
• to relate the position of an interval variable with one of a set of interval variables (spanning, synchronization, alternative) (see Constraints on groups of interval variables in CP Optimizer).

An important characteristic of scheduling problems is that time intervals may be optional and thus whether or not to execute a time interval is a decision variable. In CP Optimizer, this is represented by a Boolean presence status associated with each interval variable. Logical relations can be expressed between the presence of interval variables: for instance, it is possible to state that whenever interval a is present then interval b must also be present (see Logical constraints).

Another aspect of scheduling is the allocation of scarce resources to time intervals. The evolution of a resource over time can be modeled by two types of variables:

• The evolution of a disjunctive resource over time can be described by the sequence of intervals that represent the activities executing on the resource. For that, CP Optimizer introduces an interval sequence variable. Constraints and expressions are available to control the sequencing of a set of interval variables (see Interval variable sequencing in CP Optimizer).
• The evolution of a cumulative resource often needs a description of how the accumulated usage of a resource evolves over time. For that purpose, CP Optimizer provides cumul function expression that can be used to constrain the evolution of the resource usage over time (see Cumul functions in CP Optimizer).
• The evolution of a resource of infinite capacity, the state of which can vary over time, is represented in CP Optimizer by a state function. The dynamic evolution of a state function can be controlled via transition, and constraints are available for specifying conditions on the state function that must be satisfied during fixed or variable intervals (see State functions in CP Optimizer).

Some classical cost functions in scheduling are earliness/tardiness costs, makespan, activity execution/non-execution costs. CP Optimizer generalizes these classical cost functions and provides a set of basic expressions that can be combined together to express a large spectrum of scheduling cost functions that can be efficiently exploited by the CP Optimizer search (see Expressions over Interval Variables).