Class: IntervalVar

Interval variable is a task, action, operation, or any other interval with a start and an end. The start and the end of the interval are unknowns that the solver has to find. They could be accessed as integer expressions using IntervalVar.start and IntervalVar.end. or using Model.startOf and Model.endOf. In addition to the start and the end of the interval, the interval variable has a length (equal to end - start) that can be accessed using IntervalVar.length or Model.lengthOf.

The interval variable can be optional. In this case, the solver can decide to make the interval absent, which is usually interpreted as the fact that the interval doesn't exist, the task/action was not executed, or the operation was not performed. When the interval variable is absent, its start, end, and length are also absent. A boolean expression that represents the presence of the interval variable can be accessed using IntervalVar.presence and Model.presenceOf.

Interval variables can be created using the function Model.intervalVar. By default, interval variables are present (not optional). To create an optional interval, specify optional: true in the arguments of the function.

@example: present interval variables

In the following example we create three present interval variables x, y and z and we make sure that they don't overlap. Then, we minimize the maximum of the end times of the three intervals (the makespan):

let model = new CP.Model;
let x = model.intervalVar({ length: 10, name: "x" });
let y = model.intervalVar({ length: 10, name: "y" });
let z = model.intervalVar({ length: 10, name: "z" });
model.noOverlap([x, y, z]);
model.max([x.end(), y.end(), z.end()]).minimize();
let result = await CP.solve(model);

@example: optional interval variables

In the following example, there is a task X that could be performed by two different workers A and B. The interval variable X represents the task. It is not optional because the task X is mandatory. Interval variable XA represents the task X when performed by worker A and similarly XB represents the task X when performed by worker B. Both XA and XB are optional because it is not known beforehand which worker will perform the task. The constraint alternative links X, XA and XB together and ensures that only one of XA and XB is present and that X and the present interval are equal.

let model = new CP.Model;
let X = model.intervalVar({ length: 10, name: "X" });
let XA = model.intervalVar({ name: "XA", optional: true });
let XB = model.intervalVar({ name: "XB", optional: true });
model.alternative(X, [XA, XB]);
let result = await CP.solve(model);

Variables XA and XB can be used elsewhere in the model, e.g. to make sure that each worker is assigned to at most one task at a time:

// Tasks of worker A don't overlap:
model.noOverlap([... , XA, ...]);
// Tasks of worker B don't overlap:
model.noOverlap([... , XB, ...]);

Extends

• ModelNode

Methods

alternative()

alternative(options: IntervalVar[]): void

Creates alternative constraints for the interval variable and provided options.

Parameters

Parameter	Type	Description
options	IntervalVar[]	Interval variables to choose from.

Returns

void

Remarks

This constraint is the same as Model.alternative.

---

end()

end(): IntExpr

Creates an integer expression for the end of the interval variable.

Returns

IntExpr

Remarks

If the interval variable is absent, then the resulting expression is also absent.

Example

In the following example, we constraint interval variable y to start after the end of y with a delay of at least 10. In addition, we constrain the length of x to be less or equal to the length of y.

let model = new CP.Model;
let x = model.intervalVar({ name: "x", ... });
let y = model.intervalVar({ name: "y", ... });
model.constraint(x.end().plus(10).le(y.start()));
model.constraint(x.length().le(y.length()));

When x or y is absent then value of both constraints above is absent and therefore they are satisfied.

See

• Model.endOf is equivalent function on Model.
• Function IntervalVar.endOr is a similar function that replaces value absent by a constant.

---

endAtEnd()

endAtEnd(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.end().plus(delay).eq(successor.end())).

In other words, end of predecessor plus delay must be equal to end of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.endAtEnd is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.eq

---

endAtStart()

endAtStart(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.end().plus(delay).eq(successor.start())).

In other words, end of predecessor plus delay must be equal to start of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.endAtStart is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.eq

---

endBeforeEnd()

endBeforeEnd(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.end().plus(delay).le(successor.end())).

In other words, end of predecessor plus delay must be less than or equal to end of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.endBeforeEnd is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.le

---

endBeforeStart()

endBeforeStart(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.end().plus(delay).le(successor.start())).

In other words, end of predecessor plus delay must be less than or equal to start of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.endBeforeStart is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.le

---

endOr()

endOr(absentValue: number): IntExpr

Creates an integer expression for the end of the interval variable. If the interval is absent, then its value is absentValue.

Parameters

Parameter	Type
absentValue	number

Returns

IntExpr

Remarks

This function is equivalent to interval.end().guard(absentValue).

See

• IntervalVar.end
• IntExpr.guard

---

forbidEnd()

forbidEnd(func: IntStepFunction): void

Constrains the end of the interval variable to be outside of the zero-height segments of the step function.

Parameters

Parameter	Type
func	IntStepFunction

Returns

void

Remarks

This function is equivalent to:

  model.constraint(func.stepFunctionEval(interval.end()).ne(0));

I.e., the function value at the end of the interval variable cannot be zero.

See

• Model.forbidEnd for the equivalent function on Model.
• Model.forbidStart for similar function that constrains start an interval variable.
• Model.stepFunctionEval for evaluation of a step function.

---

forbidExtent()

forbidExtent(func: IntStepFunction): void

Forbid the interval variable to overlap with segments of the function where the value is zero.

Parameters

Parameter	Type
func	IntStepFunction

Returns

void

Remarks

This function prevents the specified interval variable from overlapping with segments of the step function where the value is zero. I.e., if $[s, e)$ is a segment of the step function where the value is zero, then the interval variable either ends before $s$ ($\mathtt{interval.end()} \le s$) or starts after $e$ ($e \le \mathtt{interval.start()}$.

See

• Model.forbidExtent for the equivalent function on Model.
• Model.forbidStart, Model.forbidEnd for similar functions that constrain the start/end of an interval variable.
• Model.stepFunctionEval for evaluation of a step function.

---

forbidStart()

forbidStart(func: IntStepFunction): void

Constrains the start of the interval variable to be outside of the zero-height segments of the step function.

Parameters

Parameter	Type
func	IntStepFunction

Returns

void

Remarks

This function is equivalent to:

  model.constraint(func.stepFunctionEval(interval.start()).ne(0));

I.e., the function value at the start of the interval variable cannot be zero.

See

• Model.forbidStart for the equivalent function on Model.
• Model.forbidEnd for similar function that constrains end an interval variable.
• Model.stepFunctionEval for evaluation of a step function.

---

getEndMax()

getEndMax(): null | number

Returns maximum end assigned to the interval variable during its construction by Model.intervalVar or later by function setEnd or function setEndMax.

If the interval is absent, the function returns null.

Note: This function returns the maximum end of the interval in the model (before the solve), not in the solution.

Returns

null | number

---

getEndMin()

getEndMin(): null | number

Returns minimum end assigned to the interval variable during its construction by Model.intervalVar or later by function setEnd or function setEndMin.

If the interval is absent, the function returns null.

Note: This function returns the minimum end of the interval in the model (before the solve), not in the solution.

Returns

null | number

---

getLengthMax()

getLengthMax(): null | number

Returns the maximum length assigned to the interval variable during its construction by Model.intervalVar or later by function setLength or function setLengthMax.

If the interval is absent, the function returns null.

Note: This function returns the maximum length of the interval in the model (before the solve), not in the solution.

Returns

null | number

---

getLengthMin()

getLengthMin(): null | number

Returns minimum length assigned to the interval variable during its construction by Model.intervalVar or later by function setLength or function setLengthMin.

If the interval is absent, the function returns null.

Note: This function returns the minimum length of the interval in the model (before the solve), not in the solution.

Returns

null | number

---

getName()

getName(): undefined | string

Returns the name assigned to the node.

Returns

undefined | string

Inherited from

ModelNode.getName

---

getStartMax()

getStartMax(): null | number

Returns maximum start value assigned to the interval variable during its construction by Model.intervalVar or later by function setStart or function setStartMax.

If the interval is absent, the function returns null.

Note: This function returns the maximum start of the interval in the model (before the solve), not in the solution.

Returns

null | number

---

getStartMin()

getStartMin(): null | number

Returns minimum start value assigned to the interval variable during its construction by Model.intervalVar or later by function setStart or function setStartMin.

If the interval is absent, the function returns null.

Note: This function returns the minimum start of the interval in the model (before the solve), not in the solution.

Returns

null | number

---

isAbsent()

isAbsent(): boolean

Returns true if the interval variable was created absent (and therefore cannot be present in the solution).

Note: This function checks the presence status of the interval in the model (before the solve), not in the solution. In particular, for an optional interval variable, this function returns false, even though there could be a solution in which the interval is absent.

Returns

boolean

See

• isOptional, isPresent
• makeOptional, makePresent, makeAbsent

---

isOptional()

isOptional(): boolean

Returns true if the interval variable was created as optional. Optional interval variable can be absent in the solution, i.e., it can be omitted.

Note: This function checks the presence status of the variable in the model (before the solve), not in the solution.

Returns

boolean

See

• isPresent, isAbsent
• makeOptional, makePresent, makeAbsent

---

isPresent()

isPresent(): boolean

Returns true if the interval variable was created present (and therefore cannot be absent in the solution).

Note: This function returns the presence status of the interval in the model (before the solve), not in the solution. In particular, for an optional interval variable, this function returns false, even though there could be a solution in which the interval is present.

Returns

boolean

See

• isOptional, isAbsent
• makeOptional, makePresent, makeAbsent

---

length()

length(): IntExpr

Creates an integer expression for the length of the interval variable.

Returns

IntExpr

Remarks

If the interval variable is absent, then the resulting expression is also absent.

Example

In the following example, we constraint interval variable y to start after the end of y with a delay of at least 10. In addition, we constrain the length of x to be less or equal to the length of y.

let model = new CP.Model;
let x = model.intervalVar({ name: "x", ... });
let y = model.intervalVar({ name: "y", ... });
model.constraint(x.end().plus(10).le(y.start()));
model.constraint(x.length().le(y.length()));

When x or y is absent then value of both constraints above is absent and therefore they are satisfied.

See

• Model.lengthOf is equivalent function on Model.
• Function IntervalVar.lengthOr is a similar function that replaces value absent by a constant.

---

lengthOr()

lengthOr(absentValue: number): IntExpr

Creates an integer expression for the length of the interval variable. If the interval is absent, then its value is absentValue.

Parameters

Parameter	Type
absentValue	number

Returns

IntExpr

Remarks

This function is equivalent to interval.length().guard(absentValue).

See

• IntervalVar.length
• IntExpr.guard

---

makeAbsent()

makeAbsent(): IntervalVar

Makes the interval variable absent. Absent interval variable cannot be present in the solution, i.e., it will be omitted in the solution (and everything that depends on it).

Returns

IntervalVar

Returns the interval variable itself to allow chaining.

See

• makeOptional, makePresent
• isOptional, isPresent, isAbsent

---

makeOptional()

makeOptional(): IntervalVar

Makes the interval variable optional. Optional interval variable can be absent in the solution i.e. can be omitted.

It is equivalent to setting optional: true in Model.intervalVar.

Returns

IntervalVar

Returns the interval variable itself to allow chaining.

See

• makePresent, makeAbsent
• isOptional, isPresent, isAbsent

---

makePresent()

makePresent(): IntervalVar

Makes the interval variable present. The present interval variable cannot be absent in the solution, i.e., cannot be omitted.

It is equivalent to setting optional: false in Model.intervalVar.

Returns

IntervalVar

Returns the interval variable itself to allow chaining.

See

• makeOptional, makeAbsent
• isOptional, isPresent, isAbsent

---

position()

position(sequence: SequenceVar): IntExpr

Creates an expression equal to the position of the interval on the sequence.

Parameters

Parameter	Type
sequence	SequenceVar

Returns

IntExpr

Remarks

This function is the same as Model.position.

---

presence()

presence(): BoolExpr

Creates a Boolean expression which is true if the interval variable is present.

Returns

BoolExpr

Remarks

This function is the same as Model.presenceOf, see its documentation for more details.

---

pulse()

pulse(height: number | IntExpr): CumulExpr

Creates cumulative function (expression) pulse for the interval variable and specified height.

Parameters

Parameter	Type
height	number | IntExpr

Returns

CumulExpr

Remarks

This function is the same as Model.pulse.

---

setEnd()

setEnd(e)

setEnd(e: number): IntervalVar

Sets the end of the interval variable to the given value.

It overwrites any previous end limits given at variable creation by Model.intervalVar or later by setEnd, setEndMin or setEndMax.

Equivalent to:

intervalVar.setEndMin(e);
intervalVar.setEndMax(e);

Note that the end of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
e	number

Returns

IntervalVar

See

• setEndMin, setEndMax
• getEndMin, getEndMax

setEnd(eMin, eMax)

setEnd(eMin: number, eMax: number): IntervalVar

Limits the possible end of the variable to the range eMin to eMax.

It overwrites any previous end limits given at variable creation by Model.intervalVar or later by setEnd, setEndMin or setEndMax.

Equivalent to:

intervalVar.setEndMin(eMin);
intervalVar.setEndMax(eMax);

Note that the end of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
eMin	number
eMax	number

Returns

IntervalVar

See

• setEndMin, setEndMax
• getEndMin, getEndMax

---

setEndMax()

setEndMax(eMax: number): IntervalVar

Sets the maximum end of the interval variable to the given value. It overwrites any previous maximum end limit given at variable creation by Model.intervalVar or later by setEnd or setEndMax. This function does not change the minimum end.

Note that the end of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
eMax	number

Returns

IntervalVar

See

• setEnd, setEndMin
• getEndMin, getEndMax

---

setEndMin()

setEndMin(eMin: number): IntervalVar

Sets the minimum end of the interval variable to the given value.

It overwrites any previous minimum end limit given at variable creation by Model.intervalVar or later by setEnd or setEndMin. This function does not change the maximum end.

Note that the end of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
eMin	number

Returns

IntervalVar

See

• setEnd, setEndMax
• getEndMin, getEndMax

---

setLength()

setLength(l)

setLength(l: number): IntervalVar

Sets the length of the interval variable to the given value. It overwrites any previous length limits given at variable creation by Model.intervalVar or later by setLength, setLengthMin or setLengthMax.

Equivalent to:

intervalVar.setLengthMin(l);
intervalVar.setLengthMax(l);

Note that the length of the interval variable must be in the range 0 to LengthMax.

Parameters

Parameter	Type
l	number

Returns

IntervalVar

See

• setLengthMin, setLengthMax
• getLengthMin, getLengthMax

setLength(lMin, lMax)

setLength(lMin: number, lMax: number): IntervalVar

Limits the possible length of the variable to the range lMin to lMax. It overwrites any previous length limits given at variable creation by Model.intervalVar or later by setLength, setLengthMin or setLengthMax.

Equivalent to:

intervalVar.setLengthMin(lMin);
intervalVar.setLengthMax(lMax);

Note that the length of the interval variable must be in the range 0 to LengthMax.

Parameters

Parameter	Type
lMin	number
lMax	number

Returns

IntervalVar

See

• setLengthMin, setLengthMax
• getLengthMin, getLengthMax

---

setLengthMax()

setLengthMax(lMax: number): IntervalVar

Sets the maximum length of the interval variable to the given value. It overwrites any previous maximum length limit given at variable creation by Model.intervalVar or later by setLength or setLengthMax. This function does not change the minimum length.

Note that the length of the interval cannot exceed than LengthMax.

Parameters

Parameter	Type
lMax	number

Returns

IntervalVar

See

• setLength, setLengthMin
• getLengthMin, getLengthMax

---

setLengthMin()

setLengthMin(lMin: number): IntervalVar

Sets the minimum length of the interval variable to the given value. It overwrites any previous minimum length limit given at variable creation by Model.intervalVar or later by setLength or setLengthMin. This function does not change the maximum length.

Note that the length of the interval variable must be in the range 0 to LengthMax.

Parameters

Parameter	Type
lMin	number

Returns

IntervalVar

See

• setLength, setLengthMax
• getLengthMin, getLengthMax

---

setName()

setName(name: string): this

Assigns a name to the node.

Parameters

Parameter	Type	Description
name	string	Named to be assigned.

Returns

this

The node itself so it can be used in chained expression.

Remarks

Assigning a name is optional. However, it is helpful for debugging because variable names appear in the development traces. It is also helpful for exporting the model to a file (see problem2json).

Example

let model = new CP.Model();
let x = model.intervalVar({ length: 10 }).setName("x");
// The line above is equivalent to:
//   let x = model.intervalVar({ length: 10, name:"x" });
let endOfX = model.endOf(x).setName("endOfX");
let result = await CP.solve(model);

Inherited from

ModelNode.setName

---

setStart()

setStart(s)

setStart(s: number): IntervalVar

Sets the start of the interval variable to the given value.

It overwrites any previous start limits given at variable creation by Model.intervalVar or later by setStart, setStartMin or setStartMax.

Equivalent to:

intervalVar.setStartMin(s);
intervalVar.setStartMax(s);

Note that the start of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
s	number

Returns

IntervalVar

See

• setStartMin, setStartMax
• getStartMin, getStartMax

setStart(sMin, sMax)

setStart(sMin: number, sMax: number): IntervalVar

Limits the possible start value of the variable to the range sMin to sMax.

It overwrites any previous start limits given at variable creation by Model.intervalVar or later by setStart, setStartMin or setStartMax.

Equivalent to:

intervalVar.setStartMin(sMin);
intervalVar.setStartMax(sMax);

Note that the start of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
sMin	number
sMax	number

Returns

IntervalVar

See

• setStartMin, setStartMax
• getStartMin, getStartMax

---

setStartMax()

setStartMax(sMax: number): IntervalVar

Sets the maximum start of the interval variable to the given value.

It overwrites any previous maximum start limit given at variable creation by Model.intervalVar or later by setStart or setStartMax. The minimum start is not changed by this function.

Note that the start of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
sMax	number

Returns

IntervalVar

See

• setStart, setStartMin
• getStartMin, getStartMax

---

setStartMin()

setStartMin(sMin: number): IntervalVar

Sets the minimum start of the interval variable to the given value.

It overwrites any previous minimum start limit given at variable creation by Model.intervalVar or later by setStart or setStartMin. This function does not change the maximum start.

Note that the start of the interval variable must be in the range IntervalMin to IntervalMax.

Parameters

Parameter	Type
sMin	number

Returns

IntervalVar

See

• setStart, setStartMax
• getStartMin, getStartMax

---

span()

span(covered: IntervalVar[]): void

Constraints the interval variable to span (cover) a set of other interval variables.

Parameters

Parameter	Type	Description
covered	IntervalVar[]	The set of interval variables to cover.

Returns

void

Remarks

This constraint is the same as Model.span.

---

start()

start(): IntExpr

Creates an integer expression for the start of the interval variable.

Returns

IntExpr

Remarks

If the interval variable is absent, then the resulting expression is also absent.

Example

In the following example, we constraint interval variable y to start after the end of y with a delay of at least 10. In addition, we constrain the length of x to be less or equal to the length of y.

let model = new CP.Model;
let x = model.intervalVar({ name: "x", ... });
let y = model.intervalVar({ name: "y", ... });
model.constraint(x.end().plus(10).le(y.start()));
model.constraint(x.length().le(y.length()));

When x or y is absent then value of both constraints above is absent and therefore they are satisfied.

See

• Model.startOf is equivalent function on Model.
• Function IntervalVar.startOr is a similar function that replaces value absent by a constant.

---

startAtEnd()

startAtEnd(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.start().plus(delay).eq(successor.end())).

In other words, start of predecessor plus delay must be equal to end of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.startAtEnd is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.eq

---

startAtStart()

startAtStart(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.start().plus(delay).eq(successor.start())).

In other words, start of predecessor plus delay must be equal to start of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.startAtStart is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.eq

---

startBeforeEnd()

startBeforeEnd(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.start().plus(delay).le(successor.end())).

In other words, start of predecessor plus delay must be less than or equal to end of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.startBeforeEnd is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.le

---

startBeforeStart()

startBeforeStart(successor: IntervalVar, delay: number | IntExpr): void

Creates a precedence constraint between two interval variables.

Parameters

Parameter	Type	Default value
successor	IntervalVar	undefined
delay	number | IntExpr	0

Returns

void

Remarks

Assuming that the current interval is predecessor, the constraint is the same as:

model.constraint(predecessor.start().plus(delay).le(successor.start())).

In other words, start of predecessor plus delay must be less than or equal to start of successor.

When one of the two interval variables is absent, then the constraint is satisfied.

See

• Model.startBeforeStart is equivalent function on Model.
• Model.constraint
• IntervalVar.start, IntervalVar.end
• IntExpr.le

---

startOr()

startOr(absentValue: number): IntExpr

Creates an integer expression for the start of the interval variable. If the interval is absent, then its value is absentValue.

Parameters

Parameter	Type
absentValue	number

Returns

IntExpr

Remarks

This function is equivalent to interval.start().guard(absentValue).

See

• IntervalVar.start
• IntExpr.guard

---

stepAtEnd()

stepAtEnd(height: number | IntExpr): CumulExpr

Creates cumulative function (expression) that changes value at end of the interval variable by the given height.

Parameters

Parameter	Type
height	number | IntExpr

Returns

CumulExpr

Remarks

This function is the same as Model.stepAtEnd.

---

stepAtStart()

stepAtStart(height: number | IntExpr): CumulExpr

Creates cumulative function (expression) that changes value at start of the interval variable by the given height.

Parameters

Parameter	Type
height	number | IntExpr

Returns

CumulExpr

Remarks

This function is the same as Model.stepAtStart.