Task

According to the APICS dictionary, a task may either be:

1. In project management, the lowest level to which work can be divided on a project

2. In activity-based cost accounting, a task, a subdivision of an activity, is the least amount of work. Tasks are used to describe activities.

In the context of this software library, the concept of a task aligns with the first definition : the lowest level to which work can be divided on a project. ProcessScheduler's primary objective is to compute a chronological sequence, or temporal order, for a collection of tasks while adhering to a specific set of constraints. Three types of Task may be used to represent a scheduling problem : ZeroDurationTask, FixedDurationTask and VariableDurationTask. They follow the inheritance class diagram represented below.

Task model

A Task instance is basically a time interval, defined by the three following parameters:

• start: a point in the \([0, horizon]\) integer interval. If the task is scheduled, then \(start>=0\)

• end: a point in the \([0, horizon]\) integer interval. If the task is scheduled, then \(end>=start\) and \(end<=horizon\)

• duration: a integer number of periods, such as \(duration=end-start\)

classDiagram
  Task <|-- ZeroDurationTask
  Task <|-- FixedDurationTask
  Task <|-- VariableDurationTask
class Task{
    +str name
    +bool optional
    +int release_date
    +int due_date
    +bool due_date_is_deadline
    +int priority
    +int work_amount
}
class FixedDurationTask{
    +int duration
}
class VariableDurationTask{
    +int min_duration
    +int max_duration
    +list allowed_durations
}

Warning

The Task class has to be considered as an abstract class that should not be instantiated. Use any of its three specialization (ZeroDurationTask, FixedDurationTask or VariableDurationTask) to represent your scheduling problem.

The Task class and its derivatives represent any activity. The parameters for the creation of a Task are the following:

Parameter name	Type	Default Value	Description
name	str	unique string	The name of the task must be unique among all other tasks
optional	bool	False	If the task is optional
release_date	int	None	Also be referred to as the ready date. It is the time the job arrives at the system, i.e., the earliest time at which the task can start its processing
due_date	int	None	the committed shipping or completion date (i.e., the date the job is promised to the customer)
due_date_is_deadline	bool	False	if False, completion of the task after its due date is allowed, but then a penalty is incurred. If True the task cannot be scheduled after its due_date
priority	int	1	A number denoting the importance of the task relative to the other tasks in the system. A task with a priority of 10 should be considered as 10 times more important than a task with a priority of 1
work_amount	int	0	the quantity of work necessary to be completed by all the resources assigned

Additional parameters for the FixedDurationTask class.

Parameter name	Type	Default Value	Description
duration	int		The task duration, such that \(duration=end-start\)

Additional parameters for the VariableDurationTask class.

Parameter name	Type	Default Value	Description
min_duration	int	0	Minimal task duration
max_duration	int	None	Maximal task duration
allowed_duration	list	None	List of possible task durations

# Example: The duration of this task depends on the number
# of workers handling boxes.
move_boxes = VariableDurationTask(name='MoveBoxesFromMachineAToInventory')

Warning

Each Task instance must have a unique name in the scheduling problem. To prevent that two tasks share the same name, ProcessScheduler raises an exception if ever a task with an existing name is already created.

Three Task derivative classes can be used to represent a task: FixedDurationTask, ZeroDurationTask, VariableDurationTask.

FixedDurationTask class

The duration of a FixedDurationTask is known a priori. You must pass the task name and duration arguments when creating the instance:

# I assume one period to be mapped to 15min, cooking will be 1.5 hour
# so the chicken requires 6*15mn=1.5h to be cooked
cook_chicken = FixedDurationTask(name='CookChicken',
                                 duration=6)

ZeroDurationTask class

A ZeroDurationTask is a FixedDurationTask where \(duration=0\), that is to say \(start=end\). Useful to represent project milestones, or other important points in time.

project_kickup = ZeroDurationTask(name='KickUp')

VariableDurationTask class

A VariableDurationTask represents a task for which the duration is not known. The solver is expected to find a duration that satisfies the constraints (the duration may depend on the number of resources assigned to the task). You can bound the duration by using max_duration and/or min_duration parameters.

# 48h max to get done
plant_wheat_seeds = VariableDurationTask(name='PlantWheatSeeds',
                                         max_duration=48)

A VariableDurationTask duration can be selected among a list of possible durations. The solver decides the duration.

# either 1 or 2 hour for an english lesson
english_lesson = VariableDurationTask(name='EnglishLesson',
                                      allowed_durations = [1, 2])

Advanced parameters

Work amount

The work_amount is the total amount of work that the Task must provide. It is set to 0 by default. The work_amount is a dimensionless positive integer value, it can be mapped to any unit according to the physical meaning of the work amount. For example, if the task target is to move small pieces of wood from one point to another, then the work_amount maybe 166000 if 166000 pieces of woods are to be moved. In a maintenance task, if there are 8 screws to unscrew, the UnScrew work_amount will be set to 8.

Temporal priority

The priority of a task is a positive integer that can take any value. It is not bounded. A task with a higher priority will be scheduled earlier than a task with a lower priority. If the solver is requested to optimize the global schedule in terms of task priorities (a "priority objective") then a task with a high priority may be scheduled before a task with a lower priority.

Optional

All tasks instances are mandatory by default: the solver has to find a solution where all tasks are actually scheduled. However, tasks instances can be turned into optional tasks, by setting the optional flag to True:

# 10mn to clean the table. This is an optional task
clean_the_table_after_meal = FixedDurationTasks(name='CleanTable',
                                                duration=10,
                                                optional=True)

An optional task may or may not be scheduled by the solver. It depends on the constraints that bound the scheduling problem.