## Representation of the concept of ‘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 task reflects the first point. The purpose of ProcessScheduler is to compute a sequence (a temporal ordering) of a collection of tasks that satisfy a set of constraints.

### Start/end/duration¶

The Task class and its derivatives represent any task. A Task instance is 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 $$end>=start$$

• duration: a integer number of periods, such as $$duration=end-start$$ # The duration of this task will depend on the number of workers that hold boxes


A VariableDurationTask duration can be bounded by lower and upper values (a number of periods), by setting the min_duration and/or max_duration. In the following example, the wash_room Task instance means: “Washing an hospital room must be completed in at most 20mn, knowing that there’s a total amount of work of 10.” The task duration will depend on how many workers the solver assign to this task. The more workers are assigned, the less the duration will be.

wash_room = VariableDurationTask('WashHospitalRoom', work_amount=10, max_duration=20)


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('EnglishLesson', allowed_durations = [1, 2])


### 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.

### 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¶

The optional attribute of a task is a boolean. It is set to False by default. If set to True the solver may, or may not, schedule the task.

Three Task derivative classes can be used to represent a task:

A ZeroDurationTask is a task such that $$duration=0$$, that is to say $$start=end$$. Useful to represent project milestones, or other important points in time.

project_kickup = ZeroDurationTask('KickUp')


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.

The duration of a FixedDurationTask is known a priori. You must pass the duration parameter value 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('CookChicken', duration=6)


A VariableDurationTask represents a task for which the duration is not known. The 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('PlantWheatSeeds', max_duration=48)


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