## Tutoring on Scheduling

Learning Objectives:

#### Understand and apply Directed Graph and Critical Paths

Math Tutoring on Scheduling

A task manager has to manage many workers completing different tasks and has to carefully arrange the activities or Schedule things so that the project gets done in a reasonable amount of time.

The problem of Scheduling is fairly universal. Some tasks have to be completed before others or some tasks can be completed at the same time. To help us visualize the ordering of tasks in math tutoring, we will create a Directed Graph or simply Digraph’.

Digraph: A Digraph is a graphical representation of a set of tasks in which tasks are represented with dots, called vertices, and arrows between vertices are used to show ordering. Some common vocabulary regarding Digraph are as follows:

1.     Processors: In scheduling, the workers completing the tasks are called Processors.

2.     Finishing Time: The Finishing Time is how long it will take to complete all the tasks. The Finishing Time will depend upon the number of processors and the specific Schedule. If we had only one processor working on a task, it is easy to determine the finishing time. Just add up the individual times of each task.

3.     Optimal Schedule: An Optimal Schedule is the schedule with the shortest possible finishing time.

4.     Idle Time: Idle Time is time in the schedule when there are no tasks available for the processor to work on, so they sit idle.

5.     Priority list: A Priority List is a list of tasks given in the order in which we desire them to be completed.

Critical Time & Critical Path:

The Critical Time is the absolute minimum time to complete the job, regardless of the number of processors working on the tasks. Critical time can be determined by looking at the longest sequence of tasks in the Digraph, called the Critical Path.

Applications of Scheduling:

1.     Contractors need to Schedule workers and subcontractors to build a house as quickly as possible.

2.     A magazine needs to Schedule writers, editors, photographers, typesetters etc. so that an article can be completed on time.

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Hook question:

1.     What are the basic necessities of Scheduling?

2.     What is Directed Graph? Regarding Digraph Define the followings:

Processors, Finishing Time, Idle Time, Optimal Schedule. Priority List.

3.     State some real time applications of Scheduling.

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