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FSP General Mathematics

Project Planning Investigation: Critical Path Analysis

Abstract

Projects such as building a house, planning a party, cooking a meal, etc. all require many separate tasks to be completed. We use Critical Path Analysis to determine the processes which are critical to finishing the project in the shortest time. Critical Path Analysis is an algorithm for scheduling a set of projects activities,   such that the project can be completed in the shortest time.

To perform critical path analysis, we firstly need to construct a model of the project in the form of a table and network. The table and network usually include the following information:

   A list of all activities required to complete the project

   The time (duration) that each activity will take to complete,

   The dependencies between the activities and,

    Logical end points such as milestones or deliverable items.

This project covers section 6.1 of the curriculum.

Your Task:

You have been hired to help students plan for they move to Adelaide and to begin their studies at The

University of Adelaide College. With such a big job ahead of you, you decided to brush up on your planning skills before you jump into helping students prepare.

Background information:

Displaying the tasks in a Precedence Table and Network.

The following table displays the tasks required to make a cup of tea.

Independent task: A task that does not depend on the completion of a previous task in order to start the task at hand.

Simultaneous tasks: tasks that can be performed at the same time, but it doesn’t have to be performed by the same person.

Prerequisites tasks: Tasks that must be completed immediately before the task at hand can start.

 

Task

Time

(sec)

Independent tasks

Simultaneous tasks

Prerequisite tasks

A

Retrieve the cups

15

 

C

-

B

Place the tea bags into the cups

10

 

D

A

C

Fill the kettle with water

20

 

A

-

D

Boil the water in the kettle

100

 

B

C

E

Pour the boiling water into the cups

10

 

 

B, D

F

Add milk and Sugar as necessary

15

 

 

E

G

Stir the tea

10

 

 

F

The table above can be represented by a Network. The respective network is displayed below. Notice that  there is a start and finish node, the edges represent the tasks, and the weight of each edge is the time for each respective task. When two tasks (edges) connect to a node, it means that both these tasks must be completed before the subsequent task can begin.

Consider: Where are the independent tasks placed on the network? How do we represent prerequisite tasks on the network? How can we display the tasks that can be completed at the same time on the network?

Part 1: Coming to study FSP at UoAC? 

Consider the tasks you had to complete to enable you to study the University of Adelaide College

Foundations Studies Program. For example, you had to complete schooling to a certain year level, you had to apply and pass the IELTS test, you had to apply to the college, purchase a device, etc.

Your Task:

1.   Identify at least 20 individual activities involved in preparing you to study the Foundation Studies Program at the University of Adelaide College. Display the 20 tasks in a table and give a brief description of each.

2.   Indicate the approximate length of time it took for each of the activities to be completed.

3.   State the prerequisite activities for each individual activity.

4.   Complete the table below to display all the information about the individual tasks. Remember you need to include at least 20 tasks and include the following:

 

 

 

Task and description

 

Time

(units)

Which task needs to

be completed directly

before we can start

the task?

Explain WHY selected

tasked must be

completed directly

before we can start

the task

A

 

 

 

 

B

 

 

 

 

5.    Construct a network diagram to represent the above information.

6.  Write a one-page summary detailing your findings from steps (1) to (5). Your summary should include    an introductory sentence, identify the key points from your analysis and conclude with the main findings from your network. Discuss any limitations. Make sure you include the precedence table, network and    critical path analysis on a separate page.

You must submit an electronic copy of your work. Everything must be typed (no handwritten work). Your networks should be constructed using technology. Some free programs that are useful include Microsoft PowerPoint and Lucid Charts. Any drawn diagrams should be clear, professional and include all necessary information.

Part 2: You’realmost done! 

Can you believe that we only almost finished Semester 1 of FSP? Although we only have a few weeks left, your General Mathematics teachers wants to impart you with worthwhile skills that you will benefit from in   the future and at university.

Your Task:

1.   Identify the remaining general steps you must accomplish to complete FSP, General Mathematics

and English for Academic Purposes. (Ask your teachers for a list of assessments and tasks required to complete the subject. These could be things like major assessments (e.g. Investigations, Exams,  Essays, etc) or other tasks (e.g. Medical School Interview, buying a plane ticket, submitting the paperwork for your choice of degree).  You should have at least 40 tasks in total.

2.   For each task, you should consider any minor tasks that you need to complete.  For example, to complete a General Mathematics Test you may need to do the following:

i.      Revise class notes and recordings (6 days)

ii.      Attempt revision practice questions (1 day)

iii.      Book a TAP session (0.1 day)

3.   There will be some compulsory tasks and prerequisites that you MUST include in your precedence table and network. They include the following:

i.      Learn how to use Harvard referencing in EAP. This is a prerequisite to (ii) and (iii).

ii.      Learn how to use Harvard in-text references. This is a prerequisite to (iii).

iii.      Start Investigation 3 for General Mathematics. This is a prerequisite to (iv).

iv.      Start Investigation 4 for General Mathematics.

v.      Book a TAP session with a subject of your choice to prepare for the Exams. This is a prerequisite to (vii).

vi.      Sit your Exams (list your subjects). This is a prerequisite to (vii)

vii.     Attend graduation.

viii.      Learn basic formula and graphing on Microsoft Excel. This is a prerequisite for (iii).

4.   Collate all the assessments and tasks you listed into a precedence table. Your precedence table

should have the following headings (remember in the Description Column to include the assessment or task description):

Task

Description

Time (days)

Prerequisite

A

Study for UCAT

6

-

B

Take UCAT

0.5

A

C

 

 

 

D

 

 

 

5.   Use your precedence table from step (3) to construct a precedence network to represent a schedule you can follow to make sure that you complete your tasks in time for graduation.

6.   Complete a forward and backward scan to determine the slack time for each task and

whether you will complete any assessments listed by the due dates. You can wish to list the slack times as a table.

7.  Write a one-page summary detailing your findings. Your summary should include an introductory    sentence, identify the key points from your analysis and conclude with the main findings from your  network. Discuss any limitations. Make sure you include the precedence table, network and critical path analysis on a separate page.

You must submit an electronic copy of your work. Everything must be typed (no handwritten work). Your networks should be constructed using technology. Some free programs that are useful include Microsoft PowerPoint and Lucid Charts. Any drawn diagrams should be clear, professional and include all necessary information.

Important points to consider:

1.  When assigning a duration for each task, consider a realistic time that will ensure you will complete   the assessment on time. Include time required for rest and everyday life. Keep your units consistent.

2.  When assigning a prerequisite task, only list the immediate prerequisites (so other subject

assessments may or may not influence each other). Listing this correctly will illustrate how you can efficiently organise your time.

3.   In real life, you may also want to consider rest time and weekends. You can include this in your network or see how much slack time you have, which will enable to you plan your rest times.

4.   Completing a forward and backward scan will help you determine the slack time for each assessment and whether you will complete all the assessments by the due dates.