Critical Paths &PERT Diagrams (TXT: 8.5 & SOL:

DM.10)

CLASSWORK (DAY 30)

WORKSHEET (1, 3)

HOMEWORK (DAY 30):

WORKSHEET (2, 4)

Critical Paths

https://www.youtube.com/watch?v=0bkw7cnZLwQ

Critical Path- The path with the longest processing time from START to FINISH. Critical Time is the total

processing time for the critical path.

5

6

4

4

8

4

10

A

B

C

D

E

F

G

Ex: How many paths are there? Find the critical path.

ABDG = 5 + 6 + 4 +10 = 25ABEG = 5 + 6 + 8 + 10 = 29ACEG = 5 + 4 + 8+ 10 = 27ACFG = 5 + 4+ 4+ 10 =23

. This is the shortest time you would have for

any schedule

The program/project evaluation and review technique, (PERT), is a statistical mathematics tool, used in General project management, which was designed to analyze and represent the tasks involved in completing a given project. This is a special type of directed graph.

Steps to Create a PERT Diagram

1.List each sub project with an estimated time line for completing them.

2.Sort the list of sub projects such that no sub project comes before a prerequisite on the list. For example, digging the foundation and running the electrical wire are both sub project in the construction of a new home, but it's not possible to run wiring before the foundation is dug, so digging the foundation goes first.

3.Number each of the sub projects, with the first sub project being the lowest number, and the last sub project being the highest number.

4.Draw a diagram with each of the listed sub projects, starting on the left with the first sub projects, and going farther right for dependent sub projects. Draw arrows between sub projects that are prerequisites for other sub projects.

Pert Diagrams

https://www.youtube.com/watch?v=iXc2Y-xDgI8

Given

Task Time Required

Preceding Task(s)

1 Train construction workers

6 None

2 Build Shell 8 None3 Build life support

systems14 None

4 Recruit colonists 12 None5 Assemble shell 10 1,26 Train colonists 10 2, 3, 47 Install life support

systems4 1, 2, 3, 5

8 Install solar energy systems

3 1, 2, 5

9 Test life support & energy

4 1, 2, 3, 5, 7, 8

10 Bring colonists to the colony

4 1, 2, 3, 4, 5, 6, 7, 8, 9

Draw a PERT Diagram. Find the Critical Path.

0

6

8

14

12

10

10

4

3

4

4 0

1

2

3

4

5

6

8

7

9

10

Critical Paths0+6+10+3+4+4+0 = 27 0+6+10+4+4+4+0 = 280+8+10+3+4+4+0 = 29 0+8+10+4+4+4+0 = 30

0+14+4+4+4+0 = 26 0+14+10+4+0 = 280+12+10+4+0 = 26 0+___+____+___+____ = 22

Takes at least 30 monthsto complete

Extra Example:Create a PERT Diagram and determine its critical path

Task Time Require

d

Preceding Tasks

1. Train construction workers 6 None

2. Build Shell 8 None

3. Build life support 14 None

4. Recruit colonist 12 None

5. Assemble Shell 10 1,2

6. Train Colonist 10 2, 3, 4

7. Install life support systems

4 1, 2, 3, 5

8. Install solar energy systems

3 1, 2, 5

9. Test life support & energy systems

4 1, 2, 3, 5, 7, 8

10. Ring colonist to the colony

4 1, 2, 3, 4, 5, 6, 7, 8, 9