1. PROJECT MANAGEMENT
WITH CPM/PERT

2. Project Management Project Definition Primarily Management Functions
Consists of a series of tasks (or activities) with following characteristics
Starting and ending dates
Well-defined objectives
Unique endeavor
Utilizing resources
Primarily Management Functions
Planning
Organizing
Controlling

3. Project Management Functions
PM functions are to manage
Cost and time
Human resources
Communication
Contract/procurement
Risk

4. Project Management When to use Complex projects Several parallel tasks
Predefined deadlines and milestones must be met
Estimate project completion time
Difficult to know when project is in trouble
Limited and conflicting resources

5. Examples Building a new airport Expanding a plant
Designing a new product
Construction projects of all types
Maintenance projects
R&D projects

6. Project Planning Process
Define project objective(s)
Identify activities
Establish precedence relationships
Make time estimates
Determine project completion time
Schedule activities
Balance resources to meet objective(s)

7. Typical Questions for PM’s
What is the the total time to complete a project?
What are the scheduled start and finished dates for each activity?
Which activities are critical and must be completed on time to keep the project on schedules?
How long can noncritical activities be delayed before they cause a delay in the project completion time?
Is there any way to reduce the project completion time?
How much money is needed to expedite the project completion time?

8. Project Management Techniques
Critical Path Method (CPM)
Developed in 1950’s
Planed and control maintenance job of a chemical plant
Reduced length of maintenance shutdown by 40%
Project Evaluation and Review Technique (PERT)
Developed in 1960’s
Planed and control the Polaris missile project
Speeded up project by 2 years

9. Critical Path Method (CPM)
Graphical method of showing relationship of project activities
An activity or task --takes resources and time to complete
Precedence relations (some must be completed before others can start) must be constructed
Critical Path Method is the longest path through the resulting project network

10. Immediate Predecessor
Precedence Relations
Activity
Immediate Predecessor
Duration (days) A
(Start) 8 B A 6 C A 8
Act. Pred. Duration
A - 4
B A 3
C A 5
D B, C 2 D A 10 E
B,C,D 4

11. Simple Project Network “Activity on Node” AON representation
Successor
Precedence relations represented by “arcs” B
Predecessor A D E B C D A C
Project Network

12. Simple Project Network “Activity on Arc” AOA representation2 B 6 4 E A C 3 1 4 6 8 D 10 4

13. Activity Start/Finish Times (AON)
Activity Name
Early
Finish
Time
Early
Start
Time ES EF LF LS D
Late
Start
Time
Activity
Duration
Late
Finish
Time
Activity Name
Earliest Start
Earliest Finish ES LS EF LF
Latest Start
Latest Finish
Activity Time

14. Finding the Critical PathB C C E A B 4 7 D 6 9 3 A D 4 9 11 4 9 11 4 2 C 4 9 4 9 5

15. Forward Pass 8 B 14 6 8 C 16 A 18 E 22 8 8 4 8 B 4 7 8 D 18 6 9 3 5 10 A D 4 9 11 4 9 11 4 2 C 4 9 4 9 5

16. Backward Pass 8 B 14 12 6 18 8 C 16 A E 8 18 22 10 8 18 18 4 22 8 8 8 D 18 5 8 10 18

17. Finding Activity Slack S =EF-ES = LF-EF8 B 14
S =18-14=4 14 6 18
S =22-22=0
S =8-8=0 8 C 16 E A 8 18 22 10 8 18 22 8 8 18 4
S =18-16=2 8 D 18 5
Critical Path: Path with
zero activity slacks 8 10 18
S =18-18=0

18. Example Consider the following activities of a project
Activity Predecessors Time (wks)
A none 4
B none 12
C B 6
D A 16
E. A,C 12
F B 16
G. E,F 10
H. D,G 0

19. Project Network D A
Finish
Start E C B G F

20. PERT (Program Evaluation and Review Technique)
Similar to Critical Path Method (CPM)
Uncertainty in activity duration
Provides estimates of project duration probabilities
Best used for highly uncertain projects
new product development
first-time projects
R&D projects

21. Dealing with Uncertain Activity Duration
The PERT three-estimate Approach
Most likely estimate (m)
estimate of the most likely value of duration
Optimistic estimate (b)
estimate of the duration under the most favorable conditions
Pessimistic estimate (a)
estimate of duration under the unfavorable conditions

22. A Simple Example
Activity
Most Optimistic
(a)
Most Likely
(m)
Most Pessimistic
(b) A 2 8 14 B 3 6 9 C 5
7.5 13
Act. Opt. Likely Pess. A B
C 4 5 6 D D 3
10.5 15 E
2.5
11.5
2.5

23. Distribution Assumption
Beta distribution
density a m b
activity
duration
Expected Time =
a + 4m + b 6
(b - a)2 36
Variance =

24. Expected Duration & Variance
Activity A
a + 4m + b 6 =
2+4(8)+14 6
ET = =
8.0
Expected time = (Most Optimistic + 4*Most Likely + Most Pessimistic)/6
Variance = (Most Pessimistic - Most Optimistic)^2/36
(b - a)2 36 =
(14-2)2 36 =4
Var =

25. Expected Duration & Variance
Activity
Expected
Time
Variance
Critical
Path? 8 4 A ? 6 1 B 8
1.77 C
Act. E(Time) Var. C.P.?
A Yes
B No
C Yes
D Yes 10 4 D ? 4
2.33 E ?

26. Probability of Completion
Probability that a project will be completed by a specified due date
Due Date - Expected Completion Date
z =
Sum of the Variances on the Critical Path
Expected Completion
Normal Distribution z
Due Date z
See Appendix 3 (pg. 886) for a table of Normal Distribution
probabilities.

27. Completion Probability Example
What is the probability of completing the project within 24 days?
= 0.624
z =
From a Z-table for standard Normal distributions:
z = ( )/sqrt( )
z = 1/1.607 = 0.622
Probability = = 73.24%
(An overhead of the Normal distribution table (pg. 886) is needed to work this example.)
Probability of completion = = 73.2%

28. Considering Time-Cost Trade-offs
If extra money is spent to expedite the project, what is the least expensive way of attempting to meet the target completion time?
Define Normal and crash points
Normal point shows the time and cost when an activity is performed in the normal way
Crash point shows the time and cost when an activity is fully crashed

29. Time-Cost Relationship
Assumed linear relationship
(Crash cost-Normal cost) (Crash time-Normal time)
Crash
Crash cost/wk=
Crash Cost
Normal Cost
Normal
Normal time
Crash time

30. Example Time (wk) Cost($1000) Activity Normal Crash Max. Red. Cost/wkB C D E 8 6 10 4 5 9 3 7 2 1
2/2=1
2/1=2
6/3=2
2/1=2
1/1=1

31. Crashing An Activity

32. Other Project Mgmt Techniques
Resource leveling
How to schedule resources (equipment, people) to minimizes
Multiple resource scheduling
How to schedule resources when activities can require more than one resource type
Cash flow and budgeting
Combine cash and budget information with project scheduling to track expenditures, project cash flows

33. Problems
1. A project involving the installation of a computer system comprises eight activities. The following table lists immediate predecessors and activity times (in weeks).
Activity Immediate Predecessor Time A B
C A 2
D B,C 5
E D 4
F E 3
G B, C 9
H F, G 3
Draw a project network.
What are the critical activities?
What is the expected project completion time?
2. Building a backyard swimming pool consists of nine major activities. The activities, their immediate predecessors, and their time estimates (in days) are shown in the following table.
Activity A B C D E F G H I
Immediate Pred. - - A,B A,B B C D D,F E,G,H
Optimistic
Most Probable
Pessimistic
What is the probability that a project can be completed in 25 or fewer days?

34. 3. Consider the following project.
Immediate Time (Weeks) Cost ($1000)
Activity Predecessor Normal Crash Normal Crash A
B A
C B
D A
E D
F C,E
Develop a project network.
Develop an activity schedule.
What are the critical activities and what is the expected project completion time?
Assume that the project manager wants to complete the project in 6 months or 26 weeks. What crashing decisions do you recommend to meet the desired completion time at the least cost? Work through the network and attempt to make the crashing decisions by inspection.
Develop an activity schedule for the crashed project.
What added project cost is required to meet the 6-month completion time?