1. Chapter 3
Project Management

2. Project Management Projects are typically characterized as:
one-time, large scale operations
consuming large amount of resources
requiring a long time to complete
a complex set of many activities
3 Important Project Management Functions:
Planning – determine what needs to be done
Scheduling – decide when to do activities
Controlling – see that it’s done right

3. PERT/CPM project management technique
(Program Evaluation & Review Technique)/
(Critical Path Method)
Inputs
list of activities
precedence relationships
activity durations
Outputs
project duration
critical activities
slack for each activity

4. Excavate & pour footings1 2
Excavate & pour footings
Pour foundation
Install drains
Project Network for House Construction 3 6 7 4 8 9 5 10 11 12 16 18 13 17 15 14
Install rough
electrical & plumbing
Pour
basement
floor
Install
cooling &
heating
Erect
frame & roof
Lay
brickwork
storm
drains
drywall
flooring
finished
plumbing
kitchen
equipment
Paint
Finish
roof
drainage
grading
floors
walks;
Landscape
electrical
work
carpeting

5. CPM
A project has the following activities and precedence relationships:
Immediate Immediate
Predecessor Predecessor
Activity Activities Activity Activities
a f c,e
b a g b
c a h b,d
d a i b,d
e b j f,g,h
Construct a CPM network for the project using:
1.) Activity on arrow
2.) Activity on node

6. Activity on Arrow (Initial Network)

7. Activity on Arrow (Final Network)b c d e f g h i j

8. Activity on Node

9. Critical Path path  any route along the network from start to finish
Critical Path  path with the longest total duration
This is the shortest time the project can be completed.
Critical Activity  an activity on the critical path
*If a critical activity is delayed, the entire project will be delayed. Close attention must be given to critical activities to prevent project delay. There may be more than one critical path.
To find critical path: (brute force approach)
identify all possible paths from start to finish
sum up durations for each path
largest total indicates critical path

10. 1 2 6 4 7 5 3
b = 2
d = 4
g = 9
h = 9
f = 8
c = 5
a = 6
k = 6
j = 7
i = 4
e = 3

11. Slack Times
Earliest Start (ES) – the earliest time an activity can start
ES = largest EF of all immediate predecessors
Earliest Finish (EF) – the earliest time an activity can finish
EF = ES + activity duration
Latest Finish (LF) – the latest time an activity can finish
without delaying the project
LF = smallest LS of all immediate followers
Latest Start (LS) – the latest time an activity can start
LS = LF – activity duration

12. Slack Times Slack  how much an activity can be delayed
without delaying the entire project
Slack = LF – EF or Slack = LS – ES
Slack EF LF ES LS

13. c = 10
g = 12
f = 17
b =15
a = 10
e = 15
i = 7
d = 20
h = 9

14. b = 4
d = 5
h = 5
i = 3
c = 5
a = 5
g = 4
j = 6
e = 5
f = 6

15. Input Table for Microsoft Project
(Example 10.1, page 387)

16. Gantt Chart for Microsoft Project
(Example 10.1, page 387)

17. Project Network for Microsoft Project
(Example 10.1, page 387)

18. Activity Crashing (Time-Cost Tradeoffs)
An activity can be performed in less time than normal, but it costs more.
Problem: If project needs to be completed earlier than normal, which activity durations should be decreased so as to minimize additional costs?
Guidelines:
Only crash critical activities
Crash activities one day at a time
Crash critical activity with lowest crashing cost per day first
Multiple critical paths must all be crashed by one day

19. Activity Crashing Example
Crash project as much as possible.
a = 3
b = 4
c = 8
d = 5
Activity
Duration
Crashed
Cost
Crashing
Cost/day a 3 2 40 45 b 4 50 54 c 8 5 68 d 30 33
Minimum duration = 9 days; Total additional cost = $30

20. Program Evaluation & Review Technique (PERT)
3 duration time estimates
optimistic (to), most likely (tm), pessimistic (tp)
Activity duration:
mean te = (to + 4tm + tp) / 6
variance Vt = [(tp – to) / 6]2
Path duration:
mean of path duration = T = Σ te
variance of path duration = σ2 = Σ Vt

21. X = T ± Zσpath
Z is number of standard deviations that X is from the mean.
Example: If the mean duration of the critical path is 55 days and the variance of this path is 16, what is the longest the project should take using a 95% confidence level?

23. probability
of being late
.05
Zσcp
actual
project
duration T 55 X

24. PERT Example
If the expected duration of a project is 40 days and the variance of the critical path is 9 days, what is the probability that the project will complete in less than 45 days?
in more than 35 days?
in less than 35 days?
in between 35 and 45 days?

25. probability
of being late
Zσcp
actual
project
duration T 40 45

26. PERT Example
The expected duration of a project is 200 days, and the standard deviation of the critical path is 10 days. Predict a completion time that you are 90% sure you can meet.