Chapter 3
Project Management
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
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
Install rough
electrical & plumbing
6
Pour
basement
floor
Install
finished
plumbing
Install
drywall
Install
cooling &
heating
7
11
8
Install
drains
10
9
Erect
frame & roof
1
Excavate
& pour
footings
2
Pour
foundation
3
Lay
flooring
12
Install
kitchen
equipment
Paint
4
Lay
brickwork
Finish
carpeting
5
16
Finish
electrical
work
Finish
roof
Lay
storm
drains
Project Network for
House Construction
13
14
Finish
floors
Install
roof
drainage
15
Finish
grading
18
Pour
walks;
Landscape
17
CPM
A project has the following activities and precedence
relationships:
Activity
a
b
c
d
e
Immediate
Predecessor
Activities
-a
a
a
b
Immediate
Predecessor
Activity Activities
f
c,e
g
b
h
b,d
i
b,d
j
f,g,h
Construct a CPM network for the project using:
1.) Activity on arrow
2.) Activity on node
Activity on Arrow
(Initial Network)
Activity on Arrow
(Final Network)
g
b
a
e
c
d
j
f
h
i
Activity on Node
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)
1. identify all possible paths from start to finish
2. sum up durations for each path
3. largest total indicates critical path
2
1
b=2
d=4
4
3
h=9
6
g=9
5
7
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
without delaying the project
LS = LF – activity duration
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
c = 10
g = 12
d=5
f=6
b=4
h=5
i=3
Input Table for Microsoft Project
(Example 10.1, page 387)
Gantt Chart for Microsoft Project
(Example 10.1, page 387)
Project Network for Microsoft Project
(Example 10.1, page 387)
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
Activity Crashing Example
Crash project as much as possible.
d=5
c=8
Activity
Duration
Crashed
Duration
Activity
Cost
Crashed
Cost
a
3
2
40
45
b
4
3
50
54
c
8
5
50
68
d
5
4
30
33
Crashing
Cost/day
Minimum duration = 9 days; Total additional cost = $30
Program Evaluation & Review Technique
(PERT)
3 duration time estimates
– optimistic (to), most likely (tm), pessimistic (tp)
Activity duration:
mean
variance
te = (to + 4tm + tp) / 6
Vt = [(tp – to) / 6]2
Path duration:
mean of path duration = T = Σ te
variance of path duration = σ2 = Σ Vt
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?
probability
of being late
.05
Zσcp
T
55
X
actual
project
duration
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?
probability
of being late
Zσcp
T
40
45
actual
project
duration
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.