Project Management: A
Managerial Approach
Chapter 8 – Scheduling
1
Overview
• WBS to Schedule Process
• PERT
• Schedule Types
• CPM
2
Scheduling
• A schedule is the conversion of a
project action plan into an operating
timetable
• It serves as the basis for monitoring
and controlling project activity
• Taken together with the plan and
budget, it is probably the major tool
for the management of projects
3
Simple Schedule – Gantt Chart
9
Network Techniques: PERT and CPM
• With the exception of Gantt charts, the most
•
•
common approach to scheduling is the use of
network techniques such as PERT and CPM
The Program Evaluation and Review
Technique (PERT) was developed by the U.S.
Navy in 1958
The Critical Path Method (CPM) was
developed by DuPont, Inc during the same
time period
10
Scheduling Terminology
• Activity - A specific task or set of tasks that
•
•
are required by the project, use up resources,
and take time to complete
Event - The result of completing one or more
activities. An identifiable end state occurring
at a particular time. Events use no resources.
Network - The combination of all activities
and events define the project and the activity
precedence relationships
12
Scheduling Terminology
• Path - The series of connected activities
(or intermediate events) between any two
events in a network
• Critical - Activities, events, or paths
which, if delayed, will delay the
completion of the project. A project’s
critical path is understood to mean that
sequence of critical activities that connect
the project’s start event to its finish event
13
Scheduling Terminology
• An activity can be in any of these conditions:
– It may have a successor(s) but no
predecessor(s) - starts a network
– It may have a predecessor(s) but no
successor(s) - ends a network
– It may have both predecessor(s) and
successor(s) - in the middle of a network
• Interconnections from horizontal links in
vertical WBS
14
Hypothetical Network
3
13
16
30
1
5
2
5
20
6
6
TE=64
4
Calculate t(e) and Z for this network……
15
Activity and Project Frequency Distributions
ACTIVITY
a
PROJECT
m
b
(A)
TE
(B)
16
PERT Activity Calculation
t(e) = a + 4m + b
6
a = Most Optimistic (MO)
m = Most Likely (ML)
b = Most Pessimistic (MP)
t(e) = Activity Duration
When a single estimate for activity time is not sufficient!
17
PERT Schedule Probability
Z = T(S) – T(E)
√SSD(T[E])2
Z = Probability of
Meeting Schedule
Z = T(S) – T(E)
√ΣVar(T[E])
T(S) = Scheduled Duration
T(E) = Critical Path Duration
Z is derived from a table of predetermined probabilities
18
PERT Activity Times & Variances
Activity
a
m
b
t(e)
1-2
17
29
47
30
2-3
6
12
24
13
2-4
16
19
28
20
3-5
13
16
19
16
4-5
2
5
14
6
5-6
2
5
8
5
19
Variance of Activity Estimates
Activity
a
m
b
t(e)
[(b-a)/6]2
Var
1-2
17
29
47
30
25
2-3
6
12
24
13
9
2-4
16
19
28
20
4
3-5
13
16
19
16
1
4-5
2
5
14
6
4
5-6
2
5
8
5
1
20
Critical Path
3
13
1
30
16
2
5
20
5
6
6
4
TE = 30 + 13 + 16 + 5 = 64
Var(TE) = 25 + 9 + 1 + 1 = 36
21
Possible Project Durations
TS=67
TE=64
Z = (67 – 64) / √(25 + 9 + 1 + 1) = 0.5
Hence, the probability of meeting the
target schedule (Ts) is 0.69 (69%)
22
Z Table
Z Value
Probability
Z Value
Probability
-2.0
0.02
+2.0
0.98
-1.5
0.07
+1.5
0.93
-1.0
0.16
+1.0
0.84
-0.7
0.24
+0.7
0.76
-0.5
0.31
+0.5
0.69
-0.3
0.38
+0.3
0.62
-0.1
0.36
+0.1
0.54
23
Gantt Charts
• The Gantt chart shows planned and actual
•
•
•
progress for a number of tasks displayed
against a horizontal time scale
It is an effective and easy-to-read method of
indicating the actual current status for each
set of tasks compared to the planned
progress for each item of the set
It can be helpful in expediting, sequencing,
and reallocating resources among tasks
Gantt charts usually do not show technical
dependencies
25
Drawing Networks
• Activity-on-Arrow (AOA) networks use arrows
•
•
to represent activities while nodes stand for
events
Activity-on-Node (AON) networks use nodes
to represent activities with arrows to show
precedence relationships
The choice between AOA and AON
representation is largely a matter of personal
preference
27
Hypothetical Network
3
1
2
5
6
4
29
AOA Network Building Blocks
Activity
Event
Install software
79
80
30
Partial Koll Business Center - AOA
1
A
Application
approval
2
B
Construction
plans
4
C
Traffic
study
D
Service
availability
check
3
5
31
Partial AOA Network
3
X
1
A
B
C
2
4
E
(A)
3
B
1
A
X
C
2
4
E
(B)
4
B
C
1
A
2
X
E
3
(C)
32
Partial AOA Network
4
B
E
X
A
1
C
2
3
D
5
(D)
4
E
B
X
1
A
2
C
?
3
5
F
D
(E)
33
Full AOA Network
B
15 X
1
A
5
Legend
Activity
Duration
2
C
10
3
D
5
4
0
0
Y
5
E
15
F
10
6
G
170
7
H
35
8
KOLL BUSINESS CENTER
County Engineers Design Department
34
Activity-on-Node Network Fundamentals
J, K, & L can all begin at
the same time, if you wish
(they need not occur
simultaneously)
J
A
B
C
K
A is preceded by nothing
B is preceded by A
C is preceded by B
M
L
(A)
(C)
but
All (J, K, L) must be
completed before M can
begin
Y
Y and Z are preceded by X
X
Z
Z is preceded by X and Y
Z
Y and Z can begin at the
same time, if you wish
Y
AA
AA is preceded by X and Y
X
(B)
(D)
35