of Elements Project Planning
Divide project into tasks, tasks into subtasks, subtasks into ... Estimate duration of each task, subtask, ... Estimate resource requirements for each task, subtask, ...(budget, personnel, facilities) Identify precedence relations among tasks
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Benefits of Project Planning
Communications tool Resource allocation Benchmarking
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Keeping Engineers Busy with Multiple Projects
this image is not available yet
Fig. 7.1
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Stages of Engineering Design Projects
Enthusiasm Disillusionment Panic Search for the guilty Punishment for the innocent Praise and honors for the nonparticipants
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Project Planning Tools
Gantt Chart Critical Path Method (CPM) Program Evaluation and Review Technique (PERT)
Variations and combinations of the above
Many available software packages contain these tools
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Gantt Chart for Automobile Bumper Project
Task N am e P r e l i m i n a r y D e s ig n B u ild P r o t o t y p e T e s t P ro to ty p e F in a l D e s ig n
1
2
3
4
5
6
7
8
9
D ays 10 11 12 13 14 15 16 17 18 26 20 21 22 23 24 25 18 37 1 0 9
Fig. 7.2
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Enhanced Gantt Chart for Automobile Bumper Project
D ays Task Nam e
P r e lim in a r y D e s ig n B u ild P r o t o t y p e T e s t P ro to ty p e F in a l D e s ig n
h rs 1
30 20 25 40
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Fig. 7.3
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Keeping Track of Project Progress on a Gantt Chart
Task N am e
P r e lim in a r y D e s ig n B u ild P r o t o t y p e T e s t P ro to ty p e F in a l D e s ig n
h rs 1
30 20 25 40
2
3
4
5
6
7
8
9
D ays 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Fig. 7.4
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Typical Electric Substation
Fig. E7.3.1(a)
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Tasks for Designing and Building an Electric Substation
Task A. Design substation B. Select site C. Prepare site D. Order transformers and related electrical equipment E. Order concrete, fencing, and related construction supplies F. Excavate for foundation G. Pour and cure concrete foundation H. Erect structural frames I. Install electrical equipment J. Erect fence K. Test electric equipment L. Connect to grid M. Clean up site 3 10 2 3 2 2 2 2 Duration (days) 10 7 3 2 2
Table E 7.3.1
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Gantt Chart for Substation Design and Construction
Week 1 Task M T W Th F M A B C D E F G H I J K L M
Week 2
Week 3
Week 4
Week 5
Week 6
T W Th F M T W Th F M T W Th F M T W Th F M T W Th F
Fig. E7.3.1(b)
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Critical Path Method (CPM)
Uses a network flow diagram to depict the precedence relations among activities (tasks) Elements of diagram are directed line segments and nodes Facilitates identification of activities whose timely completion are critical to timely completion of the project
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CPM Notation and Conventions
An activity is an ongoing effort on a project task (directed line segment). Every activity has an initiating event and a closing event (nodes).
Fig. 7.6
3
A
(a ) A c tiv itie s
(b ) E v e n ts
Events consume no time. Their primary role in CPM diagrams is to separate activities. Consecutive activities must be separated by events.
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CPM Notation and Conventions (cont.)
No pair of events can be directly connected by more than one activity with no intervening events. If an activity R must immediately precede S and T, the relationship is depicted as follows
R
S
Fig. 7.7(a)
T
If activities R and S must both immediately precede T, the relationship is depicted as follows
R
T
S
Fig. 7.7(b)
All networks must begin with a single Start event and end with a single Finish event.
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Dummy Activities
Sometimes precedence relationships require the use of a dummy activity (depicted by a dashed line) to indicate the appropriate relationships. Dummy activities do not take up any time. Dummy activity is needed to correctly depict that P and Q must precede S, and P must precede R.
P R
Q
S
Dummy activity needed when several activities have same Start and End events. Activities R and S share the same Start and End events.
R
Fig. 7.10
S
Dummy activities should be be included only when needed to display the precedence relation.
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Precedence Relations for Several Activities of Bumper Project
Activity Design bracket Build bracket Build bumper Drill holes in bumper
Preceded by
Design bracket
Build bumper, Design bracket
Table 7.2
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Using Dummy Activity for Bumper Project
n sig et de ac k br
build bumper
drill hole in bumper
(a) Shows proper precedence relations for drilling the holes but does not include building the bracket
build bumper
drill hole in bumper
(b) Improperly shows that building the bracket requires the bumper to be built first
br buil ac d ke t
(c) Inclusion of a dummy activity allows proper relations to be depicted
n sig et de ack br
Fig. 7.8
design bracket
build bracket
build bumper
drill hole in bumper
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Multiple Dummy Activities
A precedes D A and B precede E B and C precede F
A D
B
E
C
F
Fig. 7.9
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Project Activities and their Precedence Relations
Activity A B C D E F G H I J K Duration 3 3 4 1 3 2 2 4 1 3 5
Table 7.1
Preceded by A C B, D A, B, D C, F G C E, G F, H, I
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Constructing a Network Diagram
B 3
3
Start
A
1
D
C 4
I 1
Fig. 7.11
B 3
A
E 3
J
Fig. 7.12
3
F 2
3
G 2 H4 I 1
Finish
Start
1
C 4
D
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K
20
Example of Constructing a Network Diagram
Activity A B C D E F G H I J K L M
F
Preceded by
A,B C A D, E, F C H D, E I, J G L, K
G
Table E7.4.1
A
Fig. E7.4.1
D
L
B
E
C
J
H
I
K
M
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Another Example of Constructing a Network Diagram*
Activity Duration Preceded by A 4 B 5 C 4 A D 5 A E 6 A F 4 D,C G 7 F,B H 4 G,E
A Start 4
D5 C4 E6
B 5 F4 G 7 H 4
Finish
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The Critical Path
The critical path is the path of activities from the start event to the finish event for which delay in any activity along that path will delay the project finish. For projects with a small number of alternative paths, the critical path can be most efficiently identified by finding the longest of the alternative paths.
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Alternative Paths and their Length
For the project depicted in Fig. 7.12
Path A-B-E-J A-B-F-G-dummy-J A-B-F-G-H-K C-D-E-J C-D-F-G-dummy-J C-D-F-G-H-K C-I-K
Length 12 13 19 11 12 18 10
Table 7.3
Thus, A-B-F-G-H-K is the critical path
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Critical Path Depicted on Network Diagram
B 3
A
E 3
J
F 2
3
3
G 2 H4 I 1
Finish
Start
1
C 4
D
Fig. 7.13
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K
25
Example Problem of Finding the Critical Path*
Path A-E-H A-C-F-G-H A-D-dummy-F-G-H B-G-H Duration 14 23 24 16
A Start 4
D5 C4 E6
B 5 F4 G 7 H 4
Finish
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Alternate Method for Determining Critical Path
This approach is more efficient for larger networks Use forward sweep to find earliest start (ES) for each activity Use backward sweep to find latest start (LS) for each activity Calculate total float (TF) for each activity TF = LS - ES Critical Path consists of Activities with TF = 0
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Earliest Start*
Earliest Start (ES) is the earliest time an activity can start. It is found by tracing forward (from tail to head of each activity arrow) from the project Start event to the tail of the selected activity. When several paths are possible, use the longest path as determined by the sum of the activity durations on that path. For activity F, ES = 9
A Start 4
D5 C4 E6
B 5 F4 7 G H 4
Finish
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Project Duration*
Continue until we have ES for all activities that terminate in the project Finish event. When duration of each of those activities are added to their respective ES times, the largest of the resulting sums is defined as the Project Duration. For activity H, ES=20 Project Duration =20+4=24
A Start 4
D5 C4 E6
B 5 F4 G 7 H 4
Finish
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Latest Start*
Latest Start (LS) is the latest time an activity can start and still have the project completed within the Project Duration time. LS is found by tracing backwards (from head to tail of each activity) from the project Finish event to the tail of selected activity. Make sure you reach the tail of the selected activity via the head of that activity. When several paths are possible, use the longest path as determined by the sum of the activity durations on that path. The Project Duration minus the length of this longest path is the LS for the selected activity. For activity A, LS=24-24=0
A Start 4
D5 C4 E6
B 5 F4 G 7 H 4
Finish
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Total Float
Total Float for each activity is the difference between the latest start and the earliest start. TF = LS - ES
The activities for which TF=0 define the critical path.
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Summary of Total Float Calculations*
Activity A B C D E F G H Project Duration
24
Duration ES 4 5 4 5 6 4 7 4 24 0 0 4 4 4 9 13 20
LS 0 8 5 4 14 9 13 20
TF 0 8 1 0 10 0 0 0
Critical Path consists of A-D-F-G-H
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Total Float Calculations
For project shown in Fig. 7.12
Activity A B C D E F G H I J K Duration 3 3 4 1 3 2 2 4 1 3 5 19 Earliest Start 0 3 0 4 6 6 8 10 4 10 14 Latest Start 0 3 1 5 13 6 8 10 13 16 14 Total Float 0 0 1 1 7 0 0 0 9 6 0
Project Duration
Table 7.4
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Example of Critical Path Determination
I 10
H
K 5
6
B
J 2
N
5
A 1
C 3
2
G 1
E 6
F 7
L 3
M 4
O 7
D 4
Fig. E7.4.2(a)
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Summary of Example Float Calculations
Activity A B C D E F G H I J K L M N O Project Duration ES 0 1 1 3 7 7 13 3 3 14 16 14 17 21 21 28 LS 0 1 4 3 7 7 13 8 12 15 17 14 17 22 21 TF 0 0 3 0 0 0 0 5 9 1 1 0 0 1 0
Table E7.4.2
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Critical Path for Example Problem
I 10
H
K 5
6
B
J 2
N
5
A 1
C 3
2
G 1
E 6
F 7
L 3
M 4
O 7
D 4
Fig. E7.4.2(b)
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Program Evaluation and Review Technique (PERT)
Based on Critical Path Method
Replaces single estimate of activity duration by a probability distribution
Allows estimate of probability of completing project by a specified time
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Typical Beta Distributions for Activity Durations
to-optimistic estimate; the shortest time within which this activity can be completed assuming everything goes right. This is the left terminus of the pdf. tm-the most likely time required to complete the activity. This is the mode of the pdf. tp- pessimistic estimate; the longest time it will take this activity to be completed assuming everything goes wrong. This is the right terminus of the pdf.
to
tm
tp
to
tm
tp
(a) Skewed-left Beta distribution
(b) Skewed-right Beta distribution
Fig. 7.14
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Network Diagram for PERT Example Problem
B 2-3-4
F 1-2-7
1- A 33
E 2-3-6
J6 31-
Start
11
G 1-2-4
Finish
D -5
H 3-4-6
I 0-1-3
Fig. 7.15
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3- K 512
C 10 43-
39
PERT Procedure
Calculate the expected duration te (mean) of each activity
te =
to + 4tm + t p 6
Calculate the variance 2 of each activity
t p to 2 = 6
2
Use te to determine the expected project duration Te and identify the critical path
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Determination of Critical Path for PERT Example Calculation
Activity A B C D E F G H I J K Project Duration Expected Time 3.00 3.00 4.83 1.67 3.33 2.67 2.17 4.17 1.17 3.17 5.83 21.34 Variance 0.44 0.11 1.36 0.44 0.44 1.00 0.25 0.25 0.25 0.69 2.25 Earliest Start 0.00 3.00 0.00 4.83 6.50 6.50 9.17 11.34 4.83 11.34 15.51 Latest Start 0.50 3.50 0.00 4.83 14.84 6.50 9.17 11.34 14.34 18.17 15.51 Total Float 0.50 0.50 0.00 0.00 8.34 0.00 0.00 0.00 9.51 6.83 0.00
Table 7.5
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PERT Critical Path
B 2-3-4
F 1-2-7
1- A 33
E 2-3-6
J6 31-
11
G 1-2-4
H 3-4-6
Finish
Start
D -5
C 10 43-
I 0-1-3
Fig. 7.16
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3- K 512
42
Probability of Completing Project by Specified time Ts
Calculate the variance of the project duration as the sum of the variances of the activities on the critical path
2 2 2 2 2 2 T ( critical path )= C + D + F + G + H + K
= 1.36 + 0.44 + 1.00 + 0.25 + 0.25 + 1.00
T =2.36
Use the standard normal variable z to find the probability of completing the project in a specified time Ts T Te zS= s T For Ts=20
zS = Ts Te 20 21.34 = = 0.57 T 2.36
From Table 5.1 Pr (z < -0.57) = 0.285
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Space Station PERT Problem
This image is not yet available
Fig. E7.5.1(a)
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Activities for Space Station PERT Problem
Activity A B C D E F G H I J K Description Construct shell of module Order life support system and scientific experimentation package from same supplier Order components of control and navigational system Wire module Assemble control and navigational system Preliminary test of life support system Install life support in module Install scientific experimentation package in module Preliminary test of control and navigational system in module Install control and navigational system in module Final testing and debugging
Table E7.5.1(a)
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PERT Diagram for Space Station Project
D 3-3-5
25 A -3 045
G 4-5 -7
Start
B 10-15-20
C -3 5 5 -2 20
F 1-1-1
K 6-8-15
8-1 J 0- 1 4
Finish
H -3 2 -2
E 5-7-12
I 4-4-6
Fig. E7.5.1(b)
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Summary of PERT Calculations for Space Station Project
Activity A B C D E F G H I J K Project Duration te 31.67 15.00 25.83 3.33 7.50 1.00 5.17 2.17 4.33 10.33 8.83
2
11.11 2.78 6.25 0.11 1.36 0.00 0.25 0.03 0.11 1.00 2.25
ES 0.00 0.00 0.00 31.67 25.83 15.00 35.00 35.00 33.33 37.67 48.00 56.83
LS 0.50 19.50 0.00 32.17 25.83 34.50 42.83 35.50 33.33 37.67 48.00
TF 0.50 19.50 0.00 0.50 0.00 19.50 7.83 0.50 0.00 0.00 0.00
Table E7.5.1(b)
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Another PERT Example Problem*
2. 5 D -5 - 10
A Start 2-4-8
C 2-4-8
E 3-6-12
Finish B 2.5-5-10
2-4 F -8
G 3.5-7-14
H 2-4-8
Activity A B C D E F G H Project Duration
te 4.32 5.40 4.32 5.40 6.48 4.32 7.56 4.32
2 1.00 1.56 1.00 1.56 2.25 1.00 3.06 1.00
ES 0 0 4.32 4.32 4.32 9.72 14.04 21.60 25.92
LS 0 8.64 5.40 4.32 15.12 9.72 14.04 21.60
TF 0 8.64 1.08 0 10.80 0 0 0
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Probability of Completing Project by Specified time Ts*
Calculate the variance of the project duration as the sum of the variances of the activities on the critical path
2 2 2 2 2 T= A + D + F + G + H
= 1.00 + 1.56 + 1.00 + 3.06 + 1.00 = 2.76
Use the standard normal variable z to find the probability of completing the project in a specified time Ts T T z= s e T For Ts=30
z=
Ts Te 30 25.92 = =1.48 T 2.76
From Table 5.1 Pr (z < 1.48) = 1 - Pr (z < -1.48) = 1 - 0.067 = 0.932
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CPM Diagram with Nodes Numbered
2
A
B 3
4
F 2
E 3
8
J 3
3
1
Start
1
C 4
5
G 2
6
H 4
K
9
Finish
D
3
I 1
7
Fig. 7.17
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50
Calendarized Version of Network Diagram
4
E
8
J
dummy Start 1
A
2
B
4
F
5
G
6
H
7
K
9
Finish
Start
1
C
3
D
3
I
0
2
4
6
8
10
12
14
16
18
20
Fig. 7.18
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Activity on Node Network Diagram
E
4
8
A
1
4
2
B
4
F
J
8
9
5
4
Start
3
1
D 3
G
6
7
H
7
K
9
Finish
C
I
Fig. 7.19
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Refined Activity on Node Network Diagram
E,3
A,3
B,3
F,2
J,3
Start
D,1
G,2
H,4
K,5
Finish
C,4
I,1
Fig. 7.20
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