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Chapter 10
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1. Apply lag relationships to project activities.
2. Construct and comprehend Gantt charts.
3. Understand the trade-offs required in the
decision to crash project activities.
4. Develop activity networks using Activityon-Arrow techniques.
5. Understand the differences in AON and AOA
and recognize the advantages and
disadvantages of each technique.
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The logical relationship between the start
and finish of one activity and the start and
finish of another activity.
Four logical relationships between tasks
1. Finish to Start
2. Finish to Finish
3. Start to Start
4. Start to Finish
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

Most common type of sequencing
Shown on the line joining the nodes
◦ Added during forward pass
◦ Subtracted during backward pass
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A
6
Spec Design
6
6
B
11
Design Check
5
15
C
22
Blueprinting
Lag 4 days
7
4

Two activities share a similar completion
point
◦ The interior construction cannot happen until
wiring, plumbing, and HVAC installation are
complete
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R
Wiring
6
36
31
S
33
Plumbing
2
Lag 3 days
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T
HVAC
3
39
39
U
45
Interior Const.
6
5

Often two or more activities must start at the
same time
30
R
Wiring
6
36
Lag 3
31
S
33
Plumbing
2
33
T
HVAC
3
36
36
U
42
Inspection
6
6


Least common type of lag relationship
Successor’s finish dependent on
predecessor’s start
30
R
Wiring
6
36
Lag 3
22
S
28
Plumbing
6
28
T
HVAC
5
33
33
U
34
Inspection
1
7




A graphical representation of the project schedule
that illustrates how work flows over time
Shows activity start and end dates and durations
Links project activities to a project schedule baseline
Can be used as a tracking tool
Benefits of Gantt charts
1.
Easy to create, read, and comprehend
2.
Identify the project network and schedule baseline
3.
Allows for updating and control
4.
Useful to identify resource needs and assigning
resources to tasks
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
Create a Gantt chart Task Time Predecessor
based on the
Z
8
-activities listed in
Y
5
Z
the table.
X
8
Z
W
4
Y,X
V
5
W
U
3
W
T
6
V
S
7
U,T
R
9
S
9
R
Task
Z
Y
X
W
V
U
T
S
R
Start
0
8
8
16
20
20
25
31
38
Duration
8
5
8
4
5
3
6
7
9
S
T
U
V
W
X
Y
Z
0
10
20
30
40
50
http://office.microsoft.com/en-us/excel/HA102382531033.aspx
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Critical path in red
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Accelerating a project by committing more
resources.
Principal options for crashing
 Improving existing resources’ productivity
 Changing work methods used
 Increasing the quantity of resources
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



The initial schedule may be too optimistic.
Market needs change and the project is in
demand earlier than anticipated.
The project has slipped considerably behind
schedule.
The contractual situation provides even more
incentive to avoid schedule slippage.
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1. Compute the crash cost per time period. If
crash costs are linear over time:
(Crash cost – Normal cost)
Crash cost
per period = (Normal time – Crash time)
2. Using current activity times, find the critical
path and identify the critical activities.
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3. If there is only one critical path, then select the
activity on this critical path that
(a) can still be crashed, and
(b) has the smallest crash cost per period.
4. If there is more than one critical path, then
select one activity from each critical path such
that
(a) each selected activity can still be crashed, and
(b) the total crash cost of all selected activities is the
smallest.
Note: the same activity may be common to more than one
critical path.
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5. Update all activity times.
6. If the desired due date has been reached,
stop. If not, return to Step 2.
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Activity
Cost
Crash Point
$34,000 —
Crash Cost/Wk =
Crash $33,000 —
Cost
$30,000 —
Normal
Cost
$34,000 – $30,000
3–1
$4,000
=
= $2,000/Wk
2 Wks
=
$32,000 —
$31,000 —
Crash Cost – Normal Cost
Normal Time – Crash Time
How far do you
need to speed
up the process?
Normal Point
—
|
1
Crash Time
|
2
|
3
Normal Time
Time (Weeks)
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Formula
Slope =
crash cost – normal cost
normal time – crash time
Example – calculating the cost of crashing
Suppose:
Normal activity duration = 8 weeks
Normal cost = $14,000
Crashed activity duration = 5 weeks
Crashed cost = $23,000
The activity cost slope =
23,000 – 14,000
8–5
or,
$9,000
3
=
$3,000 per week
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
Determine activity fixed and variable costs

The crash point is the fully expedited activity

Optimize time-cost tradeoffs

Shorten activities on the critical path

Cease crashing when
◦ the target completion time is reached
◦ the crash cost exceeds the penalty cost
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Activity
Pred
Normal Time
Min
Time
Normal
Cost
Crash
Cost
A
--
14
9
500
1500
B
A
5
2
1000
1600
C
A
10
8
2000
2900
D
B, C
8
5
1000
2500
E
D
6
5
1600
1900
F
D
9
6
1500
3000
G
E, F
7
4
600
1800
H
G
15
11
1600
3600
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
What is the lowest cost to complete this project in
53 weeks? Times are in weeks and costs in dollars.
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




Activities represented by arrows
Event nodes easy to flag
Forward and backward pass logic
similar to AON
Two activities may not begin and
end at common nodes
Dummy activities may be
Event
required
label
Task Description
Earliest
Event
Time (ES)
Latest
Event
Time (LF)
Duration
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Figure 10.18
3
B
1
A
2
C
4
23
E
B
H
A
F
C
D
K
G
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Activity on
Node (AON)
(a)
A
Activity
Meaning
C
B
A comes before
B, which comes
before C
A
(b)
C
B
A and B must both
be completed
before C can start
Activity on
Arrow (AOA)
A
B
C
A
B
C
B
(c)
A
C
B and C cannot
begin until A is
completed
B
A
C
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Activity on
Node (AON)
A
C
B
D
(d)
A
C
(e)
B
D
Activity
Meaning
C and D cannot
begin until both
A and B are
completed
C cannot begin until
both A and B are
completed; D
cannot begin until B
is completed. A
dummy activity is
introduced in AOA
Activity on
Arrow (AOA)
A
C
B
D
A
C
Dummy activity
B
D
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Activity on
Node (AON)
A
B
(f)
C
D
Activity
Meaning
B and C cannot
begin until A is
completed. D
cannot begin until
both B and C are
completed. A
dummy activity is
again introduced
in AOA.
Activity on
Arrow (AOA)
A
Dummy
activity
B
D
C
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1. Please give examples of circumstances in which a
project would employ lag relationships between
activities using:
1.
2.
3.
4.
Finish to start
Finish to finish
Start to start
Start to finish
2. The advantage of Gantt Charts lies in their linkage
to the project schedule baseline. Explain this
concept.
3. What are the advantages in the use of Gantt charts
over PERT diagrams? In what ways might PERT
diagrams be advantageous?
4. Under what circumstances might you wish to crash
a project?
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5. In crashing a project, we routinely focus on those
activities that lie on the critical path, not activities
with slack time. Explain why this is the case.
6. What are some of the advantages in the use of AOA
notation as opposed to AON? Under what
circumstances does it seem better to apply AON
methodology in network development? Explain the
concept of a “dummy variable.” Why are they
employed in AOA notation? Why is there no need to
use dummy variables in an AON network?
7. Explain the concept of a “dummy variable.” Why are
they employed in AOA notation? Why is there no
need to use dummy variables in an AON network?
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