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1
Project Scheduling: Lagging, Crashing and
Activity NetworksChapter 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 Activity-
on-Arrow techniques. 5. Understand the differences in AON and
AOA and recognize the advantages and disadvantages of each technique.
Learning Goals
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Lags in Precedence Relationships
The logical relationship between the start and finish of one activity and the start and finish of another activity.
Four logical relationships between tasks1. Finish to Start2. Finish to Finish3. Start to Start4. 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
Finish-to-Start (FS) Lag
0 A 6Spec Design 6
6 B 11Design Check 5
15 C 22Blueprinting 7
Lag 4 days
This lag is not
the same as
activity slack
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Two activities share a similar completion point◦ The interior construction cannot happen until
wiring, plumbing, and HVAC installation are complete
Finish-to-Finish (FF) Lag
31 S 33Plumbing 2
33 T 39HVAC 3
39 U 45Interior Const. 6
30 R 36Wiring 6
Lag 3 days
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Often two or more activities must start at the same time
Start-to-Start (SS) Lag
31 S 33Plumbing 2
33 T 36HVAC 3
36 U 42Inspection 6
30 R 36Wiring 6
Lag 3
Logic must be maintained by both forward and backward pass
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Least common type of lag relationship Successor’s finish dependent on
predecessor’s start
Start-to-Finish (SF) Lag
22 S 28Plumbing 6
28 T 33HVAC 5
33 U 34Inspection 1
30 R 36Wiring 6
Lag 3
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Gantt Charts 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 charts1. Easy to create, read, and comprehend2. Identify the project network and schedule baseline3. Allows for updating and control4. Useful to identify resource needs and assigning
resources to tasks
Example
Create a Gantt chart based on the activities listed in the table.
Task Time Predecessor
Z 8 --
Y 5 Z
X 8 Z
W 4 Y,X
V 5 W
U 3 W
T 6 V
S 7 U,T
R 9 S9
Gantt Chart Example from MSExcel
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Z
Y
X
W
V
U
T
S
R
0 5 10 15 20 25 30 35 40 45 50
Task Start DurationZ 0 8Y 8 5X 8 8W 16 4V 20 5U 20 3T 25 6S 31 7R 38 9
http://office.microsoft.com/en-us/excel/HA102382531033.aspx
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Sample Tracking Gantt Chart With Critical Path A-C-D-F-H
Critical path in red
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Crashing Projects
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.
Crashing Projects – Under What Conditions?
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Steps in Project Crashing
1. Compute the crash cost per time period. If crash costs are linear over time:
Crash costper period =
(Crash cost – Normal cost)
(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.
Steps in Project Crashing
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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.
Steps in Project Crashing
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Time-Cost Tradeoffs for Crashing Activities
| | |1 2 3 Time (Weeks)
$34,000 —
$33,000 —
$32,000 —
$31,000 —
$30,000 —
—
Activity Cost
Crash Point
Normal Point
Crash Time Normal Time
Crash Cost
Normal Cost
Crash Cost/Wk = Crash Cost – Normal CostNormal Time – Crash Time
=$34,000 – $30,000
3 – 1
= = $2,000/Wk$4,0002 WksHow far do you
need to speedup the process?
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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 weeksNormal cost = $14,000
Crashed activity duration = 5 weeksCrashed cost = $23,000 The activity cost slope =
23,000 – 14,000 or, $9,000 = $3,000 per week 8 – 5 3
Crashing Activities – An Example
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Managerial Considerations
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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Crash Example
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.
Crash Example
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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
required
Activity on Arrow (AOA) Networks
Event label
Earliest Event Time (ES)
Latest Event Time (LF)
Task Description
Duration
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Sample AOA Network Diagram
1 2
3
4
A
B
C
111 2
3
4
A
B
C
222
333
444
A
B
C
Figure 10.18
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Activity on Arrow (AOA) Network
AH
F
E
D
C
B
K
G
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A Comparison of AON and AOA Network Conventions
Activity on Activity Activity onNode (AON) Meaning Arrow (AOA)
A comes before B, which comes before C
(a) A B CBA C
A and B must both be completed before C can start
(b)
A
CC
B
A
B
B and C cannot begin until A is completed
(c)
B
A
CA
B
C
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A Comparison of AON and AOA Network Conventions
Activity on Activity Activity onNode (AON) Meaning Arrow (AOA)
C and D cannot begin until both A and B are completed
(d)
A
B
C
D B
A C
D
C cannot begin until both A and B are completed; D cannot begin until B is completed. A dummy activity is introduced in AOA
(e)
CA
B D
Dummy activity
A
B
C
D
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A Comparison of AON and AOA Network Conventions
Activity on Activity Activity onNode (AON) Meaning Arrow (AOA)
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.
(f)
A
C
DB A B
C
D
Dummy activity
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1. Please give examples of circumstances in which a project would employ lag relationships between activities using:
1. Finish to start2. Finish to finish3. Start to start4. 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?
Discussion Questions
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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?
Discussion Questions