project scheduling: networks, duration estimation, and critical path
TRANSCRIPT
Project Scheduling: Networks, Duration estimation,
and Critical Path
Project Scheduling Terms• Successors
• Predecessors
• Network diagram
• Serial activities
• Concurrent activities
ED
C
B
A F
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-3
Project Scheduling Terms
ED
C
B
A F
• Merge activities
• Burst activities
• Node
• Path
• Critical Path
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-4
Network Diagrams
Show interdependence
Facilitate communication
Help schedule resources
Identify critical
activities
Determine project completion
Show start & finish dates
AOA vs. AON
The same mini-project is shown with activities on arrow…
C
ED
B F
E
C
DB F
…and activities on node.
Node Labels
Early Start
Activity Float Activity Descriptor
Late Start
ID Number
Activity Duration
Late Finish
Early Finish
Duration Estimation Methods
• Past experience• Expert opinion• Mathematical derivation – Beta distribution
– Most likely (m)– Most pessimistic (b)– Most optimistic (a)
22 =
6
b aActivity Variance s
4 = TE
6
a m bActivity Duration
Task Predecessor a m b
A -- 7 8 15
B A 13 16 19
C A 14 18 22
D B, C 12 14 16
E D 1 4 13
F D 6 10 14
G F, E 11 14 19
1. Sketch the network described in the table.
2. Determine the expected duration and variance of each activity.
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-9
Constructing the Critical Path
• Forward pass – an additive move through the network from start to finish
• Backward pass – a subtractive move through the network from finish to start
• Critical path – the longest path from end to end which determines the shortest project length
Rules for Forward/Backward Pass
Forward Pass Rules (ES & EF)– ES + Duration = EF– EF of predecessor = ES of successor– Largest preceding EF at a merge point becomes EF
for successor
Backward Pass Rules (LS & LF)– LF – Duration = LS– LS of successor = LF of predecessor– Smallest succeeding LS at a burst point becomes LF
for predecessor
Task Predecessor Time
A -- 4
B A 9
C A 11
D B 5
E B 3
F C 7
G D, F 3
H E, G 2
K H 1
1. Sketch the network described in the table.
2. Determine the ES, LS, EF, LF, and slack of each activity
Laddering Activities
Project ABC can be completed more efficiently if subtasks are used
A(3) B(6) C(9) ABC=18 days
Laddered ABC=12 days
A1(1) A2(1) A3(1)
B1(2) B2(2) B3(2)
C1(3) C2(3) C3(3)
Hammock Activities
Used as summaries for subsets of activities
0 A 5
0 5 5
5 B15
5 1015
15 C 18
15 3 18
0 Hammock 18
0 18 18
Useful with a complex project or one that has
a shared budget
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Reducing the Critical Path
• Eliminate tasks on the CP• Convert serial paths to parallel when possible• Overlap sequential tasks• Shorten the duration on critical path tasks• Shorten
– early tasks– longest tasks– easiest tasks– tasks that cost the least to speed up
Chapter 10
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-15
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-16
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 tasks
1. Finish to Start
2. Finish to Finish
3. Start to Start
4. Start to Finish
Finish to Start Lag
• Most common type of sequencing
• Shown on the line joining the modes– Added during forward pass– Subtracted during backward pass
0 A 6Spec Design
6
6 B 11Design Check
5
15 C 22Blueprinting
7
Lag 4
This lag is not the same as activity slack
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Finish to Finish Lag
Two activities share a similar completion point– The mechanical inspection cannot happen until
wiring, plumbing, and HVAC installation are complete
10 B 16Plumbing
6
16 C 24HVAC
5
24 D 25Inspection
1
15 A 21Wiring
6
Lag 3
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Start to Start Lag
Logic must be maintained by both
forward and backward pass
31 B 32Plumbing
1
33 C 36HVAC
5
36 D 37Inspection
1
30 A 36Wiring
6
Lag 3
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Start to Finish Lag
• Least common type of lag relationship
• Successor’s finish dependent on predecessor’s start
22 B 28Plumbing
6
28 C 33HVAC
5
33 D 34Inspection
1
30 A 36Wiring
6 Lag 3
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Gantt Charts
Establish a time-phased network Can be used as a tracking tool
Benefits of Gantt charts
1. Easy to create and comprehend
2. Identify the schedule baseline network
3. Allow for updating and control
4. Identify resource needs
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Create a Gantt chart based on the activities listed in the table.
Task Time Pred
A 8 --
B 5 A
C 8 A
D 4 B,C
E 5 D
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Crashing
The process of accelerating a project
Principal methods for crashing
Improving existing resources’ productivity Changing work methods Increasing the quantity of resources
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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 crashing cost exceeds the penalty cost
Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 10-25
What is the lowest cost to complete this project in 52 weeks? Times are in weeks and costs in dollars. Plot the AON & AOA networks and the GANTT chart.
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 6 1600 1600
F D 9 6 1500 3000
G E, F 7 4 600 1800
H G 15 11 1600 3600
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Activity on Arrow Networks
Activities represented by arrows
Widely used in construction
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
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1. Use AOA to sketch the network that represents the project as described in the table.
2. Calculate early and late event times for all activities.
Activity Time Pred Activity Time Pred
A 4 -- F 15 E
B 2 A G 4 E
C 10 A H 7 D,F,G
D 3 B I 11 H
E 15 B,C
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Activity on Arrow Network
A H
F
D
E
C
B I
G
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Controversies in the Use of Networks
Networks can be too complex
Poor network construction creates problems
Networks may be used inappropriately
When employing subcontractors– The master network must be available to them– All sub-networks must use common methods
Positive bias exists in PERT networks