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PLANNING ENGINEERING AND
PROJECT MANAGEMENT
By
Lec. Junaid Arshad
1
Lecture#08
DEPARTMENT OF ENGINEERING MANAGEMENT
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Topics Covered
CPM Calculations for AOA
and AON Networks Slack Time / Float Critical Path, Critical Activity Practice Problems
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CPM Calculations for AON Network
Provides activity information
Early start (ES) & late start (LS) Early finish (EF) & late finish (LF) Slack (S) / Float (FL)
Identifies critical path
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Forward and Backward Pass
Forward pass is a technique to move forward through network diagram. Backward pass is its opposite.
Early Start (ES) and Early Finish (EF) use the forward pass technique.
Late Start (LS) and Late Finish (LF) use the backward pass technique.
Note: If the float of the activity is zero, the two starts (ES and LS) and the two finish (EF and LF) are the same. Hence, If float of activity is zero, ES = LS and EF = LF.
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Early Start and Early Finish Steps
Begin at starting event and work forward ES = 0 for starting activities
ES is earliest start EF = ES + Activity time
EF is earliest finish ES = Maximum EF of all predecessors for
non- starting activities
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Late Start and Late Finish Steps
Begin at ending event and work backward LF = Maximum EF for ending activities
LF is latest finish; EF is earliest finish LS = LF - Activity time
LS is latest start LF = Minimum LS of all successors for
non-ending activities
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Latest Finish
ES
LS
EF
LF
Earliest Finish
Latest Start
Earliest Start
Activity Nam
eActivity Duration
AON Network Calculations
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Problem 04
Activity Preceding Activity
Duration (days)
A - 10
B - 07
C - 12
D A 18
E B 14
F B 13
G C 16
H D, E 12
I F, G 06CPM Calculations for an AON Network
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Slack Time is tis the amount of time an activity may be delayed without affecting the project deadline. This is also referred as float.
Total Slack Time / Total Float:
Time shared among more than one activity.
Free Slack Time /Free Float: Time associated with a single activity.
Slack Time/FloatSlack Time/Float
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An activity having zero slack time is called critical activity.
The concept of critical activities is that it draws the attention of the project manager to the activities that needs the closest monitoring.
Any delay of a critical activity leads to an equivalent delay of the total project.
Critical ActivityCritical Activity
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A path having longest duration (completion time) in the network is called critical path.
Shortest time project can be completed
Any delay on critical path activities, delays project
Critical path activities have zero slack
Critical PathCritical Path
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Total Float is valid for a chain and not for a single activity.
In the under discussion example, C and G have a float of 06 days. This means that the sum of delays for C and G may run up to 06 days without affecting the project finish time.
Analysis of float is a particularly neat tool for calculating consequences of schedule variance.
Explanation of Total FloatExplanation of Total Float
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Assume the following data with respect to
schedule (for problem 04)
B will be delayed by 04 days D will be delayed by 01 day E will be delayed by 05 days G will be delayed by 03 days
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It is recognized that D is critical, hence a delay of at least one day to the overall project is unavoidable.
Activity G has a float of 06 days. Since no other activity on that chain has a delay, the float will accommodate the 03 day delay of G.
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Further, B and E are both on the same chain. The float along the chain is 07 days and the total delay is 4+5=9 days. This means a 02 day delay of the project.
In conclusion, the project will be delayed by 02 days and B-E-H will be the new critical path. A-D will have a float of one, and C-G a float of 04.
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CPM calculation for AON Network is same as for AOA network, but the calculation of events is omitted.
CPM Calculations for AON Network
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Problem 05: General Hospital’s Activities and Predecessors
Activity
Immediate Predecessors Duration (days)
A - 2
B - 3
C A 2
D A, B 4
E C 4
F C 3
G D, E 5
H F, G 2
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AON Network for General Hospital Includes Critical Path
Slack=0
Start
A
B
C
D
F
F
G
HH
1313
2
1515
HG
88
5
1313
HF
410
3
713
HC
22
2
44
HE
44
4
88
HD
34
4
78
HB
01
3
34
HA
00
2
22
H00
0
00
Slack=0 Slack=0
Slack=0
Slack=0
Slack=6
Slack=1Slack=1
Start
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Critical Path for General Hospital
Start
A
B
C
D
F
G
HE
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Explanation of Free Float
Consider slack time of activity F. Delaying this activity decreases only its slack time and does not impact the slack time of any other activity. This type of slack time is referred as free slack / free float.
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Gantt Chart for General Hospital Early Start and Finish
GENERAL HOSPITAL GENERAL HOSPITAL
A Build internal componentsB Modify roof and floorC Construct collection stackD Pour concrete and install frameE Build high-temperature burnerF Install pollution control systemG Install air pollution deviceH Inspect and test
1 2 3 4 5 6 7 8 9 10 1112 13 1415 16
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Gantt Chart for General Hospital Late Start and Finish
A Build internal componentsB Modify roof and floorC Construct collection stackD Pour concrete and install frameE Build high-temperature burnerF Install pollution control systemG Install air pollution deviceH Inspect and test
1 2 3 4 5 6 7 8 9 10 1112 13 1415 16
GENERAL HOSPITAL
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Table for Network Scheduling
Problem 06
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Problem 06Solution - AOA Method
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Early Event Time (TE)
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Finding TE Values
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Late Event Time (TL)
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Finding TL Values
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Critical Path
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Activity Scheduling
An activity’s early starting time equals the TE of its beginning event: ES = TE.
An activity’s late finishing time equals the TL for its ending event: LF = TL.
From these, Two times are computed using the expected activity completion time t:
Early finishing time: EF = ES + t.Late starting time: LS = LF t.
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Scheduled Times must fall between ES and LF and allow at least time t to complete.
Problem 06Solution - AOA Method
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Problem 07
Activity Preceding Activity
Duration (weeks)
A - 10
B - 07
C - 12
D A 18
E B 14
F B 13
G C 16
H D, E 12
I F, G 06CPM Calculations for an AOA Network
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ActivityPredecessors
(Dependencies)
Time (Weeks)
A - 3
B - 5
C - 7
D A 8
E B 5
F C 5
G E 4
H F 5
I D 6
J G - H 4
Table for Network Scheduling
Problem 08
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