project management cpm
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LECTURE 08 & 09 LECTURER ENGR
ALI SALMANengineer348@yahoo.com
DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST
DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST
PLANNING ENGINEERING AND
PROJECT MANAGEMENT
Topics Covered
CPM Calculations for AOA
and AON Networks Slack Time / Float Critical Path, Critical Activity Practice Problems
Provides activity information
Early start (ES) & late start (LS) Early finish (EF) & late finish (LF) Slack (S) / Float (FL)
Identifies critical path
CPM Calculations for AOA Network
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.
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
Early Start and Early 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
Late Start and Late Finish Steps
Problem 04
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
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
An activity having zero slack time is called critical activity.
The concept of critical activities is quite interesting. 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
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
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
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
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.
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.
CPM calculation for AON Network is same as for AOA network, but the calculation of events is omitted.
CPM Calculations for AON Network
Latest Finish
ES
LS
EF
LF
Earliest Finish
Latest Start
Earliest Start
Activity Nam
eActivity Duration
Problem 05Problem 05AON Network for General AON Network for General
HospitalHospital
Key
AON Network for General AON Network for General Hospital Hospital Includes Critical PathIncludes Critical Path
Slack=0
Start
A
B
C
D
F
F
G
HH
1313
2
1515
HG
88
5
1313
HE
410
3
713
HC
22
2
44
HF
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
Critical Path for General Hospital
Start
A
B
C
D
F
E
G
H
Arrows show
precedence
relationships
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.
Gantt Chart for General Hospital Early Start and Finish
General HospitalGeneral HospitalGeneral HospitalGeneral 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
Gantt Chart for General Hospital Late Start and Finish
General HospitalGeneral HospitalGeneral HospitalGeneral 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
Table for Network Scheduling
Problem 06
Problem 06Solution - AOA Method
Early Event Time (TE)
Finding TE Values
Late Event Time (TL)
Finding TL Values
Critical Path
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.
Scheduled Times must fall between ES and LF and allow at least time t to complete.
Problem 06Solution - AOA Method
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 AON Network
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
Discussion
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