critical path method (cpm) · 07-04-2011 · learning outcome. at the end of this lesson, students...
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LOGO
CRITICAL PATH
TIME CALCULATION
©Sheila Belayutham
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LEARNING OUTCOME
At the end of this lesson, students willbe able to:Understand the concept of Critical
Path Method.Determine the forward and backward
pass in a CPM diagram.Calculate Total and Free Floats.Determine the critical path for a CPM.
©Sheila Belayutham
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INTRODUCTION
CPM is based on Activity on Arrow (AOA).
In network schedule, we can determine the time of Early Start, Late Start, Early Finish, Late Finish and Float time by performing forward and backward path computation.
By performing the forward and backward pass through every path of the schedule, critical path can be establish.
©Sheila Belayutham
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Calculating Start & Finish Time
Network models permit the planner to calculate the total time that a project is projected to take and the times that each activity can and must start in order for the project to be completed in the estimated amount of time.
©Sheila Belayutham
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Important Terms :
Early Activity Start (ES) The earliest time that an activity can start
as determined by the latest of the early finish times of all immediately preceding activities.
Early Activity Finish (EF) The earliest time that an activity can
finish. It is determined by adding the duration of the activity to the early start of that activity.
©Sheila Belayutham
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Important Terms :
Late activity finish (LF) The latest time that an activity can be finished
without delaying the entire project completion. It is equal to the earliest of the late starts of the immediately succeeding activities.
Late Activity Start (LS) The latest time that an activity can start
without delaying the project completion. It is determined by subtracting the duration from the late finish of the activity.
©Sheila Belayutham
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Important Terms :
Float/ Slack It is additional time available to
complete an activity beyond the activity’s work duration.
Activities on critical path have no float. Types of float:
• Total Float• Free Float
©Sheila Belayutham
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Important Terms :
Total Float Total time available to delay the start of an activity
without changing the project duration. (LF-EF) or (LS-ES) of proceeding activity
Free Float The time available to delay the start of the activity
without interfering the early start time of the activities that follows.
Free float (n)=minimum early start of all successor activities - early finish (n)
ES proceeding activity – EF current activity
©Sheila Belayutham
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Important Terms :
Critical Path Represents the path which consist of all
activities that have no float time.
If any critical activities is delayed in their start or finish time, it will affect the overall completion time of the schedule.
Can also be defined as activities that have the same early start and late start time and so did with the early finish and late finish time.
©Sheila Belayutham
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Forward Pass
Is used to find the least time required to complete the project and the earliest time an activity can be started according to the schedule that being developed.
Made through the network, adding duration times to early start times of activities.
©Sheila Belayutham
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Forward Pass
The earliest time each activity in the network can start and finish.
Early finish (n) = Early start (n) + Duration (n)n=activity
©Sheila Belayutham
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Forward Pass
If 2 or more activities terminate at a junction or node, pick the larger sum value as the early start time for the activities following.
Early start and early finish time of project is determined by performing the forward pass computation.
©Sheila Belayutham
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Forward Pass
Node Duration(Days)
ES Forward Pass Computation
EF
1-2 5 0 0+5=5 5
2-3 3 5 5+3=8 8
3-4 1 8 8+1=9 9
4-5 4 9 9+4=13 13
©Sheila Belayutham
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Forward Pass
1 2 3 4 5
©Sheila Belayutham
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Backward Pass Computation
Calculated to find the value of latest time an activity may start (LS) or late finish (LF) time without affecting overall project schedule.
Subtract duration times.
©Sheila Belayutham
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Backward Pass
Node Duration(Days)
LF Backward Pass Computation
LS
5-4 4 13 13-4=9 9
4-3 1 9 9-1=8 8
3-2 3 8 8-3=5 5
2-1 5 5 5-5=0 0
©Sheila Belayutham
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Backward Pass
1 2 3 4
0 5 8 9
5
13
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1
2
3 5 8
6
7
94
6
3
4
7
2
7 1
6
1
5
2
Calculate the ES, EF, LS & LF.
A
B C
D E
F
G
H I
J K
©Sheila Belayutham
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Calculate the TF and FF
TF = (LS-ES) or (LF-EF)
FF = (ES of next activity – EF of current activity)
©Sheila Belayutham
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EXERCISE 1
Draw an arrow diagram that depicts the proper logic for the activities in Table 1.
Calculate ES, EF, LS, LF, TF and FF for each activity in the diagram drawn.
How long will it take for the project to complete?
©Sheila Belayutham
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TABLE 1
Activity Predecessor DurationA - 1B - 2C - 2D A 2E A,B 1F C 1G E,C 4H F 3K H 2I H 2J D 2M K,G,D 3L M,I,J 3
©Sheila Belayutham