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Critical path lecture by EDP.pptxbdhshsjjdj
1. Critical & Near Critical Path,
Contingency Planning
and
Construction Group Interface
with Project Stake Holders
(Subject Code: CP)
2. Line of Discussion
•Critical Path and Project Monitoring.
•Near Critical Paths and their Importance.
•Contingencies.
•Construction Group Interface with Project Stake Holders.
Sample Project / Finding the CP (Excel Sheet)
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4. Critical Path
Once Activity Network Diagram for a project is prepared. We move on to determine
Critical Path. Following are the steps to find critical path for the Project. Following is
the sequence:
• Find the Early Start (ES) and Early Finish (EF) date by a Forward Pass. EF of an activity
can also be referred as Early Occurrence Time (EOT) of the trailing Node of the activity
arrow.
• Find the Late Start (LS) and Late Finish (LF) date by a backward pass. LF of an activity
can also be referred as Late Occurrence Time (LOT) of the trailing Node of the activity
arrow.
• Find ‘Total Float’ or ‘Slack’ for various activities using:
Total Float= LF – EF
• Activities with zero ‘Total Float’ are the ‘critical activities’ and the path from start to
the end of the project through such critical activities is the ‘critical path’.
5. Floats: Total, Free and Independent
• Float: This is the margin of time available for taking up an activity.
• Total Float (TF): TF is the time by which an activity can be delayed without
any effect on completion of the project. Quantum of this can be calculated
as:
(LF-EF) OR (LS-ES) OR (LOT of trailing Node - EOT of leading Node Duration)
• Free Float (FF): FF is the time by which an activity can be delayed without
delaying early start of its succeeding activity. Quantum of this can be
calculated as:
EOT of trailing Node - EOT of leading Node - Duration
• Independent Float (IF): IF is the time available when activity is started at its
Late start date and finishes before ES date of the successor:
EOT of Trailing Node - LOT of leading Node - Duration
6. Project Monitoring
There are two approaches of Project Monitoring:
• PERT
Program Evaluation and Review Technique is a probabilistic approach to
evaluate a project with uncertain domains.
• CPM
Critical Path Method is a method for adopted for projects with known
domains, generally with prior experience and basically a trade off between
cost and time.
7. PERT
1. As taught in time estimation for activities, we use to, tm,tp for working out
the activity time for the time estimation using the formula
te= (to + 4 tm+ tp)/6
2. Mean Project Duration ‘T’ is calculated by adding te for all activities on the
critical path.
3. Standard deviation of an individual activity is calculated by a simplified
formula: σ= (tp-to)/6 .
4. Variance is square of the Standard Deviation i.e. σ2
5. Standard deviation of the critical path duration is = (sum of variances of all
activities on the critical path)1/2.
Cont…..
8. PERT
6. Having ‘Mean Project Duration’ and ‘Standard Deviation’ of the Critical
Path, probability of completion of the project can be estimated by
assuming it a normal distribution.
7. As per ‘center limit theorem’ of statistics, in a normal distribution
‘cumulative probability’ distributes as follows:
Range Cumulative probability
Mean+/-One Standard Deviation 0.682
Mean+/- Two Standard Deviation 0.954
Mean+/- Three Standard Deviation 0.998
9. Normal distribution bell curve gives probability
distribution over a time range. It is seen that
irrespective of the sharpness of the curve,
cumulative probability is as given in the table:
Range Cumul.
Prob.
Mean+/- One Standard Deviation 0.682
Mean+/- Two Standard Deviation 0.954
Mean+/-Three Standard Deviation 0.998
a sample calculation
10. Critical Path Method (CPM)
• For project where we have sufficient experience on activity duration we
deploy this method.
• Assumptions underlying the CPM analysis are:
1. Cost associated with a project can be divided in two components. Direct
cost and Indirect Cost.
2. Activities of a project can be expedited by crashing, which involves
employing more resources.
3. Crashing reduces time but enhances direct costs.
4. Indirect cost of a project increases linearly with project duration.
13. Forward Pass
Forward pass is carried out to find out Early Start (ES) and Early Finish (EF) date. Method
works as follows:
1. For the First Project Activity (activity with no predecessor activity), ES is zero and EF
is always ES+Duration.
2. For all successive activity(ies), ES will be the EF of predecessor, and EF= EF+Duration.
3. A ‘Merge Event’ i.e. a node where more then one arrow is entering, will have more
than one EF (as they have more than one predecessor). Chose the LARGEST of all.
4. Starting from the first activity, calculate ES and EF till last.
5. EF of the Last activity of the project i.e. activity with no successor is the end date of
the project.
6. EF of an activity can also be referred as Early Occurrence Time (EOT) of the trailing
Node of the activity arrow.
14. Backward Pass
Once EF of the last activity is known. Late Start (LS) and Late Finish (LF) dates
are to be calculated. This is done by a ‘Backward Pass’. One shall proceed as
follows:
1. Start from the last activity, here LF = EF. (Project End date calculated in
‘forward pass’).
2. LS of all activities calculated as LS = LF - Duration.
3. LF of all other activities will be LS of the succeeding activity.
4. In case of a ‘Burst Event’ i. e. a node where more than one activity is leaving
the node, there will be more than one LS values, chose lowest among
these.
5. Process sequentially reaches to the first activity of the project.
