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Critical Path Analysis
CA Final Advance Management Accounting, Paper 5, Chapter 13 Dr. Kavita Sharma
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Discussion plan
Introduction to critical path analysis
Basics about techniques of PERT/CPM
Steps of critical path analysis
Errors in logical sequencing
Construction of Network
Network Analysis • Identification of Critical Path • Calculation of Floats
Resource Analysis • Crashing
PERT
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Introduction
Critical Path Analysis is the Quantitative technique used for decision making in regard to large projects in the field of construction, maintenance, fabrication, research and development and so on.
Projects in these field are not only large, but complex too.
Large amount of money, manpower and other resources are involved.
Different departments or units are in charge of these resources.
Difficult for mangers responsible for planning, scheduling and controlling such large projects to remember all the necessary information and ensure the desired progress of work.
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What is Project ?
A project is defined as a combination of inter-related activities, all of which must be executed in a certain order for its completion
There is a need for: Planning – Identification and listing of various activities Scheduling – identifying the relationship Controlling – progress review and management decisions
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Techniques of PERT/CPM
The techniques of PERT/CPM are useful and valuable techniques which a manger may use in having assistance in planning and controlling of such large projects.
PERT- is an acronym for Programme Evaluation and Review Technique, and
CPM- is an acronym for Critical Path Method
Using these techniques the managers develop the overall layout of the project with the estimates of time and resources required; and schedule timing and sequence of various activities though independent, but may bear the relationship also.
In fact it is the inherent relationship between various activities which creates complexities and necessitates the use of PERT/CPM techniques
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Specific Insights through PERT/CPM
Total time to complete the project
The scheduled start and finish dates for each specific activity
Activities which are critical to complete the project on scheduled time
The flexibility in the non-critical activities to restrict the delay in project completion
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Nature of PERT/CPM Techniques
Both the techniques have been developed independently,
They use same terminologies and have same general purpose
PERT is the probabilistic technique as it takes care of uncertainty in the completion of the project. It is based on time projections
CPM works with ‘known’ times for completion of the activities. It is therefore deterministic in nature.
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Distinguishing features of Project requiring application of PERT/CPM
The project consists of well defined collection of
activities Activities are independent of each other Though independent various activities need to be
ordered. Order or sequence is logically or technically
defined
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Steps of Critical Path Analysis 1. Project scheduling 2. Construction of the network 3. Identify the longest path through the network 4. Resource analysis
Monitor, evaluate, and control the progress of project by re-planning, re-scheduling or re-allocation of resources
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Steps in Critical Path Analysis
Example based explanations
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Step -1: Project Scheduling
Let us take the hypothetical case of an institute planning to organize a conference on IFRS.
Activity Description
A Design Conference Meeting and theme
B Design front cover of conference proceedings
C Prepare Brochure and send request
D Compile list of distinguished guests
E Finalize Brochure and Print it
F Make travel arrangements
G Dispatch Brochure H Receive Papers I Edit Papers J Print Proceedings
(a) Determination of activities
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Step -1: Project Scheduling
Activity Description Immediate Predecessor
Successding Activity
A Design Conference Meeting and theme - B,C,D
B Design front cover of conference proceedings
A J
C Prepare Brochure and send request A E
D Compile list of distinguished guests A E
E Finalize Brochure and Print it C,D G
F Make travel arrangements D I
G Dispatch Brochure E H H Receive Papers G I I Edit Papers F,H J J Print Proceedings B,I -
(b) Establishing
inter-relationship
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Step -1: Project Scheduling
Activity Description Immediate Predecessor
DURATION (days)
A Design Conference Meeting and theme
- 2
B Design front cover of conference proceedings
A 7
C Prepare Brochure and send request A 8
D Compile list of distinguished guests A 3
E Finalize Brochure and Print it C,D 6
F Make travel arrangements D 10
G Dispatch Brochure E 4 H Receive Papers G 6 I Edit Papers F,H 2 J Print Proceedings B,I 5
(c) Assessment of time and/or cost of each
activity
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Step-2 Network Construction
Network is the graphical representation of projects’ operations and it consists of activities and nodes
Activity : Task or item of work to be done that consumes time, effort, or money or other resources Predecessor Activity Succession Activity Concurrent Activity
Represented as an arrow with unit of time written on it
Activity
Description Immediate Predecessor
Successding Activity
A Design Conference Meeting and theme
- B,C,D
B Design front cover of conference proceedings
A J
C Prepare Brochure and send request
A E
D Compile list of distinguished guests
A E
E Finalize Brochure and Print it C,D G
F Make travel arrangements D I
G Dispatch Brochure E H
H Receive Papers G I
I Edit Papers F,H J
J Print Proceedings B,I -
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Contd….
Node - Each activity has nodes – representing the event
- Shown by circle
- Head Node
- Tail Node
- Numbers within the circle denotes accomplishment of activity up to that point
1 2
3
5
4 A
B
C
D
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Rules of Network Construction 1. Each activity is represented by only one arrow in
the network 2. All preceding activities to be completed before
undertaking the next activity 3. Length of the arrow has no significance 4. Direction of the arrow indicated general progression
in time. 5. More than one activity can terminate at one event
which will be regarded as ‘merge event’. 6. An event may portray the initiation of more than
one activity and is called ‘burst event’.
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Merge Event and Burst Event
1 2
3
5
4 A
B
C
D
7
4
6
5
D
E
F
G 8
Event ‘2’ is Burst Event
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Rules of Network Construction - contd.
7. There is always one initial event and one terminal event or node
8. There cannot be the loop formation in the construction of network
9. In the case of loop formation use Dummy Activities with ‘zero’ time consumption
Dummy Activities are represented by dashed
arrow
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Identity Dummy
If two or more activities are performed simultaneously, i.e., two or more activities have same nodes (initial and terminal), then dummy activity is introduced with zero time consumption
1 2
A
B
1
2
3
A
B
Dummy
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Logic Dummy
Allows for establishing logical relationship in the network. When two or more activities have common predeceasing activities , the logical dummies are used to adequately represent the precedence relationship
D
A
B
Dummy
C
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Errors in logical Sequence
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Looping
A
B C
Looping or cycling occurs when the arrows are drawn from right to left, resulting into error in relationship.
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Dangling
Dangling occurs when an activity is not connected to any succeeding activity. Excepting the starting and the terminal activities, all other activities necessarily have preceding and succeeding activities
Dummy E
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Redundancy
Redundancy in relationship occur when unnecessary predecessors are used in establishing the relationship between various activities
Relationships are given as 1-2, 1-4, 2-3 and 3-4
A<B, B<C and A<C implies that A<B<C, so A<C is redundant relationship shown
A B
1
2
3
4
C
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Srep-3 : Construction of Network
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Activity A B C D E F G H I J
Predecessor
- A A A C,D D E G H,F B,I
Time (days) 2 7 8 3 6 10 4 6 7 5
Example -1
2
3
6
5
8 9 4 7 A-2
B-7
D-3
C-8 E-6 G-4 H-6 I-7 J-5
F-10
1 10
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Example-2
Activity A B C D E F G H I J
Time 3 8 4 2 1 7 5 6 8 9
Predecessor - - A,B B A C E,F D,F G,H I
F-7 I-8
1
2 7
6
8
5 10
3
9 A-3
B-8
C-4
D-2
E-1 G-5
H-6
J-9
4
11
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Numbering the Event
Rules • Events numbers must be unique. • Event numbering should be carried out in
sequential basis from left to right. • The initial event with all outgoing arrows with no
incoming arrow is numbered 0 or 1. • The head of an arrow should always bear a
number higher than the one assigned at the tail of the arrow.
• Gaps should be left in the sequence of event numbering to accommodate subsequent inclusion of activities, if necessary.
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Step-4:Network Analysis
Identification of Critical Path
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Path Identification
Path is the sequence of connected events or nodes that leads from the start node to the finish node
Various paths in the context of second example are:
• A- E-G-I-J • A-C-F-G-I-J • A-C-F-H-I-J • B-D-H-I-J • B-C-F-G-I-J • B-C-F-H-I-J
F-7 I-8
1
2 7
6
8
5 10
3
9 A-3
B-8
C-4
D-2
E-1 G-5
H-6
J-9
4
11
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Assumption in Critical Path Identification
Analyze the network to identify critical path, with the underlying assumption that all resources needed for performing various activities are available in required amounts at the needed times
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Forward and Backward Pass Calculations
For each activity: • Earliest start and earliest finish time computed
through forward pass calculations • Latest start and latest finish time computed
through backward pass calculations
Notations used are • ES = Earliest start time for an activity • EF = Earliest finish time for an activity • LS = Latest start time for an activity • LF = Latest finish time for an activity • t = time taken by an activity
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Forward Pass Calculations EF = ES + t Earliest start time for start activity is always set equal
to ‘0’ An activity cannot start until all immediately
preceding activities have been finished The earliest start time for an activity is equal to the
largest of the earliest finish times for all the immediate predecessors
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Backward Pass Calculations Latest allowable time for project terminal event is the
time when the project is desired to be completed For each activity LS and LF calculations are done by
rolling backwards LS= LF-t Latest finish time is assigned to the terminal event,
which may or may not be the earliest finish time of the terminal event
LF time to the activity is assigned as smallest of the latest start time of it successor activities
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Determination of ES,EF, LS,LF With one time estimates ES, EF, LS, and LF
calculations for each activity in the case of first example are
Activity A B C D E F G H I J
ES 0 2 2 2 10 5 16 20 26 33
EF 2 9 10 5 16 15 20 26 33 38
LS 0 26 2 7 10 16 16 20 26 33
LF 2 33 10 10 16 26 20 26 33 38
2
3
6
5
8 9 4 7 A-2
B-7
D-3
C-8 E-6 G-4 H-6 I-7 J-5
F-10
1 10
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Determination of Critical Path Slack time (length of the time an event can be
delayed) = LS – ES = LF - EF Activity A B C D E F G H I J
ES 0 2 2 2 10 5 16 20 26 33
EF 2 9 10 5 16 15 20 26 33 38
LS 0 26 2 7 10 16 16 20 26 33
LF 2 33 10 10 16 26 20 26 33 38
2
3
6
5
8 9 4 7 A-2
B-7
D-3
C-8 E-6 G-4 H-6 I-7 J-5
F-10
1 10
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Case Example - 2
Activity A B C D E F G H I J
ES 0 0 8 8 3 12 19 19 25 33
EF 3 8 12 10 4 19 24 25 33 42
LS 5 0 8 17 19 12 20 19 25 33
LF 8 8 12 19 20 19 25 25 33 42
Slack
3 0 0 9 16 0 1 0 0 0
Time in weeks
F-7 I-8
1
2 7
6
8
5 10
3
9 A-3
B-8
C-4
D-2
E-1 G-5
H-6
J-9
4
11
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Step 3: Network Analysis
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Network Analysis
If at the end of 10 weeks, the status of activities is given as: A, B, and E completed; C,D,F,G,H,I,J not yet started.
Activities on the critical path as
per revised schedule to be crashed by 2
weeks
REVISED ACTIVITY TIME DURATIONS
Activities ES EF LS LF
C (4-5) 10 14 10 14
D (3-8) 10 12 19 21
F (5-6) 14 21 14 21
G (7-9) 21 26 22 27
H (8-9) 21 27 21 27
I (9-10) 27 35 27 35
J (10-11) 35 44 35 44
F-7 I-8
1
2 7
6
8
5 10
3
9 A-3
B-8
C-4
D-2
E-1 G-5
H-6
J-9
4
11
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Types of Floats
Float : Indicate the flexibility in the scheduling of various activities – critical as well as non-critical. It is the difference between the latest and earliest activity time
• Total Float • Interfering Float • Free Float • Independent Float
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Total Float –(TF)
Amount of time by an activity can be delayed without delaying the project completion date
• For (i,j)th activity total float (TF)ij is the difference between the latest start time and the earliest start time of the activity • (TF)ij = (LS)ij – (ES)ij , OR • (TF)ij = (LF)ij – (EF)ij, OR • (TF)ij = (LF)ij - (ES)ij - tij
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Interfering Float –(IF)
The part of total float that causes reduction in the float of the successor activity
It is the difference between the latest time of the current activity in question and the earliest starting time of the following activity, or zero, whichever is larger
• For (ij)th activity • (IF)ij = Max {0,(LF)ij – (ES)jk}
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Free Float (FF)
The part of total float which can be used without affecting the float of the succeeding
It is difference between the earliest starting time of the succeeding activity and earliest finish time of the current activity
• For (ij)th activity, free float • (FF)ij = (ES)jk – (EF)ij • OR
• (FF)ij = (TF)ij – Head slack
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Independent Float (INF)
The float which is available for use without affecting either the head or the tail events
It is the amount of float time available for an activity when its preceding activities are completed at their latest and its succeeding activities begin at their earliest time – leaving the minimum time available for its performance
• For (ij)th activity • (INF)ij = Max {0,(ES)jk – (LF)hi – tij} • OR
• (INF)ij = (FF)ij – Tail slack
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Calculation of floats
Activity (I-J)
Duration Earliest time Latest time Float
tij ES EF LS LF TF IF FF INF
A (1-2) 3 0 3 5 8 5 5 0 0
B (1-3) 8 0 8 0 8 0 0 0 0
C (4-5) 4 8 12 8 12 0 0 0 0
D (3-8) 2 8 10 17 19 9 0 9 9
E (2-7) 1 3 4 19 20 16 1 15 10
F (5-6) 7 12 19 12 19 0 0 0 0
G (7-9) 5 19 24 20 25 1 0 1 1*
H (8-9) 6 19 25 19 25 0 0 0 0
I (9=10) 8 25 33 25 33 0 0 0 0
J (10-11) 9 33 42 33 42 0 0 0 0
F-7 I-8
1
2 7
6
8
5 10
3
9 A-3
B-8
C-4
D-2
E-1 G-5
H-6
J-9
4 11
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Essential Remarks Slack is used for events and floats is applied to an
activity Latest occurrence time of an event is always greater
than or equal to its earliest occurrence time, i.e., latest time of present event ≥ earliest time of that event.
IND Float ≤ Free Float ≤ Total Float, and Total Float = Free Float + Interfering Float
An activity is critical if its total float is zero, otherwise it is non-critical
Once float of an activity is disturbed, float of all other activities of the project is changed and should be re-calculated
The calculation of floats can help the decision maker in identifying the underutilized resources the
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Chapter Summary PERT/CPM are the techniques of critical path
analysis used in planning and controlling large projects
CPM is deterministic; PERT is probabilistic Based on precedence relationship between activities
network/arrow diagram is drawn Arrow represent activity and circle/node represent
event Activities are scheduled for their earliest and latest
time and critical path is identified to plan the project completion.
Critical activities have no floats. For non-critical activities there are four types of floats: total, free,
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Thank you
Best of Luck