Critical Path Analysis

CA Final Advance Management Accounting, Paper 5, Chapter 13 Dr. Kavita Sharma

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

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.

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

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

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

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.

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

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

Steps in Critical Path Analysis

Example based explanations

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

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

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

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 -

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

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’.

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

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

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

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

Errors in logical Sequence

Looping

A

B C

Looping or cycling occurs when the arrows are drawn from right to left, resulting into error in relationship.

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

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

Srep-3 : Construction of Network

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

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

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.

Step-4:Network Analysis

Identification of Critical Path

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

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

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

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

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

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

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

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

Step 3: Network Analysis

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

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

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

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}

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

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

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

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

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,

Thank you

Best of Luck