cpm- pert.ppt

8/11/2019 cpm- pert.ppt

1/42

Network Analysis :

CPM & PERT


2/42

Introduction

Network analysis is one of the important tools for project management.

Whether major or minor a project has to be completed in a definite time

& at a definite cost.

The necessary information of any information can be represented as a

project network.


3/42

Methodology Involved in Network Analysis

Describing the Project

Diagramming the network

Estimating the time of completion

Deterministic

estimates

Probabilistic

estimates

Monitoring the project progress


4/42

Key terminology

Activity : All projects may be viewed as composed of activities. It is the

smallest unit of work consuming both time& resources that project

manager should schedule & control.

An activity is represented by an arrow in network diagram

The head of the arrow shows sequence ofactivities.


5/42

Classification of activities

Predecessor activity: Activities that must be completed immediately priorto the start of another activity are called predecessor activities.

Successor activity: activities that cannot be started until one or more ofother activities are completed but immediately succeed them are called

successor activities.

Concurrent activities: activities that can be accomplished together areknown as concurrent activities.

Dummy activity: An activity which does not consume any resource butmerely depicts the dependence of one activity on other is called dummyactivity.


6/42

Event

The beginning & end of an activities are called as events .

Events are represented by numbered circles called nodes.

i j

Event

start

Event

finish


7/42

Path & Network

An unbroken chain of activity arrows connecting the initial event to some

other event is called a path.

A network is the graphical representation of logically & sequentially

connected arrows & nodes representing activities & events of a project . Itis a diagram depicting precedence relationships between different

activities.


8/42

Application of network analysis

Construction industry

Manufacturing

Research development

Administration

Marketing planning

Inventory planning


9/42

Advantages

Planning & controlling projects

Flexibility

Designation of responsibilities

Achievement of objective with least cost

Better managerial control


10/42

Types of Events

Merge event

Burst event

Merge & Burst Event


11/42

Guidelines for Network Construction

A complete network diagram should have one stand point & one finish

point.

The flow of the diagram should be from left to right.

Arrows should not be crossed unless it is completely unavoidable.

Arrows should be kept straight & curved or bent. Angle between arrows should as large as possible.

Each activity must have a tail or head event.. No two or more activities

may have same tail & head events.

Once the diagram is complete the nodes should be numbered from left to

right. It should then be possible to address each activity uniquely by its tail& head event.


12/42

Example

Activity Predecessor

activity

A none

B none

C A

D A

E B

F C

G D & E

1

3

2

5

4

6

A

B

C

D

E

F

G


13/42

Draw the network diagram for the following

Activity Predecessor

activity

A none

B A

C A

D B

E C

F D ,E


14/42

1 2

3

4

5 6

A

B

C

D

E

F


15/42

Basic Terminologies

Earliest start time ( EI) : This is the earliest possible time that an activity

can begin. All predecessor activities must be finished before an activity

can began.

Earliest finish time ( EJ) : This is the earliest possible time in which an

activity can be finished.

= earliest start time ( EI) + Duration of the activity ( TIJ)

Latest start time ( LI) : This is the latest time that an activity can began &

not delay the completion time of overall project.

= latest finish time ( LJ) duration of the activity ( TIJ)

Latest finish time ( LJ) : This is the latest time that an activity can befinished & not delay the completion time of the overall project


16/42

Total project time : This is the shortest possible time in which

the project is completed.

Float : There are many activities where the maximum time

available to finish the activity is more than the time required

to complete the activity. The difference between the two

times is known as float available for the activity.

There are three types of float:

Total float : It is the spare time available when all preceding

activities occur at earliest possible times & all success dingactivities occur at latest possible times.

Total float = Latest start Earliest finish.


17/42

Forward pass Method

Based on the fixed occurrence time of the initial network event , the forwardpass method yields the earliest start time & earliest finish times for each activity& indirectly earliest expected occurrence of each event.

The computation begins from the start node & move to the end node. Toaccomplish this , the forward pass computations start with an assumed earliestoccurrence time of zero for the initial project event E1 = 0

Earliest start time for activity ( I,j) is the earliest event time of the tail end eventESIJ = EI

Earliest finish time of the activity is the earliest start time of the activity plus the

duration of the activity. EFij= ES ij+ tij Earliest occurrence time of the event j is the maximum of the earliest finish times

of all the activities into that event.


18/42

Backward Pass Method

The latest occurrence time specifies the time by which all the activities

entering into that event , must be completed without delaying the total

project.

These are computed by reversing the method of calculation used for

earliest event times.

Latest finish time of an activity is equal to the latest vent time j LFIJ= LJ.

Latest start time of an activity is given by latest completion time minus the

activity time .

LSIJ = LFIJ- tij

Latest event time for event is the minimum of the latest start time of allactivities originating from that event.


19/42

1

25

3 4

6

16

30

15

12

20 15

16

10 3

Network Diagram


20/42

Earliest Event Time

The total project time is the shortest time in which the project can be

completed & this is determined by sequence of activities on the critical

path. In order to calculate the total project time carry out the forward

pass.

Start from the left of the arrow of diagram

Give the first event the time 0

Proceed to each event in order & compute the earliest possible time at

which event can occur.


21/42

1/ 0

2/165/38

3/20 4/35

6/51

16

30

15

12

20 15

16

10 3

Calculation of earliest

event time

0+16

0+20+10 0+20+15+3

0+16+15

Taking the

maximum one

0+20+15

0+ 30

38+ 12

35+16

To the earliest time of each immediately preceding event add

the duration of activity which connects it & selects the highest

of the values obtained.

Forwardpass

0+ 20


22/42

Latest event time

Latest event time : carry out the backward pass

Start from right

Give to this event its earliest time i.e is 51 in this case

By subtracting the duration time for each corresponding job calculate the

latest possible occurrence time for any event , assuming that final event isfixed.


23/42

1/ 0/0

2/16/245/38/39

3/20/204/35/35

6/51/51

16

30

15

12

20 15

16

10 3

Calculation of latest

event time

24-16

39-10

39-15

Taking the

minimum one

35-15

51-30

51-12

51-16

From the latest time of each immediately succeeding event ,

subtract the duration of the job which connects it & selects

the lowest value obtained.

Backwardpass

39-3

20-20


24/42

Critical path

Those activities which contribute directly to the overall duration of the

project constitute critical activities, the critical activities form a chain

running through the network which is called critical path.

Critical event: the slack of an event is the difference between the latest &earliest events time. The events with zero slack time are called as critical

events.

Critical activities: The difference between latest start time & earliest start

time of an activity will indicate amount of time by which the activity canbe delayed without affecting the total project duration. The difference is

usually called total float. Activities with 0 total float are called as critical

activities


25/42

Critical path

The critical path is the longest path in the network from the starting event

to ending event & defines the minimum time required to complete the

project.

The critical path is denoted by darker or double lines.


26/42

1/ 0/0

2/16/245/38/39

3/20/204/35/35

6/51/51

16

30

15

12

20 15

16

10 3

Critical Path

The critical path lies along those jobs whose earliest & latest

times for the start & finish events are same & whose duration

times are equal to the difference between start & finish

events time.

Darker line is critical path


27/42

Earliest start time : (2, 5) earliest time of event 2 16 days

Earliest finish time : ( 2, 5) earliest start time + duration of activity

EI + TIJ = 16 + 15 = 31days

Latest finish time : ( 2, 5) latest event time of finish event

39 days

Latest start time : ( 2, 5) latest finish time duration of activity

LJ - TIJ

39 15 = 24 days

Calculation of time estimates


28/42

Job Duration Earliest starttime

Latest starttime

Earliestfinish

time

Latestfinish

time

(1,2) 16 0 8 16 24

(1,3) 20 0 0 20 20

(1,6) 30 0 21 30 51

(2,5) 15 16 24 31 39

(3,4) 15 20 20 35 35

(3,5) 10 20 29 30 39

(4,5) 3 35 36 38 39

(4,6) 16 35 35 51 51

(5,6) 12 38 39 50 51

Time estimations

Darker boxes indicate critical activities


29/42

Types of float

Total float : The amount of time by which completion of an activity couldbe delayed beyond the earliest expected completion time withoutaffecting the overall project duration time.

Latest finish time earliest start time duration of an activity

Free float : This is concerned commencement of subsequent activity . Itmay be defined as time by which the completion of an activity can bedelayed beyond the earliest finish time without effecting the earliest startof a subsequent activity.

Independent Float : it may be defined as the amount of time by which thestart of an activity can be delayed without affecting the earliest start timeof any successor activity , assuming that preceding activity has finished atits latest finish time.


30/42

Calculation of free & independent float

Head slack = LJ - EJ

Tail slack = LiEi

Total float = LiEi - tij

Free float = total float head slack

Independent float = total float tail slack


31/42

PERT

PERT is designed for scheduling complex projects that involve many inter-

related tasks. it improves planning process because:

1. It forms planner to define the projects various components activities.

2. It provides a basis for normal time estimates & yet allows for somemeasure of optimism or pessimism in estimating the completion dates.

3. It shows the effects of changes to overall plan s they contemplated.

4. It provides built in means for ongoing evaluation of the plan.


32/42

PERT system of 3 time estimates

Optimistic time ( a or t0) : is that time estimate of an activity when

everything is assumed to go as per plan. In other words it is the estimate

of minimum possible time which an activity takes in completion under

ideal conditions.

Most likely time (m or tm): the time which the activity will take most

frequently if repeated number of times.

Pessimistic time ( b or t): the unlikely but possible performance time if

whatever could go wrong , goes wrong in series. In other words it is thelongest time the can take.


33/42

Expected time (te)

The a , m & b are combined statically to develop the expected time te.

te = a + 4m +b

6

Standard deviation of the time of the time required to complete the

project

b- a

6


34/42

Steps in PERT

Develop list of activities.

A rough network for PERT is drawn.

Events are numbered from left to right.

Time estimates for each activity are obtained.

Expected time for each activity is calculated : a + 4m +b / 6

Using these expected times calculate earliest & latest finish & start times of activities.

Estimate the critical path.

Calculate variance of each activity by : ( b a)2/ 6

Using this estimate compute the probability of meeting a specified completion date by usingthe standard normal equation

Z = Due date expected date of completion

project variance

Where Z = number of standard deviations the due date lies from the mean or expected date.


35/42

Activity Most optimistic

time ( a)

Most likely time

(m)

Most pessimistic

time (b)

1- 2 4 8 12

2 -3 1 4 7

2- 4 8 12 16

3 - 5 3 5 7

4 - 5 0 0 0

4 - 6 3 6 9

5 - 7 3 6 9

5 - 8 4 6 8

7 - 9 4 8 12

8 - 9 2 5 8

9 10 4 10 16

6 - 10 4 6 8


36/42

Using the information given below determine the following

1. Expected task time & their variance

2. The earliest & the latest expected times to reach each event

3. The critical path

4. The probability of an event occurring at proposed completion date if

the original contract time of completing project is 48 days.


37/42

Activity ( a) (m) (b) Expected time

te= a +4m +b /6

2= 1 ( b a)2

6

1- 2 4 8 12 8 1.78

2 -3 1 4 7 4 1

2- 4 8 12 16 12 1.78

3 - 5 3 5 7 5 0.44

4 - 5 0 0 0 0 0

4 - 6 3 6 9 6 1

5 - 7 3 6 9 6 1

5 - 8 4 6 8 6 0.44

7 - 9 4 8 12 8 1.78

8 - 9 2 5 8 5 1

9 10 4 10 16 10 4

6 - 10 4 6 8 6 0.44


38/42

1/0/0 2/8/8

4/20/20

6/26/38

3/12/15

5/20/20

7/26/26

8/26/29

9/34/34

10/44/44

Network Diagram & critical path

8

12

4

5

0

6

6

8

5

6

6

10


39/42

Te = 8 + 12 +0 +6 +8 +10 = 44 days

2 = 1.78 + 1.78 + 0 + 1 + 1.78 + 4 = 10.34e

= 3.216

Probability that project will be completed in 48 days

Z = T - Te

e

= 48 - 44

3.216

= 1.24 ( from normal distribution table ) 0.895

Therefore 89% is the probability that project will be

completed on its due date.


40/42

Difference between PERT & CPM

PERT

A probability model with

uncertainty in activity

duration . The duration of

each activity is computed

from multiple time estimates

with a view to take into

account time uncertainty.

It is applied widely for

planning & schedulingresearch projects.

PERT analysis does not

usually consider costs.

CPM

A deterministic model with well

known activity times based upon the

past experience.

It is used for construction projects &

business problems.

CPM deals with cost of project

schedules & minimization.


41/42

Limitations of PERT /CPM

Network diagrams should have clear starting & ending points , which are

independent of each other which may not be possible in real life.

Another limitation is that it assumes that manager should focus on critical

activities.

Resources will be available when needed for completion for an an activity

is again unreal.


42/42

Difficulties

Difficulty in securing realistic time estimates.

The planning & implementation of networks requires trained staff.

Developing clear logical network is troublesome.

cpm- pert.ppt

Documents

Transcript of cpm- pert.ppt