AARUSH JOSEPH SONY

NETWORK SCHEDULING BY PERT/CPM

1. P.E.R.T : Programme Evaluation Review Technique

2. C.P.M : Critical Path Method

3. R.A.M.S : Resource Allocation And Multiproject Scheduling

4. P.E.P : Programme Evaluation Procedure

5. C.O.P.A.C : Critical Operating Production Allocation Control

6. M.A.P : Manpower Allocation Procedure

7. R.P.S.M : Resource Planning And Scheduling Method

8. L.C.S : Least Cost Scheduling Method

9. M.O.S.S : Multi Operation Scheduling System

10.P.C.S : Project Control System

11.G.E.R.T : Graphical Evaluation Review Technique

NETWORK TECHNIQUES

EVENT ACTIVITY CRITICAL PATH DURATION TOTAL PROJECT TIME EARLIST STARTING TIME EARLIEST FINISH TIME LATEST FINISH TIME LATEST START TIME FLOAT/SLACK NETWORK DIAGRAM/ARROW DIAGRAM

RELATED TERMS

P.E.R.T1. Probabilistic model

2. Event oriented approach

3. Network diagram, Slack, Events

4. Dummy activity required

5. Does not demarcate between critical and non critical activities

6. Finds application in projects where resources(men, material, money) are always made available as and when required

1. Deterministic model

2. Activity oriented approach

3. Arrow diagram, Nodes, Float

4. Dummy activity activity not necessary

5. Marks critical activity

6. Employed to those projects where minimum overall cost is of primary importance

DIFFERENCE BETWEEN P.E.R.T AND C.P.M

C.P.M

An event is a specific instant of time which marks the start and end of the activity. Even consumes neither time nor resources. It is represented by a circle and event number is written within the circle.

Eg. Start the motor loan approved

EVENT

Every project consists of a number of job operations or task which are called activities.

An activity is shown by an arrow and it begins and ends with an event

CLASSIFICATIONS Critical activity

Those activities which take more time Non critical activities

they have provisions (slack/ float) so if they consumes a specified time over and estimated time, the project will not be delayed.

Dummy activity

activities started at same time, they does not consumes time, joined by dotted line, may be critical or non critical

ACTIVITY

Sequence of activities which decides total project duration. It is formed by critical activities. It consumes maximum resources. It is the longest path and consumes maximum time. It has zero float. The expected completion dates cannot be met, if even one

critical activity is delayed.

CRITICAL PATH

DURATION It is the actual or estimated time required to complete the

project

TOTAL PROJECT TIME It is the time which will be taken to complete a project and

is found from the sequence of critical activities. or it is the duration of critical path.

EARLIST STARTING TIME Earliest possible time at which the activity can be started

EARLIEST FINISH TIME Earliest possible time at which the activity can be finished

EFT=EST+DURATION

LATEST FINISH TIME Calculated by moving backward from last event to first

event

LATEST START TIME Latest possible time at which the activity can be started

LST=LFT-DURATION

Float / slack Slack is with reference to an event and float is with respect to an activity.

It means spare time or extra time over and above its duration which a non critical activity can consume without delaying the project. Float is the difference between the time available for completing an activity and the time necessary to complete the same.

Total float It is the additional time which a non critical activity can consume which

increase the project duration. However, total float may affect the float in previous and subsequent activities.

Total float = (LST-EST) OR (LFT-EFT)

FREE FLOAT If all the non critical activities start as early as possible the surplus time

is the free float.

Free float = EST(tail) – EST(head) – DURATION

INDEPENDENT FLOAT It does not change the float of an activity. It can be used to

advantage if one is interested to reduce the effort on a non critical activity in order to apply the same on critical activity thereby reducing the project duration

Independent float = EST (tail) – LFT (head) – DURATION

OPTIMISTIC TIME (to )

Shortest possible time in which an activity can be completed if everything goes exceptionally well.

MOST LIKELY TIME (tm)

Time in which activity is normally expected to complete under normal contingencies

PESSIMISTIC TIME (tp)

It is the time which an activity will take to complete in case of difficulty i.e. is if mostly the things go wrong. it is the longest of all the three time estimates

Estimation of variability of activity times the purpose is to find how reliable te is

if te = tm

St = Tp-To

6 Vt = [Tp-To]2 = St

2

62

Z=D-Ts

St

where,

Ts is the total project duration

St is the standard deviation

D is the due date or scheduled days (time)

Z is the number of standard deviations by which D exceeds Te

Each activity is represented by only one and only arrow Each activity must be identified by its starting and end node

which implies that

(a) Two activities should not be identified by the same completion events, and

(b) Activities must be represented either by their symbols or by corresponding ordered pair of starting completion events

Nodes are numbered to identify an activity uniquely. Tail node (starting point) should be lower than the head node (end point) of an activity

Between any pair so node there should be one and only one activity; however more than one activity may be emanate from and terminate to a node.

Arrow should be kept straight and not curved or bend. The logical sequence must follow

an event cannot occur until previous is completed

dummy activity should only be introduced if only it is necessary

Rules for network construction

ACTIVITY TO TM TP

1-2 2 5 14

1-6 2 5 8

2-3 5 11 29

2-4 1 4 7

3-5 5 11 17

4-5 2 5 14

6-7 3 9 27

5-8 2 2 8

7-8 7 13 31

Q1: The following are the details of estimated time of activities of a certain project. Explain in detail pert technique

1. Find the critical path and the expected time of the project

2. Find the estimated time, standard deviation and variance

3. Find the total stack

ACTIVITY

TO (A)

TM

(B)TP

(C)TE= (A+4B+C)/6

EST

EFT=EST+D

LST=LFT-D

LFT TOTAL SLACK

ST

= (CA)/6

VT=ST

2

1-2 2 5 14 6 0 6 0 6 0 2 4

1-6 2 5 8 5 0 5 2 7 2 1 1

2-3 5 11 29 13 6 19 6 19 0 4 16

2-4 1 4 7 4 6 10 20 24 14 1 1

3-5 5 11 17 11 19 30 19 30 0 2 4

4-5 2 5 14 6 10 16 24 30 14 2 4

6-7 3 9 27 11 5 16 7 18 2 4 16

5-8 2 2 8 3 30 33 30 33 0 1 1

7-8 7 13 31 15 16 21 18 33 2 4 16

Q2: The following are the details of estimated times of activities of a certain project.

ACTIVITY IMMEDEATE PREDECESSORS

NORMAL TIME (DAYS)

A 16

B 20

C A 8

D A 10

E B,C 6

F D,E 12

1. Find the critical path and the expected time of the project

2. Find the total and free-float of the project

ACTIVITY

ACTIVITY

DAYS (D)

EST EFT=EST+D

LST=LFT-D

LFT TOTAL FLOAT

FREE FLOAT

A 1-2 16 0 16 0 16 0 0

B 1-3 20 0 20 4 24 4 4

C 2-3 8 16 24 16 24 0 0

D 2-4 10 16 26 20 30 4 4

E 3-5 6 24 30 24 30 0 0

F 5-6 12 30 42 30 42 0 0

Q3: Tasks A, B, C,..., H, I constitute a project . The notation X<Y means that the task X must be finished before Y can begin. With this notation

A<D, A<E, B<F, D<F, C<G, C<H, F<I, G<I

Draw a graph to represent the sequence of tasks and find the minimum time of completion of each task is as follows.TAS

KA B C D E F G H I

TIME 8 10 8 10 16 17 18 14 9

Q4: Given the following information

(i) Draw the arrow diagram(ii) Identify critical path and find the total

project duration(iii)Determine total, free and independent

floats

Activ

0-1 1-2 1-3 2-4 2-5 3-4 3-6 4-7 5-7 6-7

Time 2 8 10 6 3 3 7 5 2 8

Q5: Consider the data of the project , find its critical path and project duration:

AITY

A B C D E F G H I

PRE A B C,D B E E F,G

TIME

4 7 2 9 6 5 2 10 4

OPERATION RESEARCH by

KANTI SWARUP P.K. GUPTA MAN MOHANINDUSTRIAL ENGINEERING AND

MANAGEMENT by Dr. O.P. KHANNA

REFERENCES