PERT & CPM presentation based on mining engineering

PERT & CPM
• A project such as construction of bridge, power
plant, mine, design, development and marketing
of a new product, R&D work may be defined as
collection of interrelated activities which must be
completed in a specified time according to a
specified sequence and require resources such as
men, money, machines, materials, method, etc.…
• The process of dividing the into specific activities
is called as the work break-down structure.

The main objective before starting any project: How to schedule the required
activities so as to
✔ Complete the given project on or before a specified time limit.
✔ Minimize the cost of completion of the project on or before a specified time limit
✔ Minimize the total project completion time for a given cost.
Network:
The class of systems engineering technique used for planning, scheduling and
controlling large and complex projects are often referred as network.
PERT & CPM techniques are based on representation of the project as a network of
activities.
A network is a graphical plan consisting of certain configuration of arrows and nodes
for showing the logical sequence of various tasks to be performed to achieve project
objectives.

Basic Concepts of Network Diagrams
• The significant feature of network diagram is
that the work content termed activities as well
as their relationship are depicted by a network
of directed arrows.
• The completed network serves as basis for
estimation of the total project duration,
scheduling, establishing priorities and
integrating time, cost and manpower
information.
• The terms used in network analysis are…

Event:
✔ Event is an inexplicitly identifiable point in time at which something has happened.
✔ Event of the project represents project milestone such as the start or the completion
of an activity and occur at a particular instant of time at which some specific part of
the project has been achieved.
✔ Events are commonly represented by circles (nodes) in the network diagram.
Classification of Events:
Merge Event:
An event which represents the joint completion of more than one activity.
Burst Event :
Event which represent the initiation of more than one activity.

Events
• Events in network diagram are identified by
numbers.
• Each event should be identified by a number
higher than that allotted to its immediately
preceding event to indicate the progress of
the work.
• The numbering of event must start from left
[start of the project] to right [completion of
the project]

Fulkerson’s Rule of Numbering the Event
• In any network, there is only one event which
has arrow coming out of it and none entering it.
Number this event as 1
• Discard all arrows emerging from event 1. This
creates at least one more initial event. Number
this initial event as 2, 3, 4 and so on
• Follow above steps till the last event is obtained
which has no arrows emerging out of it. This
shall be the last event of the network diagram.

Activities:
✔ Activities of the network diagram represents project operations or tasks to be
conducted.
✔ An arrow is commonly used to represent an activity with its head indicating the
direction of the progress in the project.
✔ An arrow (i, j) extended between two events;
✔ The tail event i represents the start of the activity & the head event j represents the
completion of the activity as shown
Activity
i j
Starting Event Completion Event

Activity Classification
Predecessor Activity:
An activity which must be completed before one or more other activities start.
Successor Activity:
An activity which started immediately after one or more of the other activities are
completed
Dummy Activity:
✔ An activity which does not consume either any resource and time.
✔ A dummy activity is denoted by dotted line in the network diagram.
✔ Dummy activity serves the following purposes
▪ To maintain the uniqueness in the given system as every activity may have a
distinct set of events by which activity can be identified
▪ To maintain the logic in the network diagram
▪ To show the exact relationship between events.

Rules for Network Construction
✔In a network diagram, arrows represents activities and circles the
event. The length of the arrow is of no significance.
✔ Each activity should be represented by only one arrow and must
start & end in a circle called event. The tail of an activity
represents the start and head the completion of work.
✔The event No 1 represents the start of the project and is called as
initial event.
✔All activities emerging from event 1 should not be preceded by
any other activity.
✔Event carrying the highest no denotes the completion of project
✔General rule for numbering the event is that number at an
activities head should always be larger than that at its tail.

Rules for Network Construction
✔ An activity must be uniquely identified by its starting and completion event. No event
number should be repeated.
✔ An event is achieved when all activities leading to it are complete.
✔ No activity can begin till the preceding event of the activity is achieved.
✔ All the restraints and interdependencies must be shown on the network diagram.
✔ No more than one activity arrow should connect any two events.
1 2 3 5
Incorrect Method
3
1 2 5
4 Correct Method

Example 1:
An assembly is to be made from two parts X & Y . Both parts must be turned on a lathe and
Y must be polished whereas X need not be polished. The sequence of activities together
with their predecessors are as under:
Activit
y
Description Predecess
or Activity
A Open Work Order --
B Get material for X A
C Get material for Y A
D Turn X on Lathe B
E Turn Y on Lathe B,C
F Polish Y E
G Assemble X & Y D, F
H Pack G

1 2
3
4 5
6 7
8
A
B
C
D1
D
E
F
G
H

Example 2:
Listed in the table are the activities and sequencing necessary for a maintenance job on
the heat exchangers in a refinery
Activity Predecessor Activity
A --
B A
C B
D B
E B
F C
G C
H F,G
I D, E & H
J I
Draw the
network
diagram for
the project.

1 2 3
4 5
6
8 9
10
7
A B
C
E
D
F
G D1
H
D2
I
J

Example 3:
• A project consists of following six activities as
mentioned below.
• A is the start activity
• B, D & E depends on A;
• C depends on B
• F is the last activity and depends on C, D & E
Draw the network diagram for the project.

Practice Examples 1:
A new type of water pump is to be designed for an automobile . Major specifications are
as under
A --
B A
C A
D C
E B,C
F D,E
G E
H G
I D,F
J I,H
K J

Practice Example 2:
A --
B --
C --
D A
E B,C
F A
G C
H D,E & F
I D
J G
K G
L H,J
M K
N I,L
Draw the
network for the
activities of the
project.

CRITICAL PATH METHOD (CPM)
✔The objective of critical path analysis is to estimate the total
project duration and to assign starting and finishing times to all
activities involved in the project.
✔The sequence of activities and events which takes the greatest
amount of time to complete is called as the critical path.
✔Physically the critical path consists of bottleneck operations.
✔Any delay in critical path delay in the project completion.
✔The project can be completed earlier, if critical operations are
finished earlier. Therefore management concentrates more on
the critical path.

CPM
CPM helps in determination of;
✔Total completion time of the project.
✔Earliest and latest start time of each activity.
✔Float for each activity. It is the amount of time
by which the completion of an activity can be
delayed without delaying the total project
completion time.
✔Identifying the critical activities and the critical
path.

Notations used for the purpose of Calculating time of Events &
Activities
Ei Earliest Occurrence time of event (i) : It is the earliest time at which an event can occur
without affecting the total project time
Li Latest Occurrence time of event (i): It is the latest time at which an event can occur
Esij Earliest start time of an activity (ij): It is the time at which the activity can start
without affecting the total project time.
Lsij Latest start time for activity (ij): It is the latest possible time by which an activity
must start without affecting the total project time.
Efij Earliest finish time for activity (ij): It is the earliest possible time by which an activity
can finish without affecting the total project time
Lfij Latest finish time for activity (ij): It is the latest time by which an activity can finish
tij Time duration of the activity (ij)

Float
The float of an activity is the amount of time by which it is possible to delay its completion
time without affecting the total project completion time.
Event Float: the float of an event is the difference between latest time (Li) and its earliest
time (Ei)
Event Float = Li – Ei
Activity Float: These are classified as;
Total Float: It is the difference between time available to perform the activity and the
expected completion time of the activity.
Total Float = (Lj – Ei) – tij
Free Float: the time by which the completion of an activity can be delayed beyond its
earliest finish time without affecting the earliest start time of an succeeding activity
Free Float = (Ej – Ei) – tij
Independent Float: It is the amount of time by which it is possible to delay the completion
of an activity so that it neither affects the predecessor nor the successor activity
Independent Float = (Ej – Li) - tij

Example 1:
A building construction project has the following time schedule
Activity Time (Months)
1- 2 2
1-3 2
1-4 1
2-5 4
3-6 8
3-7 5
4-6 3
5-8 1
6-9 5
7-8 4
8-9 3
Construct the
Network and
compute critical
path & duration
of the project

1
0
0
0
2
4
3
5
6
7
8
9
2
2
1
2
1
2
4 6
7
5
3
8
10
1
4
11
5
15 15
3
10
8
12
11
7
7
2
0
0
0
5 5 1
6
1
Critical Path: 1-3-6-9
Project Duration = 15
Months

Example 2:
An architect has been awarded a contract to prepare plans for an urban renewal project.
The job consists of following activities and their estimated times
Activity Predecessor
Activity
Time (Days)
A - 2
B - 1
C A 3
D A,B 2
E C,D 1
F C,D 3
G E,F 1
Draw the network diagram and compute the critical path.

1
2
3
4
5
6
7
0
2
2
5
6 9
8
A
-
2
B - 1
D1 0
C
3
D 2
E 1
F
3
D2 0
G 1
9
8
8
5
3
2
0
0
0 0 0
0
1
2
Critical Path: A-C-F-G
Project Duration: 9 Days

Example 3:
A R&D department is developing a new power supply system. It has broken down the job
into activities mentioned below
Activity Predecessor
Activity
Time (Days)
A - 5
B A 7
C B 2
D B 3
E C 1
F D 2
G C 1
H E,F 3
I G,H 10
Drawn the critical path and compute the total project duration time

1
2 3 4
5
6
7
8
0
5 12 14
15
17
20
0
30
5 12
15
16
20
30
17
0
0
0
0
0
0
0
2
A 5
D 3
H 3
G 1
I 10
B
7
C
2
F
2
Critical Path : A - B – D – F – H - I
Total Project Duration: 30 Days
E
1

▪ Project Evaluation and Review Techniques is commonly
abbreviated to PERT.
▪ Program Evaluation and Review Technique (PERT) was
first developed in 1958 by USA Navy special project
office and a management consulting firm for planning
and control of the Polaris sub-marine missile project
▪ The technique of PERT was specially developed to help
reducing the overall project time by as much as
possible.
▪ It is a probabilistic approach for solving network
problem.
PERT Introduction

▪ PERT is a method of analyzing the tasks involved in
completing a given project, especially the time needed
to complete each task, and to identify the minimum
time needed to complete the total project.
▪ The program evaluated follows:
▪ What research has to be done to accomplished.
▪ How would the research be planned.
▪ How long would the research take.
▪ How fast it can be done.
PERT Introduction

Characteristics of CPM and PERT
Collections of unit operation/activities.
Each activities starts & ends independently within a given sequence.
Activities must perform in technological sequence.
Applicability of CPM & PERT
Construction industry
Planning & Launching new product
Maintenance of big plants
Installing & debugging of computerized system
Month closing Account.

Difference between PERT & CPM
PERT CPM
It is a probabilistic approach. It is a deterministic approach.
It emphasizes the uncertainty
of completion time of the
activities.
It is concerned with the trade
off between project duration
and cost.
It is used mostly in research
and development projects.
It is extensively used in
construction activities
It is assumed cost varies with
time. So, the aim is to
minimize the time for the
minimum cost.
Cost optimization is the
ultimate aim. The time of
completion depends on the
cost optimization.
Time is the controlling factor Cost is the controlling factor
and is not proportional to
time.

INTRODUCTION TO PERT
In a PERT model, each job/activity is defined
with three durations:
1.Most probable time (tm)
2.Pessimistic estimated time (tp)
3.Optimistic estimated time (to)

Most probable time (tm) = Time required to complete the activity
considering few uncertainty (like rain, few signal are red) which is
normal.
Pessimistic estimated time (tp) = A guess of maximum time to
complete the activity considering worsen cases and bad luck. (like
earth makes flood, war, road blocked, drill rod jamming)
Optimistic estimated time (to) = A guess of Minimum time to
complete the job considering best cases where everything goes
right. (minimum red signal, smooth drilling etc.)

The Example for understanding job duration in PERT
Consider, a job is defined as the transportation time in scheduling a
surface mining operations. The cycle time of a dumper which runs
between crushing plant and a shovel of the mine is the job duration.
Say the design engineer has the previous experience as shown.
Based on this
–the most likely activity time is 8 days
But it can be done in5 days if everything is favourable
Or, It may take 17days if any critical problem arises

Variability of Activity Time
In a probabilistic approach, not only it is essential to
estimate the mean or average (expected time), but also it
is important to understand the reliability of the estimate.
Reliability of the estimated mean/average is assessed in
terms of variability. If the variability is less then the
estimate is strong and reliable or in other word the range
of the estimate is narrow.

Variability of Activity Time
Let us consider two cases
Example 1 Example 2
Range is 5 -> 17 Range is 8 -> 10
The expected time is same for both. But the confidence on te is
more in Example 2 where the range is narrow

Probability of Completion of Projects

Float Analysis
Following notations are used for the purpose of calculating time of events and activities
Ei ------- Earliest occurrence time of event i. It is the earliest time at which an event can
occur without affecting the total project time.
Li ------- Latest occurrence time of the event. It is the latest time at which an event can
occur without affecting the total project time.
ESij ------ Earliest start time of an activity (i, j). It is the time at which the activity can start
without affecting the total project time.
LSij ------ Latest start time for activity (i, j). It is the latest possible time by which an activity
must start without affecting the total project time.
EFij ----- Earliest finish time for activity (i, j). It is the earliest possible time by which an
activity can finish without affecting the total project time.
LFij ----- Latest finish time for activity (i, j). It is the latest time by which an activity must get
completed without delaying the total project completion time.
tij ------- Duration of the activity (i,j)

Activity Float:
The float of an activity is the amount of time by which it is possible to delay its completion
time without affecting the total project completion time.
Activity Float is classified as:
Total Float:
It is the difference between the time available to perform the activity and the expected
completion time of the activity.
Total Float =
Free Float:
The time by which the completion of an activity can be delayed beyond its earliest finish
time without affecting the earliest start time of a succeeding activity

Independent Float:
It is the amount of time by which it is possible to delay the completion of an activity so that
it neither affects the predecessors nor the successor activity
Event Float:
The float or slack of an event is the difference between latest time (Li) and its earliest time
(Ei)
Ei Li Ej Lj
tij

For the project under consideration determine the critical time for the project and find
Total float, Free float and Independent Float
Activity (i,j) Duration (days)
1-2 3
2-3 3
2-4 2
3-4 0
3-5 3
3-6 2
4-5 7
4-6 5
5-6 6

1 2 5 6
3
4
0
3
3
3
6
2
6
0
7
5
3 2
6
13 19 19
0
13
0
6
0
6
0
3
0
0
0
Ei
tij
Ej Lj
Li
i j

Activity (i,j) Duration
(days)
Total Float
(Lj-tij) - Ei
Free Float
(Ej–Ei) - tij
Independen
t Float
( Ej-Li ) -
tij
1-2 3 3-3-0 = 0 3-0-3 = 0 3-0-3 = 0
2-3 3 6-3-3 = 0 6-3-3 = 0 6-3-3 = 0
2-4 2 6-2-3 = 1 6-3-2 = 1 6-3-2 = 1
3-4 0 6-0-6 = 0
3-5 3
3-6 2
4-5 7
4-6 5
5-6 6

A project is shown by the network diagram below and has the following data.
Tas
k
A B C D E F G H I
to 5 18 26 16 15 6 7 7 3
tp 10 22 40 20 25 12 12 9 5
tm 8 20 33 18 20 9 10 8 4
Draw the Critical Path and determine expected task times and their variance.
Determine the Probability of an event occurring at the proposed completion date if the
original contract time of completing the project is 41.5 weeks.
Determine the duration of the project that has 95% chance of being completed.

1
0
A
0
0
2
7.8
9
16.8
3
20
9.8
29.8
6
29
9.8
38.8
5
25.8
9
34.8
7
42.8
0
42.8
4
33
0
33
7.8
B
20
C
33
D
18
E
20
F
9
G 9.8
I
4
H
8

Activity to tp tm te
(to+4tm+tp)/6
σ2
[(tp-to)/6]2
1 – 2 5 10 8 7.8 0.694
1 – 3 18 22 20 20 0.444
1 – 4 26 40 33 33 5.444
2 – 5 16 20 18 18 0.444
2 – 6 15 25 20 20 2.778
3 – 6 6 12 9 9 1.000
4 – 7 7 12 10 9.8 0.694
5 – 7 7 9 8 8 0.111
6 – 7 3 5 4 4 0.111

PERT & CPM presentation based on mining engineering

PERT & CPM presentation based on mining engineering

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PERT & CPM presentation based on mining engineering