Chap 4- CPM & PERT.pptx

Manufacturing & Operations
Management
Topic 4
Production Planning & Control

What is Project Management
 Project management can be defined as the
coordination of activities with the potential use of
many organizations, both internal and external to
the business, in order to conduct a large scale
project from beginning to end.
 There are two management science techniques
that are used for project management:
 Program and Evaluation Review Technique
(PERT)
 Critical Path Method (CPM)

PERT/CPM
 PERT
 Program Evaluation and Review Technique
 Developed by U.S. Navy for Polaris missile project
 Developed to handle uncertain activity times
 CPM
 Critical Path Method
 Developed by Du Pont & Remington Rand
 Developed for industrial projects for which
activity times generally were known
 Today’s project management software packages have
combined the best features of both approaches.

PERT/CPM
 PERT and CPM have been used to
plan, schedule, and control a wide
variety of projects:
 R&D of new products and processes
 Construction of buildings and highways
 Maintenance of large and complex
equipment
 Design and installation of new systems

PERT/CPM
 PERT/CPM is used to plan the
scheduling of individual activities that
make up a project.
 Projects may have as many as
several thousand activities.
 A complicating factor in carrying out
the activities is that some activities
depend on the completion of other
activities before they can be started.

PERT/CPM
 Project managers rely on PERT/CPM to help
them answer questions such as:
 How can the project be displayed graphically?
 What is the total time to complete the
project?
 What are the scheduled start and finish dates
for each specific activity?
 Which activities are critical and must be
completed exactly as scheduled to keep the
project on schedule?

 How long can non critical activities be
delayed before they cause an increase
in the project completion time?
 What is the probability of completing
the project by the deadline?
 What is the least amount of money
needed to expedite the project to
obtain the bonus?
 How should costs be monitored to keep
the project within budget?

Scheduling Using PERT/CPM
 A path through a project network is
a route that follows a set of arcs
from the start node to the finish
node.
 The length of a path is defined as
the sum of the durations of the
activities of the path.
 What are the paths and their
corresponding lengths ?

Difference between PERT & CPM
 PERT
 It is usually analytical
in concept & designed
as probabilistic
network
 It is built up of event
oriented diagrams
 Three time estimates
are possible for
activities linking up
two activities
 CPM
 It is basically
synthesising in
concept and termed as
deterministic network
 It is built up of
activities oriented
diagrams
 One time estimate is
possible

Difference between PERT & CPM
 PERT
 Times are not related
to cost
 Used for R & D
Projects, product
development
 CPM
 Time are related to
costs
 Used for repetitive
work

A
START
G
H
M
F
J
K L
N
Activity Code
A. Excavate
B. Foundation
C. Rough wall
D. Roof
E. Exterior plumbing
F. Interior plumbing
G. Exterior siding
H. Exterior painting
I. Electrical work
J. Wallboard
K. Flooring
L. Interior painting
M. Exterior fixtures
N. Interior fixtures
2
4
10
7
4
6
7
9
5
8
4 5
6
2
0
0
FINISH
D I
E
C
B

Different Terminologies
 Event :
 A Particular instant in time showing the
end or beginning of an activity.
 It is a point of accomplishment or
decision
 This does not consume resources
 An activity is bound by two events

Numbering of events
 Event Numbering :
 Event numbers should in some
respect reflect their logical
sequencing

Rule for numbering events
 D R Fulkerson’s rule for numbering :
 An initial event is one which has arrows coming
out of it and none entering it. In any network
there will be one such event. Number it 1
 Delete all the arrows emerging from event 1.
This will create at least one more “initial event”
 Number these new initial events as 2,3,..
 Delete all emerging arrows from these numbered
events which will create new initial events
 Continue till the last event is obtained which has
no arrows emerging out of it

Additional rules for numbering
events
 All events must be numbered
 The same number cannot be used for
more than one event. This is
necessary for identifying each activity
 Event can be numbered in any order
but usually forward numbering
system is more familiar

 Activity :
 An activity represents efforts applied over a
period of time which has a definite beginning
and end
 Activities are graphically represented by arrows
with description and time estimates written
along the arrow
 Direction of the arrow indicates the sequence in
which events occur
 Activity is actual performance of a task
 It consumes resources i.e. manpower, material,
money
 Activity represents what is to be done between
the achievement of any two events
 An activity cannot be started until its preceding
event has been achieved

Activity & Event Relationship
 An event can only be achieved when
all activities leading to that event are
complete
 An activity can only be started when
its preceding event is achieved.
 The preceding event thus dictates the
earliest start time of an activity.
 While the succeeding event fixes the
accomplishment of that activity

 Restriction :
 When one activity must be completed
before a second activity can begin, the
first activity is considered to be restraint
or restricting activity. A<B
 Pre-requisite Activity :
 Is one which immediately precedes the
one being considered. A is pre-requisite
for B,C & F
A
F
D
B
C
E

 Post-Requisite activity :
 Is one which immediately follows one under
consideration. B,C & F are post requite to A
 Descendent Activity :
 A descendent activity is any activity restricted
by the one under consideration
 B,C,D,E F are descendent of A
 Antecedent Activity :
 Any activity which must precede the one under
consideration. A & B are antecedent of D
A
F
D
B
C
E

 Dummy Activity :
 An activity that does not consume any kind of
resources but merely depicts the technological
dependence.
 Merge :
 A merge exists when two or more activities
converge at a single event
 Burst :
 A burst exists when two or more activities have
a common beginning event

Rules for drawing network diagram
 Rule 1 :Each activity is represented
by one and only one arrow in the
network
 Rule 2 : No two activities can be
identified by the same end event
a
b
a
b
dummy
WRONG RIGHT

Rules for drawing network diagram
 Rule 3 : In order to ensure the correct
precedence relationship in the arrow
diagram, following must be checked
when every activity is added
 What activities must be completed before
this activity can start ?
 What activity must follow this activity ?
 What activity must occur simultaneously
with this activity ?

Further guidelines for network
diagrams
 Activity arrows should be drawn from
left to right indicating progressive
approach towards the ultimate
objective or final event
 Crossing of arrows should be avoided
 Unnecessary use of dummy activities
should be avoided

Network Rules
 The length of arrows bears no relationship to the time
which the activity takes
 The arrow in a network identifies logical conditions of
dependencies. The geometry of the arrow has no
significance
 The direction of the arrow indicates the direction of
work flow. Normal convention is from left to right
 All networks are constructed logically on the principle
of dependency
 No event can be reached in a project before the
activity preceding is completed
 No set of activites can form a circular loop

More Terminology
 Earliest start time of an activity (ES)
 The time at which an activity will begin if there
are no delays in a project.
 Earliest finish time of an activity (EF)
 The time at which an activity will finish if there
are no delays in a project.
 Latest start time of an activity (LS)
 The latest possible time that an activity can
start without delaying the project.

More Terminology Cont.
 Latest finish time of an activity (LF)
 The latest possible time that an activity
can be completed without delaying the
project.
 Forward pass
 The process of moving through a
project from start to finish to determine
the earliest start and finish times for
the activities in the project.

 Backward pass
 The process of moving through a project from finish
to start to determine the latest start and finish times
for the activities in the project.
 Slack for an activity
 The amount of time that a particular activity can be
delayed without delaying the whole project.
 It is calculated by taking the difference between the
latest finish time with the earliest finish time.

 Earliest start time rule
 The earliest start time for an activity is
equal to the largest of the earliest finish
times of its immediate predecessors.
 Latest finish time rule
 The latest finish time is equal to the
smallest of the latest start times of its
immediate successors.

Procedure for Obtaining
Earliest Times
 Step 1: For the activity that starts the
project, assign an earliest start time of
zero, i.e., E1=0.
 Step 2: Any activity can start immediately
when all the preceding activities are
completed
 The earliest start time for node j is given by
Ej = Max [Ei + Dij]
Where I is the collection of nodes which precede
node j

Procedure for Obtaining
Earliest Times Cont.
 Step 3 : Repeat step 2 for the next
eligible activity until the end node is
reached

Procedure for Obtaining Latest
Start Times
 In forward pass computation, the
earliest time when a particular
activity can be completed is known.
 It is seen that some activities are
not critical to the completion of the
project
 Can their starting time be delayed ?
 What can be the maximum delay ?
Such questions arises when scheduling
resources

Procedure for Obtaining Latest
Start Times
 Step 1: Set Li = Ei or Ts where Ts is the
scheduled date of completion of the project
and Ei is the earliest terminal time
 Step 2: Li = Min [Lj – Dij]
 i.e. the latest time for activities is the
minimum of the latest time of all succeeding
activities reducing their activity time.
 Step 3: Repeat step 2 until starting activity is
reached

A
START
G
H
M
F
J
FINISH
K L
N
D I
E
C
B
2
4
10
7
4
6
7
9
5
8
4 5
6
2
S = (0, 0)
F = (2, 2)
S = (2, 2)
F = (6, 6)
S = (16, 20)
F = (22, 26)
S = (16, 16)
F = (20, 20)
S = (16, 18)
F = (23, 25)
S = (20, 20)
F = (25, 25)
S = (22, 26)
F = (29, 33)
S = (6, 6)
F = (16, 16)
S = (0, 0)
F = (0, 0)
S = (25, 25)
F = (33, 33)
S = (33, 33)
F = (38, 38)
S = (38, 38)
F = (44, 44)
S = (33, 34)
F = (37, 38)
S = (29, 33)
F = (38, 42)
S = (38, 42)
F = (40, 44)
S = (44, 44)
F = (44, 44)
0
0

Ways of Finding the Critical
Path
 Examine all the paths and find the
path with the maximum length.
 Calculate the slack for an activity.
 If the slack is zero, it is on the critical
path.
 If the slack is positive, it is not on the
critical path.

Precedence
table
Activity Immediately
preceding activities
duration
A Shower - 3
B Dry hair A 8
C Fetch car - 7
D Iron clothes - 12
E Dress and make-up B,D 10
F Drive to interview C,E 20
The last activities that
must be completed
before an activity can
begin

Activity on Arc Network
A(3)
D(12)
B(8)
E(10)
C(7)
F(20)
1 5
4
3
2
The network will build up with
each mouse click, in the order
you would construct it on
paper.

Event Times
A(3)
D(12)
B(8)
E(10)
C(7)
F(20)
1 5
4
3
2
Earliest
event time
EET
Latest
event
time
LET
Each event node
needs two boxes, to
mark in the event
times.

Earliest Event Times
A(3)
D(12)
B(8)
E(10)
C(7)
F(20)
1 5
4
3
2
0
3
12
22
42
To find EETs, work
forwards through the
network from the start
node to the finish
node.
The EET for an
event occurs
when all activities
leading into that
event are
complete.

Latest Event Times
A(3)
D(12)
B(8)
E(10)
C(7)
F(20)
1 5
4
3
2
3
0
12
22
42 42
22
12
4
0
To find LETs, work
backwards through
the network from the
finish node to the start
node.
The LET for an
event is the latest
it can occur
without delaying
subsequent
events.

Critical Activities
A(3)
D(12)
B(8)
E(10)
C(7)
F(20)
1 5
4
3
2
3 4
0 0
12 12
22 22
42 42
Critical activities are activities that cannot
run late. For critical activities:
Latest finish — Earliest start = length of
activity
The green arrows mark the critical
activities, which form the critical path.
The critical path(s) must form a continuous
route from the start node to the finish
node.

Revisiting Cables By Us Using
Probabilistic Time Estimates
Activity Description
Optimistic
time
Most likely
time
Pessimistic
time
A Develop product specifications 2 4 6
B Design manufacturing process 3 7 10
C Source & purchase materials 2 3 5
D Source & purchase tooling & equipment 4 7 9
E Receive & install tooling & equipment 12 16 20
F Receive materials 2 5 8
G Pilot production run 2 2 2
H Evaluate product design 2 3 4
I Evaluate process performance 2 3 5
J Write documentation report 2 4 6
K Transition to manufacturing 2 2 2

Using Beta Probability
Distribution to Calculate
Expected Time Durations
 A typical beta distribution is shown below, note
that it has definite end points
 The expected time for finishing each activity is
a weighted average
 
6
c
pessimisti
likely
most
4
optimistic
time
Exp.




Calculating Expected Task
Times
Activity
Optimistic
time
Most likely
time
Pessimistic
time
Expected
time
A 2 4 6 4
B 3 7 10 6.83
C 2 3 5 3.17
D 4 7 9 6.83
E 12 16 20 16
F 2 5 8 5
G 2 2 2 2
H 2 3 4 3
I 2 3 5 3.17
J 2 4 6 4
K 2 2 2 2
 
6
4 c
pessimisti
likely
most
optimistic
time
Expected




Network Diagram with
Expected Activity Times

Estimated Path Durations
through the Network
 ABDEGIJK is the expected critical
path & the project has an expected
duration of 44.83 weeks
Activities on paths Expected duration
ABDEGHJK 44.66
ABDEGIJK 44.83
ACFGHJK 23.17
ACFGIJK 23.34

Estimating the Probability of
Completion Dates
 Using probabilistic time estimates offers the advantage of
predicting the probability of project completion dates
 We have already calculated the expected time for each
activity by making three time estimates
 Now we need to calculate the variance for each activity
 The variance of the beta probability distribution is:
 where p=pessimistic activity time estimate
o=optimistic activity time estimate
2
2
6
o
p
σ 




 


Project Activity Variance
Activity Optimistic Most Likely Pessimistic Variance
A 2 4 6 0.44
B 3 7 10 1.36
C 2 3 5 0.25
D 4 7 9 0.69
E 12 16 20 1.78
F 2 5 8 1.00
G 2 2 2 0.00
H 2 3 4 0.11
I 2 3 5 0.25
J 2 4 6 0.44
K 2 2 2 0.00

Variances of Each Path
through the Network
Path
Number
Activities on
Path
Path Variance
(weeks)
1 A,B,D,E,G,H,J,k 4.82
2 A,B,D,E,G,I,J,K 4.96
3 A,C,F,G,H,J,K 2.24
4 A,C,F,G,I,J,K 2.38

Calculating the Probability of
Completing the Project in Less Than
a Specified Time
 When you know:
 The expected completion time
 Its variance
 You can calculate the probability of completing the
project in “X” weeks with the following formula:
Where DT = the specified completion date
EFPath = the expected completion time of the path







 


 2
P
σ
EF
D
time
standard
path
time
expected
path
time
specified
z
P
T
path
of
variance
σ 2
Path 

Example: Calculating the probability
of finishing the project in 48 weeks
 Use the z values in Appendix B to determine
probabilities
 e.g. probability for path 1 is
Path
Number
Activities on Path Path Variance
(weeks)
z-value Probability of
Completion
1 A,B,D,E,G,H,J,k 4.82 1.5216 0.9357
2 A,B,D,E,G,I,J,K 4.96 1.4215 0.9222
3 A,C,F,G,H,J,K 2.24 16.5898 1.000
4 A,C,F,G,I,J,K 2.38 15.9847 1.000
1.52
4.82
weeks
44.66
weeks
48
z 







 


Project Network
 A project network can be constructed to
model the precedence of the activities.
 The nodes of the network represent the
activities.
 The arcs of the network reflect the
precedence relationships of the
activities.
 A critical path for the network is a path
consisting of activities with zero slack.

Network Analysis
Phases of Network Analysis
Phase I : Planning
 Collection of all information pertinent to project
 different types of works involved are separated
into activities
 Time estimates are determined for each
activity
 Activity sequencing is established by noting
their inter relationship (which must precede,
which must succeed, which are concurrent)

Network Analysis
Phase II : Scheduling
 assigning estimated start & finish time to each
activity
 cost, availability of work crew, materials & other
resources associated with each activities must be
considered.
 Showing the float on some activities and determining
the critical activities.
 Preparation of time chart and using it for manpower
leveling and resource allocation
 Cost analysis based on the time chart

Network Analysis
Phase III : Control
 Cost control of project
 updating and reporting
 proposed changes
 simplifies communication and improve
coordination

Advantages of network analysis
 It limits possibility of over looking a
job
 It shows inter relationship of all jobs
in the project
 It helps in communicating the ideas
 It contribute to disciplined thinking
 It identifies those jobs which are
critical for project completion

Advantages of network analysis
 It provides time schedule consisting much
more information than a usual bar chart
 It provides methods of resource allocation
to meet limiting condition
 It integrates all elements of a programme
to whatever detail is desired
 It facilitates reporting & project
documentation

Project Network
 A project network is a network
diagram that uses nodes and arcs to
represent the progression of the
activities is a project from start to
finish.
 Three pieces of information needed:
 Activity information
 Precedence relationship
 Time information

Project Network Cont.
 Two types of project networks
 Activity-on-Arc (AOA)
 On this diagram, the activity is
represented on an arc, while a node is
used to separate an activity from its
immediate predecessors.
 Activity-on-Node (AON)
 On this diagram, the activity is
represented by the node, while the arc is
used to showed the precedence
relationship between the activities.

Chap 4- CPM & PERT.pptx

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