This document discusses project scheduling techniques CPM and PERT. It provides background on their development in the 1950s and describes their key features. Both techniques use network diagrams to show task relationships and interdependencies. They help determine if a project is on schedule or budget, and identify critical paths and resources. The document outlines the common six steps to CPM and PERT and provides examples of network diagrams and calculations.
Introduction 1
Network is a technique used for planning and scheduling of large projects in the fields of construction, maintenance, fabrication, purchasing, computer system instantiation, research and development planning etc. There is multitude of operations research situations that can be modeled and solved as network. Some recent surveys reports that as much as 70% of the real-world mathematical programming problems can be represented by network related models. Network analysis is known by many names _PERT (Programme Evaluation and Review Technique), CPM (Critical Path Method), PEP (Programme Evaluation Procedure), LCES (Least Cost Estimating and Scheduling), SCANS (Scheduling and Control by Automated Network System), etc
This chapter will present three of algorithms.
1. PERT & CPM
2. Shortest- route algorithms
3. Maximum-flow algorithms
Introduction 1
Network is a technique used for planning and scheduling of large projects in the fields of construction, maintenance, fabrication, purchasing, computer system instantiation, research and development planning etc. There is multitude of operations research situations that can be modeled and solved as network. Some recent surveys reports that as much as 70% of the real-world mathematical programming problems can be represented by network related models. Network analysis is known by many names _PERT (Programme Evaluation and Review Technique), CPM (Critical Path Method), PEP (Programme Evaluation Procedure), LCES (Least Cost Estimating and Scheduling), SCANS (Scheduling and Control by Automated Network System), etc
This chapter will present three of algorithms.
1. PERT & CPM
2. Shortest- route algorithms
3. Maximum-flow algorithms
Yagmur Bostanci47 Hackensack Street, East Rutherford, NJ929-22.docxjeffevans62972
Yagmur Bostanci
47 Hackensack Street, East Rutherford, NJ
929-229-8834
[email protected]
EDUCATON
BERKELEY COLLEGE
YORK, UNITED STATES
· Bachelor of Business Management
· Cumulative GPA 3.00
PROFESSIONAL EXPERIENCE
Lincoln House Outreach
303 W 66th St, New York, NY
Nurse
July 2014 – September 2014
· Responsible for the old women in Lincoln House Outreach
· Managing all the payments and organizing listing
· Balancing firm objectives and old women satisfaction
CANDLEWYCK DINNER
East Rutherford, New Jersey, United States
Waitress
· Food delivery
· Fulfill costumer’s wants
· Accounting (Cash, Credit Card, and tax for prices of the food)
TECHNICAL SKILLS
· Phone Settings
· Microsoft Office (Excel, Word, Power point)
· Adobe Photoshop
Overview
1) Overview – The continued discussion of project implementation by covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a project action plan into an operating timetable.” A schedule is important because each project is unique in its own way. The basic process is to identify all tasks and sequential relationships between them, that is, which tasks must precede or succeed others. There are a number of benefits to the creation and use of these networks. Some of them are as follows:
a) It is a consistent framework for planning, scheduling, and controlling the project.
b) It can be used to determine a start and end date for every project task.
c) It identifies so-called critical activities that, if delayed will delay the project completion.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT and CPM are the most commonly used approaches to project scheduling. Both were introduced in the 1950s. PERT has been primarily associated with R&D projects, while CPM with construction projects. Today PERT is not used much since project management software generates CPM style networks. The primary difference between them is that PERT uses probabilistic techniques to determine task durations, while CPM relies on a single duration estimate for each task. Both techniques identify the critical path (tasks that cannot be delayed without delaying the project) and associated float or slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it necessary to change the names of these techniques. According to PMI, PERT is called ADM/PERT (Arrow Diagram Method) and CPM is PDM/CPM (Precedence Diagramming Method).
a) Terminology – Following are the key terms associated with the development and use of networks:
i) Activity – A specific task or set of tasks that have a start and end, and consume resources.
ii) Event – The result of completing one or more activities. Events don’t use resources.
iii) Network – The arrangement of all activities and events in their logical sequence represented by arcs and nodes.
iv) Path – The series of connected activities between any two events in a network.
v) Critical – Activities, events or paths which, if delayed, w.
CPM and PERT are most commonly used methods for project management. There are some similarities and differences between PERT and CPM. PERT can be applied to any field requiring planned, controlled and integrated work efforts to accomplish defined objectives.
Overview1) Overview – The continued discussion of project implem.docxalfred4lewis58146
Overview
1) Overview – The continued discussion of project implementation by covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a project action plan into an operating timetable.” A schedule is important because each project is unique in its own way. The basic process is to identify all tasks and sequential relationships between them, that is, which tasks must precede or succeed others. There are a number of benefits to the creation and use of these networks. Some of them are as follows:
a) It is a consistent framework for planning, scheduling, and controlling the project.
b) It can be used to determine a start and end date for every project task.
c) It identifies so-called critical activities that, if delayed will delay the project completion.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT and CPM are the most commonly used approaches to project scheduling. Both were introduced in the 1950s. PERT has been primarily associated with R&D projects, while CPM with construction projects. Today PERT is not used much since project management software generates CPM style networks. The primary difference between them is that PERT uses probabilistic techniques to determine task durations, while CPM relies on a single duration estimate for each task. Both techniques identify the critical path (tasks that cannot be delayed without delaying the project) and associated float or slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it necessary to change the names of these techniques. According to PMI, PERT is called ADM/PERT (Arrow Diagram Method) and CPM is PDM/CPM (Precedence Diagramming Method).
a) Terminology – Following are the key terms associated with the development and use of networks:
i) Activity – A specific task or set of tasks that have a start and end, and consume resources.
ii) Event – The result of completing one or more activities. Events don’t use resources.
iii) Network – The arrangement of all activities and events in their logical sequence represented by arcs and nodes.
iv) Path – The series of connected activities between any two events in a network.
v) Critical – Activities, events or paths which, if delayed, will delay the completion of the project.
To construct a network the predecessors and successors of each activity must be identified. Activities that start the network will have no predecessor. Activities that end the network will have no successor. Regardless of the technique used, it is a good practice to link the activities with no other predecessor to a START milestone. Those without any successor should be linked to an END milestone. PDM/CPM networks identify the activities as nodes in the network, called the Activity on Node (AON) network. The arrows in between the nodes depict the predecessor/successor relationships among the activities. The ADM/PERT method, on the other hand, uses Activity on Arrow (AOA) networks. Here the nodes represent .
Overview1) Overview – The continued discussion of .docxalfred4lewis58146
Overview
1)
Overview – The continued discussion of project implementation by covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a project action plan into an operating timetable.” A schedule is important because each project is unique in its own way. The basic process is to identify all tasks and sequential relationships between them, that is, which tasks must precede or succeed others. There are a number of benefits to the creation and use of these networks. Some of them are as follows:
a) It is a consistent framework for planning, scheduling, and controlling the project.
b) It can be used to determine a start and end date for every project task.
c) It identifies so-called critical activities that, if delayed will delay the project completion.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT and CPM are the most commonly used approaches to project scheduling. Both were introduced in the 1950s. PERT has been primarily associated with R&D projects, while CPM with construction projects. Today PERT is not used much since project management software generates CPM style networks. The primary difference between them is that PERT uses probabilistic techniques to determine task durations, while CPM relies on a single duration estimate for each task. Both techniques identify the critical path (tasks that cannot be delayed without delaying the project) and associated float or slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it necessary to change the names of these techniques. According to PMI, PERT is called ADM/PERT (Arrow Diagram Method) and CPM is PDM/CPM (Precedence Diagramming Method).
a) Terminology – Following are the key terms associated with the development and use of networks:
i) Activity – A specific task or set of tasks that have a start and end, and consume resources.
ii) Event – The result of completing one or more activities. Events don’t use resources.
iii) Network – The arrangement of all activities and events in their logical sequence represented by arcs and nodes.
iv) Path – The series of connected activities between any two events in a network.
v) Critical – Activities, events or paths which, if delayed, will delay the completion of the project.
To construct a network the predecessors and successors of each activity must be identified. Activities that start the network will have no predecessor. Activities that end the network will have no successor. Regardless of the technique used, it is a good practice to link the activities with no other predecessor to a START milestone. Those without any successor should be linked to an END milestone. PDM/CPM networks identify the activities as nodes in the network, called the Activity on Node (AON) network. The arrows in between the nodes depict the predecessor/successor relationships among the activities. The ADM/PERT method, on the other hand, uses Activity on Arrow (AOA) networks. Her.
Salma Karina Hayat is Conscious Digital Transformation Leader at Kudos | Empowering SMEs via CRM & Digital Automation | Award-Winning Entrepreneur & Philanthropist | Education & Homelessness Advocate
When listening about building new Ventures, Marketplaces ideas are something very frequent. On this session we will discuss reasons why you should stay away from it :P , by sharing real stories and misconceptions around them. If you still insist to go for it however, you will at least get an idea of the important and critical strategies to optimize for success like Product, Business Development & Marketing, Operations :)
Reflect Festival Limassol May 2024.
Michael Economou is an Entrepreneur, with Business & Technology foundations and a passion for Innovation. He is working with his team to launch a new venture – Exyde, an AI powered booking platform for Activities & Experiences, aspiring to revolutionize the way we travel and experience the world. Michael has extensive entrepreneurial experience as the co-founder of Ideas2life, AtYourService as well as Foody, an online delivery platform and one of the most prominent ventures in Cyprus’ digital landscape, acquired by Delivery Hero group in 2019. This journey & experience marks a vast expertise in building and scaling marketplaces, enhancing everyday life through technology and making meaningful impact on local communities, which is what Michael and his team are pursuing doing once more with Exyde www.goExyde.com
Yagmur Bostanci47 Hackensack Street, East Rutherford, NJ929-22.docxjeffevans62972
Yagmur Bostanci
47 Hackensack Street, East Rutherford, NJ
929-229-8834
[email protected]
EDUCATON
BERKELEY COLLEGE
YORK, UNITED STATES
· Bachelor of Business Management
· Cumulative GPA 3.00
PROFESSIONAL EXPERIENCE
Lincoln House Outreach
303 W 66th St, New York, NY
Nurse
July 2014 – September 2014
· Responsible for the old women in Lincoln House Outreach
· Managing all the payments and organizing listing
· Balancing firm objectives and old women satisfaction
CANDLEWYCK DINNER
East Rutherford, New Jersey, United States
Waitress
· Food delivery
· Fulfill costumer’s wants
· Accounting (Cash, Credit Card, and tax for prices of the food)
TECHNICAL SKILLS
· Phone Settings
· Microsoft Office (Excel, Word, Power point)
· Adobe Photoshop
Overview
1) Overview – The continued discussion of project implementation by covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a project action plan into an operating timetable.” A schedule is important because each project is unique in its own way. The basic process is to identify all tasks and sequential relationships between them, that is, which tasks must precede or succeed others. There are a number of benefits to the creation and use of these networks. Some of them are as follows:
a) It is a consistent framework for planning, scheduling, and controlling the project.
b) It can be used to determine a start and end date for every project task.
c) It identifies so-called critical activities that, if delayed will delay the project completion.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT and CPM are the most commonly used approaches to project scheduling. Both were introduced in the 1950s. PERT has been primarily associated with R&D projects, while CPM with construction projects. Today PERT is not used much since project management software generates CPM style networks. The primary difference between them is that PERT uses probabilistic techniques to determine task durations, while CPM relies on a single duration estimate for each task. Both techniques identify the critical path (tasks that cannot be delayed without delaying the project) and associated float or slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it necessary to change the names of these techniques. According to PMI, PERT is called ADM/PERT (Arrow Diagram Method) and CPM is PDM/CPM (Precedence Diagramming Method).
a) Terminology – Following are the key terms associated with the development and use of networks:
i) Activity – A specific task or set of tasks that have a start and end, and consume resources.
ii) Event – The result of completing one or more activities. Events don’t use resources.
iii) Network – The arrangement of all activities and events in their logical sequence represented by arcs and nodes.
iv) Path – The series of connected activities between any two events in a network.
v) Critical – Activities, events or paths which, if delayed, w.
CPM and PERT are most commonly used methods for project management. There are some similarities and differences between PERT and CPM. PERT can be applied to any field requiring planned, controlled and integrated work efforts to accomplish defined objectives.
Overview1) Overview – The continued discussion of project implem.docxalfred4lewis58146
Overview
1) Overview – The continued discussion of project implementation by covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a project action plan into an operating timetable.” A schedule is important because each project is unique in its own way. The basic process is to identify all tasks and sequential relationships between them, that is, which tasks must precede or succeed others. There are a number of benefits to the creation and use of these networks. Some of them are as follows:
a) It is a consistent framework for planning, scheduling, and controlling the project.
b) It can be used to determine a start and end date for every project task.
c) It identifies so-called critical activities that, if delayed will delay the project completion.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT and CPM are the most commonly used approaches to project scheduling. Both were introduced in the 1950s. PERT has been primarily associated with R&D projects, while CPM with construction projects. Today PERT is not used much since project management software generates CPM style networks. The primary difference between them is that PERT uses probabilistic techniques to determine task durations, while CPM relies on a single duration estimate for each task. Both techniques identify the critical path (tasks that cannot be delayed without delaying the project) and associated float or slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it necessary to change the names of these techniques. According to PMI, PERT is called ADM/PERT (Arrow Diagram Method) and CPM is PDM/CPM (Precedence Diagramming Method).
a) Terminology – Following are the key terms associated with the development and use of networks:
i) Activity – A specific task or set of tasks that have a start and end, and consume resources.
ii) Event – The result of completing one or more activities. Events don’t use resources.
iii) Network – The arrangement of all activities and events in their logical sequence represented by arcs and nodes.
iv) Path – The series of connected activities between any two events in a network.
v) Critical – Activities, events or paths which, if delayed, will delay the completion of the project.
To construct a network the predecessors and successors of each activity must be identified. Activities that start the network will have no predecessor. Activities that end the network will have no successor. Regardless of the technique used, it is a good practice to link the activities with no other predecessor to a START milestone. Those without any successor should be linked to an END milestone. PDM/CPM networks identify the activities as nodes in the network, called the Activity on Node (AON) network. The arrows in between the nodes depict the predecessor/successor relationships among the activities. The ADM/PERT method, on the other hand, uses Activity on Arrow (AOA) networks. Here the nodes represent .
Overview1) Overview – The continued discussion of .docxalfred4lewis58146
Overview
1)
Overview – The continued discussion of project implementation by covering various scheduling techniques.
2) Background – Per the text, “A schedule is the conversion of a project action plan into an operating timetable.” A schedule is important because each project is unique in its own way. The basic process is to identify all tasks and sequential relationships between them, that is, which tasks must precede or succeed others. There are a number of benefits to the creation and use of these networks. Some of them are as follows:
a) It is a consistent framework for planning, scheduling, and controlling the project.
b) It can be used to determine a start and end date for every project task.
c) It identifies so-called critical activities that, if delayed will delay the project completion.
3) Network Techniques: PERT (ADM) and CPM (PDM) – PERT and CPM are the most commonly used approaches to project scheduling. Both were introduced in the 1950s. PERT has been primarily associated with R&D projects, while CPM with construction projects. Today PERT is not used much since project management software generates CPM style networks. The primary difference between them is that PERT uses probabilistic techniques to determine task durations, while CPM relies on a single duration estimate for each task. Both techniques identify the critical path (tasks that cannot be delayed without delaying the project) and associated float or slack in the schedule. In 2005 the Project Management Institute (PMI) deemed it necessary to change the names of these techniques. According to PMI, PERT is called ADM/PERT (Arrow Diagram Method) and CPM is PDM/CPM (Precedence Diagramming Method).
a) Terminology – Following are the key terms associated with the development and use of networks:
i) Activity – A specific task or set of tasks that have a start and end, and consume resources.
ii) Event – The result of completing one or more activities. Events don’t use resources.
iii) Network – The arrangement of all activities and events in their logical sequence represented by arcs and nodes.
iv) Path – The series of connected activities between any two events in a network.
v) Critical – Activities, events or paths which, if delayed, will delay the completion of the project.
To construct a network the predecessors and successors of each activity must be identified. Activities that start the network will have no predecessor. Activities that end the network will have no successor. Regardless of the technique used, it is a good practice to link the activities with no other predecessor to a START milestone. Those without any successor should be linked to an END milestone. PDM/CPM networks identify the activities as nodes in the network, called the Activity on Node (AON) network. The arrows in between the nodes depict the predecessor/successor relationships among the activities. The ADM/PERT method, on the other hand, uses Activity on Arrow (AOA) networks. Her.
Salma Karina Hayat is Conscious Digital Transformation Leader at Kudos | Empowering SMEs via CRM & Digital Automation | Award-Winning Entrepreneur & Philanthropist | Education & Homelessness Advocate
When listening about building new Ventures, Marketplaces ideas are something very frequent. On this session we will discuss reasons why you should stay away from it :P , by sharing real stories and misconceptions around them. If you still insist to go for it however, you will at least get an idea of the important and critical strategies to optimize for success like Product, Business Development & Marketing, Operations :)
Reflect Festival Limassol May 2024.
Michael Economou is an Entrepreneur, with Business & Technology foundations and a passion for Innovation. He is working with his team to launch a new venture – Exyde, an AI powered booking platform for Activities & Experiences, aspiring to revolutionize the way we travel and experience the world. Michael has extensive entrepreneurial experience as the co-founder of Ideas2life, AtYourService as well as Foody, an online delivery platform and one of the most prominent ventures in Cyprus’ digital landscape, acquired by Delivery Hero group in 2019. This journey & experience marks a vast expertise in building and scaling marketplaces, enhancing everyday life through technology and making meaningful impact on local communities, which is what Michael and his team are pursuing doing once more with Exyde www.goExyde.com
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- Get actionable strategies you can use right away to improve your bookings, sales and retention.
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2. 2
Network techniques
Developed in 1950’s
CPM by DuPont for chemical plants (1957)
PERT by Booz, Allen & Hamilton with the U.S.
Navy, for Polaris missile (1958)
Consider precedence relationships and
interdependencies
Each uses a different estimate of activity times
PERT and CPM
3. why networks/CPM/PERT?
Gantt charts don’t explicitly show
task relationships
don’t show impact of delays or
shifting resources well
network models clearly show
interdependencies
4. 4
Is the project on schedule, ahead of schedule,
or behind schedule?
Is the project over or under cost budget?
Are there enough resources available to finish
the project on time?
If the project must be finished in less than the
scheduled amount of time, what is the way to
accomplish this at least cost?
Questions Which May Be
Addressed by PERT & CPM
5. 5
The Six Steps Common to PERT & CPM
Define the project and prepare the work breakdown
structure,
Develop relationships among the activities. (Decide
which activities must precede and which must follow
others.)
Draw the network connecting all of the activities
Assign time and/or cost estimates to each activity
Compute the longest time path through the network.
This is called the critical path
Use the network to help plan, schedule, monitor, and
control the project
6. 6
Terminology
Activity: A specific or set of tasks required by
the project
Event: Outcome of one or more activities
Network: Combination of all activities and
events
Path: Series of connected activities or
between any two events
Critical path: Longest - Any delay would delay
the project
Slack/float: Allowable slippage for a path
7. 7
Activity Relationships
Predecessor – an activity that is required to
start or finish before the next activity(s) can
proceed
Successor – an activity that must start or
finish after the previous activity can finish
Types of relationships are defined from the
predecessor to the successor
8. 8
1
A
B
A & B can occur
concurrently
2
3
Activity Relationships
10. 10
1 4
2
3
A
B E
C
B & C must be done
before E can begin
D
Activity Relationships
11. AOA Project Network for
a House
3
2 0
1
3
1 1
1
1 2 4 6 7
3
5
Lay
foundation
Design
house and
obtain
financing
Order and
receive
materials
Dummy
Finish
work
Select
carpet
Select
paint
Build
house
12. 12
Activities are defined often by beginning &
ending events
Every activity must have unique pair of
beginning & ending events
Otherwise, computer programs get confused
Dummy activities maintain precedence
Consume no time or resources
Dummy Activities
13. 13
Job on Arc Network
Not allowed: no two
jobs can have the
same starting and
ending node!
Need to introduce a
dummy job.
A
B
D
C
A
B
D
C
18. Program Evaluation and
Review Technique (PERT)
PERT is based on the assumption that an
activity’s duration follows a probability
distribution instead of being a single value.
The probabilistic information about the
activities is translated into probabilistic
information about the project.
19. PERT
reflects PROBABILISTIC nature of durations
assumes BETA distribution
same as CPM except THREE duration
estimates
optimistic
most likely
pessimistic
20. PERT Calculation
a = optimistic duration estimate
m = most likely duration estimate
b = pessimistic duration estimate
expected duration:
variance:
Te
a + 4m + b
6
V =
b - a
6
2
21. 21
3 time estimates
Optimistic times (a)
Most-likely time (m)
Pessimistic time (b)
Follow beta distribution
Expected time: t = (a + 4m + b)/6
Variance of times: v = (b - a)2/6
PERT Activity Times
22. 22
Variability of Completion Time for
Noncritical Paths
Variability of times for activities on non-critical
paths must be considered when finding the
probability of finishing in a specified time.
Variation in non-critical activity may cause
change in critical path.
23. 23
Advantages of PERT/CPM
Especially useful when scheduling and controlling
large projects.
Straightforward concept and not mathematically
complex.
Graphical networks aid perception of relationships
among project activities.
Critical path & slack time analyses help pinpoint
activities that need to be closely watched.
Project documentation and graphics point out who is
responsible for various activities.
Applicable to a wide variety of projects.
Useful in monitoring schedules and costs.
24. 24
Questions Answered by CPM & PERT
Completion date?
On Schedule?
Within Budget?
Critical Activities?
How can the project be finished early at the
least cost?
25. 25
Assumes clearly defined, independent, &
stable activities
Specified precedence relationships
Activity times (PERT) follow beta distribution
Subjective time estimates
Over-emphasis on critical path
Limitations of PERT/CPM
26. Example 2. CPM with Three Activity Time
Estimates
Ta s k
Im m e d ia t e
P re d e c e s o rs O p t im is t ic M o s t L ik e ly P e s s im is t ic
A N o n e 3 6 1 5
B N o n e 2 4 1 4
C A 6 1 2 3 0
D A 2 5 8
E C 5 1 1 1 7
F D 3 6 1 5
G B 3 9 2 7
H E , F 1 4 7
I G , H 4 1 9 2 8
27. Example 2. Expected Time
Calculations
T a s k
Im m e d i a t e
P re d e c e s o rs
E x p e c t e d
T i m e
A N o n e 7
B N o n e 5 . 3 3 3
C A 1 4
D A 5
E C 1 1
F D 7
G B 1 1
H E , F 4
I G , H 1 8
28. Example 2. Probability Exercise
What is the probability of finishing this project in
less than 53 days?
p(t < D)
TE = 54
Z =
D - TE
cp
2
t
D=53
29. Activity variance, = (
Pessim. - Optim.
6
)
2 2
Ta s k O p tim is tic M o s t L ik e ly P e s s im is tic V a ria n c e
A 3 6 1 5 4
B 2 4 1 4
C 6 1 2 3 0 1 6
D 2 5 8
E 5 1 1 1 7 4
F 3 6 1 5
G 3 9 2 7
H 1 4 7 1
I 4 1 9 2 8 1 6
(Sum the variance along the critical path.) 2
= 41
30. p(Z < -0.156) = 0.5 - 0.0636 = 0.436, or 43.6 %
Z =
D - T
=
53- 54
41
= -.156
E
cp
2
TE = 54
p(t < D)
t
D=53