Project management involves three key phases: planning, scheduling, and controlling. Planning involves setting objectives, identifying activities, and estimating resources and costs. Scheduling determines the start and finish times of activities using techniques like CPM and PERT to identify the critical path. Controlling monitors progress against the plan and allows for revisions if needed. Effective project management requires thorough planning, scheduling of activities and resources, and ongoing controlling to ensure projects are completed on time and on budget.
The presentation helps in understanding the influence of JICA (Financing authority) on the tender guidelines on DMRC. The presentation further provides a basic understanding of the Tender structure of DRMC
The presentation helps in understanding the influence of JICA (Financing authority) on the tender guidelines on DMRC. The presentation further provides a basic understanding of the Tender structure of DRMC
WHAT DOES CONSTRUCTION PROJECT MANAGEMENT (CPM) MEAN?
THE UNIQUE FEATURES OF CONSTRUCTION IN INDIA
THE DIFFERENT TYPES OF CONSTRUCTION PROJECTS
FEATURES OF A CONSTRUCTION PROJECT
PHASES OF PROJECT
AGENCIES INVOLVED AND THEIR METHODS OF EXECUTION
I am Continuously seeking to improve my competencies and skills to provide first class professional Project Management training courses; and develop my scope experience in Project Management functions.
I am confident that my innovative and results-focused approach would make significant contribution to the continued success of your organization.
For more information do not hesitate to contact me.
Ahmad H. Maharma - PMP®
Ramallah, Palestine
Phone: + (972) (2) 2968644
Mobile: + (972) (599) 001155
E-Mail: ahmad.maharma@gmail.com
Did you know that the .NET compiler turns our async methods into classes? And that .NET adds a try/catch block to each of these classes, potentially hiding thrown exceptions? It's true!
In this session, we will learn how to best use async/await in C# by analyzing how .NET compiles our async code.
Join me as we take an existing app and optimize its async code together, showing off performance gains, better exception handling, improved run-time speed, smaller app size and more using the latest tools in C#12 + .NET 8!
CONSTRUCTION PROJECT PLANING
WHAT IS CONSTRUCTION PLANNING
5 STEPS TO THE PERFECT CONSTRUCTION PLANNING PROCESS
PRE TENDER PLANNING
PRE CONTRACT PLANNING
ROLE OF CLIENT
ROLE OF CONTRACTOR
PROCESS OF DEVELOPMENT OF PLANS
PLANNING A PROJECT
INTRODUCTION TO SCHEDULING
WORK BREAKDOWN STRUCTURE
BAR CHARTS (GANTT CHARTS)
NETWORK TECHNIQUES
ACTIVITY-ON-ARROW NETWORK
DUMMY ACTIVITIES
DANGLING ACTIVITY
CYCLE IN NETWORK
PRECEDENCE NETWORKS
TIME ESTIMATES
MILESTONES IN PROJECT
TIME ANALYSIS
CRITICAL PATH, SLACK AND FLOAT
NETWORK ANALYSIS AND BAR CHART
WHAT IS NETWORK
PERT / CPM Techniques
TERMS USED IN A NETWORK
RULES OF NETWORK CONSTRUCTION
NETWORK SYMBOLS
WHAT DOES CONSTRUCTION PROJECT MANAGEMENT (CPM) MEAN?
THE UNIQUE FEATURES OF CONSTRUCTION IN INDIA
THE DIFFERENT TYPES OF CONSTRUCTION PROJECTS
FEATURES OF A CONSTRUCTION PROJECT
PHASES OF PROJECT
AGENCIES INVOLVED AND THEIR METHODS OF EXECUTION
I am Continuously seeking to improve my competencies and skills to provide first class professional Project Management training courses; and develop my scope experience in Project Management functions.
I am confident that my innovative and results-focused approach would make significant contribution to the continued success of your organization.
For more information do not hesitate to contact me.
Ahmad H. Maharma - PMP®
Ramallah, Palestine
Phone: + (972) (2) 2968644
Mobile: + (972) (599) 001155
E-Mail: ahmad.maharma@gmail.com
Did you know that the .NET compiler turns our async methods into classes? And that .NET adds a try/catch block to each of these classes, potentially hiding thrown exceptions? It's true!
In this session, we will learn how to best use async/await in C# by analyzing how .NET compiles our async code.
Join me as we take an existing app and optimize its async code together, showing off performance gains, better exception handling, improved run-time speed, smaller app size and more using the latest tools in C#12 + .NET 8!
CONSTRUCTION PROJECT PLANING
WHAT IS CONSTRUCTION PLANNING
5 STEPS TO THE PERFECT CONSTRUCTION PLANNING PROCESS
PRE TENDER PLANNING
PRE CONTRACT PLANNING
ROLE OF CLIENT
ROLE OF CONTRACTOR
PROCESS OF DEVELOPMENT OF PLANS
PLANNING A PROJECT
INTRODUCTION TO SCHEDULING
WORK BREAKDOWN STRUCTURE
BAR CHARTS (GANTT CHARTS)
NETWORK TECHNIQUES
ACTIVITY-ON-ARROW NETWORK
DUMMY ACTIVITIES
DANGLING ACTIVITY
CYCLE IN NETWORK
PRECEDENCE NETWORKS
TIME ESTIMATES
MILESTONES IN PROJECT
TIME ANALYSIS
CRITICAL PATH, SLACK AND FLOAT
NETWORK ANALYSIS AND BAR CHART
WHAT IS NETWORK
PERT / CPM Techniques
TERMS USED IN A NETWORK
RULES OF NETWORK CONSTRUCTION
NETWORK SYMBOLS
A project is an interrelated set of activities that has definite starting and ending points and that result in a unique product
or service
• Cuts across organizational lines - they need varied skills of different profession
• Uncertainties like new technology & external environment can change the character of the project
• Personnel, materials, facilities etc. are temporarily assembled to accomplish a goal within a specified time frame and then disbanded
• Upon finish, a project releases lot of resources which were engaged in execution of the project
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
4. Planning
The overall goal of project planning is to establish a
pragmatic strategy for controlling, tracking, and
monitoring a complex technical project.
Or,
A Plan is the strategy for the successful
completion of the project. It's a description of the
project steps that produce increasing maturity of
the products or processes produced by the project.
7. Project management generally consists of three phases.
Planning:
Planning involves setting the objectives of the project. Identifying
various activities to be performed and determining the requirement of
resources such as men, materials, machines, etc.
The cost and time for all the activities are estimated, and a network diagram is
developed showing sequential interrelationships (predecessor and successor)
between various activities during the planning stage.
Scheduling:
Basd on the time estimates, the start and finish times for each activity
are worked out by applying forward and backward pass techniques, critical
path is identified, along with the slack and float for the non-critical paths.
Controlling:
Controlling refers to analyzing and evaluating the actual progress
against the plan. Reallocation of resources, crashing and review of projects
with periodical reports are carried out.
8. Management of Projects
1. Planning - goal setting, defining the
project, team organization
2. Scheduling - relates people, money,
and supplies to specific activities and
activities to each other
3. Controlling - monitors resources,
costs, quality, and budgets; revises
plans and shifts resources to meet
time and cost demands
17. GANTT Chart
o A GANTT chart is a type of bar chart that illustrates a
project schedule.
o After the PERT/CPM analysis is completed, the
following phase is to construct the GANTT chart
and then to re allocate resources and re-schedule if
necessary.
o GANTT charts have become a common technique for
representing the phases and activities of a project
work breakdown structure.
o It was introduced by Henry Gantt around 1910 -1915.
18. 18
Gantt Charts
• Gantt charts are used as a tool to monitor and
control the project progress.
• A Gantt Chart is a graphical presentation that
displays activities as follows:
– Time is measured on the horizontal axis. A horizontal
bar is drawn proportionately to an activity’ s expected
completion time.
– Each activity is listed on the vertical axis.
• In an earliest time Gantt chart each bar begins
and ends at the earliest start/finish the activity
can take place.
19. 19
• Gantt chart can be used as a visual aid for
tracking the progress of project activities.
• Appropriate percentage of a bar is shaded to
document the completed work.
• The manager can easily see if the project is
progressing on schedule (with respect to the
earliest possible completion
times).
Gantt Charts-
Monitoring Project
Progress
20. 20
The Purpose of a Gantt Charts
• To illustrate the relationship between project
activities & time.
• To show the multiple project activities on one chart
• To provide a simple & easy to understand
representation of project scheduling
-
21. 21
The Purpose of a Gantt Charts
• Determine Project start date and deadline.
• Gather all information surrounding the list of activities within
project - the Work Breakdown Structure may be useful for this
• Determine how long each activity will take
• Evaluate what activities are dependent on others
• Create Graph shell including the timeline and list of activities.
• Using either Forward Scheduling or Backward Scheduling,
• Begin to add bars ensuring to include dependencies and the ful
• duration for each activity.
22. 22
Steps for Gantt Charts
• Determine Project start date and deadline.
• Gather all information surrounding the list of activities within
project - the Work Breakdown Structure may be useful for this
• Determine how long each activity will take
• Evaluate what activities are dependent on others
• Create Graph shell including the timeline and list of activities.
• Using either Forward Scheduling or Backward Scheduling,
• Begin to add bars ensuring to include dependencies and the ful
• duration for each activity.
23. Gantt Chart
J F M A M J J
Time Period
Activity
Design
Build
Test
J F M A M J J
Time Period
Activity
Design
Build
Test
24. 24
• Advantages.
– Easy to construct
– Gives earliest completion date.
– Provides a schedule of earliest possible start and finish
times of activities.
• Disadvantages
– Gives only one possible schedule (earliest).
– Does not show whether the project is behind schedule.
– Does not demonstrate the effects of delays in any one
activity on the
start of another activity, thus on the project completion time.
Gantt Charts –
Advantages and Disadvantages
25. Gantt Chart
o Characteristics:
• The bar in each row identifies the corresponding task
• The horizontal position of the bar identifies start and end times of the
task
• Bar length represents the duration of the task
• Task durations can be compared easily
• Good for allocating resources and re-scheduling
• Precedence relationships can be represented using arrows
• Critical activities are usually highlighted
• Slack times are represented using bars with doted lines
• The bar of each activity begins at the activity earliest start time (ES)
• The bar of each activity ends at the activity latest finish time (LF).
26. Gantt Chart
o The steps to construct a GANTT chart from the
information obtained by PERT/CPM are:
1. Schedule the critical tasks in the correct position.
2. Place the time windows in which the non-critical
tasks can be scheduled.
3. Schedule the non-critical tasks according to their
earliest starting times.
4. Indicate precedence relationships between tasks.
32. Construct GANTT chart
o Resource Smoothing is a technique used to
re-allocate resources and re-schedule activities.
o In resource smoothing, non-critical tasks are re-
scheduled within their time window.
o Staff Utilization:(duration of activity x staff
requiredfor each activity,all added together)/
(maximum staff required x duration of project)
38. Construct GANTT chart
o The obvious way to reduce the overall project
duration, it is by reducing the duration of the critical
activities.
o Crashing Critical Activities refers to reducing the
duration of a critical activity by allocating more
resources to it.
o The risk is that crashing activities may actually
reduce productivity and increase costs.
40. Construct GANTT chart
Task Prec
eden
ce
Duration ES EF LS LF Slack
Time
Critical
Task
A 2 0 2 17 19 17 No
B 4 0 4 2 6 2 No
C 3 0 3 0 3 0 Yes
D C 5 3 8 3 8 0 Yes
E B 3 4 7 6 9 2 No
F D 5 8 13 8 13 0 Yes
G D,E 7 8 15 9 16 1 No
H F 3 13 16 13 16 0 Yes
I G,H 3 16 19 16 19 0 Yes
45. PERT & CPM
• Network techniques
• Developed in 1950’s
• CPM by DuPont for chemical plants
• PERT by U.S. Navy for Polaris
missile
• Consider precedence relationships
& interdependencies
• Each uses a different estimate of
activity times
46. • Completion date?
• On schedule? Within budget?
• Probability of completing by ...?
• Critical activities?
• Enough resources available?
• How can the project be finished early at
the least cost?
Questions Answered by
PERT & CPM
48. Benefits
of PERT/CPM
• Useful at many stages of project
management
• Mathematically simple
• Use graphical displays
• Give critical path & slack time
• Provide project documentation
• Useful in monitoring costs
49. Limitations
of PERT/CPM
• Clearly defined, independent, &
stable activities
• Specified precedence
relationships
• Activity times (PERT) follow
beta distribution
• Subjective time estimates
• Over emphasis on critical path
50. Difference between
CPM & PERT
CPM PERT
• CPM works with fixed
deterministic time
• PERT works with probabilistic
time
• CPM is useful for repetitive
and non complex projects with
a certain degree of time
estimates.
• PERT is useful for non
repetitive and complex projects
with uncertain time estimates.
• CPM includes time-cost trade
off.
• PERT is restricted to time
variable.
• CPM- for construction projects. • PERT- used for R&D
programs.
51. Activity on Node (AoN)
2
4? Years
Enroll
Receive
Certificate
Project: Obtain a college degree (B.S.)
1 month
Attend class,
study etc.
1
1 day
3
52. Activity on Arc (AoA)
4,5 ?
Years
Enroll
Receive
Certificate
Project: Obtain a college degree (B.S.)
1 month
Attend
class,
study,
etc.
1
1 day
2 3 4
54. A Comparison of AON and
AOA Network Conventions
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
A comes before
B, which comes
before C
(a) A B C
B
A C
A and B must both
be completed
before C can start
(b)
A
C
C
B
A
B
B and C cannot
begin until A is
completed
(c)
B
A
C
A
B
C
Figure 3.5
55. A Comparison of AON and
AOA Network Conventions
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
C and D cannot
begin until both
A and B are
completed
(d)
A
B
C
D B
A C
D
C cannot begin until
both A and B are
completed; D
cannot begin until B
is completed. A
dummy activity is
introduced in AOA
(e)
C
A
B D
Dummy activity
A
B
C
D
Figure 3.5
56. A Comparison of AON and
AOA Network Conventions
Activity on Activity Activity on
Node (AON) Meaning Arrow (AOA)
B and C cannot
begin until A is
completed. D
cannot begin until
both B and C are
completed. A
dummy activity is
again introduced
in AOA.
(f)
A
C
D
B A B
C
D
Dummy
activity
Figure 3.5
57. AON Example
Activity Description
Immediate
Predecessors
A Build internal components —
B Modify roof and floor —
C Construct collection stack A
D Pour concrete and install frame A, B
E Build high-temperature burner C
F Install pollution control system C
G Install air pollution device D, E
H Inspect and test F, G
Milwaukee Paper Manufacturing's
Activities and Predecessors
Table 3.1
58. AON Network for
Milwaukee Paper
A
Start
B
Start Activity
Activity A
(Build Internal Components)
Activity B
(Modify Roof and Floor)
Figure 3.6
59. AON Network for
Milwaukee Paper
Figure 3.7
C
D
A
Start
B
Activity A Precedes Activity C
Activities A and B Precede
Activity D
60. AON Network for
Milwaukee Paper
G
E
F
H
C
A
Start
D
B
Arrows Show Precedence
Relationships
Figure 3.8
62. Determining the
Project Schedule
Perform a Critical Path Analysis
The critical path is the longest path
through the network
The critical path is the shortest time in
which the project can be completed
Any delay in critical path activities delays
the project
Critical path activities have no slack time
63. Network Example
You’re a project manager for Bechtel.
Construct the network.
Activity Predecessors
A --
B A
C A
D B
E B
F C
G D
H E, F
66. Critical Path Analysis
• Provides activity information
• Earliest (ES) & latest (LS) start
• Earliest (EF) & latest (LF) finish
• Slack (S): Allowable delay
• Identifies critical path
• Longest path in network
• Shortest time project can be
completed
• Any delay on activities delays project
• Activities have 0 slack
67. Critical Path
Analysis Example
Event
ID
Pred. Description Time
(Wks)
A None Prepare Site 1
B A Pour fdn. & frame 6
C A Buy shrubs etc. 3
D B Roof 2
E D Do interior work 3
F C Landscape 4
G E,F Move In 1
70. Earliest Start & Finish
Steps
• Begin at starting event & work forward
• ES = 0 for starting activities
• ES is earliest start
• EF = ES + Activity time
• EF is earliest finish
• ES = Maximum EF of all predecessors for
non-starting activities
71. Activity ES EF LS LF Slack
A 0 1
B
C
D
E
F
Activity A
Earliest Start Solution
For starting activities, ES = 0.
A
E
D
B
C F
G
1
6 2 3
1
4
3
72. Activity ES EF LS LF Slack
A 0 1
B 1 7
C 1 4
D 7 9
E 9 12
F 4 8
G 12 13
Earliest Start Solution
A
E
D
B
C F
G
1
6 2 3
1
4
3
73. Latest Start & Finish
Steps
• Begin at ending event & work backward
• LF = Maximum EF for ending activities
• LF is latest finish; EF is earliest finish
• LS = LF - Activity time
• LS is latest start
• LF = Minimum LS of all successors for
non-ending activities
74. Activity ES EF LS LF Slack
A 0 1
B 1 7
C 1 4
D 7 9
E 9 12
F 4 8
G 12 13 13
Earliest Start Solution
A
E
D
B
C F
G
1
6 2 3
1
4
3
75. Activity ES EF LS LF Slack
A 0 1 0 1
B 1 7 1 7
C 1 4 4 7
D 7 9 7 9
E 9 12 9 12
F 4 8 7 12
G 12 13 12 13
Latest Finish Solution
A
E
D
B
C F
G
1
6 2 3
1
4
3
76. Activity ES EF LS LF Slack
A 0 1 0 1 0
B 1 7 1 7 0
C 1 4 5 8 4
D 7 9 7 9 0
E 9 12 9 12 0
F 4 8 8 12 4
G 12 13 12 13 0
Compute Slack
77. Determining the
Project Schedule
Perform a Critical Path Analysis
Activity Description Time (weeks)
A Build internal components 2
B Modify roof and floor 3
C Construct collection stack A 2
D Pour concrete and install frame A,B 4
E Build high-temperature burner C 4
F Install pollution control system C 3
G Install air pollution device D,E 5
H Inspect and test F,G 2
Total Time (weeks) 25
Table 3.2
78. Determining the
Project Schedule
Perform a Critical Path Analysis
Figure 3.10
A
Activity Name or
Symbol
Earliest
Start ES
Earliest
Finish
EF
Latest
Start
LS Latest
Finish
LF
Activity Duration
2
81. E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
D
4
3 7
C
2
2 4
ES/EF Network for
Milwaukee Paper
B
3
0 3
Start
0
0
0
A
2
2
0
Figure 3.11
82. Backward Pass
Begin with the last event and work backwards
Latest Finish Time Rule:
If an activity is an immediate predecessor for just a single
activity, its LF equals the LS of the activity that immediately
follows it
If an activity is an immediate predecessor to more than one
activity, its LF is the minimum of all LS values of all activities
that immediately follow it
LF = Min {LS of all immediate following activities}
83. Backward Pass
Begin with the last event and work backwards
Latest Start Time Rule:
The latest start time (LS) of an activity is the difference of its
latest finish time (LF) and its activity time
LS = LF – Activity time
84. LS/LF Times for
Milwaukee Paper
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
85. Computing Slack Time
Earliest Earliest Latest Latest On
Start Finish Start Finish Slack Critical
Activity ES EF LS LF LS – ES Path
A 0 2 0 2 0 Yes
B 0 3 1 4 1 No
C 2 4 2 4 0 Yes
D 3 7 4 8 1 No
E 4 8 4 8 0 Yes
F 4 7 10 13 6 No
G 8 13 8 13 0 Yes
H 13 15 13 15 0 Yes
Table 3.3
86. Critical Path for
Milwaukee Paper
E
4
F
3
G
5
H
2
4 8 13 15
4
8 13
7
13 15
10 13
8 13
4 8
D
4
3 7
C
2
2 4
B
3
0 3
Start
0
0
0
A
2
2
0
4
2
8
4
2
0
4
1
0
0
87. LS – LF Gantt Chart
for Milwaukee Paper
A Build internal
components
B Modify roof and floor
C Construct collection
stack
D Pour concrete and
install frame
E Build high-temperature
burner
F Install pollution control
system
G Install air pollution
device
H Inspect and test
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
88. CPM assumes we know a fixed time
estimate for each activity and there is
no variability in activity times
PERT uses a probability distribution for
activity times to allow for variability
Variability in Activity
Times
89. Three time estimates are required
Optimistic time (a) – if everything goes
according to plan
Pessimistic time (b) – assuming very
unfavorable conditions
Most likely time (m) – most realistic
estimate
Variability in Activity
Times
90. Estimate follows beta distribution
Variability in Activity
Times
Expected time:
Variance of times:
t = (a + 4m + b)/6
v = [(b – a)/6]2
91. Estimate follows beta distribution
Variability in Activity
Times
Expected time:
Variance of times:
t = (a + 4m + b)/6
v = [(b − a)/6]2
Probability of
1 in 100 of > b
occurring
Probability of
1 in 100 of
< a occurring
Probability
Optimistic
Time (a)
Most Likely Time
(m)
Pessimistic Time
(b)
Activity
Time
Figure 3.12
92. Computing Variance
Most Expected
Optimistic Likely Pessimistic Time Variance
Activity a m b t = (a + 4m + b)/6 [(b – a)/6]2
A 1 2 3 2 .11
B 2 3 4 3 .11
C 1 2 3 2 .11
D 2 4 6 4 .44
E 1 4 7 4 1.00
F 1 2 9 3 1.78
G 3 4 11 5 1.78
H 1 2 3 2 .11
Table 3.4
93. Probability of Project
Completion
Project variance is computed by
summing the variances of critical
activities
s2 = Project variance
= (variances of activities
on critical path)
p
94. Probability of Project
Completion
Project variance is computed by
summing the variances of critical
activities
Project variance
s2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11
Project standard deviation
sp = Project variance
= 3.11 = 1.76 weeks
p
95. Probability of Project
Completion
PERT makes two more assumptions:
Total project completion times follow a
normal probability distribution
Activity times are statistically independent
97. Probability of Project
Completion
What is the probability this project can be
completed on or before the 16 week
deadline?
Z= – /sp
= (16 wks – 15 wks)/1.76
= 0.57
due expected date
date of completion
Where Z is the number of standard
deviations the due date or target date lies
from the mean or expected date
98. Variability of Completion
Time for Noncritical Paths
Variability of times for activities on
noncritical paths must be considered
when finding the probability of
finishing in a specified time
Variation in noncritical activity may
cause change in critical path
99. Trade-Offs And Project
Crashing
The project is behind schedule
The completion time has been
moved forward
It is not uncommon to face the
following situations:
Shortening the duration of the
project is called project crashing
100.
101.
102. An R & D project has a list of tasks to be performed whose time estimates are
given in the Table 8.11, as follows.
Example
a. Draw the project network.
b. Find the critical path.
c. Find the probability that the project is completed in 19 days. If the
probability is less that 20%, find the probability of completing it in 24 days.
103. calculate the time earliest, TE and
time Latest TL for all the activities.
Construct a network diagram:
From the network diagram Figure 8.24, the critical path is identified as
1-4, 4-6, 6-7, with a project duration of 22 days.
104.
105. The probability of completing the project within 19 days is given by, P (Z< Z0)
To find Z0 ,
we know, P (Z <Z Network Model 0) = 0.5 – z (1.3416) (from normal tables, z (1.3416) = 0.4099)
= 0.5 – 0.4099
= 0.0901
= 9.01% Thus, the probability of completing the R & D project in 19 days is 9.01%.
Since the probability of completing the project in 19 days is less than 20% As in
question, we find the probability of completing it in 24 days.
106. Project Crashing
• Projects will sometimes have deadlines that are
impossible to meet using normal procedures
• By using exceptional methods it may be possible
to finish the project in less time than normally
required
• However, this usually increases the cost of the
project
• Reducing a project’s completion time is called
crashing
Crash cost/Time period =
Crash cost – Normal cost
Normal time – Crash time
107. Time-Cost Models
1. Identify the critical path
2. Find cost per day to expedite each node on
critical path.
3. For cheapest node to expedite, reduce it as
much as possible, or until critical path
changes.
4. Repeat 1-3 until no feasible savings exist.
108. Time-Cost Example
• ABC is critical path=30
Crash cost Crash
per week wks avail
A 500 2
B 800 3
C 5,000 2
D 1,100 2
C 10
B 10
A 10
D 8
Cheapest way to gain 1
Week is to cut A
109. Time-Cost Example
• ABC is critical path=29
Crash cost Crash
per week wks avail
A 500 1
B 800 3
C 5,000 2
D 1,100 2
C 10
B 10
A 9
D 8
Cheapest way to gain 1 wk
Still is to cut A
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
110. Time-Cost Example
• ABC is critical path=28
Crash cost Crash
per week wks avail
A 500 0
B 800 3
C 5,000 2
D 1,100 2
C 10
B 10
A 8
D 8
Cheapest way to gain 1 wk
is to cut B
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
2 500 1,000
111. Time-Cost Example
• ABC is critical path=27
Crash cost Crash
per week wks avail
A 500 0
B 800 2
C 5,000 2
D 1,100 2
C 10
B 9
A 8
D 8
Cheapest way to gain 1 wk
Still is to cut B
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
2 500 1,000
3 800 1,800
112. Time-Cost Example
• Critical paths=26 ADC & ABC
Crash cost Crash
per week wks avail
A 500 0
B 800 1
C 5,000 2
D 1,100 2
C 10
B 8
A 8
D 8
To gain 1 wk, cut B and D,
Or cut C
Cut B&D = $1,900
Cut C = $5,000
So cut B&D
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
2 500 1,000
3 800 1,800
4 800 2,600
113. Time-Cost Example
• Critical paths=25 ADC & ABC
Crash cost Crash
per week wks avail
A 500 0
B 800 0
C 5,000 2
D 1,100 1
C 10
B 7
A 8
D 7
Can’t cut B any more.
Only way is to cut C
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
2 500 1,000
3 800 1,800
4 800 2,600
5 1,900 4,500
114. Time-Cost Example
• Critical paths=24 ADC & ABC
Crash cost Crash
per week wks avail
A 500 0
B 800 0
C 5,000 1
D 1,100 1
C 9
B 7
A 8
D 7
Only way is to cut C
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
2 500 1,000
3 800 1,800
4 800 2,600
5 1,900 4,500
6 5,000 9,500
115. Time-Cost Example
• Critical paths=23 ADC & ABC
Crash cost Crash
per week wks avail
A 500 0
B 800 0
C 5,000 0
D 1,100 1
C 8
B 7
A 8
D 7
No remaining possibilities to
reduce project length
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
2 500 1,000
3 800 1,800
4 800 2,600
5 1,900 4,500
6 5,000 9,500
7 5,000 14,500
116. Time-Cost Example
C 8
B 7
A 8
D 7
No remaining possibilities to
reduce project length
Wks Incremental Total
Gained Crash $ Crash $
1 500 500
2 500 1,000
3 800 1,800
4 800 2,600
5 1,900 4,500
6 5,000 9,500
7 5,000 14,500
• Now we know how much it
costs us to save any
number of days
• Customer says he will pay
$2,000 per wks saved.
• Only reduce 5 wkss.
• We get $10,000 from
customer, but pay $4,500 in
expediting costs
• Increased profits = $5,500