The document discusses Monte Carlo simulation methods. It begins by defining key terms like systems, models, simulation, random numbers, and Monte Carlo simulation. It then provides more details on Monte Carlo simulations, explaining that they are used to predict outcomes when random variables are present by running the model repeatedly with different random variable values and averaging the results. Several examples are given of fields that use Monte Carlo simulations. The document concludes by outlining the typical steps involved in a Monte Carlo simulation.
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
this ppt is helpful for BBA/B.tech//MBA/M.tech students.
the ppt is on simulation topic...its covers -
Meaning
Advantages & Disadvantages
Uses
Process
Monte Carlo SImulation
Advantages & Disadvantages
Its example
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
this ppt is helpful for BBA/B.tech//MBA/M.tech students.
the ppt is on simulation topic...its covers -
Meaning
Advantages & Disadvantages
Uses
Process
Monte Carlo SImulation
Advantages & Disadvantages
Its example
This ppt will explain you the Defintion ,detailed explanation of phases with necessory diagrams, Applications ,Limitations and scope of Operations Research
production and operations management(POM) Complete note kabul university
The Introduction to POM, Scope, Role, and Objectives of POM, Operations Mgt. – Concept; Functions
Product Design and its characteristics;
Product Development Process, Product Development Techniques.
This presentation explains about the Operations Management concept Reorder point, different cases with examples, fixed order interval model, single period model etc.
Interventions required to meet business objectives from Forecasting Methods,
Quantitative & Qualitative Methods,
Forecast Accuracy , Error Reduction to
CPFR
This ppt will explain you the Defintion ,detailed explanation of phases with necessory diagrams, Applications ,Limitations and scope of Operations Research
production and operations management(POM) Complete note kabul university
The Introduction to POM, Scope, Role, and Objectives of POM, Operations Mgt. – Concept; Functions
Product Design and its characteristics;
Product Development Process, Product Development Techniques.
This presentation explains about the Operations Management concept Reorder point, different cases with examples, fixed order interval model, single period model etc.
Interventions required to meet business objectives from Forecasting Methods,
Quantitative & Qualitative Methods,
Forecast Accuracy , Error Reduction to
CPFR
Statistical simulation technique that provides approximate solution to problems expressed mathematically.
It utilize the sequence of random number to perform the simulation.
presentation of simulation methods using monte carlo and an explanation of simulation methods in production in companies, this presentation is suitable for students and lecturers in the department of production management and marketing, industrial engineering etc.
Using Monte Carlo Simulation in Project Estimates by Akram Najjar
The PMI Lebanon is glad to announce that Akram Najjar is the speaker for the a lecture titled “Using Monte Carlo Simulation in Project Estimates” delivered on Thursday, 28 July 2016
Lecture Outline
* Why are single point estimates unreliable and what is the alternative?
* What are distributions and how do we extract random samples from them (using Excel)? Two costing examples.
* How to setup a Monte Carlo Simulation model in a spreadsheet?
* Two PM examples (in detail)
* How to statistically analyze the thousands of runs to reach reliable estimates?
Lecture Objectives
* A Project Manager usually knows how certain parameters (such as duration, resource rates or quantities) behave. However, the PM can almost never define reliable single point estimates for these parameters. The result: many projects fail due to unreliable estimates. The alternative? The PM has to use his/her knowledge of how specific parameters behave statistically. For example, the PM knows that a specific task’s duration is distributed according to the bell shaped curve OR that another is uniformly distributed (flat variation), or triangular, or Beta-PERT, etc. The PM can then use Monte Carlo Simulation (MCS) to arrive at statistically significant and robust results. Monte Carlo Simulation (MCS) is a technique that relies on two processes. Process 1 aims at developing a spreadsheet model that calculates the critical path or the total cost, etc. The calculation is setup in a single row (or Run). This row is then duplicated a large number of times (thousands). Process 2 aims at inserting Excel functions in each of the parameters (durations, costs). In each row (or Run), such functions will provide a sample drawn from a statistical distribution that properly describes the behavior of that parameter. For example, a specific duration follows a Normal (Bell) distribution with an Average A and a Standard Deviation S. The model will then generate for each run and for that duration a different value that conforms with the bell shaped curve as defined (A and S). Each of these thousands of runs will provide the PM with a different “simulation” of the duration or the total cost, etc. By statistically analyzing the thousands of results, the PM can arrive at a robust and reliable estimate. Proprietary Add On’s for Monte Carlo Simulation in Microsoft Project are available. However, it is easy, free and more flexible to use native Microsoft functions to carry out the full simulation. The talk covered all the steps needed for such simulations giving several examples
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2. System: The physical process of interest
Model: Mathematical representation of the system
◦ Models are a fundamental tool of science, engineering, business,
etc.
◦ Models always have limits of credibility
Simulation: A type of model where the computer is used to
imitate the behavior of the system
Monte Carlo simulation: Simulation that makes use of
internally generated (pseudo) random numbers
Random Number:Random numbers are numbers that occur in a
sequence such that two conditions are met: (1) the values are
uniformly distributed over a defined interval or set, and (2) it is
impossible to predict future values based on past or present
ones.
2
3. 3
Focus of course
System
Experiment w/
actual system
Experiment w/
model of system
Physical
Model
Mathematical
Model
Analytical
Model
Simulation
Model
4. “The Monte Carlo method is a numerical solution to a problem
that models objects interacting with other objects .
A Monte Carlo simulation is a model used to predict the
probability of different outcomes when the intervention of
random variables is present.
Monte Carlo simulations help to explain the impact of risk and
uncertainty in prediction and forecasting models.
A variety of fields utilize Monte Carlo simulations, including
finance, engineering, supply chain, and science.
The basis of a Monte Carlo simulation involves assigning
multiple values to an uncertain variable to achieve multiple
results and then to average the results to obtain an estimate.
It represents an attempt to model nature through direct
simulation of the essential dynamics of the system in question.
In this sense the Monte Carlo method is essentially simple in its
approach.
4
5. Business and finance are plagued by random
variables, Monte Carlo simulations have a vast
array of potential applications in these fields.
Monte Carlo Method:
A Monte Carlo simulation takes the variable that
has uncertainty and assigns it a random value.
The model is then run and a result is provided.
This process is repeated again and again while
assigning the variable in question with many
different values.
Once the simulation is complete, the results are
averaged together to provide an estimate.
5
6. let’s consider a simple system with simple
inputs:
6
• As A, B, C and D are always the same, the output will
always be the same and it can be easily calculated
• Imagine that input A has a range of possible values –
the output will also be variable. And when there are
many more possible inputs and all of them have a range
of possible values, the output is not that simple to
calculate.
• That’s where you need to use Monte Carlo simulation.
7. Steps in monte carlo simulation:
Step 1:Clearly define the problem.
Step 2:Construct the appropriate model.
Step 3:Prepare the model for
experimentation.
Step 4:Using step 1 to 3,experiment with the
model.
Step 5:Summarise and examine the results
obtained in step 4.
Step 5:Evaluate the results of the simulation.
7
8. A manufacturing company keeps stock of a special product.
Previous experience indicates the daily demand as given
below
8
Daily
demand
5 10 15 20 25 30
probability 0.01 0.20 0.15 0.50 0.12 0.02
Simulate the demand for the next 10 days. Also find the daily
average demand for that product on the basis of simulated data.
Consider the following random numbers:
82,96,18,96,20,84,56,11,52,03
9. Solution: Step 1:Generate tag values
9
Daily demands Probability Cumulative
probability
Tag
values(Random
num range)
5 0.01 0.01 00-00
10 0.20 0.21 01-20
15 0.15 0.36 21-35
20 0.50 0.86 36-85
25 0.12 0.98 86-97
30 0.02 1.00 98-99
Step 2: Simulate for 10 days
Days Random num Daily demand
1 82 20
2 96 25
3 18 10
4 96 25
5 20 10
6 84 20
7 56 20
8 11 10
9 52 20
10 03 10
Average demand=(20+25+10+25+10+20+20+10+20+10)/10
=170/10=17 units/day
10. 2)A tourist car operator finds that during the past few months the
cars use has varied so much that the cost of maintaining the car
varied considerably. During the past 200 days the demand for the
car fluctuated as below
10
Trips per week Frequency
0 16
1 24
2 30
3 60
4 40
5 30
Using random numbers 82,96,18,96,20,84,56,11,52,03,
simulate the demand for 10 week period
11. Solution: Step 1:Generate tag values
11
Trips/week frequency Probability Cumulative
probability
Tag values
0 16 16/200=0.08 0.08 00-07
1 24 24/200=0.12 0.20 08-19
2 30 30/200=0.15 0.35 20-34
3 60 60/200=0.30 0.65 35-64
4 40 40/200=0.20 0.85 65-84
5 30 30/200=0.15 1.00 85-99
Frequency-Number of occurrences, Total num of occurrences(16+24+30+60+40+30)=200
Step 2: Simulation for next 10 week
Weeks Random Num Trips/week
1 82 4
2 96 5
3 18 1
4 96 5
5 20 2
6 84 4
7 56 3
8 11 1
9 52 3
10 03 0
Avg trips/week=28/10=2.8≈3 trips/week
12. For a particular shop the daily demand of an item is given as follows, Use
random numbers 25,39,65,76,12,05,73,89,19,49.Find the average daily
demand.
Daily demand 5 10 15 20 25 30
Probability 0.01 0.20 0.15 0.50 0.12 0.02
Solution: Generate tag values
12
Daily demand Probability Cumulative
probability
Tag values
0 0.01 0.01 00
10 0.20 0.21 01-20
20 0.15 0.36 21-35
30 0.50 0.86 36-85
40 0.12 0.98 86-97
50 0.02 1.00 98-99
13. Step 2: Simulation for 10 days
13
Days Random num Daily demand
1 25 20
2 39 30
3 65 30
4 76 30
5 12 10
6 05 10
7 73 30
8 89 40
9 19 10
10 49 30
Avg daily demand= 240/10=24
14. An automobile company manufactures around 150 scooters.Daily
production varies from 146 to 154,the probability distribution is given
below.
Step 1:Generate tag values for production/day
Step 1:Generate tag values for production/day
14
Production
/day
146 147 148 149 150 151 152 153 154
probability 0.04 0.09 0.12 0.14 0.11 0.10 0.20 0.12 0.08
The finished scooters are transported in a lorry accomodading150 scooters. using the
following random numbers 80,81,76,75,64,43,18,26,10,12,65,68,69,61,57
simulate
1)Average number of scooters waiting in the factory
2)Average number of empty space in the lorry
15. Step 1:Generate tag values for production/day
15
Production/day probability Cumulative probability Tag values
146 0.04 0.04 00-03
147 0.09 0.13 04-12
148 0.12 0.25 13-24
149 0.14 0.39 25-38
150 0.11 0.50 39-49
151 0.10 0.60 50-59
152 0.20 0.80 60-79
153 0.12 0.92 80-91
154 0.08 1.00 92-99
Step 2: Simulate for 15 days to get avg no of waiting scooters and empty space, lorry can accommodate 150
scooters
Days Random
num
Production/day No of scooters
waiting
No of empty space in
lorry
1 80 153 3 -
2 81 153 3 -
3 76 152 2 -
4 75 152 2 -
5 64 152 2 -
6 43 150 - -
7 18 148 - 2
8 26 149 - 1
9 10 147 - 3
10 12 147 - 3
11 65 152 2 -
12 68 152 2 -
13 69 152 2 -
14 61 152 2 -
15 57 151 1 -
Total=21 Total=9
Avg no of scooters waiting=
21/15=1.4
Avg No of space in the
lorry= 9/15=0.6
16. An automobile production line turns out about 100 cars/day, but
deviation occur owing to many causes.Production of cars are
described by the probability distribution given below.
16
Productio
n/day
95 96 97 98 99 100 101 102 103 104 105
probabilit
y
0.0
3
0.05 0.0
7
0.10 0.1
5
0.20 0.15 0.10 0.07 0.05 0.03
Finished cars are transported across the bay at the end of each day by ferry.
If ferry has space for only 101 cars,
what will be the average number of cars waiting to be shipped and
what will be the average number of empty space on ship?
Simulate the production of cars for next 15 days,
consider the random numbers 97,02,80,66,96,55,50,29,58,51,04,86,24,39,47.
18. Step 2:Simulate for 15 days, ferry can transport 101 cars
18
Days Random
numbers
Productions/day No of cars
waiting
Empty space in
the ship
1 97 105 |105-101|=4 -
2 02 95 - (101-95) =6
3 80 102 1
4 66 101 - -
5 96 104 3 -
6 55 100 - 1
7 50 100 - 1
8 29 99 - 2
9 58 100 - 1
10 51 100 - 1
11 04 96 - 5
12 86 103 2 -
13 24 98 - 3
14 39 99 - 2
15 47 100 - 1
Total=10 Total=23
Avg num of cars waiting=10/15
Avg empty space in the ship=23/15
19. Strong is a dentist who schedules all her patients for 30 minutes
appointment. Some of the patients take more or less than 30min depending
on the type of dental works to be done. The following summary shows the
various categories of work,their probability and the time actually needed to
complete the work
19
Category Filling crown cleaning extracting checkup
Time
required
45 60 15 45 15
Number of
patients
40 15 15 10 20
Simulate the dentist clinic for 4 hrs and find out the avg waiting
time for the patients as well as the idleness of doctor.Assume
that the ptients show up at the clinic at exactly scheduled time.
Arrival time starts at 8AM.Use the following random number
for handling the same 40,82,11,34,25,66,19,79
20. category Time
required
No of
patients(Frequen
cy)
probability Cumulative
probability
Tag
values
Filling 45 40 0.40 0.40 00-39
Crown 60 15 0.15 0.55 40-54
Cleaning 15 15 0.15 0.70 55-69
Extracting 45 10 0.10 0.80 70-79
Checkup 15 20 0.20 1.00 80-99
Total=100
20
Random
num
Categor
y
Time
required
(min)
Arrival
time of
patients
Service time
Start time End
time
waiting
time for
patients(mi
n)
Idleness
of
doctor
40 crown 60 8.00 8.00 9.00 0 -
82 checkup 15 8.30 9.00 9.15 30(9-8.30) -
11 Filling 45 9.00 9.15 10.00 15 -
34 Filling 45 9.30 10.00 10.45 30 -
25 Filling 45 10.00 10.45 11.30 45 -
66 Cleaning 15 10.30 11.30 11.45 60 -
19 Filling 45 11.00 11.45 12.30 45 -
79 Extractin
g
45 11.30 12.30 1.15 60 -
Step 1:find the cumulative probability and tag values
Step 2:Simulate for 4 hrs
Avg waiting time for patients=(30+15+30+45+60+45+60)/8=285/8=35.62 min≈36min
Waiting time for patients=(start time of service-arrival time)
21. Bright Bakery keeps stock of a popular brand of
cake. Previous experience indicates the daily demand
as given below:
Consider the following sequence of random numbers;
48, 78, 19, 51, 56, 77, 15, 14, 68,09. Using this
sequence simulate the demand for the next 10 days.
Find out the stock situation if the owner of the bakery
decides to make 30 cakes every day. Also estimate
the daily average demand for the cakes on the basis
of simulated data.
21
Daily
demand
0 10 20 30 40 50
Probability 0.01 0.20 0.15 0.50 0.12 0.02
22. Daily demand Probability Cumulative
probability
Tag values
0 0.01 0.01 00
10 0.20 0.21 01-20
20 0.15 0.36 21-35
30 0.50 0.86 36-85
40 0.12 0.98 86-97
50 0.02 1.00 98-99
22
Step 1:find the cumulative probability and tag values
Step 2:Simulate for 10 days, make 30 cakes every day
Days Random num Daily Demand Stock condition
1 48 30 -
2 78 30 -
3 19 10 20
4 51 30 -
5 56 30 -
6 77 30 -
7 15 10 20
8 14 10 20
9 68 30 -
10 09 10 20
Avg daily demand=220/10=22
23. Verification and validation are critical parts of practical
implementation
Verification pertains to whether software correctly
implements specified model
Validation pertains to whether the simulation model
(perfectly coded) is acceptable representation
◦ Are the assumptions reasonable?
Accreditation is an official determination that a
simulation is acceptable for particular purpose(s)
Project Appraisal
We can evaluate the likely profitability of a project
using these techniques in the light of many
uncertainties using this technique.
23
24. RISK ANALYSIS AND MONTE CARLO SIMULATION
Risk analysis is the systematic study of uncertainties and risks we
encounter in business, engineering, public policy, and many other areas.
Risk analysts seek to identify the risks faced by an institution or
business unit, understand how and when they arise, and estimate the
impact (financial or otherwise) of adverse outcomes.
Uncertainty and risk are issues that virtually every business analyst must
deal with, sooner or later.
Monte Carlo simulation is a powerful quantitative tool often used in risk
analysis.
Uncertainty is an intrinsic feature of some parts of nature – it is the same
for all observers. But risk is specific to a person or company – it is not
the same for all observers.
Most business and investment decisions are choices that involve “taking
a calculated risk” – and risk analysis can give us better ways to make the
calculation.
Risk analysis in computers are done using what-if analysis.
24
