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

1. OPERATION RESEARCH

2. MEANING
o re-creation of a real world
process in a controlled
environment
o creating laws & models to
represent the world
o running those models to see
what happens

3. PROCESS
Define
Define the
problem
Formulate
Formulate the
model
Test
Test the model
Identify &
collect
Identify & collect
data
Run
Run simulation
Analyse
Analyse the result
Rerun
Rerun the
simulation for
new solution
Validate
Validate the
simulation

4. ADVANTAGES DISADVANTAGES
flexible
expensive
used to analyse
Require expert
knowledge
Assist in finding the pros &
cons of the real situation
complicated
Only a method
Real situation based on
it

5. USES/
APPLICATION
 Research
 Risky training
 Education
 Manufacturing
 Services
 Entertainment
 Safety engineering
 Video games
 Healthcare
 Technology

6.  first used by scientists working on the atom bomb in 1940.
 used in those situations where we need to make an estimate
and uncertain decisions such as weather forecast predictions.
 a computerized mathematical technique
 to generate random sample data based on some known
distribution for numerical experiments.
 apply to risk quantitative analysis and decision making
problems.
 used by the professionals of various profiles such as finance,
project management, energy, manufacturing, engineering,
research & development, insurance, oil & gas, transportation,
etc.
MONTE
CARLO
SIMULATION

7. ADVANTAGES & DISADVANTAGES OF MONTE
CARLO SIMULATION
ADVANTAGES DISADVANTAGES
Easy to implement Time consuming
Used for numerical experiment Expensive
Provide approximate solution Require Expert knowledge

8. Example of Monte Carlo Simulation
 Dr. Strong is dentist who schedules all her patients
for 30 minutes appointments. Some of the patients
take more or less than 30 minutes depending on
the types of dental work to be done. Summary
show the various categories of work with service
time.
 Simulate the dentist’s clinic for four hours and
determine the average waiting time for the patient
as well as the idleness of the doctor.
 Assume that all the patients show up at the clinic
at exactly their scheduled arrival time starting at
8:00 a.m.
 Use the following random numbers for handling the
above problem –
40, 82, 11, 34, 25, 66, 17, 79
Category
of service
Service
time
No. of
Patients
Filling
45
40
Crown 60 15
Cleaning 15 15
Extraction 45 10
Check-up 15 20

9. SOLUTION

10. Step – I – Establishing Probability distribution
 First of all we need to
make a probability for
each category of service
 For probability, apply
following formula –
Probability =
𝐹𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
𝑇𝑜𝑡𝑎𝑙 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
Category of
service
Service
time
No. of
Patients
Probability
Filling 45 40 40/100 = 0.40
Crown 60 15 15/100 = 0.15
Cleaning 15 15 15/100 = 0.15
Extraction 45 10 10/100 = 0.10
Check-up 15 20 20/100 = 0.20
Total 100

11. Step – II –Cumulative Probability distribution
(Next step is to calculate their cumulative probability)
Category of
service Service time
No. of Patients Probability
Cumulative
probability
Filling 45 40 0.40 0.40
Crown 60 15 0.15 0.40 + 0.15 = 0.55
Cleaning 15 15 0.15 0.55 + 0.15 = 0.70
Extraction 45 10 0.10 0.70 + 0.10 = 0.80
Check-up 15 20 0.20 0.80 + 0.20 = 1.00
Total 100

12. Step – III – Setting random number intervals
The Random number intervals corresponds exactly to the probability of outcome.
Category of
service
Probability
Cumulative
probability
Random Number
Intervals
Filling 0.40 0.40 00 – 39
Crown 0.15 0.55 40 – 54
Cleaning 0.15 0.70 55 – 69
Extraction 0.10 0.80 70 – 79
Check-up 0.20 1.00 80 - 99

13. Step – IV – Generating Random Number
 Next step is to generate
random number
 But in the question random
number are already given
 Here need to simulate the
dentist clinic for 4 hours = 8
patient (30 minutes each)*
 For select the category of
service to each patient check
the random number lies in
which random number intervals
Patient
Scheduled
arrival
Random
number
Category
Service
time
needed
(in min.)
1 8:00 40 Crown 60
2 8:30 82 Check-up 15
3 9:00 11 Filling 45
4 9:30 34 Filling 45
5 10:00 25 Filling 45
6 10:30 66 Cleaning 15
7 11:00 17 Filling 45
8 11:30 79 Extraction 45

14. Step – V – Find out the answer
 Here we need to find out the average waiting time of patient & idle time of
doctor
Patient
Scheduled
arrival
Service Start
Service
duration
(in minutes)
Service
ends
Waiting
time of
patient
(in minutes)
Idle Time of
doctor
1 8:00 8:00 60 9:00 - -
2 8:30 9:00 15 9:15 30 -
3 9:00 9:15 45 10:00 15 -
4 9:30 10:00 45 10:45 30 -
5 10:00 10:45 45 11:30 45 -
6 10:30 11:30 15 11:45 60 -
7 11:00 11:45 45 12:30 45 -
8 11:30 12:30 45 1:15 60 -
Total 285 -

15. Continue to V step
 Average waiting time =
𝑻𝒐𝒕𝒂𝒍 𝒘𝒂𝒊𝒕𝒊𝒏𝒈 𝒕𝒊𝒎𝒆
𝑵𝒐.𝒐𝒇 𝑷𝒂𝒕𝒊𝒆𝒏𝒔
𝟐𝟖𝟓
𝟖
= 35.625 minutes
 Idle time = 0

16. THANK YOU
!!!…