Seminar report on OR

1. OPERATION RESEARCH
Presented by: Tanveer Singh Solanki
Subject: Operation Research
Batch: ME (1st Semester)

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. INTRODUCTION
System: The physical process of interest
Model: Mathematical representation of the
system
Models are a fundamental tool of science,
engineering, business, etc.
Abstraction of reality
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

4. SIMULATION
TECHNIQUES
 Simulation techniques can be used to assist
management decision-making, where
analytical methods are either not available or
inappropriate.
 Typical business problems where simulation
could be used to aid management decision-
making are
 Inventory control.
 Queuing problems.
 Production planning.

5. Focus of course
System
Experiment w/
actual system
Experiment w/
model of system
Physical
Model
Mathematical
Model
Analytical
Model
Simulation
Model
5

6. SIMULATION
AND
QUEUING
PROBLEMS
 A major application of simulation has been
in the analysis of waiting line, or queuing
systems.
 Since the time spent by people and things
waiting in line is a valuable resource, the
reduction of waiting time is an important
aspect of operations management.
 Waiting time has also become more
important because of the increased
emphasis on quality. Customers equate
quality service with quick service and
providing quick service has become an
important aspect of quality service

7. QUEUING
PROBLEMS
 For queuing systems, it is usually not
possible to develop analytical formulas, and
simulation is often the only means of
analysis.
 Simulation can hence be used to
investigate problems that are common in
any situation involving customers, items or
orders arriving at a given point, and being
processed in a specified order.
 For ex:
 Customers arrive in a bank and form a single
queue, which feeds a number of service
desks. The arrival rate of the customers will
determine the number of service desks to
have open at any specific point in time

8. COMPONENTS
OF
QUEUING
SYSTEMS
 A queue system can be divided into four
components:
• Arrivals: Concerned with how customers
(people, cars etc) arrive in the system.
• Queue or waiting line: Concerned with what
happens between the arrival of an item or
customer requiring service and the time when
service is carried out.
• Service: Concerned with the time taken to
serve a customer.
• Outlet or departure: The exit from the
system.

9. 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 & examine the results obtained in step 4.
• Step 5:Evaluate the results of the simulation.

10. In various inventory problem especially storage problem cannot be solved analytically
because the distribution followed by demand or supply is very complex. The solution
can be obtained by using simulation technique. With the use of past data it is possible
to determine the probability distribution of the input and output functions and the
inventory system run artificially by generating the future observations on the
assumption of the same distributions. Trial and error method is used to find the
decision for the optimisation problems. With the help of random numbers the artificial
sample for the future can be generated. The demand during lead time to provide
adequate service to customers is the basis of the selection of reorder point in inventory
control. Simulation technique can be used to investigate the effect of different
inventory policies if the lead time and the demand of inventory per unit of time are
random variables. For wider applicability as well as those for specialised use a lot of
work has been done to develop inventory simulation models. In various inventory
problem queuing characteristics can be seen. For example, a problem concerned with
the optimal inventory of rental cars can be viewed as a queuing problem where the
servers are cars.
Inventory Problems

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

12. 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

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

14. 🗸 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

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

16. 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
Filling
45
40
Crown 60 15
Cleaning 15 15
Extraction 45 10
Check-up 15 20
Category
of service
Service
time
No. of
Patients

17. SOLUTION

18. 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

19. 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

20. 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

21. 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

22. 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 -

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

24. THANK YOU
!!!…