simulation monte carlo simulation

1. SIMULATION

2. SYNOPSIS
● Meaning and Methodology of Simulation
● Illustrate Monte Carlo method ofsimulation
● Application of Monte Carlo simulation techniquein
solving various types of businessproblems.

3. SIMULATION
● Simulation is the process of designing a model of a real system and then
performing experiments on the model (rather than on the real system
itself) for the purpose of understanding the behaviour for the Operation
of the system.
● It is a duplication of theoriginal System
● It can be used for a wide variety of practical problems.
● The simulation approach is relatively easy to explain and understand. As
a result, management confidence is increased and acceptance ismore
easily obtained.

4. Application
● Inventory Control
● Financial studies involving risky investments
● Examining a series of marketing policies to find the best product mix, price, promotion levels,
Advertising allocation.
● Analysing where to locate factories and warehouses in order to distribute goods at the
minimum cost .

5. Methodology for Simulation
● Define ( Identify ) the problem
● Identify Decision variables
● Develop or Construct Simulation Model
● Validate the model
● Specify values of decision variables to betested
● Run or Conduct the simulation
● Examine the results and implement thefindings

6. Monte Carlo Simulation
It is an Experiment on Chance.
The Monte – Carlo technique uses random number and is generally used to solve problems
requiring decision-making under uncertainty and where mathematical formulation is impossible.

7. Understanding of Monte Carlo Simulation
Technique
● 1. Establishing Probability Distribution
● 2. Cumulative Probability Distribution
● 3. Setting Random Number Intervals
● 4. Generating Random Numbers
● 5. To find the answer of question asked using the above 4 steps.

8. Simulation of an Inventory System
Example: A bakery keeps a stock of a popular brand of cake. Previous experience shows the daily
demand pattern for the item with associated probabilities , as given below:
Daily
demand
0 10 20 30 40 50
Probability 0.01 0.20 0.15 0.50 0.12 0.02

9. Contd…
● Use the following random numbers to simulate the demand for next 10 days.
Random numbers:48, 78, 19,51,56,77,15,14,68,9
Estimate the daily average demand for the cakes on the basis of simulated data.

10. Determination of Random Number
Interval
Demand Probability Cumulativ
e
Probability
Random Number
Interval
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

11. Simulation Experiment Worksheet
Day Random Number Demand
1 48 30
2 78 30
3 19 10
4 51 30
5 56 30
6 77 30
7 15 10
8 14 10
9 68 30
10 09 10

12. Simulation
● Expected Demand on the basis of the simulated data,
=220/10 = 22 cakes/day

13. Simulation
Demand/week 0 5 10 15 20 25
Frequency 2 11 8 21 5 3

14. Simulation
Random Nos: 35,52,90,13,23,73,34,57,35,83,94,56,67,66,60

15. Determination of Random Number
Interval
Demand Probability Cumulativ
e
Probability
Random Number
Intervals
0 2/50=0.04 0.04 00-03
5 11/50=0.22 0.26 04-25
10 8/50=0.16 0.42 26-41
15 21/50=0.42 0.84 42-83
20 5/50=0.10 0.94 84-93
25 3/50=0.06 1.00 94-99

16. Simulation Experiment Worksheet
Week Random Number Demand
1 35 10
2 52 15
3 90 20
4 13 5
5 23 5
6 73 15
7 34 10
8 57 15
9 83 15
10 95 25

17. Example on Production Line
Production line turns out about 50 truck per day, fluctuations occur for many reasons. The
production can be described by a probability distribution as follows: ( attached in Excel).
Finished trucks are transported by train at the end of the day. If the train capacity is only 51,what
will be average number of trucks waiting to be shipped and what will be the average number of
empty spaces on the train?
Use the given sequence of random numbers to simulate the production for next 8 days.

18. SIMULATION OF QUEING SYSTEM
Dr. Kumar is a dentist who schedules all her patients for 30
minutes appointments. Some of the patients take more or
less than 30 minutes depending on the type of dental work
to be done. The following table shows the various
categories of work, their probabilities and the time actually
needed to complete the work:

19. SIMULATION
Category of Service Time required ( minutes) Probability
Filling 45 0.40
Crown 60 0.15
Cleaning 15 0.15
Extraction 45 0.10
Check-up 15 0.20

20. SIMULATION
Simulate the dentist’s clinic for four hours and determine the average waiting time for the
patients 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 am. Use the following random numbers for
handling the above problem:
40 82 11 34 25 66 17 79

21. SIMULATION
At a service station a study was made over a period of 50 days to determine both the number of
automobiles being brought in for service and the number of automobiles serviced. The results are
given in the excel table.
Simulate the arrival service pattern for a ten-day period and estimate the mean number of
automobiles that remain in service for more than a day.
Use the following random numbers
For
arrival
s
09 54 42 01 80 06 06 26 57 79
For
Servic
e
49 16 36 76 68 91 97 85 56 84