The document discusses simulation modeling and provides examples of its applications. Simulation involves generating an artificial representation of a system over time and making inferences from it. Some key advantages of simulation include flexibility to study complex systems, answering "what if" questions without disrupting the real system, and examining variable interactions. The document also presents a case study using Monte Carlo simulation to estimate the profit/loss of a company producing 30 or 29 units per day based on random numbers representing demand probabilities. The total profit was found to be Rs. 2695 for both production levels.

1. SIMULATION MODELING
A Presentation on
K.K. Parekh Institute of Management Studies
(Amreli)
Prepared by :-
Mehul Rasadiya

2. INTRODUCTION
 It is a technique(Quantitative) for carrying out
experiments for analyzing the behavior and evaluating
the performance of a proposed system under assumed
condition of reality.
 An experiment or relatively simplified experimental model
of a system is used to examine the components or
properties of system, their behavior I relation to each
other and in relation to the entire system at a point of
time and over period of time, under different assume
condition.
 The alternative courses, inputs, components, properties
and variables of the system are experimentally
manipulated in several way to find out their interactions
and impact on the system’s operation and behavior.

3. SIMULATION DEFINATION
• Simulation is the imitation of the
operation of a real world system over
time.
• Simulation involves the generation of an
artificial history of the system and the
drawing of inferences from it.

4. REASON FOR USING SIMULATION
 Many practical problem where mathematical
simplification is not feasible.
 There is no sufficient time to allow the system to operate
extensively.
 Simulation model can be used to conduct experiments
without disrupting real system.
 Enable a manager to provide insights into certain
problem where the actual environment is difficult to
observe.
 The non technical manager can comprehend simulation
more easily than a complex mathematical model.

5. The Process of Simulation

6. ADVANTAGES
1. Flexibility
2. Can handle large and complex systems
3. Can answer “what-if” questions
4. Does not interfere with the real system
5. Allows study of interaction among
variables
6. “Time compression” is possible
7. Handles complications that other
methods can’t

7. DISADVANTAGES
1. Can be expensive and time consuming
2. Does not generate optimal solutions
3. Managers must choose solutions they
want to try (“what-if” scenarios)
4. Each model is unique

8. APPLICATION OF SIMULATION
 Manufacturing and other process
 Scheduling production processes
 Design of system(marketing, information,
inventory, weapon, manpower employment,
traffic light-timing, etc.)
 Facilities(hospitals, harbors, railways, libraries,
schools, design of parking lots, communication
system, etc)
 Resource development programmers( water
resources, human resources, petro-chemical,
energy resources, and so on)

9. Deterministic Model
All data are assumed
to be known with
certainty
Probabilistic Model
Some data are described
by probability distribution.
System Simulation
An experiment used to
describe sequences of events
that occur over time.
(inventory, queuing,
manufacturing process)
Simulation Models
Monte Carlo Simulation
A sampling experiment whose
purpose is to estimate the
distribution of an outcome variable
that depends on several
probabilistic input variables. (profit
projection, stock portfolio).

10. Steps Involved in Simulation
(Monte Carlo Technique)
 Find the cumulative Probability
 Assign random numbers Interval corresponding to the
Probability.
 From the random number tables, choose a set of
required random numbers from any part of the table.
This can be done by following any fixed pattern like
row wise, column wise, diagonal wise.
 Choice of random numbers whether single digit,
double digit, triple digit etc. depends upon the number
of places to which Probability is known. Eg- If the
prob. have been calculated to two decimal places,
which add up to 1.00, we need 100 numbers of 2 digit
to represent each point of probability. Thus we take
random no.s 00-99 to represent them.

11. CASE STUDY
A company manufactures 30 units/day. The sale of these items
depends upon demand which has the following distribution.
 The production cost and sales price of each unit are Rs. 40 and Rs.
50, respectively. Any unsold product is to be disposed off at loss of
Rs. 15. There is a penalty of Rs. 5 per unit if the demand is not met.
 Using the following random numbers, estimate the total profit/loss for
the company for the next ten days. 10, 99, 65, 99, 01, 79, 11, 16, 20
 If the company decides to produce 29 units per day, what is the
advantage or disadvantage of the company?
Sales (Unit) Probability
27 0.10
28 0.15
29 0.20
30 0.35
31 0.15
32 0.05

13. Sales (unit) Probability Cumulative
probability
Random No.
Interval
27 0.10 0.10
28 0.15
29 0.20
30 0.35
31 0.15
32 0.05

14. Sales (unit) Probability Cumulative
probability
Random No.
Interval
27 0.10 0.10
28 0.15 0.25
29 0.20 0.45
30 0.35 0.80
31 0.15 0.95
32 0.05 1.00

15. Sales (unit) Probability Cumulative
probability
Random No.
Interval
27 0.10 0.10 00-09
28 0.15 0.25 10-24
29 0.20 0.45 25-44
30 0.35 0.80 45-79
31 0.15 0.95 80-94
32 0.05 1.00 95-99
As the first step, random numbers 00-99 are allocated to various
possible sales values in production to the probabilities associated
with them.

16.  Now we simulate the demand for the next 10 days using
the given random numbers.
From the given following information, we have
Profit per unit sold = Rs. 50 – Rs. 40= Rs. 10
Loss per unit unsold = Rs. 15
Penalty for using demand = Rs. 5 per unit
 Using these inputs, the profit/loss for the 10 days is
calculated, first when production is 30 units per day and
then when it is 29 units.
 It is evident that the total profit/loss for the 10 days is Rs.
2695 when 30 units are produced. Also, if the company
decides to produce 29 units per day, the total profit works
out to be the same.

17. Days Random
Numbers
Estimat
ed
Sales
(units)
Profit/Loss per day with production
30 units 29 units
1 10 28
2 99
3 65
4 99
5 95
6 01
7 79
8 1
9 16
10 20

18. Days Random
Numbers
Estimat
ed
Sales
(units)
Profit/Loss per day with production
30 units 29 units
1 10 28
2 99 32
3 65 30
4 99 32
5 95 32
6 01 27
7 79 30
8 1 28
9 16 28
10 20 28

19. Days Random
Number
s
Estimate
d Sales
(units)
Profit/Loss per day with production
30 units 29 units
1 10 28 28*10-2*15 = Rs. 250
2 99 32
3 65 30
4 99 32
5 95 32
6 01 27
7 79 30
8 1 28
9 16 28
10 20 28

20. Days Random
Number
s
Estimate
d Sales
(units)
Profit/Loss per day with production
30 units
1 10 28 28*10-2*15 = Rs. 250
2 99 32 30*10-2*5 = Rs. 290
3 65 30 30*10 = Rs. 300
4 99 32 30*10-2*5 = Rs. 290
5 95 32 30*10-2*5 = Rs. 290
6 01 27 27*10-3*15 = Rs. 225
7 79 30 30*10 = Rs. 300
8 1 28 28*10-2*15 = Rs. 250
9 16 28 28*10-2*15 = Rs. 250
10 20 28 28*10-2*15 = Rs. 250
Total Profit = Rs. 2695

21. Days Rando
m
Number
s
Estimate
d Sales
(units)
Profit/Loss per day with production
30 units 29 units
1 10 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 265
2 99 32 30*10-2*5 = Rs. 290
3 65 30 30*10 = Rs. 300
4 99 32 30*10-2*5 = Rs. 290
5 95 32 30*10-2*15 = Rs. 290
6 01 27 27*10-3*15 = Rs. 225
7 79 30 30*10 = Rs. 300
8 1 28 28*10-2*15 = Rs. 250
9 16 28 28*10-2*15 = Rs. 250
10 20 28 28*10-2*15 = Rs. 250
Total Profit = Rs. 2695

22. Days Rando
m
Number
s
Estimate
d Sales
(units)
Profit/Loss per day with production
30 units 29 units
1 10 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 265
2 99 32 30*10-2*5 = Rs. 290 29*10-3*5 = Rs. 275
3 65 30 30*10 = Rs. 300 29*10-1*5 = Rs. 285
4 99 32 30*10-2*5 = Rs. 290 29*10-3*5 = Rs. 275
5 95 32 30*10-2*15 = Rs. 290 29*10-3*5 = Rs. 265
6 01 27 27*10-3*15 = Rs. 225 27*10-2*15 = Rs. 240
7 79 30 30*10 = Rs. 300 29*10-1*5 = Rs. 285
8 1 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 265
9 16 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 265
10 20 28 28*10-2*15 = Rs. 250 28*10-1*15 = Rs. 265
Total Profit = Rs. 2695 = Rs. 2695

23. When company decides to produce 29 units per
day, so that time no change in profit or loss.
Compare to 30 units per day.
When company
produce 30 units
When company
produce 29 units
Total Profit =
Rs. 2695
Total Profit =
Rs. 2695