SIMULATION MODELING

A Presentation on

K.K. Parekh Institute of Management Studies (Amreli)

Prepared by :-

Mehul Rasadiya

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.

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.

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.

The Process of Simulation

ADVANTAGES

1. Flexibility2. Can handle large and complex systems3. Can answer “what-if” questions4. Does not interfere with the real system5. Allows study of interaction among

variables6. “Time compression” is possible7. Handles complications that other

methods can’t

DISADVANTAGES

1. Can be expensive and time consuming

2. Does not generate optimal solutions3. Managers must choose solutions

they want to try (“what-if” scenarios)

4. Each model is unique

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)

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).

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.

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

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

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

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.

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.

Days Random Numbers

Estimated

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

Days Random Numbers

Estimated

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

Days Random Number

s

Estimated 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

Days Random Number

s

Estimated 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

Days Random

Numbers

Estimated 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

Days Random

Numbers

Estimated 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

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