simulation (qa ii)
DESCRIPTION
TRANSCRIPT
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