SIMULATION IN
OPERATION RESEARCH
Presented by:1. Ru Rutu tuja ja Wag agh( h(57 5729 29)) 2. Vai aibh bhav av Pa Pard rdal ale( e(57 5771 71)) 3. Ch Chet etaan Ang ngre re(5 (588 886) 6) 4. Abh bhiish shek ek Pat Patil il(5 (58 895 95))
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. reality.
An experiment or relatively simplified experimental model of a system is used to examine the components or properties of system, their 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 int eractions and impact on the system’s operation and behavior.
Use of system model that has the desired characteristic of reality in order to reproduce the essence of the actual operation.
Simulation is a quantitative studying alternative courses model of that system and then experiments to predict the over a period of time.
T. H. Taylor defined Simulation as “A numerical technique for conducting experiments on a digital computer, which involves certain types of mathematical mathematical & logical relationships necessary to describe the behaviour and structure of a complex real world system over extended period of time.”
technique developed for of actions by building a conducting a series of behaviour of the system
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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.
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Simulation is flexible and straightforward technique. Simulation is useful in solving problems where all values of the variables are either not known or partially known. It can be use to analyze large and complex real world system that cannot be solved by conventional quantitative techniques models. In situations where it is difficult difficult to predict or identify bottlenecks, Simulation is used to foresee these unknown difficulties. The simulation approach is useful to study a problem that involves uncertainty.
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Simulation does not produce optimal result. solution are approximate. It is often long and complicated process to develop a model. it is time consuming and expensive process.
Each simulation model is unique and its solution and inference are not usually transferable to other operation.
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Manufacturing and other process Scheduling production processes Design of system(marketing, information, inventory, 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, petro -chemical, energy resources, and so on)
Monte Carlo Simulation: This technique is based upon probability distribution and the use of random numbers. Also called computer simulation, it can be described as a numerical technique that involves modeling a stochastic system with the objective of predicting the system’s system’s behavior.
It is more popular in business applications due to its ease of implementation and low costs.
System Simulation: This technique is used in situations where business or operating environment is reproduced to study the behavior of the system under different operating parameters. The impact of alternative management actions on the system can be analyzed. This involves Simulation of an Inventory System and Simulation of Queuing System.
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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 eaach point of probability. 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.
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Sales (Unit)
Probability
27
0.10
28
0.15
29
0.20
30
0.35
31
0.15
32
0.05
The production cost cost and sales price of each unit are Rs. 40 and Rs. 50, respectively. 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, day, what is the advantage or disadvantage of the company?
Sales (unit)
Probability
Cumulative probability
27
0.10
0.10
28
0.15
29
0.20
30
0.35
31
0.15
32
0.05
Random No. Interval
Sales (unit)
Probability
Cumulative probability
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
Random No. Interval
As the first step, random numbers 00-99 are allocated to various possible sales values in production to the probabilities associated with them. Sales (unit)
Probability
Cumulative probability
Random No. Interval
27
0.10
0.10
00-09
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
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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 demand = Rs. Rs. 5 per unit •
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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 u nits are produced. Also, if the company decides to produce 29 units per day, day, the total profit works out to be the same.
Day Random Estimate
Profit/Loss per day day with with production production
Number d Sales s
(units)
1
10
28
2
99
3
65
4
99
5
95
6
01
7
79
8
1
9
16
10
20
30 units
29 units
Day Random Estimate
Profit/Loss per day day with with production production
Number d Sales s
(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
30 units
29 units
Day
Random Estimate Number d Sales s
(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
Profit/Loss per day day with with production production 30 units 28*10-2*15 = Rs. 250
29 units
Day
Random Estimate
Profit/Loss per day day with with production production
Number d Sales
30 units
s
(units)
1
10
28
28*10-2*15 = Rs. 250
2
99
32
30*10-2*5 = Rs. 290
3
65
30
30*10
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
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. 300
= Rs. 300
Rs. 2695
Day
Random Estimate
Profit/Loss per day day with with production production
Number d Sales
30 units
s
(units)
1
10
28
28*10-2*15 = Rs. 250
2
99
32
30*10-2*5 = Rs. 290
3
65
30
30*10
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
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. 300
= Rs. 300
= Rs. 2695
29 units 28*10-1*15 = Rs. 265
Day
Random Estimate
Profit/Loss per day day with with production production
Number d Sales
30 units
29 units
s
(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
