FR. CONCEICAO RODRIGUES COLLEGE OF ENGINEERING

REPORT

SIMULATIONIN OPERATION RESEARCH

1. RUTUJA WAGH (5729)

2. VAIBHAV PARDALE (5771)

3. CHETAN ANGRE (5886)

4. ABHISHEK PATIL (5895)

Signed by,

INDEX

1.INTRODUCTION TO OPERATION RESEARCH

2.HISTORICAL ORIGIN

3.INTRODUCTION TO SIMULATION

4.SIMULATION DEFINATION

5.REASON FOR USING SIMULATION

6.ADVANTAGES AND DISADVANTAGES OF SIMULATION

7.APPLICATION OF SIMULATION

8.TYPE OF SIMULATION

9.BASIC STEPS IN SIMULATION PROCESS

10. CASE STUDY

INTRODUCTION TO OPERATION RESEARCH

Operations research, or Operational Research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions. It is often considered to be a sub-field of Mathematics. The terms management science and decision science are sometimes used as more modern-sounding synonyms.

Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical

optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems. Because of its emphasis on human-technology interaction and because of its focus on practical applications, operations research has overlap with other disciplines, notablyindustrial engineering and operations management, and draws on psychology and organization science. Operations Research is often concerned with determining the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost) of some real-world objective. Originating in military efforts before World War II, its techniques have grown to concern problems in a variety of industries.

OR FUCTION AND METHODS

Data mining

Decision analysis

Engineering

Forecasting

Game theory

Industrial engineering

Logistics

Mathematical modeling

Mathematical optimization

Probability and statistics

Project management

Simulation

Social network/Transportation forecasting models

Supply chain management

Financial engineering

HISTORICAL ORIGIN

As a formal discipline, operational research originated in the efforts of military planners during World War II. In the decades after the war, the

techniques began to be applied more widely to problems in business, industry and society. Since that time, operational research has expanded into a field widely used in industries ranging from petrochemicals to airlines, finance, logistics, and government, moving to a focus on the development of mathematical models that can be used to analyse and optimize complex systems, and has become an area of active academic and industrial research.

In the World War II era, operational research was defined as "a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control”. Other names for it included operational analysis (UK Ministry of Defence from 1962) and quantitative management.

Prior to the formal start of the field, early work in operational research was carried out by individuals such as Charles Babbage. His research into the cost of transportation and sorting of mail led to England'suniversal "Penny Post" in 1840, and studies into the dynamical behaviour of railway vehicles in defence of the GWR's broad gauge. Percy Bridgman brought operational research to bear on problems in physics in the 1920s and would later attempt to extend these to the social sciences.The modern field of operational research arose during World War II.

Modern operational research originated at the Bawdsey Research Station in the UK in 1937 and was the result of an initiative of the station's superintendent, A. P. Rowe. Rowe conceived the idea as a means to analyse and improve the working of the UK's early warning radar system, Chain Home (CH). Initially, he analysed the operating of the radar equipment and its communication networks, expanding later to include the operating personnel's behaviour. This revealed unappreciated limitations of the CH network and allowed remedial action to be taken.

Scientists in the United Kingdom including Patrick Blackett (later Lord Blackett OM PRS), Cecil Gordon, C. H. Waddington, Owen Wansbrough-Jones, Frank Yates, Jacob Bronowski and Freeman Dyson, and in the United States with George Dantzig looked for ways to make better decisions in such areas as logistics and training schedules. After the war it began to be applied to similar problems in industry.

INTRODUCTION TO SIMULATION

Simulation is the one of the most widely used O.R. technique as it is a versatile tool which lends to the solution of a large variety of O.R. problems which are otherwise difficult to solve. It is a technique (Quantitative or otherwise) 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 ways to find out their interactions and impact on the system’s operation and behavior.

Simulation is the imitation of the operation of a real-world process or system over time. The act of simulating something first requires that a model be developed; this model represents the key characteristics or behaviors of the selected physical or abstract system or process. The model represents the system itself, whereas the simulation represents the operation of the system over time.

Simulation is used in many contexts, such as simulation of technology for performance optimization, safety engineering, testing, training, education, and video games. Training simulators include flight simulators for training aircraft pilots to provide them with a lifelike experience. Simulation is also used with scientific modeling of natural systems or human systems to gain insight into their functioning. Simulation can be used to show the eventual real effects

of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not exist.

Key issues in simulation include acquisition of valid source information about the relevant selection of key characteristics and behaviors, the use of simplifying approximations and assumptions within the simulation, and fidelity and validity of the simulation outcomes.

SIMULATION DEFINATION

Simulation, according to Shannon (1975), is “the process of designing a model of a real system and conducting ex- periments with this model for the purpose either of under- standing the behavior of the system or of evaluating vari- ous strategies (within the limits imposed by a criterion or set of criteria) for the operation of the system.” According to this definition, a simulation can be a discrete-event simulation, as we will discuss in this paper. Many peoplewho attend this conference will be familiar with the term “MRP simulation.” This is a model (actually a copy) of the real system (the MRP system of record) on which ex- periments (or scenarios) can be run to evaluate various strategies (such as how to respond to a drastic change in the forecast). 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 technique developed for studying alternative courses of actions by building a model of that system and then conducting a series of experiments to predict the behavior of the system 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 & logical relationships necessary to describe the behavior and structure of a complex real world system over extended period of time.”

REASON FOR USING SIMULATION

• Many practical problems 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.

• Actual operation and observation of a system is too disruptive.

ADVANTAGES AND DISADVANTAGES OF SIMULATION

Simulation is flexible and straightforward technique.

Simulations can help in cases where mathematical models are not applicable, because the system to be modeled is either too complex, the system's behavior cannot be expressed by mathematical equations, or the system involves uncertainty, i.e. stochastic elements.

Simulation is especially useful if changes in an existing system are to be made, and the effects of the changes should be tested prior to implementation. Trying out the changes in the real system may not be an option, because the system does not yet exist, the costs are too high, there are too many scenarios to test, the test would take too much time (weeks, months, years), the changes are not legal, etc. In all these cases, a simulation model allows to test various scenarios in often only a couple of minutes or hours.

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 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.

A disadvantage of simulation in comparison to exact mathematical methods is that simulation cannot naturally be used to find an optimal solution. There are methods which long to optimize the result, but simulation is not inherently an optimization tool. Simulation is often the only means to approach complex systems analysis. Many systems

cannot be modeled with mathematical equations. Simulation is then the only way to get information at all. 

• Another disadvantage is that it can be quite expensive to build a simulation model. First, the process that is to be modeled must be well understood, although a simulation can often help to understand a process better. The most expensive part of creating a simulation model is the collection of data to feed the simulation, and to determine stochastic distributions (e.g. processing times, arrival rates etc.).

• Each simulation model is unique and its solution and inference are not usually transferable to other operation.

• Another key point is to ensure the model is valid, i. e. it's behavior mirrors that of the original (physical) system. For systems that don't exist yet, because simulation is used for planning it, this is especially hard. Unsufficient validation and verfication of a simulation model is one of the top reasons for failing simulation projects. The consequence is false results, and this lessens the credibility of the method in general.

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).

Types of Simulation

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 behavior. It is more popular in business applications due to its ease of implementation and low costs.

Monte Carlo simulation methods do not always require truly random numbers to be useful — while for some applications, such as primality testing, unpredictability is vital. Many of the most useful techniques use deterministic, pseudorandom sequences, making it easy to test and re-run

simulations. The only quality usually necessary to make good simulations is for the pseudo-random sequence to appear "random enough" in a certain sense.

What this means depends on the application, but typically they should pass a series of statistical tests. Testing that the numbers are uniformly distributed or

Follow another desired distribution when a large enough number of elements of the sequence are considered is one of the simplest and most common ones.

Sawilowsky lists the characteristics of a high quality Monte Carlo simulation:

the (pseudo-random) number generator has certain characteristics (e. g., a long “period” before the sequence repeats)

the (pseudo-random) number generator produces values that pass tests for randomness

there are enough samples to ensure accurate results the proper sampling technique is used the algorithm used is valid for what is being modeled it simulates the phenomenon in question.

Pseudo-random number sampling algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given probability distribution.

Low-discrepancy sequences are often used instead of random sampling from a space as they ensure even coverage and normally have a faster order of convergence than Monte Carlo simulations using random or pseudorandom sequences. Methods based on their use are called quasi-Monte Carlo methods.

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.

BASIC STEPS IN SIMULATION PROCESS

1. The system to be simulated is defined.

2. The model, intended to be used, is formulated.

3. The model is tested by comparing its behavior with the behavior in the actual situation.

4. Require data on variable are identified and collected to compute probabilities associated with variable. The data collected on variable are presence in such a manner as to give a frequency distribution for the variable.

5. Frequency distribution is too converted to cumulative probability distribution.

6. Random number 00 to 99 are assigned to each of the value of variable which allocated to particular value of variable is being directly proportional to the cumulative probability.

7. ‘n’ sets of random number are selected from random number table and the value of the each of the variable is assign to each of the random number.

8. The simulated data are processed to generate the require information.

9. The data is summaries and analyzed for interpretation.

10. If desired, the solution to be evaluated is change.

11. Simulation is carried out to test the new solution.

12. Simulation is validated with increased chances of inference about the real solution.

CASE STUDY

A company manufactures 30 units/day. The sale of these items depends upon demand which has the following distribution.

Sales (Unit) Probability

27 0.10

28 0.15

29 0.20

30 0.35

31 0.15

32 0.05

• 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 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

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

• 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.

Day 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

Day Random Numbers

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*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

Day 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

PROBLEM

The Tit-Fit Scientific Laboratories is engaged in producing different types of high class equipment for use in science laboratories. The company has two different assembly lines to produce its most popular product “Pressurex”. The processing time for each of the assembly lines is regarded as a random variable and is described by the following distributions.

Process Time (minutes) Assembly A1 Assembly A2

10 0.10 0.20

11 0.15 0.40

12 0.40 0.20

13 0.25 0.15

14 0.10 0.05

Using the random numbers, generate data on the process times for 15 units of the item and compute the expected process time for the product. For the purpose, read the no.’s vertically taking the first two digits for the processing time on assembly A1 and the last two digits for processing time on assembly A2.

4134 8343 3602 7505 7428

7476 1183 9445 0089 3424

4943 1915 5415 0880 9309

Time (mts)

Assembly A1 Assembly A2

Prob. Cum. Prob.

RN Interval

Prob. Cum. Prob.

RN Interval

10 0.10 0.10 00-09 0.20 0.20 00-19

11 0.15 0.25 10-24 0.40 0.60 20-59

12 0.40 0.65 25-64 0.20 0.80 60-79

13 0.25 0.90 65-89 0.15 0.95 80-94

14 0.10 1.00 90-99 0.05 1.00 95-99

Solution: Firstly, we will find the cumulative Prob. And random number Intervals to the processing times on each of the assemblies.

12 08 10 80 13 23

13 74 13 28 11 24

14 34 12 24 11 23

15 93 14 09 10 24

Expected time= 349/15 = 23.27

The expected completion time for a unit works out to be 23.27 minutes.