Simulation Sonia

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Simulation

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MEANING

Simulation involves developing a model of some realphenomena and then performing experiments on themodel evolved.

It is a descriptive and optimising technique. In simulation a given system is copied and the

variables and constants associated with it aremanipulated in that artificial environment to

examine the behaviour of the system

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Simulation: is a representation of reality through theuse of a model or other device, which will react in thesimilar manner as reality under a given set of

conditions. Analogue Simulation: Reality in physical form.

Computer simulation: Complex system in formulatedinto a mathematical model for which computer

program are developed as problem is solved on highspeed computers.

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Simulation Methodology

Set up a model of a real system andconduct repetitive experiments

1. Problem Definition

2. Construction of the Simulation Model3. Testing and Validating the Model

4. Design of the Experiments

5. Conducting the Experiments

6. Evaluating the Results

7. Implementation


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Simulation: Issues

Probabilistic Simulation

Discrete distributions

Continuous distributions

Use of random numbers Replications with different random number

streams

Simulation Software

Visual Simulation


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Why use simulation?

Experience

Permits experimenting with the controllable system

parameters to identify optimal settingsPermits examining effect of environmental or

exogenous changes.

Identify which of several systems is most efficientDetermine which variables are most important.

Verify and checkrobustness of analytic solutions.


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Advantages to Simulation:

Simulations greatest strength is

its ability to answerwhat if questions...

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Advantages of Simulation

investigate effects of changes, new designs, new

models, etc. without costly implementation.

Stress testing: test systems under different scenarios(e.g. higher interest rates, different exchange rates)

What if questions.

NON-FINANCE applications Identify bottlenecks in systems and rectify

Increase experience with complex system at lower cost.


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Advantages to Simulation:

Can be used to study existing systems without disrupting the

ongoing operations.

Proposed systems can be tested before committing resources.

Allows us to control time.

Allows us to identify bottlenecks. Allows us to gain insight into which variables are most

important to system performance.

Simulation allows experimentation with a model of the real

system rather than the actual operating system. Relatively free from mathematics.

Comparatively flexible.

Easier to use than other techniques.

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Simulation is not

without its drawbacks...

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Disadvantages

Two models for same process may differ.

Simulation output is random so hard to interpret

results.Building models and running simulation is time

consuming

ANALYTIC SOLUTIONS, IF AVAILABLE,SHOULD BE USED! (analytic solutions to a similar

(simpler) model can be used to improve a simulation)


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Disadvantages to Simulation Model building is an art as well as a science. The quality

of the analysis depends on the quality of the model and the

skill of the modeler (Remember: GIGO)

Simulation results are sometimes hard to interpret.

Simulation analysis can be time consuming and expensive.Should not be used when an analytical method would

provide for quicker results.

Optimum result can not be produced.

Quantification of variable is not possible.(how many variable affecting the system).

Difficult to make program because of difficult to know the

interrelationship among many variables.

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Random Number:

It is a number in a sequence of numbers whoseprobability of occurrence is the same as that of anyother member.

When to use simulation:

When the characteristics such as uncertainty,complexity , dynamic interaction between thedecision and subsequent event and the need to

develop a detailed procedure , combine together inone situation, it becomes too complex to be solvedby any of the technique of mathematicalprogramming. Under such situation the simulation

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Non Finance Applications

Manufacturing systems: e.g. material handling,

inventory, assembly plants, scheduling,

Public Systems: health care- hospital management,emergency room, Military

Natural resource management, transportation, traffic

systems, airport (e.g. Motorway)

Construction systems: project planning, scheduling,

entertainment: restaurants, movies etc.


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Example

a manufacturing company contemplates

building a large extension onto one of its

plants, but is not sure if the potential gain inproductivity would justify the construction

cost.


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Application areas Designing and analyzing manufacturing systems

evaluating military weapons systems or their logistics requirements

determining hardware requirements or protocols for communication

networks

Determining hardware and software requirements for a computer

system

Designing and operating transportation systems such as airports,

freeways, ports and subways

Evaluating designs for service organizations such as call centers, fast-

food restaurants, hospitals, and post offices

Reengineering of business processes

Determining ordering polices for an inventory system

Analyzing financial or economic systems


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In Corporate Finance, project finance and real options

analysis, Monte Carlo Methods are used by financial

analysts who wish to construct probabilistic financialmodels as opposed to the traditional static

and deterministic models.

Here, in order to analyze the characteristics of a

projects net present value (NPV), the cash flow

components that are impacted by uncertainty are modeled,

incorporating any correlation between these,

mathematically reflecting their "random characteristics".

Then, these results are combined in histogram of NPV ,

and the average NPV of the potential investment - as well

as its volatility and other sensitivities - is observed. This

distribution allows, for example, for an estimate of the

probability that the project has a net present value greater

than zero 17
http://en.wikipedia.org/wiki/Corporate_Financehttp://en.wikipedia.org/wiki/Project_financehttp://en.wikipedia.org/wiki/Real_options_analysishttp://en.wikipedia.org/wiki/Real_options_analysishttp://en.wikipedia.org/wiki/Financial_analysthttp://en.wikipedia.org/wiki/Financial_analysthttp://en.wikipedia.org/wiki/Financial_analysthttp://en.wikipedia.org/wiki/Financial_analysthttp://en.wikipedia.org/wiki/Financial_analysthttp://en.wikipedia.org/wiki/Real_options_analysishttp://en.wikipedia.org/wiki/Real_options_analysishttp://en.wikipedia.org/wiki/Real_options_analysishttp://en.wikipedia.org/wiki/Real_options_analysishttp://en.wikipedia.org/wiki/Real_options_analysishttp://en.wikipedia.org/wiki/Project_financehttp://en.wikipedia.org/wiki/Project_financehttp://en.wikipedia.org/wiki/Project_financehttp://en.wikipedia.org/wiki/Corporate_Financehttp://en.wikipedia.org/wiki/Corporate_Financehttp://en.wikipedia.org/wiki/Corporate_Finance


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In valuing an option on equity, the

simulation generates several thousand

possible (but random) price paths for the

underlying share, with the

associated exercise value (i.e. "payoff") of

the option for each path. These payoffs arethen averaged and discounted to today, and

this result is the value of the option today.

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To value fixed income instruments and interest rate

derivatives the underlying source of uncertainty which is

simulated is the short rate - the annualized interest rate at which

an entity can borrow money for a given period of time; Forexample for bonds, and bond options, under each possible

evolution of interest rates we observe a different yield curve and a

different resultant bond price. To determine the bond value, these

bond prices are then averaged; to value the bond option, as forequity options, the corresponding exercise values are averaged

and present valued. A similar approach is used in

valuing swaps and swaptions.

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Monte Carlo Methods are used

for portfolio evaluation.

Here, for each sample,the correlated behaviour of the factors impacting the

component instruments is simulated over time, the

resultant value of each instrument is calculated, and

the portfolio value is then observed. As for corporatefinance, above, the various portfolio values are then

combined in a histogram, and the statistical

characteristics of the portfolio are observed, and the

portfolio assessed as required. A similar approach isused in calculating value at risk.

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Monte Carlo Methods are used for personal

financial planning.

For instance, bysimulating the overall market, the chances

of a 401(k) allowing for retirement on a

target income can be calculated. As

appropriate, the worker in question can then

take greater risks with the retirement

portfolio or start saving more money.

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http://en.wikipedia.org/wiki/Personal_financial_planninghttp://en.wikipedia.org/wiki/Personal_financial_planninghttp://en.wikipedia.org/wiki/401(k)http://en.wikipedia.org/wiki/401(k)http://en.wikipedia.org/wiki/Personal_financial_planninghttp://en.wikipedia.org/wiki/Personal_financial_planninghttp://en.wikipedia.org/wiki/Personal_financial_planning


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Ques-A bakery keeps stock of popular brand of cakedaily demand based on past experience is givenbelow

Using the sequence, simulate the demand for

the next 10 days.

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Number of cakes demanded in the next 10 days are35,35, 15, 35, 35, 35, 15, 15, 35 and 15.

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Ques following information was collected in a


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Ques- following information was collected in amkt analysis:

S.P PROB UNITCOST

PROB SALESVOLUME

PROB ADVERT.COST

PROB

350 .30 300 .40 80000 .15 25L .25

450 .40 350 .25 65000 .45 20L .25

500 .20 400 .15 50000 .30 18L .25

550 .10 450 .20 45000 .10 15L .25

FIND average profit and probablity of profit > 50L

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Calculation of random numbers

SP PROB Cum.P Rnsallot

350 .30 .30 00-29

450 .40 .70 30-69

500 .20 .90 70-89

550 .10 1.00 90-99

AD.

Cost

Prob Cum.

Prob

R. no

25L .25 .25 00-24

20L .25 .50 25-49

18L .25 .75 50-74

15L .25 1.00 75-99

U. Cost PROB Cum. P Rns

300 .40 .40 00-39

350 .25 .65 40-64

400 .15 .80 65-79450 .20 1.00 80-99

SV PROB Cum

prob

R. No

80k .15 .15 00-14

65k .45 .60 15-59

50k .30 .90 60-89

45k .10 1.00 90-99

For SP

For Sales volume

For unit cost

For AD cost

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Profit=(SP-Unit cost)S.V-AD cost

avg profit=105+60+100+140/4=48.9Lprob=4/10(total number of trials are 10)

Selling price Unit cost AD. Cost SalesVolume

Profit

Trials R. No Exp R. No Exp R. No Exp R. No Exp

1 78 500 23 300 58 65k 21 25L 105L

2 43 450 08 300 86 50k 93 15L 60L

3 92 550 28 300 62 50k 15 25L 100L

4 87 500 17 300 06 80k 27 20L 140L

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Simulation Sonia