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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.
6. Training the operating and personal staff.1/1/2013 9
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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.
Comparatively costlier and time consuming method.1/1/2013 12
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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
is best technique to be used. 1/1/2013
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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_Finance7/30/2019 Simulation Sonia
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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_planning7/30/2019 Simulation Sonia
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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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