09 - Crystal Ball Introduction - UCONN - Posted (5)

8/10/2019 09 - Crystal Ball Introduction - UCONN - Posted (5)

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Introduction to

Crystal BallSimulationsSession 9

UCONNOPIM 5270

Acuna / Tschiegg

Wilkins / Van Dusen


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Session 2 Goals

Understand why risk must be analyzed

Know pros / cons for three ways to analyze risk

Identify random variables in models

Know the four steps of a simulation process

Generate random numbers with Crystal Ball

Use the four steps of a simulation process

Explain how Crystal Ball supports Proj. Mgmt.

Fall 2012


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Dealing with Randomness

Most real-world business situations todayare probabilistic, but the decision modelsused to deal with them are deterministic.

How to deal with randomness?

Ignore it

Simplify problem to make it analyticallytractable, get solution, then ignore real-lifecomplications

Find a way to obtain an approximate solution to

real-world problemsFall 2012


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Monte Carlo Simulation

Monte Carlo simulation is a method by whichapproximate solutions are obtained to realistic(and therefore complicated) problems

This is in contrast to analytical methods, whichobtain exact solutions to highly stylized problems

Tradeoff between rigor and relevance

Fall 2012


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Introduction to Simulation

What is this?

Y = f(X1, X2, , Xk)

Often, the values for one or more "input" cellsare unknown or uncertain

This creates uncertainty about the value of the"output" cell

Simulation can be used to analyze these typesof models

Fall 2012


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Random Variables & Risk

A random variableis any variable whose valuecannot be predicted or set with certainty.

Many input cells in spreadsheet models are

actually random variables. For example: the future cost of raw materials

future interest rates

future number of employees in a firm

expected product demand

Decisions made using uncertain information ofteninvolve risk. What risks?

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Why Analyze Risk?

Using expected values for uncertain cells tells usnothing about the variability of the performancemeasure.

Suppose an $1,000 investment is expected to return$2,000 in two years. Would you invest if...

the outcomes could range from $1,060 to $4,000?

the outcomes could range from $0 to $2,100?

Alternatives with the same expected value mayinvolve very different levels of risk.

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Methods of Risk Analysis

Best-Case/Worst-Case Analysis

What-if Analysis

Simulation

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Best-Case/Worst-Case Analysis

Best case - plug in the most optimistic values for eachof the uncertain cells.

Worst case - plug in the most pessimistic values for

each of the uncertain cells.

This is easy to do and bounds the outcomes, but tellsus nothing about the distributionof possible outcomeswithin the best and worst-case limits.

Other problems or benefits?

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Possible Performance Measure

Distributions Within a Range

worst case best case




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What-If Analysis

Plug in different values for the uncertain cells and seewhat happens.

Benefits:

This is easy to do with spreadsheets Other?

Problems:

Values may be chosen in a biased way.

Hundreds or thousands of scenarios may be required togenerate a representative distribution.

Does not supply the tangible evidence (facts and figures)needed to justify decisions to management.

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Simulation

Values for uncertain cells are selectedrandomly (and in an unbiased manner).

The computer generates hundreds (or

thousands) of scenarios. We analyze the scenario results to better

understand the behavior of the performancemeasure.

Allows decisions based on solid empiricalevidence.

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Simulation

Proper risk assessment requires simulation.

Simulation is a 4 step process:

1) Identify the uncertain cells in the model.

2) Implement appropriate Random NumberGenerators (RNGs) for each uncertain cell.

3) Replicate the modeln

times, and record thevalue of the bottom-line performance measure.

4) Analyze the sample values collected on theperformance measure.

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Random Number Generators

A Random Number Generator is amathematical function that randomlygenerates (returns) a value from a

particular probability distribution.

We can implement Random NumberGenerators for uncertain cells to allow us tosample from the distribution of valuesexpected for different cells.

Fall 2012


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How Random Number

Generators Work

The RAND( ) function returns uniformly distributedrandom numbers between 0.0 and 0.9999999.

Suppose we want to simulate the act of tossing a fair

coin. Let 1 represent heads and 2 represent tails.

Consider the following RNG:

=IF(RAND( )


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Generating Random Numbers

With Crystal Ball

Crystal Ball provides two different ways for creating

Random Number Generators in spreadsheets

Crystal Ball functions

Used in formulas like any other Excel function

Require CB to be installed on the machine displaying thespreadsheet & do not support all CB functionality

The Distribution Gallery

Display a number (not a formula) in a cell but generates

random numbers for that cell when simulating the model

Does not require CB to be installed on the machine todisplay the spreadsheet & supports all CB functionality

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Using the Distribution Gallery

Click DefineAssumption icon

Select distribution

Specify parametersFall 2012


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Examples of Discrete

Probability Distributions

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Examples of Continuous

Probability Distributions

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What does Crystal Ball look like

in Excel? (Office 2007/2010)

Define Menu

Run Menu

Analyze Menu

Crystal Ball Toolbar

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How does Crystal Ball work?

1. Determine which model inputsare uncertain and define a

probability distribution.2. Identify which forecasts you want

to analyze/measure

(e.g., NPV, Sigma level, process efficiency)

3. Run Simulation

4. Analyze Results

5. Generate ReportFall 2012


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1. Define your Distributions

The first step to using Crystal Ball is to determine whichmodel inputs are uncertain. Which values are estimates?

Which are averages?

Once you have identifiedthese, you use your knowledgeof the uncertainty around theinput to create a probability

distribution for that cell (whatCrystal Ball calls anassumption). Crystal Ball letsyou define these distributionsusing the Distribution Gallery

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Assumption Dialog

Enter variety ofparameters to definedistributions

Can fit distributions to rawdata

Can cell reference allfields

Can correlate pairs ofassumptions

Marker lines

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3. Run Simulation

Number ofsimulation trials

performed

Display range

Certainty (probability) that the forecastwill reach $2,812,558

Parts within the spec

limits are shown inblue, parts outsidespec limits are shownred

Number of datapoints displayed inthe chart

Crystal Ball uses Monte Carlosimulation to randomly generatethousands of what-if scenarios

Each scenario is then captured and presented in a frequencychart (Forecast Chart)

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Whats responsible for most of the variation in the forecast?The sensitivity chart shows the influence each assumptioncell has on the forecast.

4. Analyze Results

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Reports

Select a pre-defined report or create yourown custom report. Reports now includenew statistics and more control over dataand charts.

Extract Data

You can extract data from both forecasts andassumptions and extract multiple types ofdata.

5. Generate Reports

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Build a Model for Simulation

Go to Crystal Ball in Excel

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Relevance to Project Management?

With simulation software (like Crystal Ball)you can account for, and manage againstthe uncertainty of:

Time (how long the project may take)

Money (how much the project may cost) Scope (variance from specification)

Fall 2012


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09 - Crystal Ball Introduction - UCONN - Posted (5)