1、Project ManagementSession 9Crystal BallOPIM 52701Session 9 GoalsqUnderstand why risk must be analyzedqKnow pros / cons for three ways to analyze riskqIdentify random variables in modelsqKnow the four steps of a simulation processqGenerate random numbers with Crystal BallqUse the four steps of a simu

2、lation processqExplain how Crystal Ball supports Proj. Mgmt.2Most real-world business situations today are probabilistic, but the decision models used to deal with them are deterministic.How to deal with randomness?Ignore itSimplify problem to make it analytically tractable, get solution, then ignor

3、e real-life complicationsFind a way to obtain an approximate solution to real-world problems3Dealing with RandomnessMonte Carlo simulation is a method by which approximate solutions are obtained to realistic (and therefore complicated) problemsThis is in contrast to analytical methods, which obtain

4、exact solutions to highly stylized problemsTradeoff between rigor and relevance4Monte Carlo SimulationWhat is this? Y = f(X1, X2, , Xk)Often, the values for one or more input cells are unknown or uncertain This creates uncertainty about the value of the output cellSimulation can be used to analyze t

5、hese types of models5Introduction to SimulationA random variable is any variable whose value cannot 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 employee

6、s in a firm expected product demandDecisions made using uncertain information often involve risk. What risks?6Random Variables & Risk Using expected values for uncertain cells tells us nothing about the variability of the performance measure. Suppose an $1,000 investment is expected to return $2

7、,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 may involve very different levels of risk. 7Why Analyze Risk?Best-Case/Worst-Case AnalysisWhat-if AnalysisSimulationMethods of

8、 Risk Analysis8Best case - plug in the most optimistic values for each of 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 tells us nothing about the distribution of possible outcomes within the best

9、and worst-case limits.Other problems or benefits?9Best-Case/Worst-Case Analysisworst casebest caseworst casebest caseworst casebest caseworst casebest case10Possible Performance Measure Distributions Within a RangePlug in different values for the uncertain cells and see what happens. Benefits:This i

10、s easy to do with spreadsheetsOther?Problems: Values may be chosen in a biased way. Hundreds or thousands of scenarios may be required to generate a representative distribution. Does not supply the tangible evidence (facts and figures) needed to justify decisions to management.What-If Analysis11Valu

11、es for uncertain cells are selected randomly (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 performance measure.Allows decisions based on solid empirical evidence.Simulation12Proper risk

12、 assessment requires simulation. Simulation is a 4 step process:1) Identify the uncertain cells in the model.2) Implement appropriate Random Number Generators (RNGs) for each uncertain cell.3) Replicate復(fù)制the model n times, and record the value of the bottom-line performance measure.4) Analyze the sa

13、mple values collected on the performance measure.Simulation Continued13A Random Number Generator is a mathematical function that randomly generates (returns) a value from a particular probability distribution.We can implement Random Number Generators for uncertain cells to allow us to sample from th

14、e distribution of values expected for different cells.Random Number Generators14The RAND( ) function returns uniformly distributed random 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 followin

15、g RNG:=IF(RAND( )0.5,1,2)How Random Number Generators Work15Crystal Ball provides two different ways for creating Random Number Generators in spreadsheets Crystal Ball functionsUsed in formulas like any other Excel functionRequire CB to be installed on the machine displaying the spreadsheet & do

16、 not support all CB functionality The Distribution GalleryDisplay a number (not a formula) in a cell but generates random numbers for that cell when simulating the modelDoes not require CB to be installed on the machine to display the spreadsheet & supports all CB functionalityGenerating Random

17、Numbers with Crystal Ball16Click Define Assumption iconSelect distributionSpecify parametersUsing the Distribution Gallery1718Discrete Probability Distributions18Continuous Probability Distributions19Define MenuRun MenuAnalyze MenuCrystal Ball ToolbarCrystal Ball in MS Excel201. Determine which mode

18、l inputs are uncertain and define a probability distribution. 2. Identify which forecasts you want to analyze/measure (e.g., NPV, Sigma level, process efficiency)3. Run Simulation4. Analyze Results5. Generate ReportHow does Crystal Ball work?21The first step to using Crystal Ball is to determine whi

19、ch model inputs are uncertain. Which values are estimates? Which are averages? Once you have identified these, you use your knowledge of the uncertainty around the input to create a probability distribution for that cell (what Crystal Ball calls an assumption). Crystal Ball lets you define these dis

20、tributions using the Distribution GalleryDefine Your Distributions22Enter variety of parameters to define distributionsCan fit distributions to raw dataCan cell reference all fieldsCan correlate pairs of assumptionsMarker linesAssumption Dialog23The next step is to identify a forecast. A forecast is

21、 a formula cell that you want to measure and analyze. In this model, you select the Net Profit (cell C23). Identify Your Forecasts24Number of simulation trials performedDisplay rangeCertainty (probability) that the forecast will reach $2,812,558Parts within the spec limits are shown in blue, parts o

22、utside spec limits are shown redNumber of data points displayed in the chartlCrystal Ball uses Monte Carlo simulation to randomly generate thousands of what-if scenarioslEach scenario is then captured and presented in a frequency chart (Forecast Chart)Run Simulation25Whats responsible for most of the variation in the forecast?The sensitivity chart shows the influence each assumption cell has on the forecast. Analyze Results26ReportsSelect a pre-defined report or create your own custom report. Reports now include new statistics and more control over data and charts. Extract DataYou can extract