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1 Spreadsheet Modeling & Decision Analysis: A Practical Introduction to Management Science, 3e by Cliff Ragsdale

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-2 Introduction to Simulation Using Crystal Ball Chapter 12

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-3 Introduction to Simulation u In many spreadsheets, the value for one or more cells representing independent variables is unknown or uncertain. u As a result, there is uncertainty about the value the dependent variable will assume: Y = f(X 1, X 2, …, X k ) u Simulation can be used to analyze these types of models.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-4 Random Variables & Risk u A random variable is any variable whose value cannot be predicted or set with certainty. u Many “input cells” in spreadsheet models are actually random variables. –the future cost of raw materials –future interest rates –future number of employees in a firm –expected product demand u Decisions made on the basis of uncertain information often involve risk. u “Risk” implies the potential for loss.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-5 Why Analyze Risk? u Plugging in expected values for uncertain cells tells us nothing about the variability of the performance measure we base decisions on. u Suppose an $1,000 investment is expected to return $10,000 in two years. Would you invest if... –the outcomes could range from $9,000 to $11,000? –the outcomes could range from -$30,000 to $50,000? u Alternatives with the same expected value may involve different levels of risk.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-6 Methods of Risk Analysis u Best-Case/Worst-Case Analysis u What-if Analysis u Simulation

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-7 Best-Case/Worst-Case Analysis u Best case - plug in the most optimistic values for each of the uncertain cells. u Worst case - plug in the most pessimistic values for each of the uncertain cells. u This is easy to do but tells us nothing about the distribution of possible outcomes within the best- case and worst-case limits.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-8 Possible Performance Measure Distributions Within a Range worst casebest caseworst casebest caseworst casebest caseworst casebest case

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-9 What-If Analysis u Plug in different values for the uncertain cells and see what happens. u This is easy to do with spreadsheets. u 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.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-10 Simulation u Resembles automated what-if analysis. u Values for uncertain cells are selected in an unbiased manner. u The computer generates hundreds (or thousands) of scenarios. u We can analyze the results of these scenarios to better understand the behavior of the performance measure and make decisions using solid empirical evidence.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-11 Example: Hungry Dawg Restaurants u Hungry Dawg is a growing restaurant chain with a self-insured employee health plan. u Covered employees contribute $125 per month to the plan, Hungry Dawg pays the rest. u The number of covered employees changes from month to month. u The number of covered employees was 18,533 last month and this is expected to increase by 2% per month. u The average claim per employee was $250 last month and is expected to increase at a rate of 1% per month.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-12 Implementing the Model See file Fig12-2.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-13 Questions About the Model u Will the number of covered employees really increase by exactly 2% each month? u Will the average health claim per employee really increase by exactly 1% each month? u How likely is it that the total company cost will be exactly $36,125,850 in the coming year? u What is the probability that the total company cost will exceed, say, $38,000,000?

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-14 Simulation u To properly assess the risk inherent in the model we need to use simulation. u Simulation is a 4 step process: 1) Identify the uncertain cells in the model. 2) Implement appropriate RNGs for each uncertain cell. 3) Replicate the model n times, and record the value of the bottom-line performance measure. 4) Analyze the sample values collected on the performance measure.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-15 What is Crystal Ball? u Crystal Ball is a spreadsheet add-in that simplifies spreadsheet simulation. u A 120-day trial version of Crystal Ball is on the CD- ROM accompanying this book. u It provides: –functions for generating random numbers –commands for running simulations –graphical & statistical summaries of simulation data u For more info see: http://www.decisioneering.com

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-16 Random Number Generators u A RNG is a mathematical function that randomly generates (returns) a value from a particular probability distribution. u We can implement RNGs for uncertain cells to allow us to sample from the distribution of values expected for different cells.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-17 How RNGs Work u The RAND() function returns uniformly distributed random numbers between 0.0 and 0.9999999. u Suppose we want to simulate the act of tossing a fair coin. u Let 1 represent “heads” and 2 represent “tails”. u Consider the following RNG: =IF(RAND()<0.5,1,2)

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-18 Simulating the Roll of a Die u We want the values 1, 2, 3, 4, 5 & 6 to occur randomly with equal probability of occurrence. u Consider the following RNG: =INT(6*RAND())+1 If 6*RAND( ) falls INT(6*RAND( ))+1 in the interval:returns the value: 0.0 to 0.9991 1.0 to 1.9992 2.0 to 2.9993 3.0 to 3.9994 4.0 to 4.9995 5.0 to 5.9996

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-19 Some of the RNGs Provided By Crystal Ball DistributionRNG Function BinomialCB.Binomial(p,n) CustomCB.Custom(range) GammaCB.Gamma(loc,shape,scale,min,max) PoissonCB.Poisson( ) Continuous UniformCB.Uniform(min,max) ExponentialCB.Exponential( ) NormalCB.Normal( , min,max TriangularCB.Triang(min, most likely, max)

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-20 Examples of Discrete Probability Distributions

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-21 Examples of Continuous Probability Distributions

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-22 Discrete vs. Continuous Random Variables u A discrete random variable may assume one of a fixed set of (usually integer) values. –Example: The number of defective tires on a new car can be 0, 1, 2, 3, or 4. u A continuous random variable may assume one of an infinite number of values in a specified range. –Example: The amount of gasoline in a new car can be any value between 0 and the maximum capacity of the fuel tank.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-23 Preparing the Model for Simulation u Suppose we analyzed historical data and found that: –The change in the number of covered employees each month is uniformly distributed between a 3% decrease and a 7% increase. –The average claim per employee follows a normal distribution with mean increasing by 1% per month and a standard deviation of $3.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-24 Revising & Simulating the Model See file Fig12-8.xls

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-25 The Uncertainty of Sampling u The replications of our model represent a sample from the (infinite) population of all possible replications. u Suppose we repeated the simulation and obtained a new sample of the same size. Q: Would the statistical results be the same? A: No! u As the sample size (# of replications) increases, the sample statistics converge to the true population values. u We can also construct confidence intervals for a number of statistics...

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-26 Constructing a Confidence Interval for the True Population Mean where: Note that as n increases, the width of the confidence decreases.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-27 Constructing a Confidence Interval for the True Population Proportion where: Note that as n increases, the width of the confidence decreases.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-28 Additional Uses of Simulation u Simulation is used to describe the behavior, distribution and/or characteristics of some bottom-line performance measure when values of one or more input variables are uncertain. u Often, some input variables are under the decision makers control. u We can use simulation to assist in finding the values of the controllable variables that cause the system to operate optimally. u The following examples illustrate this process.

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Spreadsheet Modeling and Decision Analysis, 3e, by Cliff Ragsdale. © 2001 South-Western/Thomson Learning. 12-29 Finished with Chapter 12

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