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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,OPIM 5270|Spring 2015,水晶球软件使用CrystalBall,本课件仅供大家学习学习 学习完毕请自觉删除 谢谢 本课件仅供大家学习学习 学习完毕请自觉删除 谢谢,Session 9 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.,2,Most real-world business situations today are probabilistic,but the decision models used to deal with them are deterministic.,How to deal with randomness?,Ignore it,Simplify problem to make it analytically tractable,get solution,then ignore real-life complications,Find a way to obtain an approximate solution to real-world problems,Dealing with Randomness,3,Monte Carlo simulation is a method by which approximate solutions are obtained to realistic(and therefore complicated)problems,This is in contrast to analytical methods,which obtain exact solutions to highly stylized problems,Tradeoff between rigor and relevance,Monte Carlo Simulation,4,What is this?,Y=,f,(X,1,X,2,X,k,),Often,the values for one or more input cells are unknown or uncertain,This creates uncertainty about the value of the output cell,Simulation can be used to analyze these types of models,Introduction to Simulation,5,A,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 employees in a firm,expected product demand,Decisions made using uncertain information often involve risk.What risks?,Random Variables&Risk,6,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$2,000 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.,Why Analyze Risk?,7,Best-Case/Worst-Case Analysis,What-if Analysis,Simulation,Methods of Risk Analysis,8,Best 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 and worst-case limits.,Other problems or benefits?,Best-Case/Worst-Case Analysis,9,worst case,best case,worst case,best case,worst case,best case,worst case,best case,Possible Performance Measure Distributions Within a Range,10,Plug in different values for the uncertain cells and see what 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 to generate a representative distribution.,Does not supply the tangible evidence(facts and figures)needed to justify decisions to management.,What-If Analysis,11,Values 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.,Simulation,12,Proper risk 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,复制,the model,n,times,and record the value of the bottom-line performance measure.,4)Analyze the sample values collected on the performance measure.,Simulation Continued,13,A 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 the distribution of values expected for different cells.,Random Number Generators,14,The 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 following RNG:,=IF(RAND()0.5,1,2),How Random Number Generators Work,15,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 the spreadsheet&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 to display the spreadsheet&supports all CB functionality,Generating Random Numbers with Crystal Ba
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