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1、OPIM 5270 |Spring 2015,Project ManagementSession 9Crystal Ball,OPIM 5270,OPIM 5270 |Spring 2015,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
2、 with Crystal Ball Use the four steps of a simulation process Explain how Crystal Ball supports Proj. Mgmt.,OPIM 5270 |Spring 2015,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 Sim
3、plify 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,OPIM 5270 |Spring 2015,Monte Carlo simulation is a method by which approximate solutions are obtained to real
4、istic (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,OPIM 5270 |Spring 2015,What is this? Y = f(X1, X2, , Xk) Often, the values for one or more input
5、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,OPIM 5270 |Spring 2015,A random variable is any variable whose value cannot be predicted or set with certainty. Many “input ce
6、lls” 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,OPIM 5270 |Spr
7、ing 2015,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 $2,10
8、0? Alternatives with the same expected value may involve very different levels of risk.,Why Analyze Risk?,OPIM 5270 |Spring 2015,Best-Case/Worst-Case Analysis What-if Analysis Simulation,Methods of Risk Analysis,OPIM 5270 |Spring 2015,Best case - plug in the most optimistic values for each of the un
9、certain 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 Analys
10、is,OPIM 5270 |Spring 2015,Possible Performance Measure Distributions Within a Range,OPIM 5270 |Spring 2015,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 thousand
11、s 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,OPIM 5270 |Spring 2015,Values for uncertain cells are selected randomly (and in an unbiased manner). The com
12、puter 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,OPIM 5270 |Spring 2015,Proper risk assessment requires simulation. Simulation is a 4 step
13、 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.,S
14、imulation Continued,OPIM 5270 |Spring 2015,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 ex
15、pected for different cells.,Random Number Generators,OPIM 5270 |Spring 2015,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
16、 RNG: =IF(RAND( )0.5,1,2),How Random Number Generators Work,OPIM 5270 |Spring 2015,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
