1. Software Tools for Simulation H. Scott Matthews 12-706/73-359 Lecture 17 - Oct. 26, 2005

2. Admin Issues zFinal Project proposals due today yRunning late? Friday at latest. zMidterm projects back on Monday yLook good so far. Thanks. zMidterm Grade discussion ySimple 90-80-70 scale, average of first 3-4 HW’s. No class participation/etc adjustment. yIntention to keep you working through end of semester.

3. Final Notes on Uncertainty zIt is inherent to everything we do zOur goal then is to best understand and model its existence, make better results zWe ‘internalize’ the uncertainty by making ranges or distributions of variables zWe see the effects by performing sensitivity analysis (one of three methods)

4. Monte Carlo Simulation - Background / History zInvented by Ulam in 1940’s (claim to fame - a-bomb project) yWanted to figure out odds of winning solitaire yDeveloped method for setting up problem and doing lots of iterations to guess answer yHis contribution: using the “fast computers” of the time to help the effort. zLater, named after Monte Carlo (famous for gambling)

5. Monte Carlo Simulation zWhat is it? yAttempt to mimic real world / uncertainty zHow to do it? yReplace single assumptions / variables with probability distributions yTools then randomly draw from your distributions and use these random draws as the assumptions/variables, and run them through your model

6. Monte Carlo Method zMonte Carlo analysis’ 3 steps yFirst, specify probability distributions in place of constants/ variables ySecond, trial by random draws (plug them in) yThird, repeat for many (000s) of trials xProduces some distribution of results - look at the distribution as the answer instead of a single point yDoing Monte Carlo doesn’t “give you the answer”! xLaw of large numbers says convergence

7. Monte Carlo Simulations zUse RiskSim add-in from website or @RISK zAdds special probability functions to excel yExcel has some, but these are better yAlso adds monte carlo math to excel zDistributions: Binomial, Cumulative, Discrete, Exponential, Integer, Normal, Poisson, Triangular, Uniform yCan do almost anything with these as base

8. Let’s Test It zReplace Simple Input with Random Variable, then look at results y“1” -> Normal (0,1) with 50 trials yNote difference between “one value” as shown in result cell of spreadsheet xWhat does this one cell value show? yVersus running it multiple times and looking at the result xDo “output results” match what we would expect? xWhat if we do more trials? Up to 3000.

9. Revisiting Previous Spreadsheets zPenny? zIRA? zHW 2 Dams zPhoto Sensors?

10. Using Monte Carlo Methods zInstead of our ‘point estimates’, use probabilistic functions yPhoto-RiskSim worksheet as starting point yBulb and elec. cost obvious to do with prob. functions yOther variables are constant (e.g., number of bulbs) yAssume bulb cost is triangular, 3.5, 6, 10 yElec cost normal with mean 0.05, stdev.005 yNow what kind of result will we get? xUse with “Tools-> Risk Simulation” (one output) yAgain, photo sensor case not ideal for this - look at production cost example

11. Wrap-Up zLook at effect of number of trials (50 - 300) yRiskSim Summary worksheet shows 300 trials - note if you do it again, results would be different! zCould do all of this with excel, would just be harder (as usual) (see ExcelOnly worksheet) zAdd-ins like this (or CrystalBall, @RISK) simplify this kind of analysis - you should definitely use these instead. zWe have much better models - and knowledge of our results now

12. Putting it Together zHopefully its more clear to you now why we have devoted time recently to: yUnderstanding probability distributions, and when and how to use specific ones yHow to interpret pdf/cdf figures