SimulationNotes.Week1-2 - Business Modeling and Simulation Contents 1 Week 1 2 1.1 Introduction 2 1.2 Dart Game.

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Business Modeling and Simulation Contents 1 Week 1 2 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Dart Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 A Dinner Deal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 EXCEL Skills: The Basics for Excel Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Week 2 7 2.1 A Sales Promotion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Excel Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Flextrola: a Newsvendor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Excel Hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 *Optional Reading: Mathematical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 An Insurance Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Excel hints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 EXCEL Skills: Data table, Indicator, and Random Sample Size . . . . . . . . . . . . . . . . . . . . . . . . . 11 1
1 Week 1 ASM textbook: Applied Simulation Modeling, by Seila, Ceric and Tadikamalla, Duxbury Press, 2003 Excel 2010: Data Analysis and Business Modeling, Winston, Microsoft Press, 2011. For later edi- tions of the Excel book, the chapter numbers may differ, but the chapter name and contents are the same. 1.1IntroductionSimulation is a way of thinking. It tells stories in a logical way. Just as every story has actors, plots,and contexts, so does simulation. In a story, we want to know how the actors interact, under whatcontext, and what are the outcomes of their interactions. In simulation,random variablesare ouractors, and we seek to understand how and why their interplay leads to certain outcomes.For each simulation, we must first specify the relevant random variables. Like actors, they eachhave names and behaviors (personalities, characters). For example, Bernoulli, Binomial, and Nor-mal are the names of typical random variables.Their behaviors are uniquely defined by theirdistribution functions—probability distribution function (PDF)f, or cumulative distribution func-tion (CDF)F. Depending on the problem, either one can be pleasant to work with. Their relationisF(x) =x−∞f(t)dtfor continuous case, andF(x) =tixf(ti).Second, we care about the context of the simulation. This is done by specifying the business andother environmental parameters.For example, the time horizon, the production cost, and themarket price. Along with the parameters of random variables, they constitute the INPUT of thesimulation.Third, we need to figure out the logic—the plot—of the simulation.That is, how the randomvariables interact in each context. This is the fun part of the simulation: as the logic depends onthe problem specifics, we must analyze each on its own merit.Once we have specified the INPUT and the logic, we are ready to run the simulation. The OUTPUTrecords the outcomes that interest us. For example, the mean profit and its 95 percent confidenceinternal. Typically it involves statistic analysis. Taking together, we haveOUPUT = LOGIC( INPUT ).To illustrate, we consider a dart game.1.2Dart GameJim is to play a dart game with his friend. The square frame is of two by two size, with the roundboard of radius one siting inside. Jim is a lousy shooter. He can make each shot in the square,but otherwise the shots are random. His friend makes a generous offer: Long gets free beer if heshoots on the board. What is the probabilitypthat Long gets free bee? 2