Simulation

Chapter 14SimulationPart 3 Probabilistic Decision ModelsLearning ObjectivesExplain what the term simulation means and how simulation differs from analytical techniques.Explain the difference between discrete and continuous simulations, between fixed-interval and next-event simulations, and between discrete and probabilistic simulations.List and briefly describe the steps in simulation.Use the Monte Carlo method to generate random numbers.Conduct manual simulations using various distributions.After completing this chapter, you should be able to:2Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Learning Objectives (cont’d)Conduct simulation with Excel using various distributions.Conduct simple waiting-line simulation using Excel.Conduct inventory management simulation using Excel.List the advantages and limitations of simulations.After completing this chapter, you should be able to:3Copyright © 2007 The McGraw-Hill Companies. All rights reserved. SimulationSimulationA descriptive tool for the study of the behavior of a system under various conditions.The goal in simulation is to create a model that will reflect the behavior of some real-life system in order to be able to observe how it may behave when certain inputs or parameters are changed.Unlike analytical techniques, it is not an optimizing technique.4Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Types of SimulationsDiscrete SimulationsExperimental situations in which outcome variables are discrete and are described by a count of the number of occurrences.Continuous SimulationsExperimental situations in which the variable of interest is continuous in that it can assume both integer and noninteger values over a range of values that are measured rather than counted.5Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Types of Simulations (cont’d)Fixed-Interval SimulationsExperiments simulating the value of a variable over a given or fixed interval of time, distance or area.Interest is centered on the accumulated value of a variable over a length of time or other interval.Next-Event SimulationsExperiments focused on when something happens, or how much time is required to perform a task.Interest is centered on an occurrence of an event and, perhaps, how much time or effort is required for the event.6Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Types of Simulations (cont’d)Deterministic SimulationsCases in which a specific outcome is certain, given a set of inputs.Probabilistic SimulationsCases that involve random variables and, therefore, the exact outcome cannot be predicted with certainty, given a set of inputs. Cases that incorporate some mechanism for mimicking random behavior in one or more variables.7Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 14–1 Steps in SimulationDefine the problemSet objectivesDevelop modelGather dataValidate modelDesign experimentsRun simulationsAnalyze and interpret results8Copyright © 2007 The McGraw-Hill Companies. All rights reserved. The Monte Carlo MethodMonte Carlo SimulationA commonly used approach for achieving randomness that derives its name from its similarity to games of chance.Characteristics of random numbersAll numbers are equally likely.No patterns appear in sequences of numbers.9Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 14–1 Random Numbers10Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 14–2 Simulating a Coin Toss11Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 14–3 Assigning Random Numbers for the Replacement Parts Example12Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 14–4 Simulation of Replacement Parts Usage13Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 14–2 Conversion of a Random Number to a Uniform Distribution14Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 14–3 Simulating Exponentially Distributed Random Numbers15Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 14–5 Normally Distributed Random Numbers16Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 14–4 Simulation Using Normally Distributed Random Numbers17Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 14–5 Two Common Types of Multiple-Variable Simulations18Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14-1 60 Random Numbers Generated by the RAND() Function19Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14-2 200 Random Numbers Generated Between 0 and 10020Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–3 200 Uniform Discrete Random Numbers Generated Between 20 and 10021Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–4 Histogram Specification Screen22Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–5 Histogram of the Values in Exhibit 14-323Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–6 Excel Worksheet and the Results Associated with the Andersen Quick Oil and Lube Example24Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–7 The Excel Worksheet for the Simulation of the Gas Station Waiting-Line Problem25Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–8 Excel Worksheet and the Results for the Golden Eagle Plumbing Company Inventory Problem Where Quantity =12, ROP =526Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–9 Excel Worksheet and the Results for the Golden Eagle Plumbing Company Inventory Problem Where Quantity = 10, ROP = 727Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–10 Excel Worksheet and the Results Associated with SolvedProblem 1 (Fire Station)28Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–11 Excel Worksheet and the Results Associated with SolvedProblem 229Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–12 Excel Worksheet and the Results Associated with Solved Problem 3 (Emergency Repairs)30Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 14–13 Excel Worksheet and the Results Associated with Solved Problem 3 (Emergency Repairs)31Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Advantages of SimulationIt is particularly well-suited for problems that are difficult or impossible to solve mathematically.It allows an analyst or decision maker to experiment with system behavior in a controlled environment instead of in a real-life setting that has inherent risks.It enables a decision maker to compress time in order to evaluate the long-term effects of various alternatives.It can serve as a mode for training decision makers by enabling them to observe the behavior of a system under different conditions.32Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Limitations of SimulationProbabilistic simulation results are approximations, rather than optimal solutions.Good simulations can be costly and time-consuming to develop properly; they also can be time-consuming to run, especially in cases in which a large number of trials are indicated.A certain amount of expertise is required in order to design a good simulation, and this may not be readily available.Analytical techniques may be available that can provide better answers to problems.33Copyright © 2007 The McGraw-Hill Companies. All rights reserved.