Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 14 Simulation Part 3 Probabilistic Decision Models

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–2 Learning Objectives 1.Explain what the term simulation means and how simulation differs from analytical techniques. 2.Explain the difference between discrete and continuous simulations, between fixed-interval and next-event simulations, and between discrete and probabilistic simulations. 3.List and briefly describe the steps in simulation. 4.Use the Monte Carlo method to generate random numbers. 5.Conduct manual simulations using various distributions. After completing this chapter, you should be able to:

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–3 Learning Objectives (cont’d) 6.Conduct simulation with Excel using various distributions. 7.Conduct simple waiting-line simulation using Excel. 8.Conduct inventory management simulation using Excel. 9.List the advantages and limitations of simulations. After completing this chapter, you should be able to:

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–4 SimulationSimulation Simulation –A 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.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–5 Types of Simulations Discrete Simulations –Experimental situations in which outcome variables are discrete and are described by a count of the number of occurrences. Continuous Simulations –Experimental 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.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–6 Types of Simulations (cont’d) Fixed-Interval Simulations –Experiments 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 Simulations –Experiments 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.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–7 Types of Simulations (cont’d) Deterministic Simulations –Cases in which a specific outcome is certain, given a set of inputs. Probabilistic Simulations –Cases 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.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–8 Figure 14–1Steps in Simulation Define the problem Set objectives Develop model Gather data Validate model Design experiments Run simulations Analyze and interpret results

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–9 The Monte Carlo Method Monte Carlo Simulation –A commonly used approach for achieving randomness that derives its name from its similarity to games of chance. Characteristics of random numbers –All numbers are equally likely. –No patterns appear in sequences of numbers.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–10 Table 14–1Random Numbers

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–11 Table 14–2 Simulating a Coin Toss

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–12 Table 14–3Assigning Random Numbers for the Replacement Parts Example

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–13 Table 14–4Simulation of Replacement Parts Usage

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–14 Figure 14–2Conversion of a Random Number to a Uniform Distribution

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–15 Figure 14–3Simulating Exponentially Distributed Random Numbers

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–16 Table 14–5Normally Distributed Random Numbers

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–17 Figure 14–4Simulation Using Normally Distributed Random Numbers

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–18 Figure 14–5Two Common Types of Multiple-Variable Simulations

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–19 Exhibit Random Numbers Generated by the RAND() Function

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–20 Exhibit Random Numbers Generated Between 0 and 100

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–21 Exhibit 14–3200 Uniform Discrete Random Numbers Generated Between 20 and 100

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–22 Exhibit 14–4Histogram Specification Screen

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–23 Exhibit 14–5Histogram of the Values in Exhibit 14-3

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–24 Exhibit 14–6Excel Worksheet and the Results Associated with the Andersen Quick Oil and Lube Example

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–25 Exhibit 14–7The Excel Worksheet for the Simulation of the Gas Station Waiting-Line Problem

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–26 Exhibit 14–8Excel Worksheet and the Results for the Golden Eagle Plumbing Company Inventory Problem Where Quantity =12, ROP =5

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–27 Exhibit 14–9Excel Worksheet and the Results for the Golden Eagle Plumbing Company Inventory Problem Where Quantity = 10, ROP = 7

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–28 Exhibit 14–10Excel Worksheet and the Results Associated with Solved Problem 1 (Fire Station)

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–29 Exhibit 14–11Excel Worksheet and the Results Associated with Solved Problem 2

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–30 Exhibit 14–12Excel Worksheet and the Results Associated with Solved Problem 3 (Emergency Repairs)

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–31 Exhibit 14–13Excel Worksheet and the Results Associated with Solved Problem 3 (Emergency Repairs)

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–32 Advantages of Simulation 1.It is particularly well-suited for problems that are difficult or impossible to solve mathematically. 2.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. 3.It enables a decision maker to compress time in order to evaluate the long-term effects of various alternatives. 4.It can serve as a mode for training decision makers by enabling them to observe the behavior of a system under different conditions.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 14–33 Limitations of Simulation Probabilistic 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.