Chapter 14 Simulation, after completing this chapter, you should be able to: Explain 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;...
Introduction to Management Science with Spreadsheets Stevenson and Ozgur First Edition Part Probabilistic Decision Models Chapter 14 Simulation McGrawHill/Irwin Copyright © 2007 by The McGrawHill Companies, Inc. All rights reserved Learning Objectives After completing this chapter, you should be able to: Explain 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 Copyright © 2007 The McGrawHill McGraw Companies. All rights reserved. Hill/Irwin 14–2 Learning Objectives (cont’d) After completing this chapter, you should be able to: 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 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14–3 Simulation Simulation • 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 McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14–4 Types Types of of Simulations 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 McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14–5 Types Types of of Simulations Simulations (cont’d) (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 McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14–6 Types Types of of Simulations Simulations (cont’d) (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 McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14–7 Figure Figure14–1 14–1 Steps StepsininSimulation Simulation Define the problem Set objectives Develop model Gather data Validate model Design experiments Run simulations Copyright © 2007 The McGrawHill Companies. All rights reserved. Analyze and interpret results McGraw Hill/Irwin 14–8 The The Monte Monte Carlo Carlo Method 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 McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14–9 Table Table14–1 14–1 Random RandomNumbers Numbers Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 10 Exhibit Exhibit14-1 14-1 60 60Random RandomNumbers NumbersGenerated Generatedby bythe theRAND() RAND()Function Function Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 19 Exhibit Exhibit14-2 14-2 200 200Random RandomNumbers NumbersGenerated GeneratedBetween Between00and and100 100 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 20 Exhibit Exhibit14–3 14–3 200 200Uniform UniformDiscrete DiscreteRandom RandomNumbers NumbersGenerated GeneratedBetween Between 20 20and and100 100 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 21 Exhibit Exhibit14–4 14–4 Histogram HistogramSpecification SpecificationScreen Screen Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 22 Exhibit Exhibit14–5 14–5 Histogram Histogramof ofthe theValues ValuesininExhibit Exhibit14-3 14-3 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 23 Exhibit Exhibit14–6 14–6 Excel ExcelWorksheet Worksheetand andthe theResults ResultsAssociated Associatedwith withthe the Andersen AndersenQuick QuickOil Oiland andLube LubeExample Example Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 24 Exhibit Exhibit14–7 14–7 The TheExcel ExcelWorksheet Worksheetfor forthe theSimulation Simulationofofthe theGas GasStation Station Waiting-Line Waiting-LineProblem Problem Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 25 Exhibit Exhibit14–8 14–8 Excel ExcelWorksheet Worksheetand andthe theResults Resultsfor forthe theGolden GoldenEagle EaglePlumbing Plumbing Company CompanyInventory InventoryProblem ProblemWhere WhereQuantity Quantity=12, =12,ROP ROP=5 =5 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 26 Exhibit Exhibit14–9 14–9 Excel ExcelWorksheet Worksheetand andthe theResults Resultsfor forthe theGolden GoldenEagle Eagle Plumbing PlumbingCompany CompanyInventory InventoryProblem ProblemWhere WhereQuantity Quantity==10, 10, ROP ROP==77 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 27 Exhibit Exhibit14–10 14–10 Excel ExcelWorksheet Worksheetand andthe theResults ResultsAssociated Associatedwith withSolved Solved Problem Problem11(Fire (FireStation) Station) Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 28 Exhibit Exhibit14–11 14–11 Excel ExcelWorksheet Worksheetand andthe theResults ResultsAssociated Associatedwith withSolved Solved Problem Problem22 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 29 Exhibit Exhibit14–12 14–12 Excel ExcelWorksheet Worksheetand andthe theResults ResultsAssociated Associatedwith withSolved Solved Problem Problem33(Emergency (EmergencyRepairs) Repairs) Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 30 Exhibit Exhibit14–13 14–13 Excel ExcelWorksheet Worksheetand andthe theResults ResultsAssociated Associatedwith withSolved Solved Problem Problem33(Emergency (EmergencyRepairs) Repairs) Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 31 Advantages Advantages of of Simulation Simulation It 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 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin 14– 32 Limitations Limitations of of Simulation 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 McGraw Copyright © 2007 The McGrawHill Companies. All rights reserved. Hill/Irwin 14– 33 ... Exhibit Exhibit14–5 14? ??5 Histogram Histogramof ofthe theValues ValuesininExhibit Exhibit1 4-3 1 4- 3 Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin ? ?14? ?? 23 Exhibit... Hill/Irwin ? ?14? ?? 21 Exhibit Exhibit14–4 14? ??4 Histogram HistogramSpecification SpecificationScreen Screen Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin ? ?14? ?? 22... Hill/Irwin ? ?14? ??9 Table Table14–1 14? ??1 Random RandomNumbers Numbers Copyright © 2007 The McGrawHill Companies. All rights reserved. McGraw Hill/Irwin ? ?14? ?? 10 Table Table14–2 14? ??2 Simulating