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Tiêu đề Simulation of Industrial Systems: Discrete Event Simulation Using Excel/VBA
Tác giả David Elizandro, Hamdy Taha
Trường học University of Houston
Chuyên ngành Engineering and Management
Thể loại book
Năm xuất bản 2007
Thành phố New York
Định dạng
Số trang 538
Dung lượng 8,91 MB

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Kamrani, Series Advisors University of Houston, Houston, TX Facility Logistics: Approaches and Solutions to Next Generation Challenges Maher Lahmar ISBN: 0-8493-8518-0 Simulation of Indu

Trang 2

SIMULATION OF INDUSTRIAL SYSTEMS

Trang 3

ENGINEERING AND MANAGEMENT INNOVATION SERIES

Hamid R Parsaei and Ali K Kamrani, Series Advisors

University of Houston, Houston, TX

Facility Logistics: Approaches and Solutions to Next Generation Challenges

Maher Lahmar

ISBN: 0-8493-8518-0

Simulation of Industrial Systems: Discrete Event Simulation Using Excel/VBA

David Elizandro and Hamdy Taha

Integral Logistics Management: Operations and

Supply Chain Management in Comprehensive

Value-Added Networks, Third Edition

The Portal to Lean Production: Principles

& Practices for Doing More With Less

by John Nicholas and Avi Soni

ISBN: 0-8493-5031-X

Supply Market Intelligence: A Managerial

Handbook for Building Sourcing Strategies

by Robert B Handfield

ISBN: 0-8493-2789-X

The Small Manufacturer s Toolkit: A Guide to

Selecting the Techniques and Systems to Help

You Win

by Steve Novak

ISBN: 0-8493-2883-7

Velocity Management in Logistics and Distribution:

Lessons from the Military to Secure the Speed

of Business

by Joseph L Walden

ISBN: 0-8493-2859-4

Supply Chain for Liquids: Out of the Box

Approaches to Liquid Logistics

by Wally Klatch

ISBN: 0-8493-2853-5

Supply Chain Architecture: A Blueprint for Networking

the Flow of Material, Information, and Cash

Introduction to e-Supply Chain Management:

Engaging Technology to Build Market-Winning Business Partnerships

by David C Ross ISBN: 1-57444-324-0

Supply Chain Networks and Business Process Orientation

by Kevin P McCormack and William C Johnson with William T Walker ISBN: 1-57444-327-5

Collaborative Manufacturing: Using Real-Time Information to Support the Supply Chain

by Michael McClellan ISBN: 1-57444-341-0

The Supply Chain Manager s Problem-Solver:

Maximizing the Value of Collaboration and Technology

by Charles C Poirier ISBN: 1-57444-335-6

Lean Performance ERP Project Management:

Implementing the Virtual Lean Enterprise, Second Edition

by Brian J Carroll ISBN: 0-8493-0532-2

Integrated Learning for ERP Success:

A Learning Requirements Planning Approach

by Karl M Kapp, with William F Latham and Hester N Ford-Latham

ISBN: 1-57444-296-1

Basics of Supply Chain Management

by Lawrence D Fredendall and Ed Hill ISBN: 1-57444-120-5

Lean Manufacturing: Tools, Techniques, and How to Use Them

by William M Feld ISBN: 1-57444-297-X

Back to Basics: Your Guide to Manufacturing Excellence

by Steven A Melnyk and R.T Chris Christensen ISBN: 1-57444-279-1

Enterprise Resource Planning and Beyond:

Integrating Your Entire Organization

by Gary A Langenwalter ISBN: 1-57444-260-0 ISBN: 0-8493-8515-6

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New York London

SIMULATION OF INDUSTRIAL SYSTEMS

David Elizandro • Hamdy Taha

Discrete Event Simulation Using Excel/VBA

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Microsoft, Windows, and Excel are registered trademarks of Microsoft Corporation in the United States and/

or other countries.

DEEDS is a copyright of David Elizandro.

CRC Press

Taylor & Francis Group

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Boca Raton, FL 33487-2742

© 2007 by Taylor & Francis Group, LLC

CRC Press is an imprint of Taylor & Francis Group, an Informa business

No claim to original U.S Government works

Version Date: 20140313

International Standard Book Number-13: 978-1-4200-6745-3 (eBook - PDF)

This book contains information obtained from authentic and highly regarded sources Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint.

Except as permitted under U.S Copyright Law, no part of this book may be reprinted, reproduced, ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers.

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To Marcia and Karen

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Contents

Preface xv

Acknowledgments xxi

Th e Authors xxiii

PART I SIMULATION FUNDAMENTALS 1 Simulation Modeling 3

1.1 Why Simulate? 3

1.2 Types of Simulation 5

1.3 Th e Simulation Clock 5

1.4 Randomness in Simulation 7

1.5 Discrete Simulation Languages 7

1.6 Design Environment for Event-Driven Simulation 8

1.7 Th e Two Sides of Simulation 9

1.8 Organization of the Book 10

For Further Reading 11

Problems 11

2 Probability and Statistics in Simulation 13

2.1 Role of Probability and Statistics in Simulation 13

2.2 Characterization of Common Distributions in Simulation 14

2.2.1 Properties of Common Distributions 14

2.2.1.1 Uniform Distribution 14

2.2.1.2 Negative Exponential Distribution 15

2.2.1.3 Gamma (Erlang) Distribution 16

2.2.1.4 Normal Distribution 17

2.2.1.5 Lognormal Distribution 17

2.2.1.6 Weibull Distribution 18

2.2.1.7 Beta Distribution 19

2.2.1.8 Triangular Distribution 19

2.2.1.9 Poisson Distribution 20

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viii Contents

2.2.2 Identifying Distribution on the Basis of Historical Data 21

2.2.2.1 Building Histograms 21

2.2.2.2 Goodness-of-Fit Tests 23

2.2.2.3 Maximum Likelihood Estimates of Distribution Parameters 26

2.3 Statistical Output Analysis 27

2.3.1 Confi dence Intervals 27

2.3.1.1 Satisfying the Normality Assumption in Simulation 29

2.3.2 Hypothesis Testing 29

2.4 Summary 32

References 32

Problems 33

3 Elements of Discrete Simulation 37

3.1 Concept of Events in Simulation 37

3.2 Common Simulation Approaches 38

3.2.1 Event-Scheduling Approach 38

3.2.2 Activity-Scanning Approach 44

3.2.3 Process-Simulation Approach 46

3.3 Computations of Random Deviates 48

3.3.1 Inverse Method 48

3.3.2 Convolution Method 51

3.3.3 Acceptance–Rejection Method 53

3.3.4 Other Sampling Methods 55

3.3.5 Generation of (0, 1) Random Numbers 56

3.4 Collecting Data in Simulation 57

3.4.1 Types of Statistical Variables 57

3.4.2 Histograms 59

3.4.3 Queue and Facility Statistics in Simulation 63

3.4.3.1 Queue Statistics 63

3.4.3.2 Facility Statistics 65

3.5 Summary 68

References 68

Problems 68

4 Gathering Statistical Observations in Simulation 73

4.1 Introduction 73

4.2 Peculiarities of the Simulation Experiment 73

4.2.1 Issue of Independence 74

4.2.2 Issue of Stationarity (Transient and Steady-State Conditions) 74

4.2.3 Issue of Normality 76

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Contents ix

4.3 Peculiarities of the Simulation Experiment 76

4.3.1 Normality and Independence 77

4.3.2 Transient Conditions 78

4.4 Gathering Simulation Observations 80

4.4.1 Subinterval Method 80

4.4.2 Replication Method 83

4.4.3 Regenerative Method 84

4.5 Variance Reduction 86

4.6 Summary 87

References 88

Problems 88

5 Overview of DEEDS 89

5.1 Introduction 89

5.2 DEEDS Modeling Philosophy 89

5.3 Basic Elements of DEEDS 91

5.4 Basic Features of DEEDS 93

5.4.1 Network Representation 93

5.4.2 Time Management (Simulation Clock) 93

5.4.3 DEEDS Class Defi nitions 94

5.4.4 User’s Files Management 94

5.4.5 Generation of Random Samples 96

5.4.6 Statistical Observations Gathering 96

5.4.7 Interactive Debugging and Trace 96

5.4.8 Computations of Mathematical Expressions 98

5.4.9 Initialization Capabilities 98

5.4.10 Output Capabilities 98

5.4.11 Model Documentation 99

5.5 Develop and Execute a DEEDS Model 99

5.6 Summary 99

6 DEEDS Network Representation 101

6.1 Components of the DEEDS Model 101

6.1.1 DEEDS Nodes 101

6.1.2 DEEDS Transactions 102

6.1.3 DEEDS Lists 102

6.1.4 DEEDS Classes and Procedures 103

6.1.5 DEEDS Simulation Program 104

6.2 Program Initial Conditions 108

6.3 Summary 110

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x Contents

PART II EXCEL/VBA AND DESIGN ENVIRONMENT

FOR DISCRETE EVENT SIMULATION

7 VBA Programming 113

7.1 Introduction 113

7.2 Names 113

7.3 Data Types 113

7.4 Variable Defi nitions 114

7.5 Constants 115

7.6 Expressions 116

7.7 Assignment Statements 117

7.8 Control Structures 119

7.8.1 If 119

7.8.2 Case 121

7.8.3 For 123

7.8.4 Do 123

7.9 Procedures 124

7.9.1 Subs 125

7.9.2 Functions 128

7.10 Arrays 128

7.11 Summary 131

8 User Interface 133

8.1 Introduction 133

8.2 Overview of ProgramManager 133

8.3 Source Nodes 135

8.4 Queue Nodes 136

8.5 Facility Nodes 137

8.6 Initial Model 138

8.6.1 Build VBA Code 139

8.6.2 Program Execution 142

8.6.3 Viewing Options 144

8.7 Delay Nodes 149

8.8 Statistical Variables 149

8.9 User-Defi ned Probability Functions 153

8.10 User-Defi ned Tables 155

8.11 Program Execution—Expanded 156

8.12 Summary 157

9 Modeling Procedures 159

9.1 Introduction 159

9.2 Visual Basic Procedures 159

9.3 Simulator Procedures 160

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Contents xi

9.4 DEEDS Classes 162

9.4.1 Source 163

9.4.2 Queue 165

9.4.3 Facility 169

9.4.4 Delay 176

9.4.5 Transaction 177

9.4.6 Statistic 181

9.4.7 pdf 183

9.4.8 Table 185

9.5 Distribution Functions 186

9.6 Visual Basic Functions 187

9.7 Excel WorksheetFunction 188

9.8 Summary 195

Problems 195

10 Simulation Output 205

10.1 Introduction 205

10.2 Gathering Observations 205

10.3 Simulation Messages 207

10.4 Monitoring Simulation During Execution 207

10.5 Forced Model Termination 208

10.6 Standard Output 209

10.6.1 Source Sheet 209

10.6.2 Queue Sheet 209

10.6.3 Facility Sheet 211

10.6.4 Delay Sheet 212

10.6.5 Statistics Sheet 212

10.6.6 UserOutput Sheet 213

10.7 Model Verifi cation 214

10.7.1 User-Defi ned Simulator Messages 214

10.7.2 Trace Report 215

10.7.3 Collection Report 217

10.8 VBA Interactive Debugger 218

10.9 Summary 223

11 Analysis of Simulation Results 225

11.1 Introduction 225

11.2 Eff ect of Transient State 227

11.3 Gathering Statistical Observations 232

11.4 Establishing Confi dence Intervals 234

11.5 Hypothesis Testing in Simulation Experiments 235

11.6 Summary 236

Reference 236

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xii Contents

12 Modeling Special Eff ects 237

12.1 Introduction 237

12.2 A Multi-Server Facility to Represent Independent Facilities 237

12.3 Facility Preemption Operation 240

12.4 Limit on Waiting Time in Queues 242

12.5 Time-Dependent Intercreation Times at a Source 244

12.6 Network Logic Change Using Queue Nodes 246

12.7 Controlled Blockage of a Facility 248

12.8 Assemble and Match Sets with Common Queues 250

12.9 Jackson Networks 252

12.10 Sampling without Replacement 254

Reference 255

Problems 255

13 Advanced Routing Techniques 259

13.1 Introduction 259

13.2 Routing Transactions 259

13.2.1 Always Routing 260

13.2.2 Conditional Routing 260

13.2.3 Select Routing 261

13.2.3.1 Node Independent 262

13.2.3.2 Current State of Node 264

13.2.3.3 “Recent History” of Node 264

13.2.4 Probabilistic Routing 265

13.2.5 Dependent Routing 266

13.2.6 Exclusive Routing 267

13.2.7 Last Choice 267

13.3 Synchronized Queues 270

13.3.1 Match 270

13.3.2 Assemble Transactions 272

13.4 Summary 274

Problems 274

PART III APPLICATIONS 14 Simulation Project Management 281

14.1 Introduction 281

14.2 System Specifi cation 281

14.3 Simulation Constants, Decision Variables, and Constraints 283

14.4 Data Specifi cations 286

14.5 Project Management 288

14.5.1 Problem Defi nition 289

14.5.2 Preliminary Design 290

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Contents xiii

14.5.3 Validate Design 290

14.5.4 Model Development 290

14.5.5 Verify Model 291

14.5.6 Design/Conduct Experiments 291

14.5.7 Summarize/Present Results 292

14.6 Summary 292

References 293

15 Facilities Layout Models 295

15.1 Introduction 295

15.2 Line Balancing 296

15.3 Flexible Manufacturing Environment 306

Reference 317

16 Materials-Handling Models 319

16.1 Introduction 319

16.2 Transporter Car 319

16.3 Overhead Crane 323

16.4 Carrousel Conveyor 330

16.5 Belt Conveyor—Plywood Mill Operation 334

References 342

17 Inventory Control Models 343

17.1 Introduction 343

17.2 Discount Store Model 343

17.3 Periodic Review Model 348

17.4 Continuous Review Model 352

References 357

18 Scheduling Models 359

18.1 Introduction 359

18.2 Job Shop Scheduling 359

18.3 PERT Project Scheduling 367

18.4 Daily Manpower Allocation 372

References 379

19 Maintenance and Reliability Models 381

19.1 Introduction 381

19.2 General Reliability Model 381

19.3 Maintenance Scheduling 385

20 Quality Control Models 397

20.1 Introduction 397

20.2 Costing Inspection Plans 397

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xiv Contents

20.3 Monitoring Control Charts 403

Reference 410

21 Supply Chain Models 411

21.1 Introduction 411

21.2 Port Operation 411

21.3 Automatic Warehouse Operation 421

21.4 Cross Dock Model 430

References 439

Problems 439

22 Advanced Analysis Techniques 447

22.1 Introduction 447

22.2 Evaluation of Alternatives 447

22.3 Design of Experiments 448

22.4 Simulation and Search Algorithms 450

22.5 Cross Dock Problem 452

22.6 Summary 464

References 466

Appendix A Initializing DEEDS 467

Appendix B Classes and Procedures 479

Appendix C Histograms Using Excel 489

Index 495

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Preface

Lean manufacturing describes the Toyota Production System According to Taiichi

Ohno, the focus of Toyota was “the absolute elimination of waste.” Th ere are

vari-ations on implementation of lean systems, but the essence is that a continuous

one-piece fl ow is ideal with emphasis on integrating systems of people, equipment,

materials, and facilities, to achieve improvements in quality, cost, on-time delivery,

and performance Process improvements are typically described as a reduction in

cycle time or lead time; a reduction in the cost of space, inventory, and capital

equipment; an increase in capacity utilization; and the elimination of bottlenecks

Production systems, based on the concept of lean manufacturing, are becoming

a paradigm across many industries In a broader sense, operations management is

the practice of coordinating the physical work place with the people and work of

a particular organization to support organizational objectives As such, operations

managers have responsibility for planning, operating, and maintaining complex

and diverse resources Similar to manufacturing processes, improvements in these

production systems may also be described in terms of reduced cycle time,

reduc-tion in cost, increase in capacity utilizareduc-tion, and the eliminareduc-tion of bottlenecks In

any production environment, discrete event simulation is a powerful tool for the

analysis, planning, design, and operation of those facilities

Th is book is written for the novice who wants to learn the basics of discrete

simulation as well as for professionals who wish to use discrete event simulation

to model systems described above Th e book assumes that the reader has a

funda-mental familiarity with modeling concepts and Excel; however, it does not assume

any prior programming experience Th e book is organized into three parts Part I

presents concepts of discrete simulation Part II covers the Design Environment for

Event-Driven Simulation (DEEDS), and Part III presents a variety of applications

using DEEDS Th e DEEDS environment is itself an Excel/VBA add-in

Background

Basic approaches to discrete simulation have been process simulation languages

(e.g., GPSS) and event-scheduling type (e.g., SIMSCRIPT) Th e trade-off s are that

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xvi Preface

event-scheduling languages off er more modeling fl exibility and process-oriented

languages are more intuitive to the user

Process-oriented languages are based on blocks (or nodes) that perform

func-tions in serial fashion For example, suppose that a transaction leaving a queue must

dispose of a previously acquired resource before it enters one of several available

facilities for processing Th e leaving transaction must pass through a special block/

node to dispose of the resource and then through another to select the desired

facility

In a process-oriented language, special blocks/nodes must be designed to

respond to distinct modeling needs Th e result is that the language is not as

user-friendly because of the high level of model abstractness and the large number of

blocks/nodes in the language Also, the fact that transactions must pass through

these blocks/nodes serially does indeed reduce the language fl exibility and may

create the need for external (FORTRAN, Visual Basic, or Java) program inserts A

third disadvantage is that each special block/node is designed to respond to specifi c

modeling needs, an approach that inevitably leads to a degree of redundancy, and

hence ineffi ciency, in the language

Objectives of the Book

With these considerations in mind, we embarked on the development of a new

discrete simulation environment Th e design objectives are to

Achieve the modeling fl exibility of an event-driven simulation languageAchieve the intuitive nature of a process-oriented language

Develop a user-friendly implementation environment

In essence, the goal was to design a development environment that is easy to use,

yet fl exible enough to model complex production systems

Approach

Using pioneering ideas of Q-GERT’s network simulation (nodes connected by

branches), Taha developed the simulation language SIMNET Th e basis of

SIM-NET was that the majority of discrete simulations may be viewed in some form or

other as a complex combination of simple queuing systems SIMNET has four basic

types of nodes: a source from which transactions arrive, a queue where transactions

may wait when necessary, a facility where service is performed, and a “Delay” node,

which is an infi nite-capacity generalization of a facility node

DEEDS implements the basic tenets of SIMNET in the Excel/VBA

environ-ment Each node is designed to be self-contained, in the sense that user-developed

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Preface xvii

event handlers written in Visual Basic for Applications (VBA) manage the transaction

before it enters and as it leaves the node In essence, such a defi nition implements the

sequential nature of a process-oriented language, without the many blocks, and

pro-vides for the fl exibility of event-driven simulation languages Th is approach has proven

to be eff ective and convenient in handling very complex simulation models

DEEDS is used by undergraduate industrial engineering students in the fi rst

simulation course at Tennessee Technological University Th ese students have

com-pleted an information systems course based on Excel and VBA It is gratifying to

report that these students were able to use DEEDS eff ectively to program fairly

complex models after only four weeks of instruction Some of these models are

included in this book

Th e students indicated the following advantages of DEEDS:

Excel facilitates model development and presentation of results

With a VBA background, DEEDS is easy to learn

A user interface facilitates model development and program management

An interactive VBA debugger and “like English” trace report reduce the

eff ort to validate a model

VBA class defi nitions facilitate managing the four network nodes

Explicit simulator messages detail unusual events that occur during the simulation

Contents

Th e fi rst part (Chapters 1 through 6) focuses on the fundamentals of simulation,

and the second part (Chapters 7 through 13) covers DEEDS Chapters 14 through

22, the third part, present examples of production systems models and techniques

for using DEEDS to improve decision-making

In Part I, the subject of simulation is treated in a generic sense to provide the

reader with an understanding of the capabilities and limitations of this important

tool Chapter 1 provides an overview of simulation modeling with emphasis on the

statistical nature of simulation Chapter 2 gives a summary of the role of statistics

in the simulation experiment Chapter 3 is devoted to introducing the elements

of discrete simulation including types of simulation, methods for sampling from

distributions, and methods for collecting data in simulation runs Th e material

in Chapter 4 deals with the statistical peculiarities of the simulation experiment

and ways to circumvent the diffi culties arising from these peculiarities Chapter

5 begins with an overview of the DEEDS environment Chapter 6 introduces the

network representation and VBA classes to represent sources, queues, facilities, and

delays in DEEDS

Although the material in Part I treats simulation in a general sense, it ties to

DEEDS by introducing and defi ning the terminology and the concepts used in the

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xviii Preface

development of the language Th e reader is encouraged to review at least Chapters

3 through 6 before beginning Part II

In Part II, Chapter 7 provides an overview of the VBA essentials needed for

programming in the DEEDS environment Chapter 8 presents features of the

ProgramManager, the user interface for program management Also in Chapter 8 is

a description of the EventsManager module where the simulation program resides

and how to develop and execute a program Chapter 9 presents details of developing

simulation programs in DEEDS Included in Chapter 9 are Simulator procedures

and methods for DEEDS classes In Chapter 10 are the output features of DEEDS

and model validation tools such as simulation reports and the VBA Interactive

Debugger Chapter 11 presents details on how to conduct simulation experiments

in DEEDS Chapter 12 presents a variety of programs that demonstrate the fl

ex-ibility of DEEDS In Chapter 13 are advanced features of DEEDS that assist the

modeler with complex transaction routing schemes

In Part III, Chapter 14 presents concepts on the design and development of

large and complex simulation models Also presented in Chapter 14 is an overview

of management issues related to simulation projects In Chapters 15 through 21,

DEEDS simulation programs are designed and developed for a spectrum of

tradi-tional application areas that include facilities layout, materials handling, inventory

control, scheduling, maintenance, quality control, and supply chain logistics For

the practitioner, models have been organized into chapters to address common

operations management topics However, several models could easily fi t into two

or more chapters

All of the models were developed by senior students in an advanced simulation

course at Tennessee Tech University Th eir models have been edited to

empha-size certain DEEDS features Solutions may be regarded as examples of how these

problems may be modeled in DEEDS To conserve space, only selected output

results based on a single run for each problem are presented Most of these problems

have been widely circulated in the literature as the basis for comparing simulation

languages

In Chapter 22, the capstone chapter, the research features of DEEDS are

dem-onstrated In contrast to the traditional “what if” approach to simulation, design

of experiments and genetic algorithms techniques are integrated into the DEEDS

environment to produce a powerful tool that can be used for “optimizing”

prob-lems described in Chapters 15 through 21

Use of This Book

Th e fl exibility of DEEDS makes it a great tool for students or novice to learn

con-cepts of discrete simulation Th erefore, it can be the basis for an undergraduate

course in introduction to simulation By extending the depth of coverage, it can

be the basis for a graduate simulation course It can also be a reference book for

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Preface xix

practitioners engaged in simulation projects It may also be used as a research tool

by faculty and graduate students who are interested in “optimizing” production

systems

For projects that require animation, DEEDS can be used for rapid

prototyp-ing of the model so that simulation experiments can begin before the animation is

complete For complex models, many of the VBA program segments from DEEDS

can also be used in the animation software and the DEEDS program can be used

as model documentation

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Acknowledgments

Recent simulation classes at Tennessee Tech University demonstrated that DEEDS

is a viable tool for teaching concepts of discrete event simulation Neither this book

nor the DEEDS software would have been brought to fruition without the eff orts

of Clinton Th omas, Julie Braden, Chad Watson, Jacob Manahan, Chris Potts, and

Chad Bournes Each of these students made unique contributions to the design

of DEEDS and demonstrated that DEEDS is a viable tool for modeling complex

systems Marcia Elizandro was very kind to contribute many hours by proofreading

early versions of the manuscript Diane Knight was most helpful with editing the

fi nal version Randy Smith, at Microsoft, provided valuable advice on VB

program-ming in Visual Studio Finally, a very special thanks to Brandon Malone, a master’s

degree candidate in computer science at Tennessee Tech University who did a great

job helping to move the simulator from VBA to VB.net

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The Authors

David W Elizandro is a professor of

indus-trial engineering at Tennessee Tech University where he teaches operations research and simu-lation He earned a BS in chemical engineer-ing, MBA, and PhD in industrial engineering

Professor Elizandro has served in administrative and leadership roles in science and engineering education

Professor Elizandro has written publica tions and made presentations in areas such as expert systems, data communica tions, distributed simulation, adaptive control systems, digital signal processing, and integrating technology into engineering education He has also been an industry consultant on projects that include developing computer models to assess

manpower production requirements and resource utilization; evaluation of an

over-night freight delivery network; performance of digital signal processing boards; and

response time for a fl ight controller communications system

Professor Elizandro received the Distinguished Faculty Award, Texas A&M,

Commerce, served on the National Highway Safety Advisory Commission, and is

a member of Tau Beta Pi, Alpha Pi Mu, and Upsilon Pi Epsilon

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xxiv The Authors

Hamdy A Taha is a university professor

emeritus of industrial engineering with the University of Arkansas, where he taught and conducted research in operations research and simulation He is the author of four other books on integer programming and simulation, and his works have been translated into Chi-nese, Korean, Spanish, Japanese, Malay, Rus-sian, Turkish, and Indonesian He is also the author of several book chapters, and his techni-

cal articles have appeared in the European

Jour-nal of Operations Research, IEEE Transactions on Reliability, IIE Transactions, Interfaces, Manage- ment Science, Naval Research Logistics Quarterly, Operations Research, and Simulation.

Professor Taha was the recipient of the Alumni Award for excellence in research and the universitywide Nadine Baum Award for excellence in teaching, both from the

University of Arkansas, and numerous other research and teaching awards from

the College of Engineering, University of Arkansas He was also named a Senior

Fulbright Scholar to Carlos III University, Madrid, Spain He is fl uent in three

languages and has held teaching and consulting positions in Europe, Mexico, and

the Middle East

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SIMULATION

FUNDAMENTALS

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Chapter 1

Simulation Modeling

Lean manufacturing is a term that describes the Toyota Production System

Accord-ing to Taiichi Ohno, the focus at Toyota was “the absolute elimination of waste.”

Waste is anything that prevents the value-added fl ow from raw material to fi nished

goods Th ere are variations on implementation of lean systems, but the essence is

that a continuous one-piece fl ow is ideal with emphasis on optimizing and

integrat-ing systems of people, equipment, materials, and facilities, to achieve improvements

in quality, cost, on-time delivery, and performance Process improvements are

typi-cally described as a reduction in cycle time or lead time; a reduction in the cost of

space, inventory, and capital equipment; an increase in capacity utilization; and the

elimination of bottlenecks

Production systems, based on the concept of lean manufacturing, are emerging

as a paradigm across many industries In a broader sense, operations management

is the practice of coordinating the physical workplace with the people and work of

a particular organization to support organizational objectives As such, operations

managers have responsibility for planning, operating, and maintaining complex

and diverse resources Similar to manufacturing processes, improvements in these

production systems may also be described in terms of reduced cycle time,

reduc-tion in cost, increase in capacity utilizareduc-tion, and the eliminareduc-tion of bottlenecks In

either environment, discrete event simulation is a powerful tool for the analysis,

planning, design, and operation of those facilities

Imagine the following situation Aircraft arrive at an intermediate-range

air-port Th e airport has two runways, one for landing and the other for takeoff

Aircraft that cannot land upon arrival in the air space of the facility must circle

within specifi ed “holding stacks” until a runway becomes available If the number

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4 Simulation of Industrial Systems

of “holding” planes exceeds a certain quota, the air traffi c controller must clear the

takeoff runway and allow circling planes to land Th e runways are connected to the

passenger terminal via taxiways A plane that cannot take off immediately upon

reaching the end of the taxiway waits on a holding apron Th e airport authority

is currently conducting a study with the objective of improving the landing and

takeoff services at the facility

To investigate the given situation, we specify certain system performance

mea-sures such as

1 Th e average time a plane waits in a holding apron

2 Th e average number of planes in holding stacks

3 Th e average utilization of the taxiways and runways

Considering the strict regulations under which most airports operate, such

perfor-mance measures can usually be determined from historical data In conducting a

study, however, we are more interested in assessing the impact of proposed changes

in the system (e.g., increasing the number of runways) on the desired performance

measures Th e question then becomes, How can we estimate performance measures

on a system that does not exist? It would be naive (at least in this situation) to

pro-pose experimenting with the real system Perhaps the only available alternative in

this case is to consider representing the proposed system by a model Th is is where

simulation plays an important role

Simulation modeling should be regarded as “the next best thing to observing

a real system in operation.” Indeed, the basic contribution of a simulation model

is that it allows us to observe performance characteristics of the system over time

Th ese observations may then be used to estimate expected performance measures of

the system For the airport example, a simulation model will record an observation

representing the number of circling planes each time a new aircraft enters or leaves

the holding stacks Th ese observations may then be used to calculate the

(time-weighted) average number of planes in the stacks

You may be thinking that the airport situation can be analyzed by using the

results of queueing theory However, those familiar with the capabilities of

queue-ing theory will recognize that queuequeue-ing models are rather restrictive In particular,

queueing theory is only capable of describing isolated segments of the complex

air-port operation Th is type of segmented analysis will likely fail to refl ect the impact

of the interaction of the various components on the overall behavior of the system

As a result, performance measure estimates may be severely biased For example,

in the airport situation, the landing and takeoff operations must be studied as two

dependent queues However, queueing theory models are not capable of

represent-ing the links between these two operations Th is drawback is primarily due to the

intractability of mathematical models for such systems

Why is simulation diff erent? Th e answer is that simulation typically represents

the entire system rather than in a segmented fashion as in mathematical models

All of the “cause and eff ect” relationships among the diff erent components of the

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Simulation Modeling 5

model are accounted for in a simulation model Th e purpose of a simulation model

is to imitate the behavior of the real system (as closely as possible) Collecting

obser-vations is simply monitoring the behavior of the various model components as a

function of simulation time

1.2 Types of Simulation

Th e main purpose of a simulation model is to gather observations about a particular

system as a function of time From that standpoint, there are two distinct types of

simulation:

1 Discrete

2 Continuous

In discrete simulation, observations are gathered only at points in time when

changes occur in the system On the contrary, continuous simulation requires that

observations be collected continuously at every point in time

To illustrate the diff erence between the two types of simulation, we use the

example of a single-server facility and an oil terminal supplying a number of storage

tanks through a pipeline network In the single-server model, changes in the status

of the system occur only when a customer arrives or completes service At these

two points in time, performance measures such as queue length and waiting time

in the facility will be aff ected At all other points in time, these measures remain

unchanged (e.g., queue length) and not yet ready for data collection (e.g., waiting

time) For this reason, one needs to observe the system only at selected discrete

points in time—hence the name discrete simulation.

In the oil pipeline example, one of the measures of performance could be the

oil level in each tank Because of the nature of the product, fl ow into and out of a

tank occurs on a continuous basis In other words, the system must be monitored

continuously In this case, the output must be presented as a function of the time

Because it is practically impossible to monitor a system continuously in simulation,

the actual recording of observations usually occurs at small equal intervals in time

Although continuous simulation has important applications, most attention

has been directed toward discrete simulation Th e main reason is the wide range

of problems in this area Also, continuous simulation appears straightforward,

whereas discrete simulation usually requires more user creativity

1.3 The Simulation Clock

Simulation, as we stated earlier, collects observations by monitoring the “modeled”

system over time As such, the simulation model must have an internal clock Unlike

familiar time devices, this clock is designed to initiate the collecting of observations

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6 Simulation of Industrial Systems

at the moment before changes take place in the system Such a clock in continuous

simulation is straightforward because it implies “looking” at the system at equally

spaced time intervals However, in the discrete case, the system is observed only

when system changes occur

To demonstrate how the discrete simulation clock works, we consider a simple

system with a single-server facility What simulation does in this case is to follow

the movement of each customer from the instant of arrival into the system until

a system departure occurs To achieve this goal, the simulator must be capable of

determining the exact time each customer arrives to and departs from the service

facility Such information is available from knowledge of the times between

succes-sive arrivals and customer service time

In essence, once we are given the time at which the facility “opens for business,”

together with the time interval between successive arrivals and the service time per

customer, we are able to trace the fl ow of each customer, from system arrival to

system departure

Note importantly that simulation does not operate by tracing individual

cus-tomers Instead, it identifi es the points of arrival and departure chronologically

on the timescale regardless of the identity of the customer arriving or departing

the system Th is approach, in essence, categorizes system changes into two specifi c

types of simulation events—arrivals and service completions—while suppressing

the specifi c identity of each customer

Figure 1.1 shows a typical mapping of single-server events on the timescale

Th e simulation processes these events in chronological order and specifi es actions

depending on the type of the event For example, when an arrival event takes place,

the customer will either start service if facility is available, or will wait in a queue

until the facility is free When a customer is ready to begin service, the service

completion event is scheduled (and mapped onto the timescale) by adding the

ser-vice time to the current simulation clock time In a similar manner, when a serser-vice

completion event occurs, a check is made for any waiting customers Upon service

completion, the waiting customer departs the queue and another engages the

facil-ity with a new service completion event mapped onto the timescale

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Simulation Modeling 7

As previously mentioned, the clock in discrete simulation stops at the time an

event occurs As a result, the simulation clock may be viewed as “jumping” to the

point in time that defi nes the next chronological event Th is explains the reason

that such simulations are referred to as discrete event simulation.

1.4 Randomness in Simulation

Th e discrete event scheme described for the single-server facility works only if two

basic data elements are known: (1) the interarrival time and (2) the service time You

may wonder how such information is obtained during the course of a simulation

In most real-life situations, customer interarrival times and service times occur

in a random fashion Th e only way we can represent this randomness is by using

probability distributions to describe the variables being considered For example, if

the arrivals occur in a Poisson stream, then from probability theory we know that

the interarrival distribution is exponential In general, information on customer

arrivals is based on either direct observation of the system or historical data

Oth-erwise, some plausible assumption must be made to describe the random process by

a probability distribution

Once the probability distribution has been selected, statistical theory provides

the basis for obtaining random samples based on (0, 1) uniform random numbers

Th ese random samples are used to map the occurrence of an event on the timescale

For example, if the interarrival time is exponential, then a random sample drawn

from that distribution represents the lapsed time before the next arrival

Randomness in simulation is not limited to time Suppose, for example,

arriv-ing customers may choose between one of two servers accordarriv-ing to their individual

preference To represent this situation, we must quantify an arriving customer’s

preference for one server over the other Such information is also based on

observa-tion or historical data Th e result is two ratios representing the allocation of

cus-tomers to the two servers Th is, in eff ect, is equivalent to specifying a probability

distribution from which samples can be drawn to decide on the server chosen by

an arriving customer

1.5 Discrete Simulation Languages

Discrete simulation involves a large number of repetitious computations

Conse-quently, the use of computers to carry out these computations is essential However,

the number of computations is not the only obstacle in simulation If you consider the

single-server simulation presented in Sections 1.3 and 1.4, you will conclude that it

involves a complex logical structure that requires special expertise to develop a

com-puter model Take, for example, the case of mapping generated events chronologically

on a timescale To write a procedural language (i.e., BASIC, FORTRAN, or Java)

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8 Simulation of Industrial Systems

program for this segment of the simulation model requires above-average

program-ming skills In the absence of some software development tools to relieve the user of

this burden, simulation as a tool would most certainly be the domain of “elite”

pro-grammers Fortunately, the repetitive nature of simulation computations is the basis

for the development of a suite of computer programs that are applicable to all

simula-tion models For example, routines for ordering events chronologically, as well as those

for generating random samples, apply to any simulation model

Modern computers have induced the development of full-fl edged simulation

languages that are applicable to any simulation situation Some languages have

been developed for either continuous or discrete simulations Others can be used

for combined continuous and discrete modeling All languages provide certain

standard programming facilities and diff er in the degree of detail that the user

must specify to develop a model Th ere is a trade-off Usually, languages that are

highly fl exible in representing complex situations require the user to provide a more

detailed account of the model logic Th is type of language is generally less

“user-friendly.” On the contrary, compact, easy-to-implement languages are usually more

rigid, which may make it diffi cult to represent complex interactions

In general, there are two types of discrete simulation languages:

1 Event-scheduling

2 Process-based

Event-scheduling languages deal directly with the individual actions associated

with each type of event Th ese languages are highly fl exible in representing complex

situations because the user provides most of the details Most prominent among

these languages are SIMSCRIPT and GASP

Process-based languages are usually more compact as they are designed to

rep-resent the movement of a “customer” (commonly referred to as a transaction or

entity) from the instant it enters the simulated system until it is discharged, thus

relieving the user from programming most of the details Th e oldest of these

lan-guages is GPSS More recent lanlan-guages include SLAM, SIMAN, and SIMULA

GPSS, SIMAN, and SLAM allow user-defi ned procedural language routines to

be linked to the model Additionally, SIMAN and SLAM have the capabilities of

modeling continuous systems

1.6 Design Environment for Event-Driven Simulation

Because the majority of discrete simulation systems may be viewed in some form or

another as a queueing situation, the design of available process-oriented languages

has centered around the use of three basic blocks or nodes: a source for creating

transactions, a facility where transactions are serviced, and a queue where

transac-tions may wait However, to simulate complex situatransac-tions, it is necessary to develop

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Simulation Modeling 9

special-purpose blocks to “direct traffi c” among these three basic blocks In serial

traffi c, each block contributes to satisfying the “needs” of the transaction as it fl ows

from one basic block to the next Th e disadvantage of the “serial block” design

philosophy is that the language is much less user-friendly because of the number of

blocks required to direct “traffi c fl ow” in the model In reality, only the most simple

of situations may be represented using the serial block approach

Th e design environment for event-driven simulation (DEEDS) approach

elimi-nates the use of special-purpose nodes and reduces the language to dealing with

exactly four nodes: a source, a queue, a facility, and a delay As shown in later

chapters, the delay node, which may be considered as an infi nite capacity facility,

enhances the fl exibility of the language Each node is designed to be self-contained,

in the sense that suffi cient information is provided to manage the transaction

within a given node User-developed routines written in Visual Basic for

Applica-tions (VBA) manage the transaction as it enters and leaves a node In essence, such

a defi nition focuses on “directing traffi c” without the many blocks of a process

language at the expense of minimal incremental eff ort for “serial” traffi c situations

Th is approach has proven to be eff ective and convenient in handling very complex

simulation models

1.7 The Two Sides of Simulation

Simulation studies encompass two broad phases:

1 Construction, debugging, and running of the model

2 Interpretation of model output

Th e fi rst phase usually is by far the most time-consuming It begins with selecting

a suitable simulation language (or procedural language) to represent the logic of the

model It also includes collecting input data for the model Debugging is essential

to ensure that the model logic is correct Finally, tracing simulation computations

as a function of time to verify that the results of the model “make sense” must be

done Once the model is debugged and validated, the model can then be run for an

“appropriate” length of time to estimate the system’s output

Th e second phase is the most crucial and probably the most neglected among

simulation users Simulation, by the very nature of its inherent randomness, is a

statistical experiment Th erefore, the output of simulation must be interpreted

sta-tistically Indeed, the simulation experiment has peculiar statistical properties that

must be considered when interpreting the results Otherwise, the simulation output

may be heavily biased

We must always keep in mind that, just as in any other physical experiment, a

simulation study must be subjected to all the proper statistical techniques Failing

to do so may render simulation results that are worthless Unfortunately, this aspect

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10 Simulation of Industrial Systems

of simulation is often ignored because a user may not be well trained in the use of

statistical techniques Th is defi ciency, coupled with lack of knowledge about the

peculiarities of the simulation experiment, has contributed to the misuse of

simu-lation Fortunately, there is a trend that simulation languages include automatic

features to assist with applying statistical tests on the simulation output

1.8 Organization of the Book

Th is book encompasses three major parts In the fi rst part (Chapters 2 through 4),

the prominent theoretical aspects of simulation are discussed and explained Th is

part includes the mechanics of constructing a discrete simulation model using the

concept of events It also shows how input data are prepared for use by the model

Methods for collecting data internally by a simulation language processor are also

detailed Finally, the statistical aspect of the simulation experiment is explained,

and its impact on simulation output is emphasized

Although Chapters 5 and 6 treat simulation in a general sense, they tie to

DEEDS by introducing and defi ning the terminology and the concepts used in

the development of DEEDS Th e reader is encouraged to review at least Chapters 3

through 6 before beginning Part II

In Part II, Chapter 7 provides an overview of the VBA essentials needed for

programming in the DEEDS environment Chapter 8 presents features of the

ProgramManager, the user interface for program management Also in Chapter 8 is

a description of the EventsManager module where the simulation program resides

and how to develop and execute a program Chapter 9 presents details of

develop-ing simulation programs in DEEDS It also presents Simulator procedures and

methods for DEEDS classes Chapter 10 presents the output features of DEEDS

and model validation tools such as simulation reports and the VBA Interactive

Debugger Chapter 11 details how to conduct simulation experiments in DEEDS

Chapter 12 presents a variety of programs that demonstrate the fl exibility of

DEEDS Chapter 13 presents advanced features of DEEDS that assist the modeler

with complex decision-making schemes

In Part III, Chapter 14 presents concepts on the design and development of

large and complex simulation models Also presented in Chapter 14 is an

over-view of management issues related to simulation projects In Chapters 15 through

21, DEEDS simulation programs are designed and developed for a spectrum of

traditional application areas that include facilities layout, material handling,

inventory control, scheduling, maintenance, quality control, and supply chain

logistics

In Chapter 22, the research features of DEEDS are demonstrated In contrast

to the traditional “what if” approach to simulation, design of experiments and

genetic algorithms techniques are integrated into the DEEDS environment to

pro-duce a powerful tool that can be used for “optimizing” models

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Simulation Modeling 11

For Further Reading

1 Banks, J and J Carson II, Discrete-Event System Simulation Englewood Cliff s, NJ:

Prentice-Hall, Inc., 1984

2 Gordon, G., Th e Application of GPSSV to Discrete System Simulation Englewood

Cliff s, NJ: Prentice-Hall, Inc., 1975

3 Henrickson, J and R Crain, Th e GPSSIH User’s Manual, 2nd ed Annandale, VA:

Wolverine Software Corporation, 1983

4 Law Averill, M., Simulation Modeling and Analysis, 4th ed New York: McGraw-Hill

8 Pritsker, A A B., Modeling and Analysis Using Q-GERT Networks, 2nd ed New York:

Halsted Press, Wiley, 1979

9 Pritsker, A A B and C E Sigal, Management Decision Making: A Network

Simula-tion Approval Englewood Cliff s, NJ: Prentice-Hall, Inc., 1983.

10 Russell, E., Building Simulation Models with SIMSCRIPT 11.5 Los Angeles, CA:

CACI, Inc., 1983

11 Schriber, T., Simulation Using GPSS New York: Wiley, 1974.

12 Shannon, R., Systems Simulation, Th e Art and Science Englewood Cliff s, NJ:

Prentice-Hall, Inc., 1975

Problems

1-1 Customers arrive at a two-window drive-in bank for service Each lane can

accommodate a total of three cars If both lanes are full, 25 percent of the customers that cannot be served at the windows will park in a six-space lot and seek service inside the bank Th e remaining 75 percent balk to other bank branches What measures of performance will be suitable for evaluating the eff ectiveness of drive-in service?

1-2 Categorize the following situations as either discrete or continuous (or a

com-bination of both) In each situation, specify the objective of developing a simulation model

a Orders of diff erent sizes arrive randomly for an item An order that not be fi lled from available stock must await arrival of new shipments that occur in two equal deliveries at the beginning and the middle of each month

can-b A factory produces an item at a specifi ed rate Produced goods are stocked

in an adjacent warehouse Customers place their orders through dealers, who in turn send their orders to the warehouse with intervening delay periods Demand for the item experiences seasonal fl uctuations

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12 Simulation of Industrial Systems

c World population is aff ected by the availability of natural resources, food production, environmental conditions, educational level, healthcare, and capital investments in industry and agriculture

d Goods arrive on pallets at a receiving bay of an automated warehouse

Th e pallets are loaded on a lower conveyor belt and lifted through an up- elevator to an upper conveyor that moves the pallets to corridors Th e corridors are served by cranes that pick the pallets up from the conveyor and place them in storage bins When an order is received, the pallets are moved by cranes from the bins to the upper conveyor Th ese pallets are moved by a down-elevator to the lower conveyor, which then moves them

to the shipping bay

1-3 Consider the single-server queueing situation Suppose that the time between

successive arrivals is ten minutes Th e service time is only eight minutes per customer Show how the simulation clock will advance over 100 simulation minutes Assume that the fi rst arrival occurs at time zero

1-4 In the single-queueing situation, explain how you would determine the

inter-arrival and service times of a real-life situation

1-5 Explain why you would agree or disagree with the following statement: “Th e

majority of discrete simulation situations can be viewed as (simple or

com-plex) queueing systems consisting of sources that generate customers, queues where customers may wait, and facilities where customers are served.”

1-6 Simulation is basically a statistical experiment whose output is subject to

random error Discuss your views regarding the factors that may “bias” lation results How can such bias be reduced in simulation?

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Chapter 2

Probability and Statistics

in Simulation

2.1 Role of Probability and Statistics in Simulation

Simulation is applied to environments in which randomness is a key element in the

description of the system As we stated in Chapter 1, randomness in simulation is

represented using probability distributions For example, in many service facilities,

the random arrival or departure of customers is typically described by a Poisson

process

Because randomness is synonymous with simulation, simulation output must

be viewed as a sample in a statistical experiment Th erefore, simulation output

must be subjected to proper statistical inference tests Also, performance measures

from a simulation model typically must be expressed with appropriate confi dence

intervals

Th is chapter is not intended as a review of probability or statistics Rather, it is

off ered as a quick reference for simulation users on

1 Characteristics of probability distributions commonly used in simulation

models

2 Statistical goodness-of-fi t models used to identify distributions

3 Confi dence intervals and the application of hypothesis testing to output data

Information sources to model random behavior may be from closed-form probability

distributions or histograms derived from historical data or data collection eff orts

Also, because simulation is an experimental design to estimate system performance

measures, statistical inference techniques are critical to the decision-making

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14 Simulation of Industrial Systems

process Figure 2.1 summarizes the organization of this chapter relative to the

sim-ulation experiment Further details on these topics may be found in the references

cited at the end of the chapter

in Simulation

Th is section introduces the defi nitions and properties of some continuous and

dis-crete distributions that are commonly used in simulation Th e next section then

shows how goodness-of-fi t tests are used to identify distributions from raw data

Th e following notation and defi nitions will be used throughout the chapter

Given x is a continuous random variable in the interval [a, b], we use f (x) to

repre-sent the probability density function (pdf) of x Th e cumulative density function

(CDF) is represented by the notation F x (X ).

Th e functions f (x) and F x (X ) have the following properties:

For the case where x is discrete over the values a, a + 1, …, and b, f(x) and F x (X ) are

replaced by p(x) and P x (X ), in which case integration is replaced by summation.

2.2.1 Properties of Common Distributions

The simulation experiment

Statistical inference methods (Section 2.3)

Figure 2.1 Role of probability and statistics in simulation.

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Probability and Statistics in Simulation 15

Th e shape of uniform f (x) is shown in Figure 2.2 Th e uniform [0, 1] distribution

plays a key role in simulation Specifi cally, uniform [0, 1] random numbers are used

to generate random samples from any pdf Th is technique is detailed in Section 3.3

2.2.1.2 Negative Exponential Distribution

f (x) = μe −μx , x > 0, μ > 0

F x (X ) = 1 − μe −μX , X > 0

Th e negative exponential pdf appears as shown in Figure 2.3 Th is

distribu-tion applies frequently in the simuladistribu-tion of the inter-arrival and service times of

facilities It also applies in many reliability problems to describe the time-to-failure

of a system’s component

Exponential random variables possess a unique forgetfulness or lack of memory

property Th at is, given T is the time period that elapsed since the occurrence of the

Figure 2.2 Uniform density function.

b a

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