Jack P.C. Kleijnen Design and Analysis of Simulation Experiments Second Edition ~Springer
Contents Preface vii 1 Introduction 1 1.1 What Is Simulation? 1 1.2 What Is "Design and Analysis of Simulation Experiments" (DASE)?.............. 8 1.3 DASE Symbols and Terminology 12 Solutions for Exercises 16 References................ 16 2 Classic Regression Metamodels and Their Designs 23 2.1 Introduction................ 24 2.2 Linear Regression................ 28 2.2.1 Basic Linear Regression Analysis... 28 2.2.2 Advanced Linear Regression Analysis 33 2.3 Linear Regression: First-Order Polynomials. 40 2.3.1 Scaling the Inputs........... 41 2.3.2 One-Factor-at-a-Time Designs Versus Factorial Designs..................... 44 2.4 Designs for First-Order Polynomials: Resolution-III. 49 2.4.1 2k-p Designs of Resolution-III....... 50 2.4.2 Plackett-Burman Designs of Resolution-III. 54 xi
xii Contents 2.5 Linear Regression: Interactions............... 55 2.6 Designs Allowing Two-Factor Interactions: Resolution-IV 58 2. 7 Designs for Two-Factor Interactions: Resolution-V 61 2.8 Linear Regression: Second-Order Polynomials.. 63 2.9 Designs for Second-Degree Polynomials: Central Composite Designs.......... 64 2.10 Optimal Designsand Other Designs 66 2.10.1 Optimal Designs.. 66 2.10.2 More Design Types. 67 2.11 Conclusions... 68 Solutions for Exercises 73 References....... 77 3 Classic Assumptions Versus Simulation Practice 83 3.1 Introduction............... 84 3.2 Multivariate Output................. 85 3.2.1 Linear Regression Metamodels....... 86 3.2.2 Designs for Multivariate Simulation Output 88 3.3 Nonnormal Output............. 89 3.3.1 Realistic Normality Assumption?. 89 3.3.2 Testing the Normality Assumption 91 3.3.3 Normalizing Transformations 93 3.3.4 Jackknifing........ 93 3.3.5 Bootstrapping........ 96 3.4 Heterogeneous Output Variances.. 100 3.4.1 Realistic Constant Variance Assumption? 100 3.4.2 Testing for Constant Variances.... 101 3.4.3 Variance Stabilizing Transformations... 102 3.4.4 Least Squares Estimators......... 102 3.4.5 Designs for Heterogeneous Output Variances 105 3.5 Common Random Numbers (CRN).......... 108 3.6 Validation of Metamodels............... 112 3.6.1 The Coefficients of Determination R 2 and R!ij 113 3.6.2 Cross-Validation............. 114 3.6.3 Transformations of Regression Variables 121 3.6.4 Adding High-Order Terms. 122 3.7 Conclusions... 122 Solutions for Exercises 123 References....... 124 4 Screening the Many Inputs of Realistic Simulation Models 135 4.1 Introduction....................... 136 4.2 Sequential Bifurcation (SB) for Deterministic Simulations and First-Order Polynomial Metamodels. 139
Contents xiii 4.3 SB for Deterministic Simulations and Second-Order Polynomial Metamodels............... 147 4.4 SB for Random Simulations and Constant Number of Replications................. 149 4.4.1 The SB Method............... 149 4.4.2 Case Study: Ericsson's Supply Cbain.... 151 4.5 SB for Random Simulations and Variable Number of Replications................. 154 4.5.1 Monte Carlo Experiment with SPRT.... 157 4.6 Multiresponse SB: MSB............... 159 4.6.1 Monte Carlo Experiments with MSB and SB 162 4.6.2 Case Study: Chinese Supply-Chain 166 4.7 Validating the SB and MSB Assumptions 168 4.8 Conclusions... 172 Solutions for Exercises 173 References....... 173 5 Kriging Metamodels and Their D esigns 179 5.1 Introduction....................... 180 5.2 Ordinary Kriging (OK) in Deterministic Simulation 181 5.2.1 OK Basics................... 181 5.2.2 Estimating the OK Parameters....... 187 5.3 Bootstrapping and Conditional Simulation for OK in Deterministic Simulation........... 191 5.3.1 Bootstrapped OK (BOK).......... 191 5.3.2 Conditional Simulation of OK (CSOK) 194 5.4 Universal Kriging (UK) in Deterministic Simulation 197 5.5 Designs for Deterministic Simulation... 198 5.5.1 Latin Hypercube Sampling (LHS)... 199 5.5.2 Sequential Customized Designs..... 203 5.6 Stochastic Kriging (SK) in Random Simulation 206 5.6.1 A Metamodel for SK........... 207 5.6.2 Designs for SK.............. 209 5.7 Monotonie Kriging: Bootstrapping and Acceptance/ Rejection............... 212 5.8 Global Sensitivity Analysis: Sobol's FANOVA............ 216 5.9 Risk Analysis.......... 218 5.10 Miscellaneous Issues in Kriging 222 5.11 Conclusions... 223 Solutions for Exercises 224 References....... 224
xiv Contents 6 Simulation Optimization 6.1 Introduction.... 6.2 Linear Regression for Optimization........... 6.2.1 Response Surface Methodology (RSM): Basics 6.2.2 RSM in Random Simulation........... 6.2.3 Adapted Steepest Descent (ASD) for RSM.. 6.2.4 Multiple Responses: Generalized RSM (GRSM). 6.2.5 Testing a GRSM Optimum: Karush-Kuhn-Tucker (KKT) conditions........... 6.3 Kriging Metamodels for Optimization.......... 6.3.1 Effi.cient Global Optimization (EGO).... 6.3.2 Kriging and Integer Mathematical Programming (KrIMP).... 6.4 Robust Optimization.................... 6.4.1 Taguchian Robust Optimization Through RSM. 6.4.2 Taguchian Robust Optimization Through Kriging 6.4.3 Ben-Tal et al. 's Robust Optimization. 6.5 Conclusions... Solutions for Exercises References.... Author Index Subject Index 241 242 244 244 250 252 253 259 266 266 269 273 275 280 284 285 286 286 301 317