Optimization and Dynamics with Their Applications (eBook)

Akio Matsumoto, Dept. of Economics, Chuo University

Preface 5
Contents 8
Contributors 10
Introduction 12
Numerical Analysis 12
Optimization 13
Dynamic Systems Including Simulations 13
Game Theory and Oligopoly Theory 13
Industrial Applications 14
Economics 15
Contributions 15
Operations Research 21
Developments on the Convergence of Some Iterative Methods 22
1 Introduction 22
2 Preliminaries 24
3 Semilocal Convergence 28
4 Local Convergence 33
5 Numerical Examples 38
References 41
The Non-symmetric L-Nash Bargaining Solution 42
1 Introduction 42
2 Preliminaries 43
3 The Main Result 44
4 Example 46
5 Discussion 47
References 48
3 Analyzing the Impact of Process Improvement on Lot Sizes in JIT Environment When Capacity Utilization Follows Beta Distribution 49
Abstract 49
1 Introduction 50
2 The Model with Beta Distribution 52
3 The Impact of Process Improvement on Lot Sizes and Total Costs When x/thinspace /ge /thinspace ky 64
4 Estimating the Impact of Process Quality Improvement on the Variance of the Minimum Total Annual Cost 72
5 Conclusions 76
References 77
4 Exploring Efficient Reward Strategies to Encourage Large-Scale Cooperation Among Boundedly Rational Players with the Risk and Impact of the Public Good 79
Abstract 79
1 Introduction 80
2 The Payoffs of Being a Cooperator and a Defector with Rewards in a Public Goods Game 81
3 Large-Scale Cooperation with the Risk and Impact of the Public Good 83
3.1 Behavioral Game-Theoretic Decision Model 83
3.2 The Realization of the Public Good with the Rewards 85
4 Individual Reward Strategies Based on Behavioral Game-Theoretic Decision Model 86
5 Conclusions 87
References 87
Dynamics 89
Periodicity Induced by Production Constraints in Cournot Duopoly Models with Unimodal Reaction Curves 90
1 Introduction 91
2 The Constrained Cournot-Rand Model with Piecewise Linear Reaction Functions 93
2.1 The Piecewise Linear One-Dimensional Map for the Case Without Inertia 95
3 Dynamics of the Equivalent One-Dimensional Map 99
3.1 Case N2 100
3.2 Case N3 103
3.3 Transition N2--N4 (N3--N4) 104
4 Rand Duopoly with Inertia 106
5 Conclusions and Outline of Further Investigations 108
References 109
An Adaptive Learning Model for Competing Firms in an Industry 111
1 Introduction 111
2 The Learning Model 112
3 Learning with Fixed Delays 115
4 Learning with Continuously Distributed Delays 117
5 Conclusions 118
References 118
The Coordination and Dynamic Analysis of Industrial Clusters: A Multi-agent Simulation Study 120
1 Introduction 120
2 Related Literature Review 122
2.1 Oligopoly Theory 122
2.2 The Agent-Based Industrial Cluster Model 123
3 The Agent-Based and Oligopoly Integrated Model 124
3.1 The Structure of the System 124
3.2 Agents, Interactions and Environment 125
3.3 Agents State Updating Rules Based on Oligopoly Theory 126
3.4 The Decision Rules of Productions and the Innovation Step 129
4 The Simulation Process 130
4.1 Parameters of the Model 130
4.2 Simulation Results 131
5 Conclusion 139
References 139
8 Approximation of LPV-Systems with Constant-Parametric Switching Systems 141
Abstract 141
1 Introduction 141
2 Applications 142
3 Problem Formulation 143
3.1 Introducing LPV Systems from a Buck-Boost Converter 143
4 Approximation Theorems 145
5 Conclusions 167
References 168
Love Affairs Dynamics with One Delay in Losing Memory or Gaining Affection 169
1 Introduction 169
2 Basic Model 171
3 Delay in the Gaining-Affection Process 174
4 Delay in the Losing-Memory Process 178
4.1 Stability of Nonzero Steady State 180
4.2 Stability of Zero Steady State 183
5 Concluding Remarks 187
References 192
Applications 193
10 Optimizing Baseball and Softball Bats 194
Abstract 194
1 Précis of This Endeavor 194
2 Bat-Ball Collisions 198
3 Equations for Bat-Ball Collisions 199
3.1 Collisions at the Center of Mass 199
3.2 Collisions at the Sweet Spot 199
3.2.1 Coordinate System 199
3.2.2 Assumptions 199
3.2.3 Experimental Validation Data 200
3.2.4 The Model 200
Definition of Variables 200
Condensing the Notation for the Equations 202
Conservation of Energy 203
Conservation of Linear Momentum 203
Definition of the Coefficient of Restitution 203
Newton’s Second Principle 204
Conservation of Angular Momentum 204
Finding Ball Velocity After the Collision 205
Finding Bat Velocity After the Collision 207
Finding the Bat Angular Velocity After the Collision 210
Three Output Equations in Three Formats 211
Adding Conservation of Energy and Finding KE_{{/rm lost}} 212
Adding Conservation of Angular Momentum 214
3.2.5 Analytic Sensitivity Analysis 217
3.2.6 Optimizing with Commercial Software 222
3.2.7 Optimizing the Bat 223
3.2.8 Summary of Bat Selection 227
3.2.9 The Ideal Bat WeightTM 228
3.2.10 Bat Speed 231
3.2.11 Seeing the Collision 232
4 Summary 233
Acknowledgements 234
References 235
11 Reverse Logistic Network Design for End-of-Life Wind Turbines 237
Abstract 237
1 Introduction 238
2 Wind Turbine Supply Chain 239
3 Wind Turbine Reverse Logistics Network Mathematical Model 242
3.1 Model Notation 244
3.2 Mathematical Model 246
4 Case Study 248
4.1 Input Parameters 248
4.2 Wind Turbine Reverse Logistics Network Model Run 250
4.3 Model Results 252
4.4 Sensitivity Analysis 261
4.5 Wind Turbine Reverse Logistics Network Problem with Total Profit Objective (WTRLN-TP) 264
5 Conclusions 265
References 267
Maintenance Outsourcing Contracts Based on Bargaining Theory 269
1 Introduction 269
2 Problem Description and Model Formulation 271
2.1 Customer's Payoff Function 273
2.2 Agent's Payoff Function 274
3 Nash Bargaining Solution 274
3.1 Threat Point for the Agent 276
3.2 Threat Point for the Customer 278
4 Extended Nash Bargaining Solution 280
4.1 Maximum Total Profit 281
4.2 Price Discount Contract 282
5 Numerical Examples 284
6 Conclusions and Future Research Directions 288
References 290
13 Agricultural Production Planning in a Fuzzy Environment 292
Abstract 292
1 Introduction 293
2 Mathematical Model 295
3 Model Parameters and Data 298
4 Results 300
5 Conclusions 303
References 303
14 Optimal Replacement Decisions with Mound-Shaped Failure Rates 305
Abstract 305
1 Introduction 305
2 Model for Optimum Preventive Replacement 306
3 Exponential Transformation of Random Variables 308
4 Particular Distributions 309
4.1 Lognormal Distribution 309
4.2 Log-Logistic Distribution 310
4.3 Log-Gamma Distribution 311
4.4 Log-Weibull Distribution 312
5 Examples 313
6 Conclusions 316
References 317
15 A System Dynamics Approach to Simulate the Restoration Plans for Urmia Lake, Iran 318
Abstract 318
1 Introduction 318
2 Problem Description: Urmia Lake Case Study in Iran 320
3 SD Model Framework 322
3.1 Calibration and Validation 326
3.2 Restoration Plans 327
4 Results 329
4.1 Individual Effect of Restoration Plans 329
4.2 Accumulative Effect of Plans 331
5 Conclusions 333
Acknowledgements 333
References 333
16 A Decision Support System for Managing Water Resources in Real-Time Under Uncertainty 336
Abstract 336
1 Introduction 337
2 Data Collection Systems 338
3 ANN Prediction Models 339
4 Optimization 340
5 Conceptual Study Area 340
6 Conceptual Real-Time Management System 342
7 Management Formulation 344
8 Computed Optimal Solutions 347
9 Stochastic Analysis 349
10 Conclusions 351
Acknowledgements 352
References 353