Public Systems Modeling: Methods for Identifying and Evaluating Alternative Plans and Policies (International Series in Operations Research & Management Science, 318)

This is an open access book discusses readers to various methods of modeling plans and policies that address public sector issues and problems. Written for public policy and social sciences students at the upper undergraduate and graduate level, as well as public sector decision-makers, it demonstrates and compares the development and use of various deterministic and probabilistic optimization and simulation modeling methods for analyzing planning and management issues. These modeling tools offer a means of identifying and evaluating alternative plans and policies based on their physical, economic, environmental, and social impacts. Learning how to develop and use the mathematical modeling tools introduced in this book will give students useful skills when in positions of having to make informed public policy recommendations or decisions. Preface Contents 1 Analyzing Public Policy Decisions 1.1 Introduction 1.1.1 Historical and Other Perspectives 1.2 Modeling Policy Issues 1.3 Complexity 1.4 Are You Ready? 1.5 Book Outline 1.6 Conclusion References 2 Public Sector Systems 2.1 Introduction 2.1.1 Managing Public Systems 2.2 Why Apply a Systems Approach to Public Policy? 2.2.1 When to Use the Systems Approach 2.3 Data: Are There Ever Enough? Appendix Some Case Study Summaries Lessons from These Case Studies References 3 Creating Models 3.1 Let’s Model 3.2 Types of Models 3.3 Why Model? 3.3.1 Some Cravats 3.3.2 Limitations and Common Sins 3.3.3 A Word of Caution 3.3.4 Subscripted Variables 4 Modeling Examples and Solutions 4.1 Introduction 4.2 Resource Allocation 4.3 An Example Allocation Problem 4.4 Hill Climbing 4.5 Shadow Price 5 Models for Managing Money 5.1 Introduction 5.2 The Time Value of Money 5.3 Computing Present Values of Future Cash Flows 5.4 Computing Equivalent Constant End-of-Period Amounts 5.5 Within-Year Compounding 5.6 Inflation 5.7 Income Taxes 5.8 Comparing Alternatives 5.9 Investing for Retirement 6 Solving Models Using Excel 6.1 Introduction 6.2 Using Solver in Excel 6.3 Conclusion 7 Discrete Optimization Modeling 7.1 Discrete Dynamic Programming 7.1.1 Traveling Problem 7.1.2 Resource Allocation 7.1.3 Capacity Expansion 7.2 Conclusions 8 Linear Optimization Modeling 8.1 Introduction 8.2 Dual Variables 8.3 A Production Model 8.4 Crop Production 8.5 Police Scheduling 8.6 Project Scheduling 8.7 Trash and Pollution 8.8 Modeling Fixed Cost Problems 9 Some Linearization Methods 9.1 If-Then-Else Conditions 9.2 Fixed Costs in Cost Functions 9.3 Minimizing the Maximum or Maximizing the Minimum of a Set of Unknown Variables or Functions 9.4 Minimizing the Absolute Value of the Difference Between Two Unknown Non-negative Variables 9.5 Minimizing Convex Functions or Maximizing Concave Functions 9.6 Minimizing Concave Functions or Maximizing Convex Functions 9.7 Minimizing or Maximizing Combined Concave-Convex Functions 10 Solving Models Using Calculus 10.1 Introduction 10.2 Finding Slopes 10.3 Maxima and Minima 10.4 Finding Slopes Using Differentiation 10.5 Partial Differentiation 10.6 A Review 10.7 Derivative Notation 10.8 Integration 10.8.1 An Exception 10.8.2 What is Integration? 10.8.3 Integrating Over Ranges of a Variable or Function 10.8.4 Other Examples of Integration 11 Lagrangian Models 11.1 Introduction 11.2 Constructing Lagrangian Optimization Models 11.3 Example Lagrangian Models 12 Dealing with Uncertainty 12.1 Introduction 12.2 Discrete Random Variables 12.3 Continuous Random Variables 12.4 Mean 12.5 Variance 12.6 Normal Distribution 12.7 Median 12.8 Mode 12.9 Conditional and Joint Probabilities 12.10 Marginal Distributions 12.11 Pedestrian Safety 12.12 Sources of Uncertainty 13 Modeling Stochastic Processes 13.1 Introduction 13.2 Changing Weather 13.3 The Stock Market 13.4 Human Health 13.5 Reducing Crime 14 Chance Constrained and Monte Carlo Modeling 14.1 Chance Constraints 14.2 Monte Carlo Sampling 14.3 Another Example 15 Simulation Modeling 15.1 Introduction 15.2 Stochastic Simulations 15.3 Water Quality Simulation 15.4 Lake Quality Simulation with Random Wasteloads 15.5 Possible Chaos 15.6 Endowment Giving 15.7 Forest Management 15.8 Military Battle 15.9 Disease Epidemic 16 Multi-criteria Analyses 16.1 Introduction 16.2 Efficiency Concept 16.3 Dominance 16.4 Satisficing 16.5 Lexicography 16.6 Indifference Analysis 16.7 The Weighting Method 16.8 The Constraint Method 16.9 Goal Attainment 16.10 Goal-Programming 16.11 Interactive Methods 16.12 Plan Simulation Performance Measures 17 Fuzzy Optimization 17.1 Introduction 17.2 Fuzzy Membership Functions 17.3 Optimization in Fuzzy Environments 17.4 Fuzzy Sets in Resource Allocation 17.5 Summary 18 Conclusion Exercise Solutions Index