Public Systems Modeling
Methods for Identifying and Evaluating Alternative Plans and Policies
- Open Access
- 2022
- Open Access
- Book
- Author
- Prof. Daniel P. Loucks
- Publisher
- Springer International Publishing
About this book
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.
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Table of Contents
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Chapter 1. Analyzing Public Policy Decisions
- Open Access
Download PDF-versionThis chapter delves into the use of deterministic and probabilistic optimization and simulation models to address public policy issues. It highlights the importance of systems analysis in identifying and evaluating policy solutions, considering multiple goals and uncertain data. The text emphasizes the role of models in informing decision-makers and facilitating more informed policy-making. It also discusses the limitations of models and the need for human judgment in the decision-making process. Additionally, the chapter introduces soft systems methodology and participatory modeling frameworks as tools for addressing complex public policy issues.AI Generated
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AbstractAn introduction to the contents of the book that focus on the art of building and using various optimization and simulation modeling methods for analyzing public systems planning and management issues. Emphasized is on the use of models for informing policy makers and for assisting in decision making processes. -
Chapter 2. Public Sector Systems
- Open Access
Download PDF-versionThis chapter delves into the definition and application of systems analysis in public policy modeling, emphasizing the importance of understanding interdependent components to achieve desired outcomes. It discusses the challenges and complexities of public sector systems, such as wicked problems, and the need for holistic approaches to inform policymakers. The text also introduces the concept of robust and adaptive policies, essential for navigating the volatile, uncertain, complex, and ambiguous nature of public policy. Additionally, it underscores the role of systems analysis in addressing contemporary issues like climate change, obesity, and income inequality, making it a valuable resource for professionals seeking to improve policy-making processes.AI Generated
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AbstractA discussion of the nature of public systems and their management. Examples of public systems and the services they provide show how complicated and complex they can be, and the challenges analysts have in providing information useful to those responsible for providing and managing them. Case studies involving modeling to improve system performance are briefly described as are the lessons learned from them. -
Chapter 3. Creating Models
- Open Access
Download PDF-versionThe chapter 'Creating Models' delves into the essentials of mathematical modeling, emphasizing the use of notation to define systems and their performance measures. Through simple examples such as calculating the perimeter of a park or optimizing the dimensions of a tank, the chapter demonstrates how to develop and solve optimization models. It highlights the importance of understanding constraints and objectives in modeling and introduces the concepts of simulation versus optimization. The chapter also discusses the purpose of modeling, the trade-offs between simplicity and detail, and the importance of sensitivity analysis. Throughout, the chapter aims to enhance the reader's understanding of modeling techniques and their practical applications, making it a valuable resource for anyone seeking to improve their modeling skills.AI Generated
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AbstractIntroduces the approach to developing optimization models for identifying and evaluating alternative designs of some infrastructure. The chapter distinguishes between two general types of models, optimization and simulation, and continues the discussion of the advantages and possible pitfalls of modeling. -
Chapter 4. Modeling Examples and Solutions
- Open Access
Download PDF-versionThis chapter delves into the complex problem of allocating scarce resources among multiple users, using the hill climbing method to find the best allocations. It begins by introducing the resource allocation problem, where the goal is to maximize total benefits while distributing resources equitably. The chapter then presents a detailed example involving the allocation of apples among three farmer’s markets, using concave benefit functions to model income. The hill climbing approach is explained step-by-step, showing how to allocate resources to maximize total income. Additionally, the concept of shadow prices is introduced, providing insight into the value of additional resources. The chapter concludes with exercises that apply the learned methods to real-world scenarios, making it a valuable resource for practitioners and students in the field.AI Generated
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AbstractThis chapter illustrates the development of optimization models for various example problems and introduces the hill-climbing approach for solving them, as and if appropriate. -
Chapter 5. Models for Managing Money
- Open Access
Download PDF-versionThe chapter delves into the concept of the time value of money, illustrating how money can grow over time through compound interest. It explains how to compute present and future values of cash flows, and discusses the impact of inflation and taxes on investment returns. The chapter also covers within-year compounding and provides examples of retirement planning and investment strategies. It concludes with exercises to reinforce understanding of the concepts discussed.AI Generated
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AbstractThe chapter reviews ways of computing equivalent present, future, or equal annual values that can be used to compare different time series of costs and benefits. It defines both simple and compound interest modeling, and the impacts of within-year compounding, inflation, and income taxes. -
Chapter 6. Solving Models Using Excel
- Open Access
Download PDF-versionThis chapter focuses on solving optimization models using Microsoft Excel's Solver tool. It begins by introducing the necessity of solving optimization models and the advantages and limitations of various methods. The chapter then delves into the practical application of Solver in Excel, guiding readers through the installation process and providing detailed examples. These examples include a benefit-cost analysis, designing a cylindrical tank, and resource allocation, each showcasing how to set up and solve optimization problems in Excel. The chapter also highlights the importance of understanding the underlying principles of optimization and the role of computers in problem-solving. Additionally, it offers exercises to further enhance the reader's understanding and application of the Solver tool.AI Generated
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AbstractThis chapter offers examples illustrating how the ‘Solver’ feature of Excel can be used to solve simultaneous equations and unconstrained and constrained optimization models. This and other features of Excel can be used to solve any of the optimization or simulation models or equations introduced in this book. -
Chapter 7. Discrete Optimization Modeling
- Open Access
Download PDF-versionThe chapter introduces discrete dynamic programming as a powerful method for solving discrete optimization problems where traditional methods like hill climbing fall short. It transforms multi-variable, multi-stage problems into networks of nodes and links, representing different states and decisions at each stage. The chapter demonstrates this approach through examples such as the traveling problem and resource allocation, showing how to identify the best paths through these networks to minimize or maximize objective functions. It also discusses capacity expansion problems, highlighting the practical applications and challenges of dynamic programming in real-world scenarios. The chapter concludes with exercises that allow readers to apply the concepts to solve complex optimization problems, emphasizing the versatility and effectiveness of discrete dynamic programming in addressing a wide range of optimization challenges.AI Generated
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AbstractUsing examples, the chapter introduces discrete dynamic programming that converts an overall optimization problem into many simpler sub-optimization problems. The chapter discusses the advantages and limitations of this optimization method. -
Chapter 8. Linear Optimization Modeling
- Open Access
Download PDF-versionThe chapter delves into the fundamental concepts of linear optimization modeling, emphasizing its widespread use due to the efficiency of its solution methods. It begins with an introduction to linear programming and its applications across diverse fields such as military, government, industry, and agriculture. The text then illustrates how to solve linear optimization models graphically, focusing on finding the feasible region and optimizing the objective function. It also discusses the transformation of non-linear components into linear ones to leverage the efficient algorithms available for linear models. The chapter includes practical examples, such as production models, police scheduling, project scheduling, and cost optimization, to demonstrate the application of linear optimization techniques in real-world scenarios. Additionally, it introduces the concept of dual variables and their significance in sensitivity analysis, providing insights into the impact of constraint changes on the objective function. The chapter concludes with exercises that allow readers to apply the learned concepts to various problems, further reinforcing the practical value of linear optimization modeling.AI Generated
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AbstractThe chapter introduces linear programming, arguably the most used optimization method applicable when all the model terms are linear. Graphical solution approaches to solve two-variable linear models are used to illustrate how linear programming algorithms solve models containing many more variables as are typical of most real-world problems. -
Chapter 9. Some Linearization Methods
- Open Access
Download PDF-versionThis chapter delves into the integration of non-linear and conditional elements into linear programming models, leveraging the efficiency of linear programming algorithms. It focuses on if-then-else and and/or conditions, illustrating how to represent these complexities using additional binary and continuous variables. The chapter presents four detailed examples, each showcasing a unique conditional scenario, and provides linear constraints to model these conditions effectively. By doing so, it offers a comprehensive guide to enhancing the versatility of linear programming models in decision-making processes.AI Generated
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AbstractBecause linear programming algorithms are so efficient and in widespread use, together with the limitations of non-linear optimization solvers applied to large models, modelers faced wanting to solve very large models often attempt to linearize the non-linear terms in their models. This chapter introduces various approaches for accomplishing this, often using binary (0, 1) variables. -
Chapter 10. Solving Models Using Calculus
- Open Access
Download PDF-versionThe chapter 'Solving Models Using Calculus' delves into the application of calculus to optimize models with continuous non-linear objective functions. It begins by explaining how slopes, or marginal values, play a crucial role in economic decision-making, with examples drawn from previous chapters. The core of the chapter introduces differentiation, a method of calculus used to find slopes of functions, and demonstrates how these slopes can help address policy issues. The text assumes a basic understanding of calculus and provides clear, step-by-step explanations of differentiation and its application to power functions. It also covers partial differentiation for multivariable functions and integration, the reverse process of differentiation. The chapter concludes with exercises and examples to reinforce the concepts, making it a valuable resource for those seeking to understand the practical applications of calculus in model optimization.AI Generated
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AbstractSolutions to many economic models are based on marginal values of functions, such as marginal costs, marginal benefits, and marginal net benefits, or whatever the function being maximized or minimized represent. These marginal values are the slopes of functions. This chapter introduces how to use differential calculus to find the slopes and solutions to problems characterized by continuous non-linear functions. The reverse, called integral calculus, is also introduced for finding areas under functions that can represent total costs, benefits, and/or other values such as probabilities that are discussed in later chapters. -
Chapter 11. Lagrangian Models
- Open Access
Download PDF-versionThe chapter delves into the historical background of Joseph-Louis Lagrange and his pioneering work in differential calculus and optimization. It introduces Lagrangian models, explaining how they are used to find solutions to constrained non-linear models. The text covers the construction of Lagrangian optimization models, focusing on the determination of shadow prices or dual variables. Practical examples, such as optimizing the dimensions of a storage tank and resource allocation problems, are provided to illustrate the application of these models. The chapter also discusses the significance of shadow prices and their interpretation in different contexts, making it a valuable resource for professionals seeking to deepen their understanding of optimization techniques.AI Generated
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AbstractLagrangian models use calculus to solve multi-variable non-linear constrained optimization models of problems and for identifying the marginal changes (‘shadow prices’) of optimal solutions to changes in constraint bounds. This is especially useful when the constraints represent resource limitations. -
Chapter 12. Dealing with Uncertainty
- Open Access
Download PDF-versionThis chapter introduces the concept of random variables, categorizing them into discrete and continuous types. Discrete random variables are those that can take on a finite set of values, such as the outcome of a dice roll, while continuous random variables can take on an infinite number of values within a range, like measurements of weather. The chapter delves into the statistical characteristics of these variables, including mean, variance, and probability distributions. It also covers the normal distribution, which is a common type of continuous probability distribution with a bell-shaped curve. The chapter highlights the importance of understanding these concepts for making informed decisions in various fields, such as finance and healthcare, where uncertainty is a significant factor.AI Generated
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AbstractThis chapter introduces how probability and statistical measures can be incorporated into models to reflect the uncertainties of model inputs, parameter values and output variable values. -
Chapter 13. Modeling Stochastic Processes
- Open Access
Download PDF-versionThe chapter delves into the concept of stochastic processes, which involve uncertain outcomes over time. It introduces the idea of first-order discrete stochastic processes, defined by conditional probabilities of states. The chapter illustrates these concepts through various examples, including weather forecasting, stock market analysis, and health state transitions. It also discusses the application of stochastic processes in optimization problems, such as minimizing crime rates through community interventions. The chapter further explores the computation of steady-state probabilities and the use of linear programming and dynamic programming to find optimal policies. The practical applications and real-world examples make this chapter particularly engaging and relevant for professionals seeking to understand and apply stochastic processes in their fields.AI Generated
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AbstractMany public systems must deal with uncertain inputs over time. This chapter illustrates how models incorporating uncertain inputs over time can be developed and solved. Stochastic linear and dynamic programming models are developed to show the difference in output that define optimal sequential conditional decision making strategies. -
Chapter 14. Chance Constrained and Monte Carlo Modeling
- Open Access
Download PDF-versionThe chapter delves into the application of chance constraints in optimization models, where constraints may not always hold due to random variables. It introduces the concept of chance constraints and their conversion to deterministic equivalents using cumulative distribution functions. Additionally, the chapter explores Monte Carlo sampling techniques for generating random inputs that fit specified probability distributions, essential for simulating systems with random variables. Practical examples and exercises are included to illustrate these methods, making the chapter a valuable resource for professionals seeking to optimize systems under uncertainty.AI Generated
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AbstractConstraints of models that contain random variables may be applicable only some of the time. Constraints that apply only a specified fraction of the time are called chance constraints. This chapter illustrates how chance constraints can be included in optimization models. In addition, the chapter demonstrates how to generate values of random variables fitting user defined probability distributions. These random variable values often serve as inputs to stochastic simulation models. -
Chapter 15. Simulation Modeling
- Open Access
Download PDF-versionThe chapter delves into simulation modeling, a method used to address 'what if' questions by predicting system performance under various conditions. It discusses the advantages of simulation over optimization methods, including the ability to model systems in detail without restrictions. Applications range from traffic congestion and disease spread to endowment fundraising and military combat simulations. The chapter also explores stochastic simulations using Monte Carlo methods and provides examples of how simulation models can be used to predict outcomes in different scenarios, such as water quality and forest management. Additionally, it highlights the importance of considering human behavior and decision-making in simulations, as seen in examples like flight training and disease epidemics. The chapter concludes with exercises that encourage readers to apply the concepts discussed to real-world problems.AI Generated
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AbstractAn introduction to deterministic and stochastic system simulation modeling and various statistical measures of their outputs. -
Chapter 16. Multi-criteria Analyses
- Open Access
Download PDF-versionThe chapter delves into the complexities of multi-criteria analyses, essential for decision-making processes where multiple, often conflicting, goals need to be satisfied. It introduces the role of modelers in informing political debates by identifying and evaluating alternative plans or policies. The focus is on defining tradeoffs among conflicting stakeholder goals, using methods such as efficiency concepts, dominance analysis, satisficing, lexicography, and indifference analysis. The chapter also explores continuous methods like the weighting and constraint methods to identify efficient combinations of objective values. Additionally, it discusses goal attainment, goal programming, and interactive methods to assist decision-makers in selecting the best non-dominated plans. Performance measures such as reliability, resilience, and vulnerability are introduced to evaluate alternative plans or policies based on simulation model outputs. The chapter highlights the importance of these methods in guiding political decisions and ensuring that the best compromise is reached among conflicting objectives.AI Generated
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AbstractAn introduction to various approaches for modeling systems where different policy makers and/or stakeholders have different and often conflicting goals regarding desired system performance. -
Chapter 17. Fuzzy Optimization
- Open Access
Download PDF-versionThis chapter delves into the concept of fuzzy optimization, a technique used when precise quantification of system performance criteria and decision values is not possible or necessary. It introduces the use of fuzzy membership functions to quantify uncertain or qualitative variables, such as adjectives like 'hot' or 'cold.' The chapter illustrates how these functions can be incorporated into optimization models, providing a comprehensive approach to handling imprecision in decision-making processes. Through detailed examples, such as water quality management and resource allocation, the chapter demonstrates the practical application of fuzzy optimization in real-world scenarios. It also discusses the advantages of using fuzzy sets in environments where traditional crisp sets fall short, offering a more flexible and adaptable modeling approach.AI Generated
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AbstractThe chapter introduces methods of quantifying and modeling qualitative statements concerning system objectives and constraints and thus enabling the analyses of such systems. -
Chapter 18. Conclusion
- Open Access
Download PDF-versionThe chapter explores the critical role of systems analysts in informing policymakers, emphasizing the need for effective communication and collaboration. It delves into the challenges of conveying complex model results, the importance of building trust, and the iterative nature of policy modeling. The text underscores the political dynamics of the decision-making process and the necessity of considering stakeholder perspectives and uncertainties. It offers valuable insights into how analysts can ensure their work is relevant and impactful in the policy-making landscape.AI Generated
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AbstractConcluding thoughts on the successful implementation of modeling in policy making processes and the relationships between analysts and policy makers.
- Title
- Public Systems Modeling
- Author
-
Prof. Daniel P. Loucks
- Copyright Year
- 2022
- Publisher
- Springer International Publishing
- Electronic ISBN
- 978-3-030-93986-1
- Print ISBN
- 978-3-030-93985-4
- DOI
- https://doi.org/10.1007/978-3-030-93986-1
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