Synthesis Lectures on Operations Research and Applications – serie

This text is an introduction to Operations Management. Three themes are woven throughout the book: optimization or trying to do the best we can, managing tradeoffs between conflicting objectives, and dealing with uncertainty. After a brief introduction, the text reviews the fundamentals of probability including commonly used discrete and continuous distributions and functions of a random variable. The next major section, beginning in Chapter 7, examines optimization. The key fundamentals of optimization—inputs, decision variables, objective(s), and constraints—are introduced. Optimization is applied to linear regression, basic inventory modeling, and the newsvendor problem, which incorporates uncertain demand. Linear programming is then introduced. We show that the newsvendor problem can be cast as a network flow linear programming problem. Linear programming is then applied to the problem of redistributing empty rental vehicles (e.g., bicycles) at the end of a day and the problem of assigning students to seminars. Several chapters deal with location models as examples of both simple optimization problems and integer programming problems. The next major section focuses on queueing theory including single-and multi-server queues. This section also introduces a numerical method for solving for key performance metrics for a common class of queueing problems as well as simulation modeling. Finally, the text ends with a discussion of decision theory that again integrates notions of optimization, tradeoffs, and uncertainty analysis. The text is designed for anyone with a modest mathematical background. As such, it should be readily accessible to engineering students, economics, statistics, and mathematics majors, as well as many business students.

This book provides a blend of quantitative and qualitative approaches to decision making, while also bridging the gap between the theory of how to make good decisions versus how people actually make decisions.  The authors present the tools and techniques of decision analysis to learn how to become a FOCCUSSED decision maker: Identify and properly Frame the decision or problem at handSpecify the goals, Objectives, and values that you are trying to achieveDevelop creative, meaningful Choices from among which you can chooseEvaluate the Consequences of selecting each alternative using your goals, objectives, and valuesThink about the key Uncertainties that could impact the decisionUnderstand the Swaps and trade-offs that you are willing to makeDevelop an approach for implementing your SolutionElicit the data you’ll need from a variety of sourcesand Disseminate and communicate your decisions to others.  The authors define a decision as the choice among alternatives, based on how we value and trade-off their pros and cons, made in the face of uncertainty about what will actually happen. The decision-making process is presented as having three pillars to support the decision maker: Preferences–what we prefer, what meets our goals and objectives, and the recognition that preferences are personal to the one making the decision; Alternatives–the choices, options, or courses of action that we have, and over which we have some degree of control; and Information–what we know about the situation, what we don’t know, how we connect choices to outcomes, and how we deal with uncertainty.  Key components of good decision-making include how to define your goals and objectives, how to incorporate uncertainties that we all face, and how to develop better alternatives, all of which are discussed.  Sophisticated techniques are presented in a way that is accessible to the average decision maker. Probability theory is utilized to improve decisions, and uncertainties are captured in decision trees.  Risk avoidance, risk transfer, and risk mitigation are also discussed.  Readers will gain a clear understanding of how to articulate the goals and objectives that should be the focal point of any decision.

This book provides a blend of quantitative and qualitative approaches to decision making, while also bridging the gap between the theory of how to make good decisions versus how people actually make decisions.  The authors present the tools and techniques of decision analysis to learn how to become a FOCCUSSED decision maker: Identify and properly Frame the decision or problem at handSpecify the goals, Objectives, and values that you are trying to achieveDevelop creative, meaningful Choices from among which you can chooseEvaluate the Consequences of selecting each alternative using your goals, objectives, and valuesThink about the key Uncertainties that could impact the decisionUnderstand the Swaps and trade-offs that you are willing to makeDevelop an approach for implementing your SolutionElicit the data you’ll need from a variety of sourcesand Disseminate and communicate your decisions to others.  The authors define a decision as the choice among alternatives, based on how we value and trade-off their pros and cons, made in the face of uncertainty about what will actually happen. The decision-making process is presented as having three pillars to support the decision maker: Preferences–what we prefer, what meets our goals and objectives, and the recognition that preferences are personal to the one making the decision; Alternatives–the choices, options, or courses of action that we have, and over which we have some degree of control; and Information–what we know about the situation, what we don’t know, how we connect choices to outcomes, and how we deal with uncertainty.  Key components of good decision-making include how to define your goals and objectives, how to incorporate uncertainties that we all face, and how to develop better alternatives, all of which are discussed.  Sophisticated techniques are presented in a way that is accessible to the average decision maker. Probability theory is utilized to improve decisions, and uncertainties are captured in decision trees.  Risk avoidance, risk transfer, and risk mitigation are also discussed.  Readers will gain a clear understanding of how to articulate the goals and objectives that should be the focal point of any decision.

This book provides a concerted supply chain perspective for dealing with pandemics on the scale of COVID-19.  Specifically, this book describes a new approach, supply chain immunity, to illustrate what is needed to fix our economy and healthcare systems.  The authors of this book are experts in supply chain management, health care supply chains, major systems acquisition, and contingency sourcing methods.  Based on first-hand experiences working during COVID in the depths of the nation’s supply chain failures, the authors develop important themes for private and public sector supply chain managers to consider in rebuilding a more immune supply chain.  The book is targeted at policy makers, academics, practitioners, and students of disaster response, public policy, healthcare, and supply chain management who are interested in learning contemporary lessons from the COVID-19 pandemic.  From the perspective of those who lived through the chaos, the authors furtherexplore the application of novel concepts in joint planning, market intelligence, and governance related to a national pandemic or other global contingency.

This book presents state-of-the-art research and practice in optimization routing, specifically the vehicle routing problem (VRP).   Since its introduction in the late 1950s, the VRP has been a very significant area of research and practice in operations research.  Vehicles are used to make deliveries and for pick-ups every day and everywhere.  Companies such as Amazon, UPS, FedEx, and DHL use route optimization to reduce mileage, fuel use, number of trucks on the road, and carbon dioxide emissions.  The authors compile and analyze 135 survey and review articles on vehicle routing topics published between 2005 and 2022 in an effort to make key observations about publication and trend history, summarize the overall contributions in the field, and identify trends in VRP research and practice.   The authors have compiled published research on models, algorithms, and applications for specific areas, including: alternative and multiple objectives; arc routing and general routing; drones, last-mile delivery, and urban distribution; dynamic and stochastic routing; green routing; inventory routing; loading constraints; location-routing; multiple depots; pickup and delivery and dial-a-ride problems; rich and multi-attribute routing; routing over time; shipping; two-echelon, collaborative, and inter-terminal problems; specific variants, benchmark datasets, and software; and exact algorithms and heuristics.  In addition, the book discusses how vehicle routing problems are among the most widely studied problems in combinatorial optimization due to the mathematical complexity and practical significance.

This book presents state-of-the-art research and practice in optimization routing, specifically the vehicle routing problem (VRP).   Since its introduction in the late 1950s, the VRP has been a very significant area of research and practice in operations research.  Vehicles are used to make deliveries and for pick-ups every day and everywhere.  Companies such as Amazon, UPS, FedEx, and DHL use route optimization to reduce mileage, fuel use, number of trucks on the road, and carbon dioxide emissions.  The authors compile and analyze 135 survey and review articles on vehicle routing topics published between 2005 and 2022 in an effort to make key observations about publication and trend history, summarize the overall contributions in the field, and identify trends in VRP research and practice.   The authors have compiled published research on models, algorithms, and applications for specific areas, including: alternative and multiple objectives; arc routing and general routing; drones, last-mile delivery, and urban distribution; dynamic and stochastic routing; green routing; inventory routing; loading constraints; location-routing; multiple depots; pickup and delivery and dial-a-ride problems; rich and multi-attribute routing; routing over time; shipping; two-echelon, collaborative, and inter-terminal problems; specific variants, benchmark datasets, and software; and exact algorithms and heuristics.  In addition, the book discusses how vehicle routing problems are among the most widely studied problems in combinatorial optimization due to the mathematical complexity and practical significance.

This book presents a new search paradigm for solving the Traveling Salesman Problem (TSP). The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. The author introduces the idea of using the attractor concept in dynamical systems theory to reduce the search space for exhaustive search for the TSP. Numerous examples are used to describe how to use this new search algorithm to solve the TSP and its variants including: multi-objective TSP, dynamic TSP, and probabilistic TSP. This book is intended for readers in the field of optimization research and application.

This book presents a new search paradigm for solving the Traveling Salesman Problem (TSP). The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. The author introduces the idea of using the attractor concept in dynamical systems theory to reduce the search space for exhaustive search for the TSP. Numerous examples are used to describe how to use this new search algorithm to solve the TSP and its variants including: multi-objective TSP, dynamic TSP, and probabilistic TSP. This book is intended for readers in the field of optimization research and application.

This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution.  The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method.  It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems.  On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams.  It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming.  On the practical side, it explains how LBBD has been applied to a rapidly growingvariety of problem domains.  After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand.  In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

This book is the first comprehensive guide to logic-based Benders decomposition (LBBD), a general and versatile method for breaking large, complex optimization problems into components that are small enough for practical solution.  The author introduces logic-based Benders decomposition for optimization, which substantially generalizes the classical Benders method.  It can reduce solution times by orders of magnitude and allows decomposition to be applied to a much wider variety of optimization problems.  On the theoretical side, this book provides a full account of inference duality concepts that underlie LBBD, as well as a description of how LBBD can be combined with stochastic and robust optimization, heuristic methods, and decision diagrams.  It also clarifies the connection between LBBD and combinatorial Benders cuts for mixed integer programming.  On the practical side, it explains how LBBD has been applied to a rapidly growingvariety of problem domains.  After describing basic theory, this book provides a comprehensive review of the rapidly growing literature that describes these applications, in each case explaining how LBBD is adapted to the problem at hand.  In doing so this work provides a sourcebook of ideas for applying LBBD to new problems as they arise.

This book provides a novel and unifying perspective on the structural properties of fair solutions in optimization formulations.  The book also addresses a growing interest in incorporating fairness into the models that lie behind many business and public policy decisions.   Since there are several ways to formulate fairness mathematically, the authors characterize optimal solutions that result from different formulations with the aim of informing the choice of an appropriate model for a given application.  The focus is on fairness criteria that combine efficiency with fairness since typically both are important in practice.  Most of these results are new and do not appear in the current literature. The book is directed towards a wide range of audiences including practitioners, researchers in mathematical optimization, and welfare economists. In addition, this book:Presents practical linear, nonlinear, or mixed integer programming formulations and a wide variety of fairness modelsIncludes detailed proofs that provide insight into the properties of each criterionProvides guidelines for selecting a fairness model and the tendency to incentivize cooperation or competition About the AuthorsÖzgün Elçi, Ph.D., is a Research Scientist on the Modeling and Optimization team at Amazon.John Hooker, Ph.D. is University Professor of Operations Research and T. Jerome Holleran Professor of Business Ethics and Social Responsibility, Emeritus, at Carnegie Mellon University.Peter Zhang, Ph.D, is an Assistant Professor at Carnegie Mellon University’s Heinz College of Information Systems and Public Policy.

This book provides a novel and unifying perspective on the structural properties of fair solutions in optimization formulations.  The book also addresses a growing interest in incorporating fairness into the models that lie behind many business and public policy decisions.   Since there are several ways to formulate fairness mathematically, the authors characterize optimal solutions that result from different formulations with the aim of informing the choice of an appropriate model for a given application.  The focus is on fairness criteria that combine efficiency with fairness since typically both are important in practice.  Most of these results are new and do not appear in the current literature. The book is directed towards a wide range of audiences including practitioners, researchers in mathematical optimization, and welfare economists. In addition, this book:Presents practical linear, nonlinear, or mixed integer programming formulations and a wide variety of fairness modelsIncludes detailed proofs that provide insight into the properties of each criterionProvides guidelines for selecting a fairness model and the tendency to incentivize cooperation or competition About the AuthorsÖzgün Elçi, Ph.D., is a Research Scientist on the Modeling and Optimization team at Amazon.John Hooker, Ph.D. is University Professor of Operations Research and T. Jerome Holleran Professor of Business Ethics and Social Responsibility, Emeritus, at Carnegie Mellon University.Peter Zhang, Ph.D, is an Assistant Professor at Carnegie Mellon University’s Heinz College of Information Systems and Public Policy.

This book presents a comprehensive examination of crime patrolling problems across various domains, including robotics, security, and law enforcement, with a focus on the mathematical models used to optimize patrolling strategies. Patrolling is a critical crime prevention and deterrence strategy, requiring the effective allocation of resources to address evolving security challenges.  In addition, patrolling is one of the most effective and widely adopted crime prevention and deterrence strategies worldwide. It is integral to security agencies such as police and military forces across various domains, including land, air, and maritime areas. As such, effective patrolling requires the coordination of manpower, technological resources, and policies to address evolving security challenges.  The authors review recent research on robotic patrolling, multirobot systems, and police patrolling and also explore advances in modeling, optimization, and practical applications.  In addition, the author’s analysis categorizes studies by core modeling themes, such as Game Theory, Mathematical Optimization, and Stochastic methods, and highlights the secondary modeling themes that frequently complement the primary approaches.  Each study is categorized by fields including, but not limited to domain, patrolling focus, area representation, and solution methodology to facilitate cross-comparison. The book identifies gaps in current research, particularly the lack of a holistic examination of patrolling from robotic, autonomous, human, and hybrid perspectives, and proposes future directions for research in this evolving field.