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Dimitris Bertsimas: Decision Making in the Age of Uncertainty
Introduction:
In a world grappling with increasingly complex challenges, the ability to make sound, data-driven decisions is paramount. Dimitris Bertsimas, a renowned professor at MIT and a leading expert in optimization and decision science, offers a revolutionary approach to decision-making that transcends traditional methods. This comprehensive guide delves into the core principles of the "Bertsimas Decision" framework, exploring its practical applications across various fields and demonstrating how you can leverage its power to enhance your own decision-making process. We'll unpack the methodology, explore its strengths, and address potential limitations, providing you with a complete understanding of this impactful approach.
Understanding the Bertsimas Decision Framework: A Robust Approach
The Bertsimas Decision framework isn't simply about maximizing expected value; it's about understanding and managing uncertainty. Traditional decision-making models often falter when confronted with incomplete information or unpredictable events. Bertsimas’ approach addresses this head-on by explicitly incorporating robustness into the decision-making process. This means focusing on decisions that perform well not just in the most likely scenario, but also under a range of plausible, albeit less likely, outcomes.
Key Principles of the Bertsimas Method
1. Defining the Uncertainty Set: This crucial first step involves identifying and quantifying the sources of uncertainty influencing the decision. This might involve using historical data, expert opinions, or scenario planning to define a range of possible values for uncertain parameters.
2. Formulating a Robust Optimization Model: Instead of focusing solely on optimizing for a single, best-case scenario, a robust optimization model seeks to find a solution that remains near-optimal across the entire uncertainty set. This ensures resilience even if the actual outcome deviates from the initially anticipated one.
3. Balancing Performance and Robustness: The method allows for a trade-off between maximizing expected value and ensuring robustness against uncertainty. This is crucial as a perfectly robust solution might sacrifice too much potential payoff, while a purely optimistic solution risks significant losses under unfavorable conditions. This balance is achieved by carefully tuning parameters within the optimization model.
4. Data-Driven Insights: The Bertsimas Decision framework is fundamentally data-driven. The effectiveness of the approach hinges on having access to relevant data that allows for accurate modeling of the uncertainty set. The quality of the data directly impacts the quality of the resulting decision.
Applications of the Bertsimas Decision Across Industries
The versatility of the Bertsimas Decision framework extends across diverse sectors. Its impact is felt in:
Finance:
Portfolio optimization is a prime example. Traditional models often fail to adequately account for market volatility. The Bertsimas approach allows for the construction of portfolios that are robust against unexpected market downturns, providing better risk management.
Supply Chain Management:
Supply chains are inherently susceptible to disruptions. The Bertsimas framework can be applied to create robust supply chain designs that are resilient against unforeseen events like natural disasters or geopolitical instability, ensuring continued operations even in adverse circumstances.
Healthcare:
In healthcare, resource allocation is often constrained by limited budgets and unpredictable patient demand. The robust optimization principles enable the development of effective allocation strategies that maintain high quality of care even under fluctuating demands.
Energy:
Managing energy grids requires accounting for unpredictable fluctuations in energy consumption and production. The Bertsimas approach enables the creation of robust energy management systems that ensure grid stability even in the face of uncertainty.
Limitations and Considerations
While the Bertsimas Decision framework provides a powerful approach to decision-making, it's essential to acknowledge its limitations:
Data Dependency: The quality of the decision is directly tied to the quality and quantity of data available. Poor data can lead to flawed models and suboptimal decisions.
Computational Complexity: Solving robust optimization problems can be computationally intensive, particularly for large-scale applications. This requires specialized software and expertise.
Defining the Uncertainty Set: Accurately defining the uncertainty set can be challenging. Overly restrictive or overly permissive sets can lead to suboptimal solutions.
Conclusion: Embracing Robustness in Decision-Making
The Dimitris Bertsimas decision framework represents a significant advancement in decision science. By explicitly incorporating uncertainty into the decision-making process, it empowers individuals and organizations to make more robust and resilient choices in the face of complexity. While challenges exist, the potential benefits of adopting this approach are substantial, leading to improved outcomes and reduced risk across diverse domains. By understanding and applying its core principles, you can significantly enhance your own decision-making capabilities in today's uncertain world.
FAQs:
1. What is the difference between the Bertsimas method and traditional expected value maximization? The Bertsimas method goes beyond simply maximizing expected value by explicitly considering a range of possible outcomes (the uncertainty set), ensuring the decision performs well even under less-likely scenarios, unlike traditional methods which focus solely on the most likely scenario.
2. Is the Bertsimas method suitable for all types of decisions? While applicable to many, its effectiveness depends on the availability of data to define the uncertainty set. Decisions with highly unpredictable or unknowable factors might be less suited for this framework.
3. What software tools are typically used for implementing the Bertsimas Decision framework? Specialized optimization software packages, such as those based on mathematical programming languages like AMPL or Gurobi, are commonly used.
4. How can I learn more about applying the Bertsimas Decision framework in my specific field? Researching published papers and case studies applying robust optimization in your industry is a good starting point. Attending workshops or courses on optimization and decision science could also be beneficial.
5. What is the role of data analytics in the Bertsimas Decision framework? Data analytics plays a crucial role in defining the uncertainty set. Accurate and comprehensive data analysis is essential for building robust and effective decision models.
| dimitris bertsimas decision: Data, Models, and Decisions Dimitris Bertsimas, Robert Michael Freund, 2004 Combines topics from two traditionally distinct quantitative subjects, probability/statistics and management science/optimization, in a unified treatment of quantitative methods and models for management. Stresses those fundamental concepts that are most important for the practical analysis of management decisions: modeling and evaluating uncertainty explicitly, understanding the dynamic nature of decision-making, using historical data and limited information effectively, simulating complex systems, and allocating scarce resources optimally. |
| dimitris bertsimas decision: Machine Learning Under a Modern Optimization Lens Dimitris Bertsimas, Jack William Dunn, 2019 |
| dimitris bertsimas decision: The Analytics Edge Dimitris Bertsimas, Allison K. O'Hair, William R. Pulleyblank, 2016 Provides a unified, insightful, modern, and entertaining treatment of analytics. The book covers the science of using data to build models, improve decisions, and ultimately add value to institutions and individuals--Back cover. |
| dimitris bertsimas decision: Introduction to Linear Optimization Dimitris Bertsimas, John N. Tsitsiklis, 1997-01-01 |
| dimitris bertsimas decision: DATA, MODELS, AND DECISIONS DIMITRIS BERTSIMAS, ROBERT FREUND, |
| dimitris bertsimas decision: Robust Optimization Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski, 2009-08-10 Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject. |
| dimitris bertsimas decision: Optimization and Decision Science: Operations Research, Inclusion and Equity Paola Cappanera, Matteo Lapucci, Fabio Schoen, Marco Sciandrone, Fabio Tardella, Filippo Visintin, 2023-07-15 This volume collects peer-reviewed short papers presented at the Optimization and Decision Science conference (ODS 2022) held in Florence (Italy) from August 30th to September 2nd, 2022, organized by the Global Optimization Laboratory within the University of Florence and AIRO (the Italian Association for Operations Research). The book includes contributions in the fields of operations research, optimization, problem solving, decision making and their applications in the most diverse domains. Moreover, a special focus is set on the challenging theme Operations Research: inclusion and equity. The work offers 30 contributions, covering a wide spectrum of methodologies and applications. Specifically, they feature the following topics: (i) Variational Inequalities, Equilibria and Games, (ii) Optimization and Machine Learning, (iii) Global Optimization, (iv) Optimization under Uncertainty, (v) Combinatorial Optimization, (vi) Transportation and Mobility, (vii) Health Care Management, and (viii) Applications. This book is primarily addressed to researchers and PhD students of the operations research community. However, due to its interdisciplinary content, it will be of high interest for other closely related research communities. |
| dimitris bertsimas decision: Monotonicity in Markov Reward and Decision Chains Ger Koole, 2007 Monotonicity in Markov Reward and Decision Chains: Theory and Applications focuses on monotonicity results for dynamic systems that take values in the natural numbers or in more-dimensional lattices. The results are mostly formulated in terms of controlled queueing systems, but there are also applications to maintenance systems, revenue management, and so forth. The focus is on results that are obtained by inductively proving properties of the dynamic programming value function. A framework is provided for using this method that unifies results obtained for different models. The author also provides a comprehensive overview of the results that can be obtained through it, in which he discusses not only (partial) characterizations of optimal policies but also applications of monotonicity to optimization problems and the comparison of systems. Monotonicity in Markov Reward and Decision Chains: Theory and Applications is an invaluable resource for anyone planning or conducting research in this particular area. The essentials of the topic are presented in an accessible manner and an extensive bibliography guides towards further reading. |
| dimitris bertsimas decision: Fundamentals of Management Science Efraim Turban, Jack R. Meredith, 1998 |
| dimitris bertsimas decision: Artificial Intelligence in Control and Decision-making Systems Yuriy P. Kondratenko, Vladik Kreinovich, Witold Pedrycz, Arkadii Chikrii, Anna M. Gil-Lafuente, 2023-04-17 This book presents an authoritative collection of contributions reporting on computational intelligence, fuzzy systems as well as artificial intelligence techniques for modeling, optimization, control and decision-making together with applications and case studies in engineering, management and economic sciences. Dedicated to the Academician of the Polish Academy of Sciences, Professor Janusz Kacprzyk in recognition of his pioneering work, the book reports on theories, methods and new challenges in artificial intelligence, thus offering not only a timely reference guide but also a source of new ideas and inspirations for graduate students and researchers alike. The book consists of the 18 chapters, presented by distinguished and experienced authors from 16 different countries (Australia, Brazil, Canada, Chile, Germany, Hungary, Israel, Italy, China, R.N.Macedonia, Saudi Arabia, Spain, Turkey, United States, Ukraine, and Vietnam). All chapters are grouped into three parts: Computational Intelligence and Fuzzy Systems, Artificial Intelligence Techniques in Modelling and Optimization, and Computational Intelligence in Control and Decision Support Processes. The book reflects recent developments and new directions in artificial intelligence, including computation method of the interval hull to solutions of interval and fuzzy interval linear systems, fuzzy-Petri-networks in supervisory control of Markov processes in robotic systems, fuzzy approaches for linguistic data summaries, first-approximation analysis for choosing fuzzy or neural systems and type-1 or type-2 fuzzy sets, matrix resolving functions in game dynamic problems, evolving stacking neuro-fuzzy probabilistic networks and their combined learning in online pattern recognition tasks, structural optimization of fuzzy control and decision-making systems, neural and granular fuzzy adaptive modeling, state and action abstraction for search and reinforcement learning algorithms. Among the most successful and perspective implementations in practical areas of human activity are tentative algorithms for neurological disorders, human-centric question-answering system, OWA operators in pensions, evaluation of the perception of public safety through fuzzy and multi-criteria approach, a multicriteria hierarchical approach to investment location choice, intelligent traffic signal control and generative adversarial networks in cybersecurity. |
| dimitris bertsimas decision: Surgical Decision Making, Evidence, and Artificial Intelligence, An Issue of Surgical Clinics, E-Book Jason Bingham, Matt Eckert, 2023-03-26 In this issue, guest editors bring their considerable expertise to this important topic.Provides in-depth reviews on the latest updates in the field, providing actionable insights for clinical practice. Presents the latest information on this timely, focused topic under the leadership of experienced editors in the field. Authors synthesize |
| dimitris bertsimas decision: An Introduction to Robust Combinatorial Optimization Marc Goerigk, |
| dimitris bertsimas decision: Decision Diagrams for Optimization David Bergman, Andre A. Cire, Willem-Jan van Hoeve, John Hooker, 2016-11-01 This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world. [Pascal Van Hentenryck] |
| dimitris bertsimas decision: Optimization Over Integers Dimitris Bertsimas, Robert Weismantel, 2005 |
| dimitris bertsimas decision: Handbook of Markov Decision Processes Eugene A. Feinberg, Adam Shwartz, 2012-12-06 Eugene A. Feinberg Adam Shwartz This volume deals with the theory of Markov Decision Processes (MDPs) and their applications. Each chapter was written by a leading expert in the re spective area. The papers cover major research areas and methodologies, and discuss open questions and future research directions. The papers can be read independently, with the basic notation and concepts ofSection 1.2. Most chap ters should be accessible by graduate or advanced undergraduate students in fields of operations research, electrical engineering, and computer science. 1.1 AN OVERVIEW OF MARKOV DECISION PROCESSES The theory of Markov Decision Processes-also known under several other names including sequential stochastic optimization, discrete-time stochastic control, and stochastic dynamic programming-studiessequential optimization ofdiscrete time stochastic systems. The basic object is a discrete-time stochas tic system whose transition mechanism can be controlled over time. Each control policy defines the stochastic process and values of objective functions associated with this process. The goal is to select a good control policy. In real life, decisions that humans and computers make on all levels usually have two types ofimpacts: (i) they cost orsavetime, money, or other resources, or they bring revenues, as well as (ii) they have an impact on the future, by influencing the dynamics. In many situations, decisions with the largest immediate profit may not be good in view offuture events. MDPs model this paradigm and provide results on the structure and existence of good policies and on methods for their calculation. |
| dimitris bertsimas decision: Handbook of Semidefinite Programming Henry Wolkowicz, Romesh Saigal, Lieven Vandenberghe, 2012-12-06 Semidefinite programming (SDP) is one of the most exciting and active research areas in optimization. It has and continues to attract researchers with very diverse backgrounds, including experts in convex programming, linear algebra, numerical optimization, combinatorial optimization, control theory, and statistics. This tremendous research activity has been prompted by the discovery of important applications in combinatorial optimization and control theory, the development of efficient interior-point algorithms for solving SDP problems, and the depth and elegance of the underlying optimization theory. The Handbook of Semidefinite Programming offers an advanced and broad overview of the current state of the field. It contains nineteen chapters written by the leading experts on the subject. The chapters are organized in three parts: Theory, Algorithms, and Applications and Extensions. |
| dimitris bertsimas decision: Testing Macroeconometric Models Ray C. Fair, 1994 In this book Ray Fair expounds powerful techniques for estimating and analyzing macroeconometric models. He takes advantage of the remarkable decrease in computational costs that has occurred since the early 1980s by implementing such sophisticated techniques as stochastic simulation. Testing Macroeconometric Models also incorporates the assumption of rational expectations in the estimation, solution, and testing of the models. And it presents the latest versions of Fair's models of the economies of the United States and other countries. After estimating and testing the U.S. model, Fair analyzes its properties, including those relevant to economic policymakers: the optimal monetary policy instrument, the effect of a government spending reduction on the government deficit, whether monetary policy is becoming less effective over time, and the sensitivity of policy effects to the assumption of rational expectations. Ray Fair has conducted research on structural macroeconometric models for more than twenty years. With interest increasing in the area, this book will be an essential reference for macroeconomists. |
| dimitris bertsimas decision: Proceedings of the Third SIAM International Conference on Data Mining Daniel Barbara, Chandrika Kamath, 2003-01-01 The third SIAM International Conference on Data Mining provided an open forum for the presentation, discussion and development of innovative algorithms, software and theories for data mining applications and data intensive computation. This volume includes 21 research papers. |
| dimitris bertsimas decision: Cognitive Operations Konstantinos V. Katsikopoulos, 2023-07-05 This book examines how people make decisions under risk and uncertainty in operational settings and opens the black box by specifying the cognitive processes that lead to human behavior. Drawing on economics, psychology and artificial intelligence, the book provides an innovative perspective on behavioral operations. It shows how to build optimization as well as heuristic models for describing human behavior and how to compare such models on various dimensions such as predictive power and transparency, as well as discussing interventions for improving human behavior. This book will be particularly valuable to academics and practitioners who seek to select a modeling approach that suits the operational decision at hand. |
| dimitris bertsimas decision: Dynamic Programming and Optimal Control Dimitri P. Bertsekas, 2005 The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The treatment focuses on basic unifying themes, and conceptual foundations. It illustrates the versatility, power, and generality of the method with many examples and applications from engineering, operations research, and other fields. It also addresses extensively the practical application of the methodology, possibly through the use of approximations, and provides an extensive treatment of the far-reaching methodology of Neuro-Dynamic Programming/Reinforcement Learning. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use. The second volume is oriented towards mathematical analysis and computation, treats infinite horizon problems extensively, and provides an up-to-date account of approximate large-scale dynamic programming and reinforcement learning. The text contains many illustrations, worked-out examples, and exercises.--Publisher's website. |
| dimitris bertsimas decision: Quantitative Analysis in Financial Markets Marco Avellaneda, 1999 Contains lectures presented at the Courant Institute's Mathematical Finance Seminar. |
| dimitris bertsimas decision: Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies Edward K. Baker, Anito Joseph, Anuj Mehrotra, Michael A. Trick, 2007-04-30 This book represents the results of cross-fertilization between OR/MS and CS/AI. It is this interface of OR/CS that makes possible advances that could not have been achieved in isolation. Taken collectively, these articles are indicative of the state-of-the-art in the interface between OR/MS and CS/AI and of the high caliber of research being conducted by members of the INFORMS Computing Society. |
| dimitris bertsimas decision: New Designs for Bio-Explorations Janet Lanza, 2005-03 This collection of laboratory exercises provides small groups of students with the background information and materials needed to design and conduct their own inquiry-based projects, and report their work-orally or through posters-to the rest of the group. Laboratory exercises are supported by a detailed Instructor's Manual that offers ideas for projects, addresses difficulties that instructors may encounter using these exercises, and provides lists of needed supplies. |
| dimitris bertsimas decision: Robust Discrete Optimization and Its Applications Panos Kouvelis, Gang Yu, 2013-03-09 This book deals with decision making in environments of significant data un certainty, with particular emphasis on operations and production management applications. For such environments, we suggest the use of the robustness ap proach to decision making, which assumes inadequate knowledge of the decision maker about the random state of nature and develops a decision that hedges against the worst contingency that may arise. The main motivating factors for a decision maker to use the robustness approach are: • It does not ignore uncertainty and takes a proactive step in response to the fact that forecasted values of uncertain parameters will not occur in most environments; • It applies to decisions of unique, non-repetitive nature, which are common in many fast and dynamically changing environments; • It accounts for the risk averse nature of decision makers; and • It recognizes that even though decision environments are fraught with data uncertainties, decisions are evaluated ex post with the realized data. For all of the above reasons, robust decisions are dear to the heart of opera tional decision makers. This book takes a giant first step in presenting decision support tools and solution methods for generating robust decisions in a variety of interesting application environments. Robust Discrete Optimization is a comprehensive mathematical programming framework for robust decision making. |
| dimitris bertsimas decision: Mechanism Design Rakesh V. Vohra, 2011-05-09 Mechanism design is an analytical framework for thinking clearly and carefully about what exactly a given institution can achieve when the information necessary to make decisions is dispersed and privately held. This analysis provides an account of the underlying mathematics of mechanism design based on linear programming. Three advantages characterize the approach. The first is simplicity: arguments based on linear programming are both elementary and transparent. The second is unity: the machinery of linear programming provides a way to unify results from disparate areas of mechanism design. The third is reach: the technique offers the ability to solve problems that appear to be beyond solutions offered by traditional methods. No claim is made that the approach advocated should supplant traditional mathematical machinery. Rather, the approach represents an addition to the tools of the economic theorist who proposes to understand economic phenomena through the lens of mechanism design. |
| dimitris bertsimas decision: Commercial Transactions Lynn M. LoPucki, 2012 Commercial Transactions: A Systems Approach explores the nuances of transaction law from a systems' perspective, examining the infrastructure that supports commercial transactions and how the law is applied in real-world situations. Its outstanding team of co-authors uses an assignment-based structure that allows professors to adapt the text to a variety of class levels and approaches. Well-crafted problems challenge students' understanding of the material in this comprehensive, highly teachable text. All sections of the Fifth Edition have been revised to include new case law and problems, and the 2010 Amendments to Article 9. Hallmark features: Extraordinary authorship all four authors are standouts in the field of secured credit, payment systems and sales law. The Systems Approach examines the infrastructure that supports actual transactions; code is taught in the context of the transactions. Teachable problems prefaced by straightforward textual explanations. Assignment-based organization offers flexibility in teaching. Cutting-edge coverage, including key court cases. The revised Fifth Edition has been thoroughly updated by section: Part One: Sales Systems At least 20% new cases. Part Two: Financial Systems Updated problems that reflect the types of disputes arising out of the new electronic payment systems. Important new cases, including: Wachovia Bank, N.A. v. Foster Bancshares, Inc. Triffin v. Third Federal Savings Bank In re PTI Holding Corp. Chemical Bank v. Meltzer Data Sales Co. v. Diamond Z Manufacturing Banco Nacional de Mexico v. Societe Generale In re Kang Jin Hwang Korea Export Insurance Corp. v. Audiobahn, Inc. Davis v. Stern, Agee and& Leach, Inc. Part Three: Secured Credit The 2010 Amendments to Article 9. |
| dimitris bertsimas decision: Rollout, Policy Iteration, and Distributed Reinforcement Learning Dimitri Bertsekas, 2021-08-20 The purpose of this book is to develop in greater depth some of the methods from the author's Reinforcement Learning and Optimal Control recently published textbook (Athena Scientific, 2019). In particular, we present new research, relating to systems involving multiple agents, partitioned architectures, and distributed asynchronous computation. We pay special attention to the contexts of dynamic programming/policy iteration and control theory/model predictive control. We also discuss in some detail the application of the methodology to challenging discrete/combinatorial optimization problems, such as routing, scheduling, assignment, and mixed integer programming, including the use of neural network approximations within these contexts. The book focuses on the fundamental idea of policy iteration, i.e., start from some policy, and successively generate one or more improved policies. If just one improved policy is generated, this is called rollout, which, based on broad and consistent computational experience, appears to be one of the most versatile and reliable of all reinforcement learning methods. In this book, rollout algorithms are developed for both discrete deterministic and stochastic DP problems, and the development of distributed implementations in both multiagent and multiprocessor settings, aiming to take advantage of parallelism. Approximate policy iteration is more ambitious than rollout, but it is a strictly off-line method, and it is generally far more computationally intensive. This motivates the use of parallel and distributed computation. One of the purposes of the monograph is to discuss distributed (possibly asynchronous) methods that relate to rollout and policy iteration, both in the context of an exact and an approximate implementation involving neural networks or other approximation architectures. Much of the new research is inspired by the remarkable AlphaZero chess program, where policy iteration, value and policy networks, approximate lookahead minimization, and parallel computation all play an important role. |
| dimitris bertsimas decision: Nonlinear Programming Dimitri P. Bertsekas, 1999 |
| dimitris bertsimas decision: Proceedings of the 33rd IEEE Conference on Decision and Control IEEE Control Systems Society, 1994 |
| dimitris bertsimas decision: Understanding and Using Linear Programming Jiri Matousek, Bernd Gärtner, 2007-07-04 The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is what every theoretical computer scientist should know about linear programming. A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming behind the scenes. |
| dimitris bertsimas decision: Operations Strategy Jan A. Van Mieghem, Gad Allon, 2015 |
| dimitris bertsimas decision: Introduction to Probability Dimitri Bertsekas, John N. Tsitsiklis, 2008-07-01 An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems. |
| dimitris bertsimas decision: Tools and Algorithms for the Construction and Analysis of Systems Hubert Garavel, John Hatcliff, 2003-07-01 This book constitutes the refereed proceedings of the 9th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2003, held in Warsaw, Poland, in April 2003. The 43 revised full papers presented were carefully reviewed and selected from 160 submissions. The papers are organized in topical sections on bounded model checking and SAT-based methods, mu-calculus and temporal logics, verification of parameterized systems, abstractions and counterexamples, real-time and scheduling, security and cryptography, modules and compositional verification, symbolic state spaces and decision diagrams, performance and mobility, state space reductions, constraint solving and decision procedures, and testing and verification. |
| dimitris bertsimas decision: Managerial Decision Modeling , 2002 |
| dimitris bertsimas decision: Electric Energy Systems Antonio Gomez-Exposito, Antonio J. Conejo, Claudio Canizares, 2018-06-14 Electric Energy Systems, Second Edition provides an analysis of electric generation and transmission systems that addresses diverse regulatory issues. It includes fundamental background topics, such as load flow, short circuit analysis, and economic dispatch, as well as advanced topics, such as harmonic load flow, state estimation, voltage and frequency control, electromagnetic transients, etc. The new edition features updated material throughout the text and new sections throughout the chapters. It covers current issues in the industry, including renewable generation with associated control and scheduling problems, HVDC transmission, and use of synchrophasors (PMUs). The text explores more sophisticated protections and the new roles of demand, side management, etc. Written by internationally recognized specialists, the text contains a wide range of worked out examples along with numerous exercises and solutions to enhance understanding of the material. Features Integrates technical and economic analyses of electric energy systems. Covers HVDC transmission. Addresses renewable generation and the associated control and scheduling problems. Analyzes electricity markets, electromagnetic transients, and harmonic load flow. Features new sections and updated material throughout the text. Includes examples and solved problems. |
| dimitris bertsimas decision: Expert Systems Joseph C. Giarratano, Gary Riley, 1994 In this book, the authors present rule-based programming in CLIPS (a rule-based programming language developed at NASA in part by Gary Riley). This book covers the construction of expert systems using rule-based programming methodologies. In this new edition the CLIPS software has been completely updated from version 4.2 to 6.0 and new CLIPS features have been included. The prerequisites are a structured programming and a data structures courses. |
| dimitris bertsimas decision: 数据、模型与决策:管理科学基础 伯特西马斯, 弗罗因德, 2002 本书由中信出版社与汤姆森学习集团合作出版。 |
| dimitris bertsimas decision: Robust Markov Decision Processes with Uncertain Transition Matrices Arnab Nilim, 2004 |
| dimitris bertsimas decision: Predictive Clustering Hendrik Blockeel, Saso Dzeroski, Jan Struyf, Bernard Zenko, 2012-05-31 This book introduces a novel paradigm for machine learning and data mining called predictive clustering, which covers a broad variety of learning tasks and offers a fresh perspective on existing techniques. The book presents an informal introduction to predictive clustering, describing learning tasks and settings, and then continues with a formal description of the paradigm, explaining algorithms for learning predictive clustering trees and predictive clustering rules, as well as presenting the applicability of these learning techniques to a broad range of tasks. Variants of decision tree learning algorithms are also introduced. Finally, the book offers several significant applications in ecology and bio-informatics. The book is written in a straightforward and easy-to-understand manner, aimed at varied readership, ranging from researchers with an interest in machine learning techniques to practitioners of data mining technology in the areas of ecology and bioinformatics. |
| dimitris bertsimas decision: Convex Optimization Theory Dimitri Bertsekas, 2009-06-01 An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. Convexity theory is first developed in a simple accessible manner, using easily visualized proofs. Then the focus shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex functions in terms of points, and in terms of hyperplanes. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework. This on-line version of the book, includes an extensive set of theoretical problems with detailed high-quality solutions, which significantly extend the range and value of the book. The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years. It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory). It is an excellent supplement to several of our books: Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2017), Network Optimization(Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998). |
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From Predictive to Prescriptive Analytics - arXi…
Bertsimas and Kallus: 2 From Predictive to Prescriptive Analytics c) A decision …
Global Optimization via Optimal Decision Trees arX…
Bertsimas and Ozturk: Global Optimization via Optimal Decision …
t Problems and Semidenite Optimization - MIT - Mass…
Dimitris Bertsimas y Ioana P op escu Ja y Seth uraman z April Abstract …
Abhishek Cauligi , Preston Culbertson , Bartolomeo St…
x are continuous decision variables, 2 f0;1gn are binary decision variables, …
From Predictive to Prescriptive Analytics - arXi…
Bertsimas and Kallus: 2 From Predictive to Prescriptive Analytics c) A decision …
Data-driven assortment optimization Dimitris Ber…
Dimitris Bertsimas, Velibor Misic. Data-driven assortment optimization 1 …
MIT Open Access Articles Theory and Applications of …
466 DIMITRIS BERTSIMAS, DAVID B. BROWN, AND CONSTANTINE …
Reshaping National Organ Allocation Policy - MIT Sloan
Theodore Papalexopoulos,1 James Alcorn,2 Dimitris Bertsimas,1 …
MIT Open Access Articles Interpretable clustering: a…
However, in many other decision-making applications, there is a need …
Optimal control of execution costs - MIT
Dimitris Bertsimas, Andrew W. Lo* Sloan School of Management, MIT, …
From Predictive to Prescriptive Analytics arXiv:…
Dimitris Bertsimas Sloan School of Management, Massachusetts …
MIT Open Access Articles The Airlift Planning Problem
Dimitris Bertsimas Sloan School of Management and Operations …
CV Oct2024 External - University of Southern Calif…
Oct 24, 2024 · Decision- INTERESTS Aware Learning. Applications in …
Interpretable Clustering via Optimal Trees - arXiv.org
Interpretable Clustering via Optimal Trees Prof. Dimitris Bertsimas …
A data-driven approach to multi-stage stochastic linea…
Dimitris Bertsimas Operations Research Center, Massachusetts Institute of …
Algorithmic Insurance arXiv:2106.00839v2 [cs.LG] …
Dimitris Bertsimas Sloan School of Management, Massachusetts …
Personalized Diabetes Management Using Electro…
Dimitris Bertsimas, Nathan Kallus, Alexander M. Weinstein, and Ying …
Dynamic optimization with side information - arXiv.org
Dimitris Bertsimas, Christopher McCord, Bradley Sturt Operations …
Adaptive Robust Optimization for the Securi…
Dimitris Bertsimas, Member, IEEE, Eugene Litvinov, ... Also, since the UC …
Learning Preferences Under Noise and Loss Aversion: A…
Dimitris Bertsimas, Allison O’Hair Sloan School of Management and …
Pricing Algorithmic Insurance - arXiv.org
Dimitris Bertsimas Sloan School of Management, Massachusetts …
Introduction To Linear Optimization Bertsimas So…
Introduction to Linear Optimization by Dimitris Bertsimas & John N. …
INFORMS Journal on Optimization - MIT - Massa…
1 2 2
Machine Learning in Oncology: Methods, Applica…
Dimitris Bertsimas, PhD1,2; and Holly Wiberg, BS2 INTRODUCTION …
Dimitris Bertsimas - dspace.mit.edu
Dimitris Bertsimas OR 310-95 June 1995. The achievable region method in the …
Theory and Applications of Robust Optimization
Dimitris Bertsimas^ David B. Brown* Constantine Caramanis5 Abstract. In …
MIT Open Access Articles Theory and Applications of …
466 DIMITRIS BERTSIMAS, DAVID B. BROWN, AND CONSTANTINE …
THE ANALYTICS EDGE - MIT OpenCourseWare
Dimitris Bertsimas • MIT professor since 1988 • Allison O’Hair • Received …
On the Efficiency-Fairness Trade-off - JSTOR
Jul 8, 2018 · Bertsimas, Farias, and Trichakis: On the Efficiency-Fairness …
Data Models And Decisions The Fundamentals Of Mana…
Data Models and Decisions Dimitris (Massachusetts Institute of …
A Mathematical Programming Approach to …
Dimitris Bertsimas WP# -3668-94 MSA March, 1994. A mathematical …
Inventory Management in the Era of Big Data - MIT
Dimitris Bertsimas MIT Sloan School of Management and Operations …
Restless Bandits, Linear Programming Relaxations a…
Dimitris Bertsimas * Jos6 Nifio-Mora t August 1994 Abstract We propose a …
A Hierarchy of Near-Optimal Policies for Multi-stage Ada…
Dimitris Bertsimas ∗ Dan A. Iancu† ... for the decision rules is rarely …
Optimal classification trees Dimitris Bertsimas & Jack …
Dimitris Bertsimas & Jack Dunn. 123 Your article is protected by copyright …
Optimization-based Scenario Reduction for Data-Driven …
Bertsimas and Mundru: Optimization-based Scenario Reduction 2 More …
Curriculum Vita Dimitris Bertsimas Sloan School of …
Jan 12, 2023 · Dimitris Bertsimas Sloan School of Management, MIT I. …
arXiv:2303.06515v1 [math.OC] 11 Mar 2023
2 Dimitris Bertsimas, Kimberly Villalobos Carballo remains an …
Theory and applications of Robust Optimization
Dimitris Bertsimas⁄, David B. Brown y, Constantine Caramanis z July 6, 2007 …
Velibor V. Mišic´ - MIT - Massachusetts Institute of …
Thesis advisor: Professor Dimitris Bertsimas University of Toronto …
