The book combines topics from two traditionally distinct quantitative subjects: probability/statistics and optimization models, into one unified treatment of quantitative methods and models for management and business. The book 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.

Data, Models, and Decisions: The Fundamentals of Management Science

Business & Money

Dimitris Bertsimas

Robert M. Freund

Economics

South-Western College Publishing

The paperback version is only available for international sales only. This book represents a departure from existing textbooks. Rather than covering methodology, the book introduces decision support systems through real world applications, and uses spreadsheets to model and solve problems. It uses management science techniques (statistics, simulation, probabilistic modeling and optimization), but only as tools to facilitate problem solving. The book embraces George Dantzig's dictum as its premise: "The final test of any theory is its capacity to solve the problems which originated it." 
The book is used in the core MBA program at MIT's, Sloan School of Management for the class titled: "Data, Models and Decisions". It is used in over ten universities in both core and elective classes, including Stanford University, Chicago's graduate school of Business, Babson College, among several others. 
The book contains many real business cases from the authors consulting experience. There are Powerpoint presentation slides for lecture material, a solution manual and other instructor resources available that can be obtained by contacting the authors directly ( dbertsim@mit.edu , rfreund@mit.edu )

Robert Freund

Management & Leadership

Dynamic Ideas

The book provides a unified, insightful, and modern treatment of the theory of integer optimization. 
The book is used in the doctoral level course, "Integer and Combinatorial Optimization" at the Massachusetts Institute of Technology. 
For solutions to exercises and other instructor resources, please contact Dimitris Bertsimas (dbertsim@mit.edu). 
The chapters of the book are logically organized in four parts: 
Part I: Formulations and relaxations includes Chapters 1-5 and discusses how to formulate integer optimization problems, how to enhance the formulations to improve the quality of relaxations, how to obtain ideal formulations, the duality of integer optimization and how to solve the resulting relaxations both practically and theoretically. 
Part II: Algebra and geometry of integer optimization includes Chapters 6-8 and develops the theory of lattices, oulines ideas from algebraic geometry that have had an impact on integer optimization, and most importantly discusses the geometry of integer optimization, a key feature of the book. These chapters provide the building blocks for developing algorithms. 
Part III: Algorithms for integer optimization includes Chapters 9-12 and develops cutting plane methods, integral basis methods, enumerative and heuristic methods and approximation algorithms. The key characteristic of our treatment is that our development of the algorithms is naturally based on the algebraic and geometric developments of Part II. 
Part IV: Extensions of integer optimization includes Chapters 13 and 14, and treats mixed integer optimization and robust discrete optimization. Both areas are practically significant as real world problems have very often both continuous and discrete variables and have elements of uncertainty that need to be addressed in a tractable manner. 
Distinguishing Characteristics Of This Book: 
* Develops the theory of integer optimization from a new geometric perspective via integral generating sets; 
* Emphasizes strong formulations, ways to improve them, integral polyhedra, duality, and relaxations; 
* Discusses applications of lattices and algebraic geometry to integer optimization, including Grobner bases, optimization over polynomials and counting integer points in polyhedra; 
* Contains a unified geometric treatment of cutting plane and integral basis methods; 
* Covers enumerative and heuristic methods, including local search over exponential neighborhoods and simulated annealing; 
* Presents the major methods to construct approximation algorithms: primal-dual, randomized rounding, semidefinite and enumerative methods; 
* Provides a unified treatment of mixed integer and robust discrete optimization; 
* Includes a large number of examples and exercises developed through extensive classroom use.

Optimization Over Integers

Robert Weismantel

The Analytics Edge 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. The philosophical underpinnings of the book are that real world problems are usually complex and often will defined; they do not come with labels, meaning that they are not necessarily regression problems or optimization problems. The only objective reality is data, which itself may be incomplete and of questionable quality, and the role of models is to facilitate the solution of real world problems. Problems and data play a leading role in this book, while models play an essential but supporting role. This is in contrast with the vast majority of books and classes available today, in which methods play the leading role. Dimitris Bertsimas is the Boeing Professor of Operations Research and the co-director of the Operations Research Center at the Massachusetts Institute of Technology. He is a member of the National Academy of Engineering, recipient of numerous research awards and co-founder of six Analytics companies. Allison K. O'Hair is a Lecturer in Operations, Information and Technology at the Stanford Graduate School of Business. She has a Ph.D. in Operations Research from MIT, and is a former Lecturer at the MIT Sloan School of Management. William R. Pulleyblank is Professor of Operations Research at the United States Military Academy, West Point. Previously he was Vice President of Business Optimization in IBM and before that led the BlueGene supercomputing project in IBM Research. He is a member of the National Academy of Engineering and has served on a broad range of business and government advisory boards.

The Analytics Edge

Allison O'Hair

William Pulleyblank

Dynamic Ideas LLC

On the Spacefilling Curve Heuristic for the Euclidean Traveling Salesman Problem (Classic Reprint)

Forgotten Books

The book provides an original treatment of machine learning (ML) using convex, robust and mixed integer optimization that leads to solutions to central ML problems at large scale that can be found in seconds/minutes, can be certified to be optimal in minutes/hours, and outperform classical heuristic approaches in out-of-sample experiments. 
 Structure of the book: 
 Part I covers robust, sparse, nonlinear, holistic regression and extensions.
 Part II contains optimal classification and regression trees. 
 Part III outlines prescriptive ML methods. 
Part IV shows the power of optimization over randomization in design of experiments, exceptional responders, stable regression and the bootstrap. 
Part V describes unsupervised methods in ML: optimal missing data imputation and interpretable clustering. 
Part VI develops matrix ML methods: sparse PCA, sparse inverse covariance estimation, factor analysis, matrix and tensor completion .
 Part VII demonstrates how ML leads to interpretable optimization. 
Philosophical principles of the book: Interpretability is materially important in the real world. Practical tractability not polynomial solvability leads to real world impact. 
NP-hardness is an opportunity not an obstacle. 
 ML is inherently linked to optimization not probability theory. Data represent an objective reality; models only exist in our imagination. 
Optimization has a significant edge over randomization .
 The ultimate objective in the real world is prescription, not prediction.

Machine Learning Under a Modern Optimization Lens

This book provides an original treatment of robust (RO) and adaptive robust optimization (ARO) based on over twenty years of research by each of the authors.\nStructure of the Book\nPart I describes linear RO and the underlying uncertainty sets. 
Part II treats modeling, exact and approximate algorithms for ARO. 
Part III introduces nonlinear RO for concave uncertainty. Part IV outlines nonlinear RO for concave uncertainty. 
Part V discusses the theory of distributional RO and ARO. 
Part VI contains a variety of RO and ARO applications including queueing theory, auction design, option pricing and energy unit commitment. 
ORIGINAL CHARACTERISTICS OF THE BOOK: 
Emphasis on modeling in RO and ARO. 
Integrated treatment of RO and ARO and of nonlinear RO for concave and convex uncertainty, as opposed to robust conic optimization. 
Interplay of probability theory to select parameters in RO and of optimization for tractability.

Robust and Adaptive Optimization

Dick Den Hertog

STRUCTURE OF THE BOOK: Part I describes single and multi-server queues. Part II treats single and multiclass queueing networks (MQNETs). Part III introduces asymptotic methods, including queueing networks in heavy traffic, large deviations, call centers, queues in space, and the supermarket model. Part IV outlines the use of optimization in queueing networks. Part V presents Markov chains and processes, Brownian motion, and weak convergence in the Appendix.

Queueing Theory: Classical and Modern Methods

David Gamarnik

This book provides a unified, insightful, and modern treatment of linear optimization, that is, linear programming, network flow problems, and discrete optimization. It includes classical topics as well as the state of the art, in both theory and practice.

Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6)

Science & Math

John Tsitsiklis

Tsitsiklis, John

John N. Tsitsiklis

Bertsimas, Dimitris

Mathematics

Athena Scientific

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