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"Decision making Mathematics."
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Markov chains and decision processes for engineers and managers
\"This book presents an introduction to finite Markov chains and Markov decision processes, with applications in engineering and management. It introduces discrete-time, finite-state Markov chains, and Markov decision processes. The text describes both algorithms and applications, enabling students to understand the logical basis for the algorithms and be able to apply them. The applications address problems in government, business, and nonprofit sectors. The author uses Markov models to approximate the random behavior of complex systems in diverse areas, such as management, production, science, education, health services, finance, and marketing\"-- Provided by publisher.
Book
Understanding uncertainty
Praise for the First Edition
\"...a reference for everyone who is interested in knowing and handling uncertainty.\"
— Journal of Applied Statistics
The critically acclaimed First Edition of Understanding Uncertainty provided a study of uncertainty addressed to scholars in all fields, showing that uncertainty could be measured by probability, and that probability obeyed three basic rules that enabled uncertainty to be handled sensibly in everyday life. These ideas were extended to embrace the scientific method and to show how decisions, containing an uncertain element, could be rationally made.
Featuring new material, the Revised Edition remains the go-to guide for uncertainty and decision making, providing further applications at an accessible level including:
* A critical study of transitivity, a basic concept in probability
* A discussion of how the failure of the financial sector to use the proper approach to uncertainty may have contributed to the recent recession
* A consideration of betting, showing that a bookmaker's odds are not expressions of probability
* Applications of the book's thesis to statistics
* A demonstration that some techniques currently popular in statistics, like significance tests, may be unsound, even seriously misleading, because they violate the rules of probability
Understanding Uncertainty, Revised Edition is ideal for students studying probability or statistics and for anyone interested in one of the most fascinating and vibrant fields of study in contemporary science and mathematics.
eBook
Fuzzy Multiple Objective Decision Making
Focusing on the methodologies and applications of the field, this book presents mathematical tools for complex decision making. The first part of the book introduces the most popular methods used to calculate the solution of MOP in the field of MODM. The authors describe multi-objective evolutionary algorithms; expand de novo programming to changeable spaces, such as decision and objective spaces; and cover network data envelopment analysis. The second part focuses on various applications, giving readers a practical, in-depth understanding of MODM.
eBook
Supermodularity and complementarity
The economics literature is replete with examples of monotone comparative statics; that is, scenarios where optimal decisions or equilibria in a parameterized collection of models vary monotonically with the parameter. Most of these examples are manifestations of complementarity, with a common explicit or implicit theoretical basis in properties of a super-modular function on a lattice. Supermodular functions yield a characterization for complementarity and extend the notion of complementarity to a general setting that is a natural mathematical context for studying complementarity and monotone comparative statics. Concepts and results related to supermodularity and monotone comparative statics constitute a new and important formal step in the long line of economics literature on complementarity.
This monograph links complementarity to powerful concepts and results involving supermodular functions on lattices and focuses on analyses and issues related to monotone comparative statics. Don Topkis, who is known for his seminal contributions to this area, here presents a self-contained and up-to-date view of this field, including many new results, to scholars interested in economic theory and its applications as well as to those in related disciplines. The emphasis is on methodology. The book systematically develops a comprehensive, integrated theory pertaining to supermodularity, complementarity, and monotone comparative statics. It then applies that theory in the analysis of many diverse economic models formulated as decision problems, noncooperative games, and cooperative games.
eBook
Cooperation, Coopetition and Innovation
In presenting the concepts and the logical structure of the reasoning offered by game theory and their applications, the book explains the rational process of decision making in the framework of firm management and market competition. The book will expose both general teachings and a comprehensive analysis applied to specific case studies of various sectors of the economy.
eBook
Fuzzy Multi-Criteria Decision Making
In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the most recently developed methods. Each one of the 22 chapters include practical applications along with new results.
eBook
Robust Optimization
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 Optimizationalso makes an ideal graduate textbook on the subject.
eBook
Robust sample average approximation
Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA’s tractability and asymptotic properties and, additionally, enjoys strong finite-sample performance guarantees. The key to our method is linking SAA, distributionally robust optimization, and hypothesis testing of goodness-of-fit. Beyond Robust SAA, this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data-driven procedures that are based upon distributionally robust optimization. This analysis provides insight into the practical performance of these various methods in real applications. We present examples from inventory management and portfolio allocation, and demonstrate numerically that our approach outperforms other data-driven approaches in these applications.
Journal Article