More related to mathematical optimization

On February 27 and 28 of 2006, the University of Arizona held a workshop entitled, “Decision Modeling and Behavior in Uncertain and Complex En- ronments,” sponsored by the Air Force O?ce of Scienti?c Research under a Multidisciplinary University Research Initiative (MURI) grant. The purpose of the workshop was to assemble preeminent researchers studying problems at the interface of behavioral and cognitive science, decision analysis, and operations research. This book is a compilation of 14 chapters based on the presentations given during the workshop. These contributions are grouped into four general areas, which describe in some detail the challenges in conducting novel research in this ?eld. Part One is concerned with the need for integrating decision analysis and behavioral models. Robert T. Clemen discusses how the ?elds of behavioral - search and decision analysis have diverged over time, and makes a compelling case to establish new links between the disciplines. He recommends leveraging lessons learned from behavioral studies within prescriptive decision analysis studies and evaluating the practical impact of those prescriptive techniques in helping decision makers achieve their objectives. Jenna L. Marquard and Stephen M. Robinson address eleven common “traps” that face decision model analysts and users. An understanding of these traps leads to an understanding of modeling features that either help or hurt the decision-making process. The authors link theory and practice by examining a set of case studies across a diverse array of model scenarios, and provide a checklist of recommendations for analysts confronted by these eleven traps.
Goal Programming Applications in Accounting 74 Goal Programming Applications in Agriculture 76 Goal Programming Applications in Economics 78 Goal Programming Applications in Engineering 79 Goal Programming Applications in Finance 80 Goal Programming Applications in Government 83 Goal Programming Applications in an International Context 88 Goal Programming Applications in Management 90 Goal Programming Applications in Marketing 97 Summary 98 CHAPTER 5. FUTURE TRENDS IN GOAL PROORAMMING 101 GP is Positioned for Growth 101 Shifting the Life Cycle of GP Research to Growth 103 Summary 107 Reference 108 APPENDIX A TEXTBOOKS, READINGS BOOKS AND MONOORAPHS ON GOAL PROORAMMING 109 APPENDIX B. JOURNAL RESEARCH PUBLICATIONS ON GOAL PROORAMMING 113 INDEX 213 viii LIST OF FIGURES Figure 1-1. Summary Relationship of GP with MS/OR and MCDM Figure 1-2. Frequency Distribution for GP Journal Publications Figure 1-3. Life Cycle ofGP Research Figure 2-1. Set of GP Efficient Solutions Figure 5-1. Life Cycle of GP Research ix LIST OF TABLES Table 1-1. MS/OR Topics and Their Related GP Topics Table 1-2. MCDM Subareas and Their Related GP Topics Table 1-3. Frequency Listing ofGP Journal Publications and Book Titles Table 2-1. Solutions for a Dominated GP Problem Table 2-2. Conversion ofLP Constraints to Goal Constraints Table 2-3. GP Citations on Dominance, Inferiority and Inefficiency Table 2-4. GP Citations on Relative Weighting, Prioritization and Incommensurability Table 2-5. MS/OR Topics and Their Related GP Topics Table 3-1. Citations on WeightedlPreemptive GP Methodology Table 3-2. Citations on Pure/Mixed Integer GP Methodology Table 3-3.
​This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises.

The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes.


"This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study."

Professor Ilan Adler,
IEOR Department,
UC Berkeley
"A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields."

Michael P. Friedlander,
IBM Professor of Computer Science,
Professor of Mathematics,
University of British Columbia

DYNAMIC OPTIMIZATION AND DIFFERENTIAL GAMES has been written to address the increasing number of Operations Research and Management Science problems (that is, applications) that involve the explicit consideration of time and of gaming among multiple agents. It is a book that will be used both as a textbook and as a reference and guide to engineers, operation researchers, applied mathematicians and social scientists whose work involves the theoretical aspects of dynamic optimization and differential games. Included throughout the text are detailed explanations of several original dynamic and game-theoretic mathematical models, which are of particular relevance in today’s technologically-driven-global economy: revenue management, supply chain management, electric power systems, urban freight systems, dynamic congestion pricing, dynamic traffic assignment, electronic commerce and the Internet. In addition, there will be some more traditional applications with useful pedagogical content included in Chapter 1.

The book combines an emphasis on deterministic models and methods along with an introduction to stochastic optimal control and stochastic differential games. And most important, the book covers both theory and applications. It develops the key results of deterministic, continuous time, optimal control theory from both the classical calculus of variations perspectives and the more modern approach of infinite dimensional mathematical programming. Infinite dimensional mathematical programming provides greater utility for solving continuous-time-differential-game problems.

Aiding Decisions With Multiple Criteria: Essays in Honor of Bernard Roy is organized around two broad themes: Graph Theory with path-breaking contributions on the theory of flows in networks and project scheduling, Multiple Criteria Decision Aiding with the invention of the family of ELECTRE methods and methodological contribution to decision-aiding which lead to the creation of Multi-Criteria Decision Analysis (MCDA). Professor Bernard Roy has had considerable influence on the development of these two broad areas. £/LIST£ Part one contains papers by Jacques Lesourne, and Dominique de Werra & Pierre Hansen related to the early career of Bernard Roy when he developed many new techniques and concepts in Graph Theory in order to cope with complex real-world problems. Part two of the book is devoted to Philosophy and Epistemology of Decision-Aiding with contributions from Valerie Belton & Jacques Pictet and Jean-Luis Genard & Marc Pirlot. Part three includes contributions based on Theory and Methodology of Multi-Criteria Decision-Aiding based on a general framework for conjoint measurement that allows intrasitive preferences. Denis Bouyssou & Marc Pirlot; Alexis Tsoukiàs, Patrice Perny & Philippe Vincke; Luis Dias & João Clímaco; Daniel Vanderpooten; Michael Doumpos & Constantin Zopounidis; and Marc Roubens offer a considerable range of examinations of this aspect of MCDA. Part four is devoted to Perference Modeling with contributions from Peter Fishburn; Salvatore Greco, Benedetto Matarazzo & Roman Slowinski; Salem Benferhat, Didier Dubois & Henri Prade; Oscar Franzese & Mark McCord; Bertrand Munier; and Raymond Bisdorff. Part five groups Applications of Multi-Criteria Decision-Aiding, and Carlos Henggeler Antunes, Carla Oliveira & João Clímaco; Carlos Bana e Costa, Manuel da Costa-Lobo, Isabel Ramos & Jean-Claude Vansnick; Yannis Siskos & Evangelos Grigoroudis; Jean-Pierre Brans, Pierre Kunsch & Bertrand Mareschal offer a wide variety of application problems. Finally, Part six includes contributions on Multi-Objective Mathematical Programming from Jacques Teghem, Walter Habenicht and Pekka Korhonen.
Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems.

Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity.

This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike.

The Handbook’s thirty-one chapters are organized into four parts:

Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization;Algorithms, documenting the directions of current algorithmic development;Software, providing an overview of the state-of-the-art;Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.
In February 2002, the Industrial and Systems Engineering (ISE) De partment at the University of Florida hosted a National Science Founda tion Workshop on Collaboration and Negotiation in Supply Chain Man agement and E Commerce. This workshop focused on characterizing the challenges facing leading edge firms in supply chain management and electronic commerce, and identifying research opportunities for de veloping new technological and decision support capabilities sought by industry. The audience included practitioners in the areas of supply chain management and E Commerce, as well as academic researchers working in these areas. The workshop provided a unique setting that has facilitated ongoing dialog between academic researchers and industry practitioners. This book codifies many of the important themes and issues around which the workshop discussions centered. The editors of this book, all faculty members in the ISE Department at the University of Florida, also served as the workshop's coordinators. In addition to workshop participants, we also invited contributions from leading academics and practitioners who were not able to attend. As a result, the chapters herein represent a collection of research contributions, monographs, and case studies from a variety of disciplines and viewpoints. On the aca demic side alone, chapter authors include faculty members in supply chain and operations management, marketing, industrial engineering, economics, computer science, civil and environmental engineering, and building construction departments.
At a practical level, mathematical programming under multiple objectives has emerged as a powerful tool to assist in the process of searching for decisions which best satisfy a multitude of conflicting objectives, and there are a number of distinct methodologies for multicriteria decision-making problems that exist. These methodologies can be categorized in a variety of ways, such as form of model (e.g. linear, non-linear, stochastic), characteristics of the decision space (e.g. finite or infinite), or solution process (e.g. prior specification of preferences or interactive). Scientists from a variety of disciplines (mathematics, economics and psychology) have contributed to the development of the field of Multicriteria Decision Making (MCDM) (or Multicriteria Decision Analysis (MCDA), Multiattribute Decision Making (MADM), Multiobjective Decision Making (MODM), etc.) over the past 30 years, helping to establish MCDM as an important part of management science. MCDM has become a central component of studies in management science, economics and industrial engineering in many universities worldwide.
Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory and Applications aims to bring together `state-of-the-art' reviews and the most recent advances by leading experts on the fundamental theories, methodologies and applications of MCDM. This is aimed at graduate students and researchers in mathematics, economics, management and engineering, as well as at practicing management scientists who wish to better understand the principles of this new and fast developing field.
The availability of today’s online information systems rapidly increases the relevance of dynamic decision making within a large number of operational contexts. Whenever a sequence of interdependent decisions occurs, making a single decision raises the need for anticipation of its future impact on the entire decision process. Anticipatory support is needed for a broad variety of dynamic and stochastic decision problems from different operational contexts such as finance, energy management, manufacturing and transportation. Example problems include asset allocation, feed-in of electricity produced by wind power as well as scheduling and routing. All these problems entail a sequence of decisions contributing to an overall goal and taking place in the course of a certain period of time. Each of the decisions is derived by solution of an optimization problem. As a consequence a stochastic and dynamic decision problem resolves into a series of optimization problems to be formulated and solved by anticipation of the remaining decision process.

However, actually solving a dynamic decision problem by means of approximate dynamic programming still is a major scientific challenge. Most of the work done so far is devoted to problems allowing for formulation of the underlying optimization problems as linear programs. Problem domains like scheduling and routing, where linear programming typically does not produce a significant benefit for problem solving, have not been considered so far. Therefore, the industry demand for dynamic scheduling and routing is still predominantly satisfied by purely heuristic approaches to anticipatory decision making. Although this may work well for certain dynamic decision problems, these approaches lack transferability of findings to other, related problems.

This book has serves two major purposes:

‐ It provides a comprehensive and unique view of anticipatory optimization for dynamic decision making. It fully integrates Markov decision processes, dynamic programming, data mining and optimization and introduces a new perspective on approximate dynamic programming. Moreover, the book identifies different degrees of anticipation, enabling an assessment of specific approaches to dynamic decision making.

‐ It shows for the first time how to successfully solve a dynamic vehicle routing problem by approximate dynamic programming. It elaborates on every building block required for this kind of approach to dynamic vehicle routing. Thereby the book has a pioneering character and is intended to provide a footing for the dynamic vehicle routing community.

Practical Goal Programming is intended to allow academics and practitioners to be able to build effective goal programming models, to detail the current state of the art, and to lay the foundation for its future development and continued application to new and varied fields. Suitable as both a text and reference, its nine chapters first provide a brief history, fundamental definitions, and underlying philosophies, and then detail the goal programming variants and define them algebraically. Chapter 3 details the step-by-step formulation of the basic goal programming model, and Chapter 4 explores more advanced modeling issues and highlights some recently proposed extensions.

Chapter 5 then details the solution methodologies of goal programming, concentrating on computerized solution by the Excel Solver and LINGO packages for each of the three main variants, and includes a discussion of the viability of the use of specialized goal programming packages. Chapter 6 discusses the linkages between Pareto Efficiency and goal programming. Chapters 3 to 6 are supported by a set of ten exercises, and an Excel spreadsheet giving the basic solution of each example is available at an accompanying website.

Chapter 7 details the current state of the art in terms of the integration of goal programming with other techniques, and the text concludes with two case studies which were chosen to demonstrate the application of goal programming in practice and to illustrate the principles developed in Chapters 1 to 7. Chapter 8 details an application in healthcare, and Chapter 9 describes applications in portfolio selection.

The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the ?nite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has bene?ted from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, ?nancial, and spatial).
Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters discuss briefly two concrete nlodels (linear fractional vector optimization and the traffic equilibrium problem) whose analysis can benefit a lot from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty of a characteristic map or function is investigated, we always try first to establish necessary conditions for it to hold, then we go on to study whether the obtained necessary conditions are suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration.
This volume contains selected papers presented at the International Conference on Operations Research SOR 2002 held at the University of Klagenfurt from Sep tember 2 to September 5, 2002. The conference was organized under the auspices of the German, the Swiss and the Austrian Operations Research societies - Gesellschaft fiir Operations Research e.V. (GOR) - Schweizerische Vereinigung fiirOperations Research (SVOR) - Osterreichische Gesellschaft fiirOperations Research (OGOR). After Vienna (1990), Berlin (1994) and Ziirich (1998) this has been the fourth time that the three societies organized ajoint conference. The conference was attended by more than 400 participants from countries all over the world which demonstrates the broad interest in all aspects ofOperations Research. The scientific program of the conference consisted of 4 plenary lectures, 5 semi plenary lectures, and about 320 contributed papers which have been presented in 16 sections. Due to the limited number of pages available for the proceedings vol ume, the length of each article as well as the total number ofcontributions had to be restricted. The decision on the acceptance of papers for the proceedings has been made in close eo operation with the section chairmen and was based on their suggestions. We wish to express our sincere thanks to the chairmen for supporting our editorial work by refereeing the manuscripts and letting us have their advice. We also would like to thank Dr. Wemer Muller from Springer-Verlag for his support in publishing this proceedings volume so quickly.
Multicriterion Decision in Management: Principles and Practice is the first multicriterion analysis book devoted exclusively to discrete multicriterion decision making. Typically, multicriterion analysis is used in two distinct frameworks: Firstly, there is multiple criteria linear programming, which is an extension of the results of linear programming and its associated algorithms. Secondly, there is discrete multicriterion decision making, which is concerned with choices among a finite number of possible alternatives such as projects, investments, decisions, etc. This is the focus of this book.
The book concentrates on the basic principles in the domain of discrete multicriterion analysis, and examines each of these principles in terms of their properties and their implications. In multicriterion decision analysis, any optimum in the strict sense of the term does not exist. Rather, multicriterion decision making utilizes tools, methods, and thinking to examine several solutions, each having their advantages and disadvantages, depending on one's point of view. Actually, various methods exist for reaching a good choice in a multicriterion setting and even a complete ranking of the alternatives. The book describes and compares these methods, so-called `aggregation methods', with their advantages and their shortcomings. Clearly, organizations are becoming more complex, and it is becoming harder and harder to disregard complexity of points of view, motivations, and objectives. The day of the single objective (profit, social environment, etc. ) is over and the wishes of all those involved in all their diversity must be taken into account. To do this, a basic knowledge of multicriterion decision analysis is necessary. The objective of this book is to supply that knowledge and enable it to be applied.
The book is intended for use by practitioners (managers, consultants), researchers, and students in engineering and business.
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