Springer Series in Operations Research and Financial Engineering – serie

This book covers the classical theory of Markov chains on general state-spaces as well as many recent developments. Part I lays the foundations of the theory of Markov chain on general states-space. Part II covers the basic theory of irreducible Markov chains on general states-space, relying heavily on regeneration techniques.

Integer programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely ef?cient LP software packages exist, solving an integer program can remain a formidable challenge, even for some small size problems. For instance, the following small (5-variable) IP problem (called the unbounded knapsack problem) min{213x?1928x?11111x?2345x +9123x} 1 2 3 4 5 s.t. 12223x +12224x +36674x +61119x +85569x = 89643482, 1 2 3 4 5 x ,x ,x ,x ,x?N, 1 2 3 4 5 taken from a list of dif?cult knapsack problems in Aardal and Lenstra [2], is not solved even by hours of computing, using for instance the last version of the ef?cient software package CPLEX. However,thisisnotabookonintegerprogramming,asverygoodonesonthistopicalreadyexist. For standard references on the theory and practice of integer programming, the interested reader is referred to, e.g., Nemhauser and Wolsey [113], Schrijver [121], Wolsey [136], and the more recent Bertsimas and Weismantel [21]. On the other hand, this book could provide a complement to the above books as it develops a rather unusual viewpoint.

Services requiring parts has become a USD1.5 trillion business annually worldwide, creating a tremendous incentive to manage the logistics of these parts efficiently by making planning and operational decisions in a rational and rigorous manner. This book provides a broad overview of modeling approaches and solution methodologies for addressing service parts inventory problems found in high-powered technology and aerospace applications. The focus in this work is on the management of high cost, low demand rate service parts found in multi-echelon settings.The text may be used in a variety of courses for first-year graduate students or senior undergraduates, as well as for practitioners, requiring only a background in stochastic processes and optimization. It will serve as an excellent reference for key mathematical concepts and a guide to modeling a variety of multi-echelon service parts planning and operational problems.

Extreme Value Theory offers a careful, coherent exposition of the subject starting from the probabilistic and mathematical foundations and proceeding to the statistical theory.

This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of many phenomena where the probability of a single huge value impacts heavily. Record-breaking insurance losses, financial-log returns, files sizes stored on a server, transmission rates of files are all examples of heavy-tailed phenomena. Key features: * Unique text devoted to heavy-tails * Emphasizes both probability modeling and statistical methods for fitting models. Most treatments focus on one or the other but not both * Presents broad applicability of heavy-tails to the fields of data networks, finance (e.g., value-at- risk), insurance, and hydrology * Clear, efficient and coherent exposition, balancing theory and actual data to show the applicability and limitations of certain methods * Examines in detail the mathematical properties of the methodologies as well as their implementation in Splus or R statistical languages * Exposition driven by numerous examples and exercises Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus.This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.

Ensuring the availability of materials and goods is one of the major responsibilities and goals of inventory management, requiring various techniques such as mathematical modeling and computational methods. This unique textbook is devoted to models and solutions in inventory management. It begins with an introductory chapter in which the basics of inventory systems and mathematical assumptions for all models are grouped together, thereafter mathematical principles and applications are treated as they relate to one another. In this clearly organized systematic exposition, a unique balance is maintained between simplicity and rigor. Topics related to multiechelon systems are discussed in the latter chapters. An important feature of this work can be found in the beautiful examples in the final chapter in which a relationship between different kinds of real situations in industry and theoretical models are discussed in detail.This graduate textbook will appeal to senior and first year graduate students in operations research, industrial engineering, and quantitative MBA programs and serves as a reference resource for the industrial world.

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations.Review by Jakub Marecek (Computer Journal) The emphasis put on mixed integer rounding and mixing sets, heuristics in-built in general purpose integer programming solvers, as well as on decompositions and heuristics using integer programming should be praised...There is no doubt that this volume offers the present best introduction to integer programming formulations of lotsizing problems, encountered in production planning. (2007)

Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research.

Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It presents a coherent treatment of the distributional and sample path fundamental properties of extremes and records. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.The book is self-contained and requires an introductory measure-theoretic course in probability as a prerequisite. Almost all sections have an extensive list of exercises which extend developments in the text, offer alternate approaches, test mastery and provide for enjoyable muscle flexing by a reader. The material is aimed at students and researchers in probability, statistics, financial engineering, mathematics, operations research, civil engineering and economics who need to know about: asymptotic methods for extremes; models for records and record frequencies; stochastic process and point process methods and their applications to obtaining distributional approximations; pervasive applications of the theory of regular variation in probability theory, statistics and financial engineering.“This book is written in a very lucid way. The style is sober, the mathematics tone is pleasantly conversational, convincing and enthusiastic. A beautiful book!”Bulletin of the Dutch Mathematical Society“This monograph is written in a very attractive style. It contains a lot of complementary exercises and practically all important bibliographical reference.”Revue Roumaine deMathématiques Pures et Appliquées

Since its introduction by Isaac Newton (1669) and Joseph Raphson (1690) more than three hundred years ago, Newton's method or the Newton-Raphson method has become the most important technique for solving the system of smooth algebraic equations. Despite its simple structure, Newton's method possesses a fast local convergence rate - superlinear or quadratic. This outstanding feature of Newton's method leads to numerous extensions in the literature. Most of these extensions focus on systems of smooth equations. Since the 1980s, researchers the fields of optimization and numerical analysis have been working on extending Newton's method to non-differentiable system of algebraic equations. This book presents a comprehensive treatment of the development of the generalized Newton method for solving nonsmooth equations and related problems which grow out of science, engineering, economics and business and sheds light on further investigations of this fascinating topic oriented towards applications in optimization. Semismooth analysis, which form the backbone of further developments, is developed in Chapter 1. Topics then unfold systematically, with apposite illustrations and examples. Graduate students and researchers in this area will find the book useful.

Classical probability theory provides information about random walks after a fixed number of steps. For applications, however, it is more natural to consider random walks evaluated after a random number of steps. Stopped Random Walks: Limit Theorems and Applications shows how this theory can be used to prove limit theorems for renewal counting processes, first passage time processes, and certain two-dimensional random walks, as well as how these results may be used in a variety of applications. The present second edition offers updated content and an outlook on further results, extensions and generalizations. A new chapter introduces nonlinear renewal processes and the theory of perturbed random walks, which are modeled as random walks plus "noise". This self-contained research monograph is motivated by numerous examples and problems. With its concise blend of material and over 300 bibliographic references, the book provides a unified and fairly complete treatment of the area. The book may be used in the classroom as part of a course on "probability theory", "random walks" or "random walks and renewal processes", as well as for self-study.From the reviews: "The book provides a nice synthesis of a lot of useful material." N.H. Bingham "...[a] clearly written book, useful for researcher and student." A.J. Stam

This volume presents a comprehensive first course in the Monte Carlo method which will be suitable for graduate and undergraduate students in the mathematical sciences and engineering, principally operations research, statistics, mathematics, and computer science. The reader is assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained. As well as a thorough exploration of all the important concepts of the Monte Carlo method, the volume includes over 75 algorithms which allow the reader to move rapidly from the concepts to putting them into practice. The book also contains numerous exercises, many of them hands-on implementations of selected algorithms to demonstrate the application of these ideas in realistic settings.

Facility location is concerned with the siting of one or more facilities in a way that optimizes certain objectives such as minimizing transportation costs, providing equitable service to customers, or minimizing the time taken to deliver emergency services. This handbook presents a wide-ranging survey of location analysis. Both researchers in the subject and practitioners concerned with the solution of real-world problems will find this an up-to-date and comprehensive volume which addresses all the major methods and applications in the field. Each chapter has been written by an expert on that particular topic, and the editor has taken care to ensure a uniformity of style and notation throughout. The book is organized into four parts: Methodology and analysis of facility location. - Various objectives in facility location. - Competitive facility location. - Routing and location.

One of the most important tasks faced by decision-makers in business and government is that of selection. Selection problems are challenging in that they require the balancing of multiple, often conflicting, criteria. In recent years, a number of interesting decision aids have become available to assist in such decisions. The aim of this book is to provide a comparative survey of many of the decision aids currently available. The first chapters present general ideas which underpin the methodologies used to design these aids. Subsequent chapters then focus on specific decision aids and demonstrate some of the software which implement these ideas. A final chapter provides a comparative analysis of their strengths and weaknesses.

The past two decades have seen a great deal of research into the stochastic modelling of production, manufacturing, and inventory systems for the purpose of improving their performance. This book provides a graduate-level introduction to these techniques covering exact, approximate, and numerical techniques. The author has aimed to strike a balance between theoretical issues and the practical aspects of modelling manufacturing systems. It is based on graduate courses given to operations research and industrial engineering students and includes numerous examples and exercises.

This book provides a comprehensive introduction to linear programming which encompasses all the major topics students will encounter in courses on the subject. The authors aim to teach both the underlying mathematical foundations and how these ideas are implemented in practice. The book illustrates all the concepts with both worked examples and plenty of exercises. In addition, Windows software is provided with the book so that students can try out numerical methods using the examples and exercises and hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time.Authors'note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States. The new version of Formula One, when ready, will be posted on WWW.

Discrete-event simulation consists of a collection of techniques that when applied to a discrete-event dynamical system, generates sequences called sample paths that characterize its behavior. The collection includes modelling concepts for abstracting the essential features of a system, using specially designed software for converting these relationships into computer executable code capable of generating the requisite sample-path data; outlining procedures for converting these data into estimates of systems performances; and then illustrating methods for assessing how well these estimates approximate true, but unknown system behavior.This book is intended for upper level undergraduate and graduate students in operations research and management science, mathematics, industrial engineering, computer science, and business and features extensive exercises throughout. This concept of modelling complex sytems allows a relatively low-cost way of gathering information for decision-making.Principally offered are four problems for student exercises; each is progressively brought forward through the modelling, programming, and analysis chapters, providing continuity to the learning process.

Stochastic Process Limits are useful and interesting because they generate simple approximations for complicated stochastic processes and also help explain the statistical regularity associated with a macroscopic view of uncertainty. This book emphasizes the continuous-mapping approach to obtain new stochastic-process limits from previously established stochastic-process limits. The continuous-mapping approach is applied to obtain heavy-traffic-stochastic-process limits for queueing models, including the case in which there are unmatched jumps in the limit process. These heavy-traffic limits generate simple approximations for complicated queueing processes and they reveal the impact of variability upon queueing performance. The book will be of interest to researchers and graduate students working in the areas of probability, stochastic processes, and operations research. In addition this book won the 2003 Lanchester Prize for the best contribution to Operation Research and Management in English, see: http://www. informs. org/Prizes/LanchesterPrize. html

Written by a leading researcher this book presents an introduction to Stochastic Petri Nets covering the modeling power of the proposed SPN model, the stability conditions and the simulation methods. Its unique and well-written approach provides a timely and important addition to the literature. Appeals to a wide range of researchers in engineering, computer science, mathematics and OR.

Quality control is a scientific means for conducting observations, tests, and inspections and thereby making decisions that improve the perfomance of industrial processes. This book develops a set of dynamic approaches characterized by coordination. In practice, quality control problems almost never exist in isolation. The basic methodology underlying the studies is Markov decision programming. The book can be used as a graduate text for a new course on statistical process control, or as a reference for researchers and practitioners in mathematics, operations research and operations management, quality control, production planning, and logistics.

Everyday life bears a multitude of location problems and locational de- sions. These may be as simple as how best to place a pencil on a desk without having to reach too far and still keeping the work space clear, up to the question of where to place the next out of hundreds of thousands of transistors on a microchip. Some of these questions have easy answers, while others are so complex that not even satisfactory solutions are ava- able, never mind asking for optimized placement. The scales of problems reach from microchip design up to global trade and may demand consid- ation of one, two, three, or even more dimensions. As modern life encounters an ever increasing concentration in many - spects, usually a multitude of restrictions will be imposed on a problem. Theserestrictionsmaybeclassi?edasregionsoflimitedorforbiddenpla- ment of a new facility or as regions with limitations on traveling. Areas where the placement of a new facility is forbidden, referred to as forbidden regions,canbeusedtomodel,forexample,protectedareasorregionswhere thegeographiccharacteristicsforbidtheconstructionofthedesiredfacility. Limitations on traveling are constituted by barrier regions or obstacles like military regions,mountainranges,lakes,big rivers,interstatehighways,or, on smaller scales, machinery and conveyor belts in an industrial plant.

This two volume work presents a comprehensive treatment of the finite dimensional variational inequality and complementarity problem, covering the basic theory, iterative algorithms, and important applications. The authors provide a broad coverage of the finite dimensional variational inequality and complementarity problem beginning with the fundamental questions of existence and uniqueness of solutions, presenting the latest algorithms and results, extending into selected neighboring topics, summarizing many classical source problems, and suggesting novel application domains. This first volume contains the basic theory of finite dimensional variational inequalities and complementarity problems. This book should appeal to mathematicians, economists, and engineers working in the field.A set price of EUR 199 is offered for volume I and II bought at the same time. Please order at: orders@springer.de

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).

Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method; interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will find this volume of particular interest.

This book presents general results for discussing local optimality and computation of the expansion of value function and approximate solution of optimization problems. These results may be applied to various fields, from physics to economics, as various examples in the book show. Therefore, the book is an opportunity for popularizing these techniques among researchers involved in other sciences. Consequently the readership should be not only researchers in the field of optimization, nonlinear programming and optimal control, but also users of optimization in a wide sense, in mechanics (elasticity and plasticity theory), physics, statistics, finance and economics. The book will be useful to research professionals, including graduate students at an advanced level.

This book aims to present a comprehensive, self-contained, and concise overview of extreme value theory for time series, incorporating the latest research trends alongside classical methodology.

Integer programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely ef?cient LP software packages exist, solving an integer program can remain a formidable challenge, even for some small size problems. For instance, the following small (5-variable) IP problem (called the unbounded knapsack problem) min{213x?1928x?11111x?2345x +9123x} 1 2 3 4 5 s.t. 12223x +12224x +36674x +61119x +85569x = 89643482, 1 2 3 4 5 x ,x ,x ,x ,x?N, 1 2 3 4 5 taken from a list of dif?cult knapsack problems in Aardal and Lenstra [2], is not solved even by hours of computing, using for instance the last version of the ef?cient software package CPLEX. However,thisisnotabookonintegerprogramming,asverygoodonesonthistopicalreadyexist. For standard references on the theory and practice of integer programming, the interested reader is referred to, e.g., Nemhauser and Wolsey [113], Schrijver [121], Wolsey [136], and the more recent Bertsimas and Weismantel [21]. On the other hand, this book could provide a complement to the above books as it develops a rather unusual viewpoint.

Services requiring parts has become a $1.5 trillion business annually worldwide, creating a tremendous incentive to manage the logistics of these parts efficiently by making planning and operational decisions in a rational and rigorous manner. This book provides a broad overview of modeling approaches and solution methodologies for addressing service parts inventory problems found in high-powered technology and aerospace applications. The focus in this work is on the management of high cost, low demand rate service parts found in multi-echelon settings.The text may be used in a variety of courses for first-year graduate students or senior undergraduates, as well as for practitioners, requiring only a background in stochastic processes and optimization. It will serve as an excellent reference for key mathematical concepts and a guide to modeling a variety of multi-echelon service parts planning and operational problems.