Project scheduling problems are, generally speaking, the problems of allocating scarce resources over time to perform a given set of activities. The resources are nothing other than the arbitrary means which activities complete for. Also the activities can have a variety of interpretations. Thus, project scheduling problems appear in a large spectrum of real-world situations, and, in consequence, they have been intensively studied for almost fourty years. Almost a decade has passed since the multi-author monograph: R. Slowinski, 1. W~glarz (eds. ), Advances in Project Scheduling, Elsevier, 1989, summarizing the state-of-the-art across project scheduling problems, was published. Since then, considerable progress has been made in all directions of modelling and finding solutions to these problems. Thus, the proposal by Professor Frederick S. Hillier to edit a handbook which reports on the recent advances in the field came at an exceptionally good time and motivated me to accept the challenge. Fortunately, almost all leading experts in the field have accepted my invitation and presented their completely new advances often combined with expository surveys. Thanks to them, the handbook stands a good chance of becoming a key reference point on the current state-of-the-art in project scheduling, as well as on new directions in the area. The contents are divided into four parts. The first one, dealing with classical models -exact algorithms, is preceded by a proposition of the classification scheme for scheduling problems.

This book is the result of over ten (10) years of research and development in flexible robots and structures at Sandia National Laboratories. The authors de cided to collect this wealth of knowledge into a set of viewgraphs in order to teach a graduate class in Flexible Robot Dynamics and Controls within the Mechanical En gineering Department at the University of New Mexico (UNM). These viewgraphs, encouragement from several students, and many late nights have produced a book that should provide an upper-level undergraduate and graduate textbook and a reference for experienced professionals. The content of this book spans several disciplines including structural dynam ics, system identification, optimization, and linear, digital, and nonlinear control theory which are developed from several points of view including electrical, me chanical, and aerospace engineering as well as engineering mechanics. As a result, the authors believe that this book demonstrates the value of solid applied theory when developing hardware solutions to real world problems. The reader will find many real world applications in this book and will be shown the applicability of these techniques beyond flexible structures which, in turn, shows the value of mul tidisciplinary education and teaming.

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."

Books on computation in the marketplace tend to discuss the topics within specific fields. Many computational algorithms, however, share common roots. Great advantages emerge if numerical methodologies break the boundaries and find their uses across disciplines. Interdisciplinary Computing In Java Programming Language introduces readers of different backgrounds to the beauty of the selected algorithms. Serious quantitative researchers, writing customized codes for computation, enjoy cracking source codes as opposed to the black-box approach. Most C and Fortran programs, despite being slightly faster in program execution, lack built-in support for plotting and graphical user interface. This book selects Java as the platform where source codes are developed and applications are run, helping readers/users best appreciate the fun of computation. Interdisciplinary Computing In Java Programming Language is designed to meet the needs of a professional audience composed of practitioners and researchers in science and technology. This book is also suitable for senior undergraduate and graduate-level students in computer science, as a secondary text.

Iterative methods for finding fixed points of non-expansive operators in Hilbert spaces have been described in many publications. In this monograph we try to present the methods in a consolidated way. We introduce several classes of operators, examine their properties, define iterative methods generated by operators from these classes and present general convergence theorems. On this basis we discuss the conditions under which particular methods converge. A large part of the results presented in this monograph can be found in various forms in the literature (although several results presented here are new). We have tried, however, to show that the convergence of a large class of iteration methods follows from general properties of some classes of operators and from some general convergence theorems.

During the last half century, the development and testing of prediction models of combustion chamber performance have been an ongoing task at the International Flame Research Foundation (IFRF) in IJmuiden in the Netherlands and at many other research organizations. This task has brought forth a hierarchy of more or less standard numerical models for heat transfer predictions, in particular for the prediction of radiative heat transfer. Unfortunately all the methods developed, which certainly have a good physical foundation, are based on a large number of extreme sim plifications or uncontrolled assumptions. To date, the ever more stringent requirements for efficient production and use of energy and heat from com bustion chambers call for prediction algorithms of higher accuracy and more detailed radiative heat transfer calculations. The driving forces behind this are advanced technology requirements, the costs of large-scale experimen tal work, and the limitation of physical modeling. This interest is growing more acute and has increased the need for the publication of a textbook for more accurate treatment of radiative transfer in enclosures. The writing of a textbook on radiative heat transfer, however, in ad dition to working regularly on other subjects is a rather difficult task for which some years of meditation are necessary. The book must satisfy two requirements which are not easily reconciled. From the mathematical point of view, it must be written in accordance with standards of mathemati cal rigor and precision."

This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem."

Driven by the request for increased productivity, flexibility, and competitiveness, modern civilization increasingly has created high-performance discrete event dynamic systems (DEDSs). These systems exhibit concurrent, sequential, competitive activities among their components. They are often complex and large in scale, and necessarily flexible and thus highly capital-intensive. Examples of systems are manufacturing systems, communication networks, traffic and logistic systems, and military command and control systems. Modeling and performance evaluation play a vital role in the design and operation of such high-performance DEDSs and thus have received widespread attention from researchers over the past two decades. One methodology resulting from this effort is based on timed Petri nets and related graphical and mathematical tools. The popularity that Petri nets have been gaining in modeling of DEDSs is due to their powerful representational ability of concurrency and synchronization; however these properties of DEDSs cannot be expressed easily in traditional formalisms developed for analysis of `classical' systems with sequential behaviors. This book introduces the theories and applications of timed Petri nets systematically. Moreover, it also presents many practical applications in addition to theoretical developments, together with the latest research results and industrial applications of timed Petri nets. Timed Petri Nets: Theory and Application is intended for use by researchers and practitioners in the area of Discrete Event Dynamic Systems.

Modeling, Control And Optimization Of Complex Systems is a collection of contributions from leading international researchers in the fields of dynamic systems, control theory, and modeling. These papers were presented at the Symposium on Modeling and Optimization of Complex Systems in honor of Larry Yu-Chi Ho in June 2001. They include exciting research topics such as:

-modeling of complex systems,
-power control in ad hoc wireless networks,
-adaptive control using multiple models,
-constrained control,
-linear quadratic control,
-discrete events,
-Markov decision processes and reinforcement learning,
-optimal control for discrete event and hybrid systems,
-optimal representation and visualization of multivariate data and functions in low-dimensional spaces.

While domain decomposition methods have a long history dating back well over one hundred years, it is only during the last decade that they have become a major tool in numerical analysis of partial differential equations. This monograph emphasizes domain decomposition methods in the context of so-called virtual optimal control problems and treats optimal control problems for partial differential equations and their decompositions using an all-at-once approach.

Supervision of Petri Nets presents supervisory control theory for Petri nets with a legal set as the control goal. Petri nets model discrete event systems - dynamic systems whose evolution is completely determined by the occurrence of discrete events. Control laws, which guarantee that the system meets a set of specifications in the presence of uncontrollable and unobservable events, are studied and constructed, using application areas such as automated manufacturing and transportation systems. Supervision of Petri Nets introduces a new and mathematically sound approach to the subject. Existing results are unified by proposing a general mathematical language that makes extensive use of order theoretical ideas, and numerous new results are described, including ready-to-use algorithms that construct supervisory control laws for Petri nets. Supervision of Petri Nets is an excellent reference for researchers, and may also be used as a supplementary text for advanced courses on control theory.

During the last four decades there has been a remarkable development in optimization and optimal control. Due to its wide variety of applications, many scientists and researchers have paid attention to fields of optimization and optimal control. A huge number of new theoretical, algorithmic, and computational results have been observed in the last few years. This book gives the latest advances, and due to the rapid development of these fields, there are no other recent publications on the same topics.

Key features:

Provides a collection of selected contributions giving a state-of-the-art account of recent developments in the field

Covers a broad range of topics in optimization and optimal control, including unique applications

Includes chapters written by experts in their respective disciplines

Appeals to a broad audience of researchers, practitioners, and advanced graduate students in applied mathematics and engineering

Variational calculus has been the basis of a variety of powerful methods in the ?eld of mechanics of materials for a long time. Examples range from numerical schemes like the ?nite element method to the determination of effective material properties via homogenization and multiscale approaches. In recent years, however, a broad range of novel applications of variational concepts has been developed. This c- prises the modeling of the evolution of internal variables in inelastic materials as well as the initiation and development of material patterns and microstructures. The IUTAM Symposium on "Variational Concepts with Applications to the - chanics of Materials" took place at the Ruhr-University of Bochum, Germany, on September 22-26, 2008. The symposium was attended by 55 delegates from 10 countries. Altogether 31 lectures were presented. The objective of the symposium was to give an overview of the new dev- opments sketched above, to bring together leading experts in these ?elds, and to provide a forum for discussing recent advances and identifying open problems to work on in the future. The symposium focused on the developmentof new material models as well as the advancement of the corresponding computational techniques. Speci?c emphasis is put on the treatment of materials possessing an inherent - crostructure and thus exhibiting a behavior which fundamentally involves multiple scales. Among the topics addressed at the symposium were: 1. Energy-based modeling of material microstructures via envelopes of n- quasiconvex potentials and applications to plastic behavior and pha- transformations.

The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium." So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality, our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions."

The numerous advances in mathematical programming have opened up new insights about sensitivity analysis. The paradigm 'What if...?' question is no longer the only question of interest. Often, we want to know 'Why...?' and 'Why not...?' Such questions were not analyzed in the early years of mathematical programming to the same extent that they are now, and we have not only expanded our thinking about 'post-optimal analysis', but also about 'solution analysis', even if the solution obtained is not optimal. Therefore, it is now time to examine all the recent advances on sensitivity analysis and parametric programming. This book combines the origins of sensitivity analysis with the state of the art. It covers much of the traditional approaches with a modern perspective, and shows recent results using the optimal partition approach, stemming from interior methods, for both linear and quadratic programming. It examines the special case of network models. It presents a neglected topic, qualitative sensitivity analysis, as well as elements of mixed integer programming and gives a modern perspective of nonlinear programming.It provides recent advances in multi-criteria mathematical programming and also describes the state-of-the-art in stochastic programming. It covers recent advances in understanding redundancy in quadratic programs, considers an approach to diagnosing infeasibility in linear and nonlinear programs, and gives an overview of sensitivity analysis for fuzzy mathematical programming.

This work is a revised and enlarged edition of a book with the same title published in Romanian by the Publishing House of the Romanian Academy in 1989. It grew out of lecture notes for a graduate course given by the author at the University if Ia i and was initially intended for students and readers primarily interested in applications of optimal control of ordinary differential equations. In this vision the book had to contain an elementary description of the Pontryagin maximum principle and a large number of examples and applications from various fields of science. The evolution of control science in the last decades has shown that its meth ods and tools are drawn from a large spectrum of mathematical results which go beyond the classical theory of ordinary differential equations and real analy ses. Mathematical areas such as functional analysis, topology, partial differential equations and infinite dimensional dynamical systems, geometry, played and will continue to play an increasing role in the development of the control sciences. On the other hand, control problems is a rich source of deep mathematical problems. Any presentation of control theory which for the sake of accessibility ignores these facts is incomplete and unable to attain its goals. This is the reason we considered necessary to widen the initial perspective of the book and to include a rigorous mathematical treatment of optimal control theory of processes governed by ordi nary differential equations and some typical problems from theory of distributed parameter systems."

This IMA Volume in Mathematics and its Applications ESSAYS ON MATHEMATICAL ROBOTICS is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory." The workshop featured a mathematicalintroductionto kinematics and fine motion planning; dynam- ics and control of kinematically redundant robot arms including snake-like robots, multi-fingered robotic hands; methods of non-holonomic motion planning for space robots, multifingered robot hands and mobile robots; new techniques in analytical mechanics for writing the dynamics of com- plicated multi-body systems subject to constraints on angular momentum or other non-holonomic constraints. In addition to papers representing proceedings of the Workshop, this volume contains several longer papers surveying developments of the intervening years. We thank John Baillieul, Shankar S. Sastry, and Hector J. Sussmann for organizing the workshop and editing the proceedings. We also take this opportunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. Avner Friedman Willard Miller, Jr.

During the last three decades, interest has increased significantly in the representation and manipulation of imprecision and uncertainty. Perhaps the most important technique in this area concerns fuzzy logic or the logic of fuzziness initiated by L. A. Zadeh in 1965. Since then, fuzzy logic has been incorporated into many areas of fundamental science and into the applied sciences. More importantly, it has been successful in the areas of expert systems and fuzzy control. The main body of this book consists of so-called IF-THEN rules, on which experts express their knowledge with respect to a certain domain of expertise. Fuzzy IF-THEN Rules in Computational Intelligence: Theory and Applications brings together contributions from leading global specialists who work in the domain of representation and processing of IF-THEN rules. This work gives special attention to fuzzy IF-THEN rules as they are being applied in computational intelligence. Included are theoretical developments and applications related to IF-THEN problems of propositional calculus, fuzzy predicate calculus, implementations of the generalized Modus Ponens, approximate reasoning, data mining and data transformation, techniques for complexity reduction, fuzzy linguistic modeling, large-scale application of fuzzy control, intelligent robotic control, and numerous other systems and practical applications. This book is an essential resource for engineers, mathematicians, and computer scientists working in fuzzy sets, soft computing, and of course, computational intelligence.

Production costs are being reduced by automation, robotics, computer-integrated manufacturing, cost reduction studies and more. These new technologies are expensive to buy, repair, and maintain. Hence, the demand on maintenance is growing and its costs are escalating. This new environment is compelling industrial maintenance organizations to make the transition from fixing broken machines to higher-level business units for securing production capacity. On the academic front, research in the area of maintenance management and engineering is receiving tremendous interest from researchers. Many papers have appeared in the literature dealing with the modeling and solution of maintenance problems using operations research (OR) and management science (MS) techniques. This area represents an opportunity for making significant contributions by the OR and MS communities. Maintenance, Modeling, and Optimization provides in one volume the latest developments in the area of maintenance modeling. Prominent scholars have contributed chapters covering a wide range of topics. We hope that this initial contribution will serve as a useful informative introduction to this field that may permit additional developments and useful directions for more research in this fast-growing area. The book is divided into six parts and contains seventeen chapters. Each chapter has been subject to review by at least two experts in the area of maintenance modeling and optimization. The first chapter provides an introduction to major maintenance modeling areas illustrated with some basic models. Part II contains five chapters dealing with maintenance planning and scheduling. Part III deals with preventive maintenance in six chapters. Part IV focuses on condition-based maintenance and contains two chapters. Part V deals with integrated production and maintenance models and contains two chapters. Part VI addresses issues related to maintenance and new technologies, and also deals with Just-in-Time (JIT) and Maintenance.

Control theory methods in economics have historically developed over three phases. The first involved basically the feedback control rules in a deterministic framework which were applied in macrodynamic models for analyzing stabilization policies. The second phase raised the issues of various types of inconsistencies in deterministic optimal control models due to changing information and other aspects of stochasticity. Rational expectations models have been extensively used in this plan to resolve some of the inconsistency problems. The third phase has recently focused on the various aspects of adaptive control. where stochasticity and information adaptivity are introduced in diverse ways e.g . risk adjustment and risk sensitivity of optimal control, recursive updating rules via Kalman filtering and weighted recursive least squares and variable structure control methods in nonlinear framework. Problems of efficient econometric estimation of optimal control models have now acquired significant importance. This monograph provides an integrated view of control theory methods, synthesizing the three phases from feedback control to stochastic control and from stochastic control to adaptive control. Aspects of econometric estimation are strongly emphasized here, since these are very important in empirical applications in economics."

The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive.

Since the building of all the Universe is perfect and is cre- ated by the wisdom Creator, nothing arises in the Universe in which one cannot see the sense of some maXImum or mInImUm Euler God moves the Universe along geometrical lines Plato Mathematical models of most closed physical systems are based on vari- ational principles, i.e., it is postulated that equations describing the evolu- tion of a system are the Euler~Lagrange equations of a certain functional. In this connection, variational methods are one of the basic tools for studying many problems of natural sciences. The first problems related to the search for extrema appeared as far back as in ancient mathematics. They go back to Archimedes, Appolonius, and Euclid. In many respects, the problems of seeking maxima and minima have stimulated the creation of differential calculus; the variational prin- ciples of optics and mechanics, which were discovered in the seventeenth and eighteenth centuries, gave impetus to an intensive development of the calculus of variations. In one way or another, variational problems were of interest to such giants of natural sciences as Fermat, Newton, Descartes, Euler, Huygens, 1. Bernoulli, J. Bernoulli, Legendre, Jacobi, Kepler, La- grange, and Weierstrass.

Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.

An increasing interest to scheduling theory can be attributed to the high level of automation of all branches of human activity. The quality of modern production essentially depends on the planning decisions taken at different stages of a production process. Moreover, while the quality of these decisions is improving, the time and flexibility requirements for decision-making are becoming more important. All this stimulates scheduling research. Started as an independent discipline in the early fifties, it now has become an important branch of operations research. In the eighties, the largest Russian publishing house for scientific literature Nauka Publishers, Moscow, issued two books by a group of Byelorussian mathematicians: Scheduling Theory. Single-Stage Systems by V. S. Tanaev, V. S. Gordon and Y. M. Shafransky (1984) and Scheduling Theory. Multi-Stage Systems by V. S. Tanaev, Y. N. Sotskov and V. A. Strusevich (1989). Originally published in Russian, these two books cover two different major problem areas of scheduling theory and can be considered as a two-volume monograph that provides a systematic and comprehensive exposition of the subject. The authors are grateful to Kluwer Academic Publishers for creating the opportunity to publish the English translations of these two books. We are indebted to M. Hazewinkel, J. K. Lenstra, A. H. G. Rinnooy Kan, D. B. Shmoys and W. Szwarc for their supporting the idea of translating the books into English.