Quantitativeapproachesforsolvingproductionplanningandinventorymanagement problems in industry have gained growing importance in the past years. Due to the increasinguse of AdvancedPlanningSystems, a widespreadpracticalapplicationof the sophisticated optimization models and algorithms developed by the Production Management and Operations Research community now seem within reach. The possibility that productscan be replaced by certain substitute productsexists in various application areas of production planning and inventory management. Substitutions can be useful for a number of reasons, among others to circ- vent production and supply bottlenecks and disruptions, increase the service level, reduce setup costs and times, and lower inventories and thereby decrease ca- tal lockup. Considering the current trend in industry towards shorter product life cycles and greater product variety, the importance of substitutions appears likely to grow. Closely related to substitutions are ?exible bills-of-materials and recipes in multi-level production systems. However, so far, the aspect of substitutions has not attracted much attention in academic literature. Existing lot-sizing models matching complex requirements of industrial optimization problems (e.g., constrained capacities, sequence-dependent setups, multiple resources) such as the Capacitated Lot-Sizing Problem with Sequence-Dependent Setups (CLSD) and the General Lot-Sizing and Scheduling Problem for Multiple Production Stages (GLSPMS) do not feature in substitution options.

In the twenty-first century the sustainability of energy and transportation systems is on the top of the political agenda in many countries around the world.

Environmental impacts of human economic activity necessitate the consideration of conflicting goals in decision making processes to develop sustainable systems. Any sustainable development has to reconcile conflicting economic and environmental objectives and criteria. The science of multiple criteria decision making has a lot to offer in addressing this need. Decision making with multiple (conflicting) criteria is the topic of research that is at the heart of the International Society of Multiple Criteria Decision Making. This book is based on selected papers presented at the societies 19th International Conference, held at The University of Auckland, New Zealand, from 7th to 12th January 2008 under the theme "MCDM for Sustainable Energy and Transportation Systems''.

Support for addressing the on-going global changes needs solutions for new scientific problems which in turn require new concepts and tools. A key issue concerns a vast variety of irreducible uncertainties, including extreme events of high multidimensional consequences, e.g., the climate change. The dilemma is concerned with enormous costs versus massive uncertainties of extreme impacts. Traditional scientific approaches rely on real observations and experiments. Yet no sufficient observations exist for new problems, and "pure" experiments, and learning by doing may be expensive, dangerous, or impossible. In addition, the available historical observations are often contaminated by past actions, and policies. Thus, tools are presented for the explicit treatment of uncertainties using "synthetic" information composed of available "hard" data from historical observations, the results of possible experiments, and scientific facts, as well as "soft" data from experts' opinions, and scenarios.

Supply relations are often governed by so-called relational contracts. These are informal agreements sustained by the value of future cooperation. Although relational contracts persist in practice, research on these types of contract is only emerging in Operations and Supply Chain Management. This book studies a two-firm supply chain, where repeated transactions via well-established supply contracts and continued quality-improvement efforts are governed by a relational contract. We are able to characterize an optimal relational contract, i.e., to develop policies for supplier and buyer that structure investments in quality and flexibility in a way that no other self-enforcing contract generates higher expected joint surplus. A second goal is to compare the performance of different returns mechanisms in the context of relational contracting (quantity flexibility and buy-back contracts). Industry studies motivate the presented model.

This book provides a complete and comprehensive guide to Pyomo (Python Optimization Modeling Objects) for beginning and advanced modelers, including students at the undergraduate and graduate levels, academic researchers, and practitioners. Using many examples to illustrate the different techniques useful for formulating models, this text beautifully elucidates the breadth of modeling capabilities that are supported by Pyomo and its handling of complex real-world applications. In the third edition, much of the material has been reorganized, new examples have been added, and a new chapter has been added describing how modelers can improve the performance of their models. The authors have also modified their recommended method for importing Pyomo. A big change in this edition is the emphasis of concrete models, which provide fewer restrictions on the specification and use of Pyomo models. Pyomo is an open source software package for formulating and solving large-scale optimization problems. The software extends the modeling approach supported by modern AML (Algebraic Modeling Language) tools. Pyomo is a flexible, extensible, and portable AML that is embedded in Python, a full-featured scripting language. Python is a powerful and dynamic programming language that has a very clear, readable syntax and intuitive object orientation. Pyomo includes Python classes for defining sparse sets, parameters, and variables, which can be used to formulate algebraic expressions that define objectives and constraints. Moreover, Pyomo can be used from a command-line interface and within Python's interactive command environment, which makes it easy to create Pyomo models, apply a variety of optimizers, and examine solutions.

In a world with highly competitive markets and economic instability due to capitalization, industrial competition has increasingly intensified. In order for many industries to survive and succeed, they need to develop highly effective coordination between supply chain partners, dynamic collaborative and strategic alliance relationships, and efficient logistics and supply chain network designs. Consequently, in the past decade, there has been an explosion of interest among academic researchers and industrial practitioners in innovative supply chain and logistics models, algorithms, and coordination policies. Mathematically distinct from classical supply chain management, this emerging research area has been proven to be useful and applicable to a wide variety of industries. This book brings together recent advances in supply chain and logistics research and computational optimization that apply to a collaborative environment in the enterprise.

Structural Optimization is intended to supplement the engineer s box of analysis and design tools making optimization as commonplace as the finite element method in the engineering workplace. It begins with an introduction to structural optimization and the methods of nonlinear programming such as Lagrange multipliers, Kuhn-Tucker conditions, and calculus of variations. It then discusses solution methods for optimization problems such as the classic method of linear programming which leads to the method of sequential linear programming. It then proposes using sequential linear programming together with the incremental equations of structures as a general method for structural optimization. It is furthermore intended to give the engineer an overview of the field of structural optimization."

The international conference \Operations Research 2008," the annual meeting of the German Operations Research Society (GOR), was held at the University of Augsburg on September 3-5, 2008. About 580 p- ticipants from more than 30 countries presented and listened to nearly 400 talks on a broad range of Operations Research. The general subject \Operations Research and Global Business" str- ses the important role of Operations Research in improving decisions in the increasingly complex business processes in a global environment. The plenary speakers Morris A. Cohen (Wharton School) and Bernd Liepert (Executive Board of KUKA Robotics) addressed this subject. Moreover, one of the founders of Operations Research, Saul Gass (U- versity of Maryland), gave the opening speech on the early history of Operations Research. This volume contains 93 papers presented at the conference, selected by the program committee and the section chairs, forming a representative sample of the various subjects dealt with at Operations Research 2008. The volume follows the structure of the conference, with 12 sections, grouped into six \Fields of Applications" and six \Fields of Methods and Theory." This structure in no way means a separation of theory and application, which would be detrimental in Operations Research, but displays the large spectrum of aspects in the focus of the papers. Of course, most papers present theory, methods and applications together.

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content.

Today, the optimization of production planning processes by means of IT and quantitative methods is a de-facto standard in the energy industry. Franch et al. inChapter1andIkenouyeinChapter2giveanintroduction, overview, and reasonsforthis. Furthermore, theenergyproblemnowisnotonlyachallenging one but also one of the most important issues in the world from the political and economical points of view. In every country, the government is faced with the problem of how to adopt the system of 'Cap and Trade. ' Especially energy consuming industries, such as steel, power, oil and chemicals, are seriously confronted with this problem. VIII Preface This is also the reason why the German Operations Research Society (GOR) and one of its working groups, held a symposium with the title "Stochastic Optimization in the Energy Industry. " During the 78th meeting of the GOR working group "Praxis der Mathematischen Optimierung/Real World Optimization" in Aachen at Procom GmbH on April 21/22, 2007, the speakers with an application background explained their requirements for stochasticoptimizationsolutionsbasedonpracticalexperiences. Thespeakers from the research side and the software system suppliers examined di?erent aspects of the whole subject - from the integration of wind energy, the chain of errors in nuclear power plants and the scheduling of hydroelectric power stations, and the risk assessment in trading activities to the various software systems which support stochastic optimization methods. The symposium o?ered an interesting overview which re?ected the - quirements, possibilities and restrictions of "Stochastic Optimization in the Energy Industry.

Data-driven discovery is revolutionizing how we model, predict, and control complex systems. Now with Python and MATLAB (R), this textbook trains mathematical scientists and engineers for the next generation of scientific discovery by offering a broad overview of the growing intersection of data-driven methods, machine learning, applied optimization, and classical fields of engineering mathematics and mathematical physics. With a focus on integrating dynamical systems modeling and control with modern methods in applied machine learning, this text includes methods that were chosen for their relevance, simplicity, and generality. Topics range from introductory to research-level material, making it accessible to advanced undergraduate and beginning graduate students from the engineering and physical sciences. The second edition features new chapters on reinforcement learning and physics-informed machine learning, significant new sections throughout, and chapter exercises. Online supplementary material - including lecture videos per section, homeworks, data, and code in MATLAB (R), Python, Julia, and R - available on databookuw.com.

The editors and authors dedicate this book to Bernhard Korte on the occasion of his seventieth birthday. We, the editors, are happy about the overwhelming feedback to our initiative to honor him with this book and with a workshop in Bonn on November 3-7,2008.Althoughthiswouldbeareasontolookback,wewouldratherliketolook forward and see what are the interesting research directions today. This book is written by leading experts in combinatorial optimization. All - pers were carefully reviewed, and eventually twenty-three of the invited papers were accepted for this book. The breadth of topics is typical for the eld: combinatorial optimization builds bridges between areas like combinatorics and graph theory, submodular functions and matroids, network ows and connectivity, approximation algorithms and mat- matical programming, computational geometry and polyhedral combinatorics. All these topics are related, and they are all addressed in this book. Combi- torial optimization is also known for its numerous applications. To limit the scope, however, this book is not primarily about applications, although some are mentioned at various places. Most papers in this volume are surveys that provide an excellent overview of an activeresearcharea,butthisbookalsocontainsmanynewresults.Highlightingmany of the currently most interesting research directions in combinatorial optimization, we hope that this book constitutes a good basis for future research in these areas.

In the latter part of the twentieth century, the topic of generalizations of convexfunctions has attracted a sizable number of researchers,both in ma- ematics and in professional disciplines such as economics/management and engineering. In 1994 during the 15th International Symposium on Mathem- ical Programming in Ann Arbor, Michigan, I called together some colleagues to start an a?liation of researchers working in generalized convexity. The international Working Group of Generalized Convexity (WGGC) was born. Its website at www.genconv.org has been maintained by Riccardo Cambini, University of Pisa. Riccardo's father, Alberto Cambini, and Alberto's long-term colleague Laura Martein in the Faculty of Economics, University of Pisa, are the - authors of this volume. My own contact with generalized convexity in Italy datesbacktomy?rstvisittotheirdepartmentin1980,atatimewhenthe?rst international conference on generalized convexity was in preparation. Thirty years later it is now referred to as GC1, an NATO Summer School in V- couver, Canada. Currently WGGC is preparing GC9 which is to take place in Kaohsiung, Taiwan. As founding chair and also current chair of WGGC, I am delighted to see the continued interest in generalized convexity of functions, augmented by the topic of generalized monotonicity of maps. Eight international conferences have taken place in this research area, in North America (2), Europe (5) and Asia (1). We thought it was now time to return to Asia since our membership has shifted towards Asia. AsanappliedmathematicianIhavetaughtmostlyinmanagementschools.

Financial globalization has increased the significance of methods used in the evaluation of country risk, one of the major research topics in economics and finance. Written by experts in the fields of multicriteria methodology, credit risk assessment, operations research, and financial management, this book develops a comprehensive framework for evaluating models based on several classification techniques that emerge from different theoretical directions. This book compares different statistical and data mining techniques, noting the advantages of each method, and introduces new multicriteria methodologies that are important to country risk modeling. Key topics include: (1) A review of country risk definitions and an overview of the most recent tools in country risk management, (2) In-depth analysis of statistical, econometric and non-parametric classification techniques, (3) Several real-world applications of the methodologies described throughout the text, (4) Future research directions for country risk assessment problems. This work is a useful toolkit for economists, financial managers, bank managers, operations researchers, management scientists, and risk analysts. Moreover, the book can also be used as a supplementary text for graduate courses in finance and financial risk management.

• Provides well-written self-contained chapters, including problem sets and exercises, making it ideal for the classroom setting;
• Introduces applied optimization to the hazardous waste blending problem;
• Explores linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control and stochastic optimal control;
• Includes an extensive bibliography at the end of each chapter and an index;
• GAMS files of case studies for Chapters 2, 3, 4, 5, and 7 are linked to http: //www.springer.com/math/book/978-0-387-76634-8;

Solutions manual available upon adoptions.

In trying to make a satisfactory decision when imprecise and multicriteria situations are involved, a decision maker has to use a fuzzy multicriteria decision making method. "Fuzzy Multi-Criteria Decision Making" (MCDM) presents fuzzy multiattribute and multiobjective decision-making methodologies by distinguished MCDM researchers.

In summarizing the concepts and results of the most popular fuzzy multicriteria methods, using numerical examples, this work examines all the fuzzy multicriteria methods recently developed, such as fuzzy AHP, fuzzy TOPSIS, interactive fuzzy multiobjective stochastic linear programming, fuzzy multiobjective dynamic programming, grey fuzzy multiobjective optimization, fuzzy multiobjective geometric programming, and more. Each of the 22 chapters includes practical applications along with new developments/results.

This book may be used as a textbook in graduate operations research, industrial engineering, and economics courses. It will also be an excellent resource, providing new suggestions and directions for further research, for computer programmers, mathematicians, and scientists in a variety of disciplines where multicriteria decision making is needed.

This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis.

Chapters are self-contained with exercises provided at the end of most sections. Nonlinear Optimization with Engineering Applications is ideal for self-study and classroom use in engineering courses at the senior undergraduate or graduate level. The book will also appeal to postdocs and advanced researchers interested in the development and use of optimization algorithms.

This comprehensive work examines important recent developments and modern applications in the fields of optimization, control, game theory and equilibrium programming. In particular, the concepts of equilibrium and optimality are of immense practical importance affecting decision-making problems regarding policy and strategies, and in understanding and predicting systems in different application domains, ranging from economics and engineering to military applications. The book consists of 29 survey chapters written by distinguished researchers in the above areas.

The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic "silver bullet" polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

Operations research often solves deterministic optimization problems based on elegantand conciserepresentationswhereall parametersarepreciselyknown. In the face of uncertainty, probability theory is the traditional tool to be appealed for, and stochastic optimization is actually a signi?cant sub-area in operations research. However, the systematic use of prescribed probability distributions so as to cope with imperfect data is partially unsatisfactory. First, going from a deterministic to a stochastic formulation, a problem may becomeintractable. Agoodexampleiswhengoingfromdeterministictostoch- tic scheduling problems like PERT. From the inception of the PERT method in the 1950's, it was acknowledged that data concerning activity duration times is generally not perfectly known and the study of stochastic PERT was launched quite early. Even if the power of today's computers enables the stochastic PERT to be addressed to a large extent, still its solutions often require simplifying assumptions of some kind. Another di?culty is that stochastic optimization problems produce solutions in the average. For instance, the criterion to be maximized is more often than not expected utility. This is not always a meaningful strategy. In the case when the underlying process is not repeated a lot of times, let alone being one-shot, it is not clear if this criterion is realistic, in particular if probability distributions are subjective. Expected utility was proposed as a rational criterion from ?rst principles by Savage. In his view, the subjective probability distribution was - sically an artefact useful to implement a certain ordering of solutions.

Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.

Optimization problems are of great importance across a broad range of fields. They can be tackled, for example, by approximate algorithms such as metaheuristics. This book is intended both to provide an overview of hybrid metaheuristics to novices of the field, and to provide researchers from the field with a collection of some of the most interesting recent developments. The authors involved in this book are among the top researchers in their domain.

Metaheuristics have been shown to be e?ective for di?cult combinatorial - timization problems appearing in various industrial, economical, and scienti?c domains. Prominent examples of metaheuristics are evolutionary algorithms, tabu search, simulated annealing, scatter search, memetic algorithms, variable neighborhood search, iterated local search, greedy randomized adaptive search procedures, ant colony optimization and estimation of distribution algorithms. Problems solved successfully include scheduling, timetabling, network design, transportation and distribution, vehicle routing, the travelling salesman pr- lem, packing and cutting, satis?ability and general mixed integer programming. EvoCOPbeganin2001andhasbeenheldannuallysincethen.Itwasthe?rst event speci?cally dedicated to the application of evolutionary computation and related methods to combinatorial optimization problems. Originally held as a workshop, EvoCOPbecameaconferencein2004.Theeventsgaveresearchersan excellent opportunity to present their latest research and to discuss current - velopments and applications. Following the general trend of hybrid metaheur- tics and diminishing boundaries between the di?erent classes of metaheuristics, EvoCOP has broadened its scope over the last years and invited submissions on any kind of metaheuristic for combinatorial optimization

Optimization has become an essential tool in addressing the limitation of resources and need for better decision-making in the medical field. Both continuous and discrete mathematical techniques are playing an increasingly important role in understanding several fundamental problems in medicine. This volume presents a wide range of medical applications that can utilize mathematical computing. Examples include using an algorithm for considering the seed reconstruction problem in brachytherapy and using optimization-classification models to assist in the early prediction, diagnosis and detection of diseases. Discrete optimization techniques and measures derived from the theory of nonlinear dynamics, with analysis of multi-electrode electroencephalographic (EEG) data, assist in predicting impending epileptic seizures. Mathematics in medicine can also be found in recent cancer research. Sophisticated mathematical models and optimization algorithms have been used to generate treatment plans for radionuclide implant and external beam radiation therapy. Optimization techniques have also been used to automate the planning process in Gamma Knife treatment, as well as to address a variety of medical image registration problems. This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization."

Constrained optimization models are core tools in business, science, government, and the military with applications including airline scheduling, control of petroleum refining operations, investment decisions, and many others. Constrained optimization models have grown immensely in scale and complexity in recent years as inexpensive computing power has become widely available. Models now frequently have many complicated interacting constraints, giving rise to a host of issues related to feasibility and infeasibility. For example, it is sometimes difficult to find any feasible point at all for a large model, or even to accurately determine if one exists, e.g. for nonlinear models. If the model is feasible, how quickly can a solution be found? If the model is infeasible, how can the cause be isolated and diagnosed? Can a repair to restore feasibility be carried out automatically? Researchers have developed numerous algorithms and computational methods in recent years to address such issues, with a number of surprising spin-off applications in fields such as artificial intelligence and computational biology. Over the same time period, related approaches and techniques relating to feasibility and infeasibility of constrained problems have arisen in the constraint programming community. Feasibility and Infeasibility in Optimization is a timely expository book that summarizes the state of the art in both classical and recent algorithms related to feasibility and infeasibility in optimization, with a focus on practical methods. All model forms are covered, including linear, nonlinear, and mixed-integer programs. Connections to related work in constraint programming are shown. Part Iof the book addresses algorithms for seeking feasibility quickly, including new methods for the difficult cases of nonlinear and mixed-integer programs. Part II provides algorithms for analyzing infeasibility by isolating minimal infeasible (or maximum feasible) subsets of constraints, or by finding the best repair for the infeasibility. Infeasibility analysis algorithms have arisen primarily over the last two decades, and the book covers these in depth and detail. Part III describes applications in numerous areas outside of direct infeasibility analysis such as finding decision trees for data classification, analyzing protein folding, radiation treatment planning, automated test assembly, etc. A main goal of the book is to impart an understanding of the methods so that practitioners can make immediate use of existing algorithms and software, and so that researchers can extend the state of the art and find new applications. The book is of interest to researchers, students, and practitioners across the applied sciences who are working on optimization problems.