This book explores the meta-heuristics approach called tabu search, which is dramatically changing our ability to solve a host of problems that stretch over the realms of resource planning, telecommunications, VLSI design, financial analysis, scheduling, space planning, energy distribution, molecular engineering, logistics, pattern classification, flexible manufacturing, waste management, mineral exploration, biomedical analysis, environmental conservation and scores of other problems. The major ideas of tabu search are presented with examples that show their relevance to multiple applications. Numerous illustrations and diagrams are used to clarify principles that deserve emphasis, and that have not always been well understood or applied. The book's goal is to provide hands-on' knowledge and insight alike, rather than to focus exclusively either on computational recipes or on abstract themes. This book is designed to be useful and accessible to researchers and practitioners in management science, industrial engineering, economics, and computer science. It can appropriately be used as a textbook in a masters course or in a doctoral seminar. Because of its emphasis on presenting ideas through illustrations and diagrams, and on identifying associated practical applications, it can also be used as a supplementary text in upper division undergraduate courses. Finally, there are many more applications of tabu search than can possibly be covered in a single book, and new ones are emerging every day. The book's goal is to provide a grounding in the essential ideas of tabu search that will allow readers to create successful applications of their own. Along with the essential ideas, understanding of advanced issues is provided, enabling researchers to go beyond today's developments and create the methods of tomorrow.

Risk models are models of uncertainty, engineered for some purposes. They are "educated guesses and hypotheses" assessed and valued in terms of well-defined future states and their consequences. They are engineered to predict, to manage countable and accountable futures and to provide a frame of reference within which we may believe that "uncertainty is tamed". Quantitative-statistical tools are used to reconcile our information, experience and other knowledge with hypotheses that both serve as the foundation of risk models and also value and price risk. Risk models are therefore common to most professions, each with its own methods and techniques based on their needs, experience and a wisdom accrued over long periods of time. This book provides a broad and interdisciplinary foundation to engineering risks and to their financial valuation and pricing. Risk models applied in industry and business, heath care, safety, the environment and regulation are used to highlight their variety while financial valuation techniques are used to assess their financial consequences. This book is technically accessible to all readers and students with a basic background in probability and statistics (with 3 chapters devoted to introduce their elements). Principles of risk measurement, valuation and financial pricing as well as the economics of uncertainty are outlined in 5 chapters with numerous examples and applications. New results, extending classical models such as the CCAPM are presented providing insights to assess the risks and their price in an interconnected, dependent and strategic economic environment. In an environment departing from the fundamental assumptions we make regarding financial markets, the book provides a strategic/game-like approach to assess the risk and the opportunities that such an environment implies. To control these risks, a strategic-control approach is developed that recognizes that many risks resulting by "what we do" as well as "what others do". In particular we address the strategic and statistical control of compliance in large financial institutions confronted increasingly with a complex and far more extensive regulation.

Discrete event simulation and agent-based modeling are increasingly recognized as critical for diagnosing and solving process issues in complex systems. Introduction to Discrete Event Simulation and Agent-based Modeling covers the techniques needed for success in all phases of simulation projects. These include: * Definition - The reader will learn how to plan a project and communicate using a charter. * Input analysis - The reader will discover how to determine defensible sample sizes for all needed data collections. They will also learn how to fit distributions to that data. * Simulation - The reader will understand how simulation controllers work, the Monte Carlo (MC) theory behind them, modern verification and validation, and ways to speed up simulation using variation reduction techniques and other methods. * Output analysis - The reader will be able to establish simultaneous intervals on key responses and apply selection and ranking, design of experiments (DOE), and black box optimization to develop defensible improvement recommendations. * Decision support - Methods to inspire creative alternatives are presented, including lean production. Also, over one hundred solved problems are provided and two full case studies, including one on voting machines that received international attention. Introduction to Discrete Event Simulation and Agent-based Modeling demonstrates how simulation can facilitate improvements on the job and in local communities. It allows readers to competently apply technology considered key in many industries and branches of government. It is suitable for undergraduate and graduate students, as well as researchers and other professionals.

Dynamic Systems (DEDS) are almost endless: military C31 Ilogistic systems, the emergency ward of a metropolitan hospital, back offices of large insurance and brokerage fums, service and spare part operations of multinational fums . . . . the point is the pervasive nature of such systems in the daily life of human beings. Yet DEDS is a relatively new phenomenon in dynamic systems studies. From the days of Galileo to Newton to quantum mechanics and cosmology of the present, dynamic systems in nature are primarily differential equations based and time driven. A large literature and endless success stories have been built up on such Continuous Variable Dynamic Systems (CVDS). It is, however, equally clear that DEDS are fundamentally different from CVDS. They are event driven, asynchronous, mostly man-made and only became significant during the past generation. Increasingly, however, it can be argued that in the modem world our lives are being impacted by and dependent upon the efficient operations of such DEDS. Yet compared to the successful paradigm of differential equations for CVDS the mathematical modelling of DEDS is in its infancy. Nor are there as many successful and established techniques for their analysis and synthesis. The purpose of this series is to promote the study and understanding of the modelling, analysis, control, and management of DEDS. The idea of the series came from editing a special issue of the Proceedings of IEEE on DEOS during 1988.

This volume presents selected contributions by top researchers in the field of operations research, originating from the XVI Congress of APDIO. It provides interesting findings and applications of operations research methods and techniques in a wide variety of problems. The contributions address complex real-world problems, including inventory management with lateral transshipments, sectors and routes in solid-waste collection and production planning for perishable food products. It also discusses the latest techniques, making the volume a valuable tool for researchers, students and practitioners who wish to learn about current trends. Of particular interest are the applications of nonlinear and mixed-integer programming, data envelopment analysis, clustering techniques, hybrid heuristics, supply chain management and lot sizing, as well as job scheduling problems. This biennial conference, organized by APDIO, the Portuguese Association of Operational Research, held in Braganca, Portugal, in June 2013, presented a perfect opportunity to discuss the latest development in this field and to narrow the gap between academic researchers and practitioners.

This is the first comprehensive book to present, in English, the multicriteria methodology for decision aiding. In the foreword the distinctive features and main ideas of the European School of MCDA are outlined. The twelve chapters are essentially expository in nature, but scholarly in treatment. Some questions, which are too often neglected in the literature on decision theory, such as how is a decision made, who are the actors, what is a decision aiding model, how to define the set of alternatives, are discussed. Examples are used throughout the book to illustrate the various concepts. Ways to model the consequences of each alternative and building criteria taking into account the inevitable imprecisions, uncertainties and indeterminations are described and illustrated. The three classical operational approaches of MCDA: synthesis in one criterion (including MAUT), synthesis by outranking relations, interactive local judgements, are studied. This methodology tries to be a theoretical or intellectual framework directed towards formulating recommendations for action. The book is addressed to graduate students, postgraduates and researchers in management sciences, or operations research or decision analysis, as well as all scientists who use models and methods for guiding decisions. In addition all those who, in business and administration, wish to take part in decision-making through scientific reasoning will be interested.

With the ever increasing growth of services and the corresponding demand for Quality of Service requirements that are placed on IP-based networks, the essential aspects of network planning will be critical in the coming years. A wide number of problems must be faced in order for the next generation of IP networks to meet their expected performance. With Performance Evaluation and Planning Methods for the Next Generation Internet, the editors have prepared a volume that outlines and illustrates these developing trends.

A number of the problems examined and analyzed in the book are:

-The design of IP networks and guaranteed performance

-Performances of virtual private networks

-Network design and reliability

-The issues of pricing, routing and the management of QoS

-Design problems arising from wireless networks

-Controlling network congestion

-New applications spawned from Internet use

-Several new models are introduced that will lead to better Internet performance

These are a few of the problem areas addressed in the book and only a selective example of some of the coming key areas in networks requiring performance evaluation and network planning.

This book covers the latest results in the field of risk analysis. Presented topics include probabilistic models in cancer research, models and methods in longevity, epidemiology of cancer risk, engineering reliability and economical risk problems. The contributions of this volume originate from the 5th International Conference on Risk Analysis (ICRA 5). The conference brought together researchers and practitioners working in the field of risk analysis in order to present new theoretical and computational methods with applications in biology, environmental sciences, public health, economics and finance.

Each chapter in Equilibrium and Advanced Transportation Modelling develops a topic from basic concepts to the state-of-the-art, and beyond. All chapters relate to aspects of network equilibrium. Chapter One advocates the use of simulation models for the representation of traffic flow movements at the microscopic level. Chapter Two presents travel demand systems for generating trip matrices from activity-based models, taking into account the entire daily schedule of network users. Chapter Three examines equilibrium strategic choices adopted by the passengers of a congested transit system, carefully addressing line selection at boarding and transfer nodes. Chapter Four provides a critical appraisal of the traditional process that consists in sequentially performing the tasks of trip generation, trip distribution, mode split and assignment, and its impact on the practice of transportation planning. Chapter Five gives an insightful overview of stochastic assignment models, both in the static and dynamic cases. Chapters Six and Seven investigate the setting of tolls to improve traffic flow conditions in a congested transportation network. Chapter Eight provides a unifying framework for the analysis of multicriteria assignment models. In this chapter, available algorithms are summarized and an econometric perspective on the estimation of heterogeneous preferences is given. Chapter Nine surveys the use of hyperpaths in operations research and proposes a new paradigm of equilibrium in a capacitated network, with an application to transit assignment. Chapter Ten analyzes the transient states of a system moving towards equilibrium, using the mathematical framework of projected dynamical systems. Chapter Eleven discusses an in-depth survey of algorithms for solving shortest path problems, which are pervasive to any equilibrium algorithm. The chapter devotes special attention to the computation of dynamic shortest paths and to shortest hyperpaths. The final chapter considers operations research tools for reducing traffic congestion, in particular introducing an algorithm for solving a signal-setting problem formulated as a bilevel program.

Beginning in the mid-2010s, the Fourth Industrial Revolution has seen remarkable changes in information technology which have blurred the boundaries between the physical, digital, and biological worlds. Industry 4.0 has enabled so-called "smart factories" in which computer systems equipped with machine learning algorithms can learn and control robotics with minimal need for human input. While smart technology has enabled many manufacturing businesses to increase efficiency and cut costs, many others are still struggling with implementing it. This book aims to help students, practitioners and industry leaders to become change agents and take their first steps on the path of transformation. Smart Business and Digital Transformation addresses the challenge of becoming "smart" from three different perspectives: smart factory, smart industry, and smart environment. Covering technologies including the Internet of Things (IoT), cloud, artificial intelligence (AI), mobility, 5G, Big Data analytics, the book shows how enterprises can take advantage of them and ultimately beat the competition. The book considers the importance of operational processes, business models, and organizational culture. The contributing authors and editors, based at Corvinus University, present a multi-dimensional picture of industry 4.0 which is both diverse in its voices and unified in its vision. Smart Business and Digital Transformation meets the growing demand for a textbook that not only presents the latest concepts and theories but is also practical for planning, managing, and implementing digital transformation in practice. The chapters include case studies to demonstrate the practical applications, and each chapter ends with review and discussion questions to develop students' skills and competencies. Students of business and digital transformation on advanced undergraduate and MBA courses will find it an indispensable guide to a vibrant and challenging topic.

The Practice of Quality Management presents the results of eleven ground-breaking research projects in quality management. It is the first collection of research papers by academics in this area. The projects are empirical studies on total quality management that suggest new ways to think about quality. The objective of the research found in this book is to develop theory and to assist practice. Thus, this volume is of interest to both academic researchers and practising managers. The chapters fall into four categories: `Performance', `Understanding TQM', `Organizations', and `Using TQM'. All of the chapters show that there are many different applications and research issues associated with quality. The chapters on `Understanding TQM' suggest that it is possible to develop and test theories of quality. The chapters on `Performance' demonstrate that studies of the operational and financial effect of quality can yield positive results. Many thinkers on quality consider that organizational impacts of quality are the most important drivers of the quality process. The chapters on `Organizations' present evidence on how quality programs affect human resource management, and organizational structure. Finally, the chapters on `Using TQM' present several studies of applications of quality management.

These proceedings consist of 30 selected research papers based on results presented at the 10th Balkan Conference & 1st International Symposium on Operational Research (BALCOR 2011) held in Thessaloniki, Greece, September 22-24, 2011. BALCOR is an established biennial conference attended by a large number of faculty, researchers and students from the Balkan countries but also from other European and Mediterranean countries as well. Over the past decade, the BALCOR conference has facilitated the exchange of scientific and technical information on the subject of Operations Research and related fields such as Mathematical Programming, Game Theory, Multiple Criteria Decision Analysis, Information Systems, Data Mining and more, in order to promote international scientific cooperation. The carefully selected and refereed papers present important recent developments and modern applications and will serve as excellent reference for students, researchers and practitioners in these disciplines. "

Operations Research and Cyber-Infrastructure is the companion volume to the Eleventh INFORMS Computing Society Conference (ICS 2009), held in Charleston, South Carolina, from January 11 to 13, 2009. It includes 24 high-quality refereed research papers.

As always, the focus of interest for ICS is the interface between Operations Research and Computer Science, and the papers in this volume reflect that interest. This is naturally an evolving area as computational power increases rapidly while decreasing in cost even more quickly. The papers included here illustrate the wide range of topics at this interface. For convenience, they are grouped in broad categories and subcategories. There are three papers on modeling, reflecting the impact of recent development in computing on that area. Eight papers are on optimization (three on integer programming, two on heuristics, and three on general topics, of which two involve stochastic/probabilistic processes). Finally, there are thirteen papers on applications (three on the conference theme of cyber-infrastructure, four on routing, and six on other interesting topics). Several of the papers could be classified in more than one way, reflecting the interactions between these topic areas.

This book presents a close look at the main developments in IT, business processes and offshore outsourcing. The authors study these topics in both theory and practice, exploring the rising prominence of outsourcing with a multi-dimensional, contextual perspective.

TEODOR GABRIEL CRAINIC, DIRECTOR The Centre for Research on Transportation (C.R.T.) was founded in 1971 by the Universite de Montreal. From 1988 on, it is jointly managed by the Universite de Montreal and its affiliated schools, the Ecole des Hautes Etudes Commerciales and Ecole Poly technique. Professors, students and researchers from many institutions in the Montreal area join forces at the C.R.T. to analyze transportation, logistics and telecommunication systems from a multidisciplinary perspective. The C.R.T. pursues three major, complementary objectives: training of high-level specialists; the advancement of knowledge and technology; the transfer of technology towards industry and the public sector. Its main field of expertise is the develop ment of quantitative and computer-based models and methods for the analysis of urban, regional and intercity transportation networks, as well as telecommunication systems. This applies to the study of passenger and commodity flows, as well as to the socioeconomic aspects of transportation: policy, regulation, economics. The twenty-fifth anniversary of the C.R.T. offered the opportunity to evaluate past accomplishments and to identify future trends and challenges. Five colloquia were thus organized on major research and application themes that also reflected our main research areas. They gathered together internationally renowned researchers who linked recent scientific and technological advances to modeling and methodological challenges waiting to be tackled, particularly concerning new problems and applica tions, and the increasingly widespread use of new technologies."

3. 2 The Busy Period 43 3. 3 The M 1M IS System with Last Come, First Served 50 3. 4 Comparison of FCFS and LCFS 51 3. 5 Time-Reversibility of Markov Processes 52 The Output Process 54 3. 6 3. 7 The Multi-Server System in a Series 55 Problems for Solution 3. 8 56 4 ERLANGIAN QUEUEING SYSTEMS 59 4. 1 Introduction 59 4. 2 The System M I E/c/1 60 4. 3 The System E/cl Mil 67 4. 4 The System MIDI1 72 4. 5 Problems for Solution 74 PRIORITY SYSTEMS 79 5 5. 1 Description of a System with Priorities 79 Two Priority Classes with Pre-emptive Resume Discipline 5. 2 82 5. 3 Two Priority Classes with Head-of-Line Discipline 87 5. 4 Summary of Results 91 5. 5 Optimal Assignment of Priorities 91 5. 6 Problems for Solution 93 6 QUEUEING NETWORKS 97 6. 1 Introduction 97 6. 2 A Markovian Network of Queues 98 6. 3 Closed Networks 103 Open Networks: The Product Formula 104 6. 4 6. 5 Jackson Networks 111 6. 6 Examples of Closed Networks; Cyclic Queues 112 6. 7 Examples of Open Networks 114 6. 8 Problems for Solution 118 7 THE SYSTEM M/G/I; PRIORITY SYSTEMS 123 7. 1 Introduction 123 Contents ix 7. 2 The Waiting Time in MIGI1 124 7. 3 The Sojourn Time and the Queue Length 129 7. 4 The Service Interval 132 7.

Data Mining introduces in clear and simple ways how to use existing data mining methods to obtain effective solutions for a variety of management and engineering design problems. Data Mining is organised into two parts: the first provides a focused introduction to data mining and the second goes into greater depth on subjects such as customer analysis. It covers almost all managerial activities of a company, including: * supply chain design, * product development, * manufacturing system design, * product quality control, and * preservation of privacy. Incorporating recent developments of data mining that have made it possible to deal with management and engineering design problems with greater efficiency and efficacy, Data Mining presents a number of state-of-the-art topics. It will be an informative source of information for researchers, but will also be a useful reference work for industrial and managerial practitioners.

Evolutionary computation techniques have attracted increasing att- tions in recent years for solving complex optimization problems. They are more robust than traditional methods based on formal logics or mathematical programming for many real world OR/MS problems. E- lutionary computation techniques can deal with complex optimization problems better than traditional optimization techniques. However, most papers on the application of evolutionary computation techniques to Operations Research /Management Science (OR/MS) problems have scattered around in different journals and conference proceedings. They also tend to focus on a very special and narrow topic. It is the right time that an archival book series publishes a special volume which - cludes critical reviews of the state-of-art of those evolutionary com- tation techniques which have been found particularly useful for OR/MS problems, and a collection of papers which represent the latest devel- ment in tackling various OR/MS problems by evolutionary computation techniques. This special volume of the book series on Evolutionary - timization aims at filling in this gap in the current literature. The special volume consists of invited papers written by leading - searchers in the field. All papers were peer reviewed by at least two recognised reviewers. The book covers the foundation as well as the practical side of evolutionary optimization.

The customer orientation philosophy of modern business organizations and the implementation of the main principles of continuous improvement, justifies the importance of evaluating and analyzing cust omer satisfaction. In fact, customer satisfaction isconsidere d today as a baseline standard of performance and a possi ble standardo f excellence forany business organization. Extensive research has defined several alternative approaches, which examine the customer satisfaction evaluation prob lem from very different perspectives. These approaches include simple quantitative tools, statistical and data analysis techniques, consumer behavioral models, etc. and adopt the following main prin ciples: * The data of the problem are based on th e customers' judgments and are directly collected from them. * This is a multivariate evaluation problem given that customer's overall satisfac tion depends on a setof variables representing product/service characteristic dimensions. * Usually, an additive formula is used in order to aggregate partial evaluations in ano verall satisfaction measure. Many of the aforementioned approaches don ot consider the qualitative form of customers' judgments, although this information constitutes the main satisfaction input data. Furthermore, insev eral cases , the measurements are not sufficient enough to analyze in detail customer sa tisfaction because models' results are mainly focused on a simple descriptive analysis.

The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems.
In this extensively updated new edition there is more material on methods and examples including several new approaches for discrete variables, new results on risk measures in modeling and Monte Carlo sampling methods, a new chapter on relationships to other methods including approximate dynamic programming, robust optimization and online methods.

The book is highly illustrated with chapter summaries and many examples and exercises. Students, researchers and practitioners in operations research and the optimization area will find it particularly of interest.

Review of First Edition:

"The discussion on modeling issues, the large number of examples used to illustrate the material, and the breadth of the coverage make'Introduction to Stochastic Programming' an ideal textbook for the area." (Interfaces, 1998)

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This handbook gathers state-of-the-art research on optimization problems in power distribution systems, covering classical problems as well as the challenges introduced by distributed power generation and smart grid resources. It also presents recent models, solution techniques and computational tools to solve planning problems for power distribution systems and explains how to apply them in distributed and variable energy generation resources. As such, the book therefore is a valuable tool to leverage the expansion and operation planning of electricity distribution networks.

Traditional mathematical programming has concentrated on problems that can be solved by achieving a single objective. In reality, many multi-objective situations exist; concentrating on a single goal limits the applicability of math programming models. Accordingly, multiobjective optimization has emerged as a rapdily growing area. In this monograph the author draws from the more mature body of literature on multicriterion decision theory to enhance understanding of multiobjective optimization. There are obvious commonalities between the two areas, but to date no one has presented a book which unifies the two. That is the aim of "Multiobjective Optimization: Behavioural and Computational Considerations". There are many behavioural and computational issues which are relevant to multiobjective optimization. These issues cross the disciplines of behavioural decision theory, information and decision support systems, and computational analysis.

A logic view of 0-1 integer programming problems, providing new insights into the structure of problems that can lead the researcher to more effective solution techniques depending on the problem class. Operations research techniques are integrated into a logic programming environment. The first monographic treatment that begins to unify these two methodological approaches. Logic-based methods for modelling and solving combinatorial problems have recently started to play a significant role in both theory and practice. The application of logic to combinatorial problems has a dual aspect. On one hand, constraint logic programming allows one to declaratively model combinatorial problems over an appropriate constraint domain, the problems then being solved by a corresponding constraint solver. Besides being a high-level declarative interface to the constraint solver, the logic programming language allows one also to implement those subproblems that cannot be naturally expressed with constraints. On the other hand, logic-based methods can be used as a constraint solving technique within a constraint solver for combinatorial problems modelled as 0-1 integer programs.

This book presents a selection of studies that have applied Operational Research methods to improve emergency planning in healthcare, to include both A&E and public health emergencies like epidemic and natural disasters. The studies have delved into qualitative Operational Research like Problem Structuring, Critical Systems Thinking, Soft Systems Methodology, and Qualitative System Dynamics, and also quantitative techniques such as Monte Carlo Simulation, Discrete-event Simulation, and System Dynamics. These techniques have been applied for review and assessment of emergency services, for policy formulation and for facilitating broader public engagement in emergency preparedness and response. Furthermore, this book presents rigorous reviews on the applications of Operational Research in the wider healthcare context. This volume focuses mainly on emergency planning at the strategic level, whereas volume 1 focuses on planning at the operational level. The OR Essentials series presents a unique cross-section of high quality research work fundamental to understanding contemporary issues and research across a range of Operational Research (OR) topics. It brings together some of the best research papers from the highly respected journals of the Operational Research Society, also published by Palgrave Macmillan.

Project management can be broadly defined as the process of managing, allocating and timing resources to achieve given objectives in an efficient and expedient manner. The builders of the pyramids in Egypt and the Maya temples in Central America are often cited as the world's first project managers. Without the help of computers or planning software, they managed exceptionally complex projects, using the simplest of tools. Nowadays projects, sets of activities which have a defined start point and a defined end state and which pursue a defined goal and use a defined set of resources, come in many and various forms. The Manhattan project which created the first atom bomb, the Apollo moon program, the construction of the Channel tunnel, the design of the Airbus, the development of new products, the construction of large office buildings, the relocation of a factory, the installation of a new information system, as well as the development of a marketing plan are all well-known examples of projects.

Our objectives in writing Project Scheduling: A Research Handbook are threefold: (1) Provide a unified scheme for classifying the numerous project scheduling problems occurring in practice and studied in the literature; (2) Provide a unified and up-to-date treatment of the state-of-the-art procedures developed for their solution; (3) Alert the reader to various important problems that are still in need of considerable research effort. As such, this book should differ from other project scheduling books in its use of an innovative unified resource scheduling classification scheme, and a unified treatment of both exact and heuristic solution procedures.

Project Scheduling: A ResearchHandbook has been divided into four parts. Part I consists of three chapters on the scope and relevance of project scheduling, on the nature of project scheduling, and finally on the introduction of a unified scheme that will be used in subsequent chapters for the identification and classification of the project scheduling problems studied in this book. Part II focuses on the time analysis of project networks. Part III carries the discussion further into the crucial topic of scheduling under scarce resources. Part IV deals with robust scheduling and stochastic scheduling issues. Numerous tables and figures are used throughout the book to enhance the clarity and effectiveness of the discussions. For the interested and motivated reader, the problems at the end of each chapter should be considered as an integral part of the presentation.