Applied Optimization – serie

In February 2002, the Industrial and Systems Engineering (ISE) De partment at the University of Florida hosted a National Science Founda tion Workshop on Collaboration and Negotiation in Supply Chain Man agement and E Commerce. This workshop focused on characterizing the challenges facing leading edge firms in supply chain management and electronic commerce, and identifying research opportunities for de veloping new technological and decision support capabilities sought by industry. The audience included practitioners in the areas of supply chain management and E Commerce, as well as academic researchers working in these areas. The workshop provided a unique setting that has facilitated ongoing dialog between academic researchers and industry practitioners. This book codifies many of the important themes and issues around which the workshop discussions centered. The editors of this book, all faculty members in the ISE Department at the University of Florida, also served as the workshop's coordinators. In addition to workshop participants, we also invited contributions from leading academics and practitioners who were not able to attend. As a result, the chapters herein represent a collection of research contributions, monographs, and case studies from a variety of disciplines and viewpoints. On the aca demic side alone, chapter authors include faculty members in supply chain and operations management, marketing, industrial engineering, economics, computer science, civil and environmental engineering, and building construction departments.

The idea of this book came to us in October 2002 at the international conference “Production systems design, supply chain management and logistics” (Miedzyzdroje, Poland). This conference was organized by an initiative group from certain French and Polish Universities with the objective to find a new synergy and to develop a Pan European (West – East) cooperation in the areas of: Design of production systems Supply and inventory management Production planning and scheduling Facility location, transportation and logistics Supply chain optimisation via simulation The conference was focused on a wide spectrum of optimisation problems taking into account Supply Chain paradigms, which create a pivotal idea to increase the productivity of modern production systems. The editors proposed to the group members, to present their results for this book. Some well-known scientists agreed also to participate in this work and sent us their contribution. The main idea of this book is that now, it is necessary to consider all the stages of product life cycle in an integrated approach, from the product/process design to the customer delivering. For example at the product design stage, we need to analyse and to optimise all the supply chain. The book is composed of 20 chapters divided into three parts.

This book reports initial efforts in providing some useful extensions in - nancial modeling; further work is necessary to complete the research agenda. The demonstrated extensions in this book in the computation and modeling of optimal control in finance have shown the need and potential for further areas of study in financial modeling. Potentials are in both the mathematical structure and computational aspects of dynamic optimization. There are needs for more organized and coordinated computational approaches. These ext- sions will make dynamic financial optimization models relatively more stable for applications to academic and practical exercises in the areas of financial optimization, forecasting, planning and optimal social choice. This book will be useful to graduate students and academics in finance, mathematical economics, operations research and computer science. Prof- sional practitioners in the above areas will find the book interesting and inf- mative. The authors thank Professor B.D. Craven for providing extensive guidance and assistance in undertaking this research. This work owes significantly to him, which will be evident throughout the whole book. The differential eq- tion solver “nqq” used in this book was first developed by Professor Craven. Editorial assistance provided by Matthew Clarke, Margarita Kumnick and Tom Lun is also highly appreciated. Ping Chen also wants to thank her parents for their constant support and love during the past four years.

A collection of 28 refereed papers grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. Suitable for researchers, practitioners and postgrads.

Supply Chain Optimization captures the latest results in a segment of current research activity in supply chain management. This research area focuses on applying optimization techniques to supply chain management problems. The research papers that make up the volume provide a snapshot of state-of-the-art optimization methods within the field. This book presents rigorous modelling approaches for supply chain operations problems with a goal of improving supply chain performance (or the performance of some segment thereof). It contains high-quality works from leading researchers in the field whose expertise fits within this scope. The book provides a diverse blend of research topics and novel modelling and solution approaches for difficult classes of supply chain operations, planning, and design problems.

Continuous optimization is the study of problems in which we wish to opti­ mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza­ tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re­ search in continuous optimization has produced a variety of theoretical devel­ opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin­ uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.

Although transportation economists have advocated the tolling of urban streets as a mechanism for controlling congestion and managing travel demands for over 50 years, it is only recently that this idea has become practical. When compared to the alternative of building more roads, congestion pricing - in particular via electronic tolling - is attractive and has been adopted in countries around the world. Recent implementations in London, Singapore, and various cities in Norway, as well as a number of projects in the United States, have been judged successful. This book presents rigorous treatments of issues related to congestion pricing. The chapters describe recent advances in areas such as mathematical and computational models for predicting traffic congestion, determining when, where, and how much to levy tolls, and analyzing the impact of tolls on transporation systems. The analyses and methodologies developed in this book provide:- Mechanisms that aid in determining and comparing congestion pricing schemes- Methodologies for evaluating the efficiency of existing and proposed congestion pricing schemes- A means to predict the impact of pricing on urban transporation systems- Information essential to the financial and political success of congestion pricing programs.

A basic problem for the interconnection of communications media is to design interconnection networks for specific needs. For example, to minimize delay and to maximize reliability, networks are required that have minimum diameter and maximum connectivity under certain conditions. The book provides a recent solution to this problem. The subject of all five chapters is the interconnection problem. The first two chapters deal with Cayley digraphs which are candidates for networks of maximum connectivity with given degree and number of nodes. Chapter 3 addresses Bruijn digraphs, Kautz digraphs, and their generalizations, which are candidates for networks of minimum diameter and maximum connectivity with given degree and number of nodes. Chapter 4 studies double loop networks, and Chapter 5 considers broadcasting and the Gossiping problem. All the chapters emphasize the combinatorial aspects of network theory. Audience: A vital reference for graduate students and researchers in applied mathematics and theoretical computer science.

Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

Primary Audience for the Book • Specialists in numerical computations who are interested in algorithms with automatic result verification. • Engineers, scientists, and practitioners who desire results with automatic verification and who would therefore benefit from the experience of suc­ cessful applications. • Students in applied mathematics and computer science who want to learn these methods. Goal Of the Book This book contains surveys of applications of interval computations, i. e. , appli­ cations of numerical methods with automatic result verification, that were pre­ sented at an international workshop on the subject in EI Paso, Texas, February 23-25, 1995. The purpose of this book is to disseminate detailed and surveyed information about existing and potential applications of this new growing field. Brief Description of the Papers At the most fundamental level, interval arithmetic operations work with sets: The result of a single arithmetic operation is the set of all possible results as the operands range over the domain. For example, [0. 9,1. 1] + [2. 9,3. 1] = [3. 8,4. 2], where [3. 8,4. 2] = {x + ylx E [0. 9,1. 1] and y E [3. 8,4. 2]}. The power of interval arithmetic comes from the fact that (i) the elementary operations and standard functions can be computed for intervals with formulas and subroutines; and (ii) directed roundings can be used, so that the images of these operations (e. g.

This work treats the integral economic models with embodied technological change and the controlled lifetime of technologies. Features of the book include: the theoretical basis and algorithmic tools for the analysis of industrial renovation under technical change; a variety of models and optimization problems with simulation examples of real economic systems; a qualitative study of optimal trajectories, including turnpike theorems, and their extended economic analysis; the development of the theory of the models in parallel with numerical algorithms and software.

One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every­ body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro­ gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin­ cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob­ lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).

Operations research and mathematical programming would not be as advanced today without the many advances in interior point methods during the last decade. These methods can now solve very efficiently and robustly large scale linear, nonlinear and combinatorial optimization problems that arise in various practical applications. The main ideas underlying interior point methods have influenced virtually all areas of mathematical programming including: analyzing and solving linear and nonlinear programming problems, sensitivity analysis, complexity analysis, the analysis of Newton's method, decomposition methods, polynomial approximation for combinatorial problems etc. This book covers the implications of interior techniques for the entire field of mathematical programming, bringing together many results in a uniform and coherent way. For the topics mentioned above the book provides theoretical as well as computational results, explains the intuition behind the main ideas, gives examples as well as proofs, and contains an extensive up-to-date bibliography.

During the last three decades, breakthroughs in computer technology have made a tremendous impact on optimization. In particular, parallel computing has made it possible to solve larger and computationally more difficult prob­ lems. This volume contains mainly lecture notes from a Nordic Summer School held at the Linkoping Institute of Technology, Sweden in August 1995. In order to make the book more complete, a few authors were invited to contribute chapters that were not part of the course on this first occasion. The purpose of this Nordic course in advanced studies was three-fold. One goal was to introduce the students to the new achievements in a new and very active field, bring them close to world leading researchers, and strengthen their competence in an area with internationally explosive rate of growth. A second goal was to strengthen the bonds between students from different Nordic countries, and to encourage collaboration and joint research ventures over the borders. In this respect, the course built further on the achievements of the "Nordic Network in Mathematical Programming" , which has been running during the last three years with the support ofthe Nordic Council for Advanced Studies (NorFA). The final goal was to produce literature on the particular subject, which would be available to both the participating students and to the students of the "next generation" .

Thisvolume starts with the basicconceptsof FuzzyLogic: the membership function, the intersection and the union of fuzzy sets, fuzzy numbers, and the extension principle underlying the algorithmic operations. Several chapters are devoted to applications of FuzzyLogic in various branches of Operations Research: PERT planning with uncertain activity durations, SMART and the AHP for Multi-Criteria Decision Analysis (MCDA) with vague preferential statements, ELECTRE usingthe ideasof the AHP and SMART, and Multi-Objective Optimization (MOO) with weighted degrees of satisfaction. Finally, earlierstudiesof colour perception illustrate the attemptsto find a physiological basisfor the set-theoretical and the algorithmic operations in Fuzzy Logic. The last chapter also discusses somekey issues in linguistic categorization and the prospectsof FuzzyLogicas a multi-disciplinary research activity.I am greatly indebted to the Department of Mechanical Engineering and Applied Mechanics, College of Engineering, University of Michigan, Ann Arbor, for the splendid opportunity to start the actual work on this book during my sabbatical leavefrom Delft (1993 - 1994); to LAMSADE, Universite de Paris-Dauphine, where many ideas emerged duringtwo winter visits (1989, 1990); to the International Institute for Applied Systems Analysis, Laxenburg, Austria, whereI got further inspiration duringa number of summer visits (1992, 1995, and 1996); and to the NISSAN Foundation in The Netherlands who enabled me to visit several Japanese universities (June 1996). Moreover, I gratefully acknowledge the stimulating supportgiven by many colleagues inthe International Society on Multi-Criteria Decision Making and in the European Working Group "Aide Multicritere Ii la Decision".

grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional pro­ grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field C­ programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. [104]), Sniedovich shows how the study of such com­ positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. [9]) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. [16]). The distinction between global optimization problems (Ref. [54]) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.

The input data for data processing algorithms come from measurements and are therefore not precise. It is therefore necessary to estimate the accuracy of the results of data processing. Even for the simplest data processing algorithms, this problem is, however, intractable. This book describes for what classes of problems interval computations (i.e. data processing with automatic results verification) are feasible, and when they are intractable. This knowledge is important for algorithm developers, because it will enable them to concentrate on the classes of problems for which general algorithms are possible.

This work deals fundamentally with two of the most important aspects of personnel management, namely selection and job mobility. These topics are treated using late-1990s techniques created from all-purpose logic for handling uncertainty. Personnel recruitment is covered from the angle of selection techniques for improved efficiency for the company and greater satisfaction and self-realization for the employee. When considering workplaces, the suitability of each person and their mobility are studied under the best economic conditions. An alternative type of mathematics is used within this subject-matter is used for the development of models and algorithms. Complex subjects such as uncertainty are explained pedagogically starting from a low level and, when necessary, recourse has been made to reminders of basic aspects to enable a wide readership to profit from this work. This volume should be of interest to those whose work involves personnel management, production operation and manufacturing management, labour economics, industrial organization, operations research and management sciences.

This book provides a new point of view on the subject of business failure prediction, through the application of multicriteria analysis methods. The aim of the book is to provide a review of the research in the area and to explore the adequacy of these methods to one of the most complex problems in the area of financial management. In addition, the book explores the applications of the methods so that it can become a very useful tool for researchers and practitioners. The analysis of the modeling and the results in these applications provides the background for further employment of the methods.

This text is dedicated to the memory of Steven Vajda, one of the pioneers of mathematical programming, who was born in Hungary. The 22 invited chapters written by 36 authors from 12 countries provide the reader with an insight into some advances in mathematical programming. The book is addressed to researchers and postgraduate students with an interest in the theoretical and algorithmic aspects of the field.

Containing some of the most recent results in nonlinear programming (in 1998), this text includes results on trust region algorithms, interior point methods, quasi-Newton methods, conjugate gradient methods, and methods for variational problems. The work should be useful as a reference source for researchers, engineers and graduate students.

February 27 - March 1, 1997, the conference Optimal Control: The­ ory, Algorithms, and Applications took place at the University of Florida, hosted by the Center for Applied Optimization. The conference brought together researchers from universities, industry, and government laborato­ ries in the United States, Germany, Italy, France, Canada, and Sweden. There were forty-five invited talks, including seven talks by students. The conference was sponsored by the National Science Foundation and endorsed by the SIAM Activity Group on Control and Systems Theory, the Mathe­ matical Programming Society, the International Federation for Information Processing (IFIP), and the International Association for Mathematics and Computers in Simulation (IMACS). Since its inception in the 1940s and 1950s, Optimal Control has been closely connected to industrial applications, starting with aerospace. The program for the Gainesville conference, which reflected the rich cross-disci­ plinary flavor of the field, included aerospace applications as well as both novel and emerging applications to superconductors, diffractive optics, non­ linear optics, structural analysis, bioreactors, corrosion detection, acoustic flow, process design in chemical engineering, hydroelectric power plants, sterilization of canned foods, robotics, and thermoelastic plates and shells. The three days of the conference were organized around the three confer­ ence themes, theory, algorithms, and applications. This book is a collection of the papers presented at the Gainesville conference. We would like to take this opportunity to thank the sponsors and participants of the conference, the authors, the referees, and the publisher for making this volume possible.

Industries rely more and more on advanced technology. Accelerated computer evolution makes large-scale computation practical. Many enterprises are be­ ginning to benefit from more efficient allocation of resources and more effective planning, scheduling, manufacturing, and distribution by adopting state-of-the­ art decision support systems. Academics increasingly emphasize application­ driven research. All these forces have moved optimization from a pure class­ room and textbook terminology to an accepted tool in today's business world. This book chronicles and describes applications of combinatorial optimization in industry. A wide range of applications is included: manpower planning • production planning • job sequencing and scheduling • manufacturing layout design • facility planning • vehicle scheduling and routing • retail seasonal planning • I! space shuttle scheduling, and telecommunication network design . • The applications covered in this book comprise a representative set of industry sectors including electronics, airlines, manufacturing, tobacco, retail, telecom­ munication, defense, and livestock. These examples should encourage opera­ tions researchers and applied mathematicians by pointing out how the impor­ tance and practicality of optimization is starting to be realized by the manage­ ment of various organizations and how some pioneering developments in this field are beginning to bear fruit.

This text presents a unified framework for theory and practice, which is proven theoretically and by many cases from various engineering fields. There are four major aspects to the book. Firstly, it develops a formal systems approach to design (including theorems, analysis of principles of design and information theory). Secondly, methods for efficient design are rigorously derived from the theory, based on AI and optimization. Thirdly, the text covers many engineering disciplines under a unified framework, including mechanical, electrical, civil, industrial, manufacturing systems, and apparel industry. It also provides the methodology for developing the next generation computer software for advanced intelligent CAD (Computer Aided Design). Audience: The book is especially appropriate for courses in engineering (mechanical, industrial, electrical, and civil). It should be useful reference for practicing engineers interested in design and optimization, and for applied mathematicians and computer software developers engaged in smart CAD applications.

This book presents a unified optimal control approach to a large class of problems arising in the field of production planning and scheduling. It introduces a leading optimal flow control paradigm which results in efficient solutions for planning and scheduling problems. This book also introduces the reader to analytical and numerical methods of the maximum principle, used here as a mathematical instrument in modeling and solving production planning and scheduling problems. The book examines control of production flows rather than sequencing of distinct jobs. Methodologically, this paradigm allows us to progress from initial assumptions about a manufacturing environment, through mathematical models and construction of numerical methods, up to practical applications which prove the relevance of the theory developed here to the real world. Given a manufacturing system, the goal is to control the production, subject to given constraints, in such a way that the demands are tracked as closely as possible. The book considers a wide variety of problems encountered in actual production planning and scheduling. Among the problems are production flow sequencing and timing, capacity expansion and deterioration, subcontracting and overtime. The last chapter is entirely devoted to applications of the theory to scheduling production flows in real-life manufacturing systems. The enclosed disk provides software implementations of the developed methods with easy, convenient user interface. We aimed this book at a student audience - final year undergraduates as weIl as master and Ph. D.

This book provides a new point of view on the subject of the management of uncertainty. It covers a wide variety of both theoretical and practical issues involving the analysis and management of uncertainty in the fields of finance, management and marketing. Audience: Researchers and professionals from operations research, management science and economics.

This is a presentation of the basic ideas of optimization methods that are applicable to strategic planning and operations management, particularly in the field of transportation. The material of the book covers almost all parts of optimization, and the author describes the ideas behind the methods (with which the study of the methods usually starts) and facilitates further study of the methods using original scientific articles rather than just textbooks. The book is also designed to be a manual for those specialists who work in the field of management and who recognize optimization as a powerful tool for numerical analysis of the potential and of the competitiveness of enterprises. A special chapter contains the basic mathematical notation and concepts useful for understanding the book and covers all the necessary mathematical information.

FIRST PART Preparation of the Investment 1. Investments in the Company 19 The decline of stability . . 19 The change in direction of studies on the investment process. 25 Basic elements for arithmetical study of selection 29 Thc study of selection from non-numerical elements. 37 2. Programming Investment Activity 49 Classical programming techniques. 49 Handling of an investment programme. 56 Incorporation of costs into investment projects . . . . . . . . . . . . . . . . . . 66 Estimating financial needs throughout the process. 72 3. Financial Risk of Investment 85 Financial aspects of the investment process. 85 Determination of the financial capacity of the investment . . 89 From pre-diagnosis to diagnosis. 102 Numerical determination of the financial risk of an investment. 106 4. Analysis of financial products for the investment 113 Aspects prior to product analysis. 113 Analysis by means of the clan concept . . . . . . . . . . . . . . . . . . . 117 Obtaining affinities and thc use of codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Grouping the characteristics of the products by means of the Moore closing. 126 From product grouping to affinities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 10 / Index SECOND PART Selection 5. A first approximation to selection models 145 Updating of monetary currents 145 Incorporation of the lack of precision of interests rates . . . . . . . . . . . . . . . . 153 The hypothesis of known net values and fuzzy rate of interest . . . . . . 157 6. Selection of investments in an economy with inflation 165 Estimate of monetary currents at constant prices . . . . . . . . . . . . . . . . . . . 165 Estimate of monetary currents at prices for each period . . . . . . . 172 The hypothesis of different rates of inflation . . . . 180 7.

The concept of "reformulation" has long been playing an important role in mathematical programming. A classical example is the penalization technique in constrained optimization that transforms the constraints into the objective function via a penalty function thereby reformulating a constrained problem as an equivalent or approximately equivalent unconstrained problem. More recent trends consist of the reformulation of various mathematical programming prob­ lems, including variational inequalities and complementarity problems, into equivalent systems of possibly nonsmooth, piecewise smooth or semismooth nonlinear equations, or equivalent unconstrained optimization problems that are usually differentiable, but in general not twice differentiable. Because of the recent advent of various tools in nonsmooth analysis, the reformulation approach has become increasingly profound and diversified. In view of growing interests in this active field, we planned to organize a cluster of sessions entitled "Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods" in the 16th International Symposium on Mathematical Programming (ismp97) held at Lausanne EPFL, Switzerland on August 24-29, 1997. Responding to our invitation, thirty-eight people agreed to give a talk within the cluster, which enabled us to organize thirteen sessions in total. We think that it was one of the largest and most exciting clusters in the symposium. Thanks to the earnest support by the speakers and the chairpersons, the sessions attracted much attention of the participants and were filled with great enthusiasm of the audience.