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| integer programming problems and solutions: Integer Programming and Combinatorial Optimization Matteo Fischetti, David P. Williamson, 2007-06-26 This book constitutes the refereed proceedings of the 12th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2007, held in Ithaca, NY, USA, in June 2007. Among the topics addressed in the 36 revised full papers are approximation algorithms, algorithmic game theory, computational biology, integer programming, polyhedral combinatorics, scheduling theory and scheduling algorithms, as well as semidefinite programs. |
| integer programming problems and solutions: Applied Integer Programming Der-San Chen, Robert G. Batson, Yu Dang, 2010-01-12 An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems. |
| integer programming problems and solutions: Integer Programming Hamdy A. Taha, 2014-05-10 Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming. Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other chapters consider the branch-and-bound methods, the cutting-plane method, and its closely related asymptotic problem. This book discusses as well several specialized algorithms for certain well-known integer models and provides an alternative approach to the solution of the integer problem. The final chapter deals with a number of observations about the formulations and executions of integer programming models. This book is a valuable resource for industrial engineers and research workers. |
| integer programming problems and solutions: Applied Integer Programming Der-San Chen, Robert G. Batson, Yu Dang, 2011-09-20 An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently. The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems. Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book. Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems. |
| integer programming problems and solutions: Elementary Linear Programming with Applications Bernard Kolman, Robert E. Beck, 2014-05-10 Elementary Linear Programming with Applications presents a survey of the basic ideas in linear programming and related areas. It also provides students with some of the tools used in solving difficult problems which will prove useful in their professional career. The text is comprised of six chapters. The Prologue gives a brief survey of operations research and discusses the different steps in solving an operations research problem. Chapter 0 gives a quick review of the necessary linear algebra. Chapter 1 deals with the basic necessary geometric ideas in Rn. Chapter 2 introduces linear programming with examples of the problems to be considered, and presents the simplex method as an algorithm for solving linear programming problems. Chapter 3 covers further topics in linear programming, including duality theory and sensitivity analysis. Chapter 4 presents an introduction to integer programming. Chapter 5 covers a few of the more important topics in network flows. Students of business, engineering, computer science, and mathematics will find the book very useful. |
| integer programming problems and solutions: 50 Years of Integer Programming 1958-2008 Michael Jünger, Thomas M. Liebling, Denis Naddef, George L. Nemhauser, William R. Pulleyblank, Gerhard Reinelt, Giovanni Rinaldi, Laurence A. Wolsey, 2009-11-06 In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the field by distinguished members of the integer programming community. Useful for anyone in mathematics, computer science and operations research, this book exposes mathematical optimization, specifically integer programming and combinatorial optimization, to a broad audience. |
| integer programming problems and solutions: Chemical Production Scheduling Christos T. Maravelias, 2021-05-06 Understand common scheduling as well as other advanced operational problems with this valuable reference from a recognized leader in the field. Beginning with basic principles and an overview of linear and mixed-integer programming, this unified treatment introduces the fundamental ideas underpinning most modeling approaches, and will allow you to easily develop your own models. With more than 150 figures, the basic concepts and ideas behind the development of different approaches are clearly illustrated. Addresses a wide range of problems arising in diverse industrial sectors, from oil and gas to fine chemicals, and from commodity chemicals to food manufacturing. A perfect resource for engineering and computer science students, researchers working in the area, and industrial practitioners. |
| integer programming problems and solutions: Integer Programming John K. Karlof, 2005-09-22 Integer Programming: Theory and Practice contains refereed articles that explore both theoretical aspects of integer programming as well as major applications. This volume begins with a description of new constructive and iterative search methods for solving the Boolean optimization problem (BOOP). Following a review of recent developments |
| integer programming problems and solutions: Mixed Integer Nonlinear Programming Jon Lee, Sven Leyffer, 2011-12-02 Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances. |
| integer programming problems and solutions: Integer Programming Laurence A. Wolsey, 2020-10-20 A PRACTICAL GUIDE TO OPTIMIZATION PROBLEMS WITH DISCRETE OR INTEGER VARIABLES, REVISED AND UPDATED The revised second edition of Integer Programming explains in clear and simple terms how to construct custom-made algorithms or use existing commercial software to obtain optimal or near-optimal solutions for a variety of real-world problems. The second edition also includes information on the remarkable progress in the development of mixed integer programming solvers in the 22 years since the first edition of the book appeared. The updated text includes information on the most recent developments in the field such as the much improved preprocessing/presolving and the many new ideas for primal heuristics included in the solvers. The result has been a speed-up of several orders of magnitude. The other major change reflected in the text is the widespread use of decomposition algorithms, in particular column generation (branch-(cut)-and-price) and Benders’ decomposition. The revised second edition: Contains new developments on column generation Offers a new chapter on Benders’ algorithm Includes expanded information on preprocessing, heuristics, and branch-and-cut Presents several basic and extended formulations, for example for fixed cost network flows Also touches on and briefly introduces topics such as non-bipartite matching, the complexity of extended formulations or a good linear program for the implementation of lift-and-project Written for students of integer/mathematical programming in operations research, mathematics, engineering, or computer science, Integer Programming offers an updated edition of the basic text that reflects the most recent developments in the field. |
| integer programming problems and solutions: Multiobjective Linear and Integer Programming Carlos Henggeler Antunes, Maria Joao Alves, Joao Climaco, 2016-04-08 This book opens the door to multiobjective optimization for students in fields such as engineering, management, economics and applied mathematics. It offers a comprehensive introduction to multiobjective optimization, with a primary emphasis on multiobjective linear programming and multiobjective integer/mixed integer programming. A didactic book, it is mainly intended for undergraduate and graduate students, but can also be useful for researchers and practitioners. Further, it is accompanied by an interactive software package - developed by the authors for Windows platforms - which can be used for teaching and decision-making support purposes in multiobjective linear programming problems. Thus, besides the textbook’s coverage of the essential concepts, theory and methods, complemented with illustrative examples and exercises, the computational tool enables students to experiment and enhance their technical skills, as well as to capture the essential characteristics of real-world problems. |
| integer programming problems and solutions: Integer Programming Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli, 2014-11-15 This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader’s understanding and serving as a gateway to deeper study. Key topics include: formulations polyhedral theory cutting planes decomposition enumeration semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field. |
| integer programming problems and solutions: An Introduction to Linear Programming and Game Theory Paul R. Thie, Gerard E. Keough, 2011-09-15 Praise for the Second Edition: This is quite a well-done book: very tightly organized, better-than-average exposition, and numerous examples, illustrations, and applications. —Mathematical Reviews of the American Mathematical Society An Introduction to Linear Programming and Game Theory, Third Edition presents a rigorous, yet accessible, introduction to the theoretical concepts and computational techniques of linear programming and game theory. Now with more extensive modeling exercises and detailed integer programming examples, this book uniquely illustrates how mathematics can be used in real-world applications in the social, life, and managerial sciences, providing readers with the opportunity to develop and apply their analytical abilities when solving realistic problems. This Third Edition addresses various new topics and improvements in the field of mathematical programming, and it also presents two software programs, LP Assistant and the Solver add-in for Microsoft Office Excel, for solving linear programming problems. LP Assistant, developed by coauthor Gerard Keough, allows readers to perform the basic steps of the algorithms provided in the book and is freely available via the book's related Web site. The use of the sensitivity analysis report and integer programming algorithm from the Solver add-in for Microsoft Office Excel is introduced so readers can solve the book's linear and integer programming problems. A detailed appendix contains instructions for the use of both applications. Additional features of the Third Edition include: A discussion of sensitivity analysis for the two-variable problem, along with new examples demonstrating integer programming, non-linear programming, and make vs. buy models Revised proofs and a discussion on the relevance and solution of the dual problem A section on developing an example in Data Envelopment Analysis An outline of the proof of John Nash's theorem on the existence of equilibrium strategy pairs for non-cooperative, non-zero-sum games Providing a complete mathematical development of all presented concepts and examples, Introduction to Linear Programming and Game Theory, Third Edition is an ideal text for linear programming and mathematical modeling courses at the upper-undergraduate and graduate levels. It also serves as a valuable reference for professionals who use game theory in business, economics, and management science. |
| integer programming problems and solutions: Modeling and Solving Linear Programming with R Jose M. Sallan, Oriol Lordan, Vicenc Fernandez, 2015-09-09 Linear programming is one of the most extensively used techniques in the toolbox of quantitative methods of optimization. One of the reasons of the popularity of linear programming is that it allows to model a large variety of situations with a simple framework. Furthermore, a linear program is relatively easy to solve. The simplex method allows to solve most linear programs efficiently, and the Karmarkar interior-point method allows a more efficient solving of some kinds of linear programming. The power of linear programming is greatly enhanced when came the opportunity of solving integer and mixed integer linear programming. In these models all or some of the decision variables are integers, respectively. In this book we provide a brief introduction to linear programming, together with a set of exercises that introduce some applications of linear programming. We will also provide an introduction to solve linear programming in R. For each problem a possible solution through linear programming is introduced, together with the code to solve it in R and its numerical solution. |
| integer programming problems and solutions: Linear and Integer Optimization Gerard Sierksma, Yori Zwols, 2015-05-01 Presenting a strong and clear relationship between theory and practice, Linear and Integer Optimization: Theory and Practice is divided into two main parts. The first covers the theory of linear and integer optimization, including both basic and advanced topics. Dantzig's simplex algorithm, duality, sensitivity analysis, integer optimization models |
| integer programming problems and solutions: Integer Programming and Network Models H.A. Eiselt, Carl-Louis Sandblom, 2013-03-14 The purpose of this book is to provide readers with an introduction to the very active field of integer programming and network models. The idea is to cover the main parts of the field without being too detailed or too technical. As a matter of fact, we found it somewhat surprising that most--especially newer---books are strongly algorithmically oriented. In contrast, the main emphasis of this book is on models rather than methods. This focus expresses our view that methods are tools to solve actual problems and not ends in themselves. As such, graduate (and with some omissions, undergraduate) students may find this book helpful in their studies as will practitioners who would like to get acquainted with a field or use this text as a refresher. This premise has resulted in a coverage that omits material that is standard fare in other books, whereas it covers topics that are only infrequently found elsewhere. There are some, yet relatively few, prerequisites for the reader. Most material that is required for the understanding of more than one chapter is presented in one of the four chapters of the introductory part, which reviews the main results in linear programming, the analysis of algorithms, graphs and networks, and dynamic programming, respectively. Readers who are familiar with the issues involved can safely skip that part. The three main parts of the book rely on intuitive reasoning and examples, whenever practical, instead of theorems and proofs. |
| integer programming problems and solutions: The Linear Ordering Problem Rafael Martí, Gerhard Reinelt, 2011-01-03 Faced with the challenge of solving the hard optimization problems that abound in the real world, existing methods often encounter great difficulties. Important applications in business, engineering or economics cannot be tackled by the techniques that have formed the predominant focus of academic research throughout the past three decades. Exact and heuristic approaches are dramatically changing our ability to solve problems of practical significance and are extending the frontier of problems that can be handled effectively. This monograph details state-of-the-art optimization methods, both exact and heuristic, for the LOP. The authors employ the LOP to illustrate contemporary optimization technologies as well as how to design successful implementations of exact and heuristic procedures. Therefore, they do not limit the scope of this book to the LOP, but on the contrary, provide the reader with the background and practical strategies in optimization to tackle different combinatorial problems. |
| integer programming problems and solutions: Disjunctive Programming Egon Balas, 2018-11-27 Disjunctive Programming is a technique and a discipline initiated by the author in the early 1970's, which has become a central tool for solving nonconvex optimization problems like pure or mixed integer programs, through convexification (cutting plane) procedures combined with enumeration. It has played a major role in the revolution in the state of the art of Integer Programming that took place roughly during the period 1990-2010. The main benefit that the reader may acquire from reading this book is a deeper understanding of the theoretical underpinnings and of the applications potential of disjunctive programming, which range from more efficient problem formulation to enhanced modeling capability and improved solution methods for integer and combinatorial optimization. Egon Balas is University Professor and Lord Professor of Operations Research at Carnegie Mellon University's Tepper School of Business. |
| integer programming problems and solutions: Theory of Linear and Integer Programming Alexander Schrijver, 1998-06-11 Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index |
| integer programming problems and solutions: Large Scale Linear and Integer Optimization: A Unified Approach Richard Kipp Martin, 1999 In this book, Kipp Martin has systematically provided users with a unified treatment of the algorithms and the implementation of the algorithms that are important in solving large problems. Parts I and II of Large Scale Linear and Integer Programming provide an introduction to linear optimization using two simple but unifying ideas-projection and inverse projection. The ideas of projection and inverse projection are also extended to integer linear optimization. With the projection-inverse projection approach, theoretical results in integer linear optimization become much more analogous to their linear optimization counterparts. Hence, with an understanding of these two concepts, the reader is equipped to understand fundamental theorems in an intuitive way. Part III presents the most important algorithms that are used in commercial software for solving real-world problems. Part IV shows how to take advantage of the special structure in very large scale applications through decomposition. Part V describes,how to take advantage of special structure by modifying and enhancing the algorithms developed in Part III. This section contains a discussion of the current research in linear and integer linear programming. The author also shows in Part V how to take different problem formulations and appropriately 'modify' them so that the algorithms from Part III are more efficient. Again, the projection and inverse projection concepts are used in Part V to present the current research in linear and integer linear optimization in a very unified way. |
| integer programming problems and solutions: Linear and Mixed Integer Programming for Portfolio Optimization Renata Mansini, Włodzimierz Ogryczak, M. Grazia Speranza, 2015-06-10 This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features. Other linear models, such as models for portfolio rebalancing and index tracking, are also covered. The book discusses computational issues and provides a theoretical framework, including the concepts of risk-averse preferences, stochastic dominance and coherent risk measures. The material is presented in a style that requires no background in finance or in portfolio optimization; some experience in linear and mixed integer models, however, is required. The book is thoroughly didactic, supplementing the concepts with comments and illustrative examples. |
| integer programming problems and solutions: Computer Optimization Techniques William Conley, 1984 |
| integer programming problems and solutions: Problems in Operations Research (Principles and Solutions) D S Hira, 1995 We take great pleasure in presenting to the readers the second throughly revised edition of the book after a number of reprints.The suggestions received from the readers have been carefully incorporated in this edition and almost the entire subject matter has been reorganised,revised and rewritten. |
| integer programming problems and solutions: Linear Programming G. V. Shenoy, 2007 Due To The Availability Of Computer Packages, The Use Of Linear Programming Technique By The Managers Has Become Universal. This Text Has Been Written Primarily For Management Students And Executives Who Have No Previous Background Of Linear Programming. The Text Is Oriented Towards Introducing Important Ideas In Linear Programming Technique At A Fundamental Level And Help The Students In Understanding Its Applications To A Wide Variety Of Managerial Problems. In Order To Strengthen The Understanding, Each Concept Has Been Illustrated With Examples. The Book Has Been Written In A Simple And Lucid Language And Has Avoided Mathematical Derivations So As To Make It Accessible To Every One.The Text Can Be Used In Its Entirely In A Fifteen Session Course At Programmes In Management, Commerce, Economics, Engineering Or Accountancy. The Text Can Be Used In One/Two Week Management/Executive Development Programmes To Be Supplemented With Some Cases. Practicing Managers And Executives, Computer Professionals, Industrial Engineers, Chartered And Cost Accountants And Economic Planners Would Also Find This Text Useful. |
| integer programming problems and solutions: Linear Programming and Algorithms for Communication Networks Eiji Oki, 2012-08-24 Explaining how to apply to mathematical programming to network design and control, Linear Programming and Algorithms for Communication Networks: A Practical Guide to Network Design, Control, and Management fills the gap between mathematical programming theory and its implementation in communication networks. From the basics all the way through to m |
| integer programming problems and solutions: Solving Optimization Problems with MATLAB® Dingyü Xue, 2020-04-06 This book focuses on solving optimization problems with MATLAB. Descriptions and solutions of nonlinear equations of any form are studied first. Focuses are made on the solutions of various types of optimization problems, including unconstrained and constrained optimizations, mixed integer, multiobjective and dynamic programming problems. Comparative studies and conclusions on intelligent global solvers are also provided. |
| integer programming problems and solutions: Integer Linear Programming in Computational and Systems Biology Dan Gusfield, 2019-06-13 This hands-on tutorial text for non-experts demonstrates biological applications of a versatile modeling and optimization technique. |
| integer programming problems and solutions: Encyclopedia of Optimization Christodoulos A. Floudas, Panos M. Pardalos, 2008-09-04 The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as Algorithms for Genomics, Optimization and Radiotherapy Treatment Design, and Crew Scheduling. |
| integer programming problems and solutions: Computational Combinatorial Optimization Michael Jünger, Denis Naddef, 2001-11-21 This tutorial contains written versions of seven lectures on Computational Combinatorial Optimization given by leading members of the optimization community. The lectures introduce modern combinatorial optimization techniques, with an emphasis on branch and cut algorithms and Lagrangian relaxation approaches. Polyhedral combinatorics as the mathematical backbone of successful algorithms are covered from many perspectives, in particular, polyhedral projection and lifting techniques and the importance of modeling are extensively discussed. Applications to prominent combinatorial optimization problems, e.g., in production and transport planning, are treated in many places; in particular, the book contains a state-of-the-art account of the most successful techniques for solving the traveling salesman problem to optimality. |
| integer programming problems and solutions: Large-scale Optimization Vladimir Tsurkov, 2013-03-09 Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control. |
| integer programming problems and solutions: Computational Mathematical Programming Klaus Schittkowski, 2013-06-29 This book contains the written versions of main lectures presented at the Advanced Study Institute (ASI) on Computational Mathematical Programming, which was held in Bad Windsheim, Germany F. R., from July 23 to August 2, 1984, under the sponsorship of NATO. The ASI was organized by the Committee on Algorithms (COAL) of the Mathematical Programming Society. Co-directors were Karla Hoffmann (National Bureau of Standards, Washington, U.S.A.) and Jan Teigen (Rabobank Nederland, Zeist, The Netherlands). Ninety participants coming from about 20 different countries attended the ASI and contributed their efforts to achieve a highly interesting and stimulating meeting. Since 1947 when the first linear programming technique was developed, the importance of optimization models and their mathematical solution methods has steadily increased, and now plays a leading role in applied research areas. The basic idea of optimization theory is to minimize (or maximize) a function of several variables subject to certain restrictions. This general mathematical concept covers a broad class of possible practical applications arising in mechanical, electrical, or chemical engineering, physics, economics, medicine, biology, etc. There are both industrial applications (e.g. design of mechanical structures, production plans) and applications in the natural, engineering, and social sciences (e.g. chemical equilibrium problems, christollography problems). |
| integer programming problems and solutions: Algorithms Sanjoy Dasgupta, Christos H. Papadimitriou, Umesh Virkumar Vazirani, 2006 This text, extensively class-tested over a decade at UC Berkeley and UC San Diego, explains the fundamentals of algorithms in a story line that makes the material enjoyable and easy to digest. Emphasis is placed on understanding the crisp mathematical idea behind each algorithm, in a manner that is intuitive and rigorous without being unduly formal. Features include:The use of boxes to strengthen the narrative: pieces that provide historical context, descriptions of how the algorithms are used in practice, and excursions for the mathematically sophisticated. Carefully chosen advanced topics that can be skipped in a standard one-semester course but can be covered in an advanced algorithms course or in a more leisurely two-semester sequence.An accessible treatment of linear programming introduces students to one of the greatest achievements in algorithms. An optional chapter on the quantum algorithm for factoring provides a unique peephole into this exciting topic. In addition to the text DasGupta also offers a Solutions Manual which is available on the Online Learning Center.Algorithms is an outstanding undergraduate text equally informed by the historical roots and contemporary applications of its subject. Like a captivating novel it is a joy to read. Tim Roughgarden Stanford University |
| integer programming problems and solutions: Understanding and Using Linear Programming Jiri Matousek, Bernd Gärtner, 2007-07-04 The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is what every theoretical computer scientist should know about linear programming. A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming behind the scenes. |
| integer programming problems and solutions: Metaheuristics El-Ghazali Talbi, 2009-05-27 A unified view of metaheuristics This book provides a complete background on metaheuristics and shows readers how to design and implement efficient algorithms to solve complex optimization problems across a diverse range of applications, from networking and bioinformatics to engineering design, routing, and scheduling. It presents the main design questions for all families of metaheuristics and clearly illustrates how to implement the algorithms under a software framework to reuse both the design and code. Throughout the book, the key search components of metaheuristics are considered as a toolbox for: Designing efficient metaheuristics (e.g. local search, tabu search, simulated annealing, evolutionary algorithms, particle swarm optimization, scatter search, ant colonies, bee colonies, artificial immune systems) for optimization problems Designing efficient metaheuristics for multi-objective optimization problems Designing hybrid, parallel, and distributed metaheuristics Implementing metaheuristics on sequential and parallel machines Using many case studies and treating design and implementation independently, this book gives readers the skills necessary to solve large-scale optimization problems quickly and efficiently. It is a valuable reference for practicing engineers and researchers from diverse areas dealing with optimization or machine learning; and graduate students in computer science, operations research, control, engineering, business and management, and applied mathematics. |
| integer programming problems and solutions: Integer Programming Ellis L. Johnson, 1980-01-01 This monograph considers pure integer programming problems which concern packing, partitioning or covering. For this class of problems, an algorithmic framework using a duality approach is offered. Furthermore, the author proposes for the first time a general framework for both packing and covering problems characterizing the convex whole of integer solutions. |
| integer programming problems and solutions: Decision-making in a Fuzzy Environment Richard Bellman, Lotfi Asker Zadeh, 1970 |
| integer programming problems and solutions: Advances in Sensitivity Analysis and Parametric Programming Tomas Gal, H.J. Greenberg, 2012-12-06 The standard view of Operations Research/Management Science (OR/MS) dichotomizes the field into deterministic and probabilistic (nondeterministic, stochastic) subfields. This division can be seen by reading the contents page of just about any OR/MS textbook. The mathematical models that help to define OR/MS are usually presented in terms of one subfield or the other. This separation comes about somewhat artificially: academic courses are conveniently subdivided with respect to prerequisites; an initial overview of OR/MS can be presented without requiring knowledge of probability and statistics; text books are conveniently divided into two related semester courses, with deterministic models coming first; academics tend to specialize in one subfield or the other; and practitioners also tend to be expert in a single subfield. But, no matter who is involved in an OR/MS modeling situation (deterministic or probabilistic - academic or practitioner), it is clear that a proper and correct treatment of any problem situation is accomplished only when the analysis cuts across this dichotomy. |
| integer programming problems and solutions: A Branch-and-Bound Algorithm for Multiobjective Mixed-integer Convex Optimization Stefan Rocktäschel, 2020-01-21 Stefan Rocktäschel introduces a branch-and-bound algorithm that determines a cover of the efficient set of multiobjective mixed-integer convex optimization problems. He examines particular steps of this algorithm in detail and enhances the basic algorithm with additional modifications that ensure a more precise cover of the efficient set. Finally, he gives numerical results on some test instances. |
| integer programming problems and solutions: Applications of Optimization with Xpress-MP Christelle Guéret, Christian Prins, Marc Sevaux, 2002 |
| integer programming problems and solutions: Linear and Integer Programming Gerard Sierksma, 2001-11-01 Combines the theoretical and practical aspects of linear and integer programming. Provides practical case studies and techniques, including rounding-off, column-generation, game theory, multiobjective optimization, and goal programming, as well as real-world solutions to the transportation and transshipment problem, project scheduling, and decentralization. |
Integer Programming 9 - MIT - Massachusetts Institute of …
why many practitioners feel that the integer-programming model is one of the most important models in management science. Second, we consider basic approaches that have been …
Integer Programming. Exercises - OCW
Solve the problem using the 0-1 branch and bound algorithm, and determine which of the 6 components will be selected to be carried in the box so as to maximize the total value of the …
Solving Integer Programming with Branch-and-Bound Technique
We will use the linear programming relaxation to estimate the optimal solution of an integer programming. — The LP problem has no feasible solution, done; — The LP problem has an …
Integer Programming. Solutions - OCW
Integer Programming. Solutions 1. The optimal solutions to the IP problems, using the graphical solution: 1.1 x∗ 1 = 5, x ∗ 2 = 2, z ∗ = 13. 1.2 x∗ 1 = 14, x ∗ 2 = 2, z ∗ = 100. 2. The optimal …
B6.3 Integer Programming - University of Oxford
What is integer programming? Introductory Examples fire station built considered location considered location considered location considered location fire station built …
Integer Programming - MIT - Massachusetts Institute of Technology
What are integer programming problems? §In many applications, integrality restrictions reflect natural indivisibilities of the problem under study. For example, when deciding how many …
Integer Programming - MIT - Massachusetts Institute of Technology
What are integer programming problems? Linear programming problems in which fractional solutions are not realistic. Mixed integer programs: when some, but not all, variables are …
Solving Real-Life Problems with Integer Programming - DTU
Linear Programming is a strong tool for many real-life optimization problems. We can solve large problems (thousands of constraints and millions of variables). We can solve problems fast …
Lecture 5 Integer Programming
1 Integer Programming Overview The Integer Programming problem (IP) is that of deciding whether there exists an integer solution to a given set of m rational inequalities on n variables. …
Integer programming (part 1)
polynomial-time algorithms for solving integer programs. Solving the associated convex relaxation (ignoring integrality constraints) results in an lower bound on the optimal value.
12 Integer Programming - Ohio University
The mathematical model for integer programming is the linear programming model (see Sec. 3.2) with the one additional restriction that the variables must have integer val-ues. If only some of …
11 Formulating and Solving Integer Programs - LINDO
methods for formulating and solving problems with integrality requirements are called integer programming. 11.1.1 Types of Variables One general classification is according to types of …
Introduction to integer programming - MIT OpenCourseWare
Integer Programming is a combinatorial optimization problem. Every instance of a combinatorial optimization problem has data, a method for determining which solutions are feasible, and an …
Integer Programming Formulation 1 Integer Programming …
However, for real problems this approach will take practically inflnite amount of time. The solution procedures for IP’s are still under development. Two approaches are common: Branch and …
Linear Programming Notes X: Integer Programming
Integer programming problems are typically much harder to solve than linear programming problems and there are no fundamental theoretical results like duality or computational …
The Lagrangian Relaxation Method for Solving Integer …
Solving Integer Programming Problems Marshall L. Fisher University of Pennsylvania, Philadelphia, Pennsylvania One of the most computationally useful ideas of the 1970s is the …
Integer programming formulations - MIT OpenCourseWare
Write Nooz’s problem as an integer program. Modeling logical constraints that include only two binary variables. Step 1. Graph the feasible region as restricted to the two variables. Step 2. …
INTEGER LINEAR PROGRAMMING - INTRODUCTION
GLPK integer solver • GLPK has a very good integer solver. • Uses branch-and-bound + Gomory cut techniques • We will examine these techniques soon. • In this lecture, • Show how to solve …
Integer programming formulation examples - wmich.edu
formulate their problem as an integer program. Hint: first formulate the problem allowing non-linear constraints and then attempt to make all the constraints linear.
A Tutorial on Integer Programming - Mathematical and Statistical …
The purpose of this chapter is to show some interesting integer programming applications and to describe some of these solution techniques as well as possible pitfalls.
Integer Programming 9 - MIT - Massachusetts Institute of Technology
why many practitioners feel that the integer-programming model is one of the most important models in management science. Second, we consider basic approaches that have been …
Integer Programming. Exercises - OCW
Solve the problem using the 0-1 branch and bound algorithm, and determine which of the 6 components will be selected to be carried in the box so as to maximize the total value of the …
Solving Integer Programming with Branch-and-Bound Technique
We will use the linear programming relaxation to estimate the optimal solution of an integer programming. — The LP problem has no feasible solution, done; — The LP problem has an …
Integer Programming. Solutions - OCW
Integer Programming. Solutions 1. The optimal solutions to the IP problems, using the graphical solution: 1.1 x∗ 1 = 5, x ∗ 2 = 2, z ∗ = 13. 1.2 x∗ 1 = 14, x ∗ 2 = 2, z ∗ = 100. 2. The optimal solutions …
B6.3 Integer Programming - University of Oxford
What is integer programming? Introductory Examples fire station built considered location considered location considered location considered location fire station built …
Integer Programming - MIT - Massachusetts Institute of Technology
What are integer programming problems? §In many applications, integrality restrictions reflect natural indivisibilities of the problem under study. For example, when deciding how many nuclear …
Integer Programming - MIT - Massachusetts Institute of Technology
What are integer programming problems? Linear programming problems in which fractional solutions are not realistic. Mixed integer programs: when some, but not all, variables are …
Solving Real-Life Problems with Integer Programming - DTU
Linear Programming is a strong tool for many real-life optimization problems. We can solve large problems (thousands of constraints and millions of variables). We can solve problems fast (even …
Lecture 5 Integer Programming
1 Integer Programming Overview The Integer Programming problem (IP) is that of deciding whether there exists an integer solution to a given set of m rational inequalities on n variables. …
Integer programming (part 1)
polynomial-time algorithms for solving integer programs. Solving the associated convex relaxation (ignoring integrality constraints) results in an lower bound on the optimal value.
12 Integer Programming - Ohio University
The mathematical model for integer programming is the linear programming model (see Sec. 3.2) with the one additional restriction that the variables must have integer val-ues. If only some of …
11 Formulating and Solving Integer Programs - LINDO
methods for formulating and solving problems with integrality requirements are called integer programming. 11.1.1 Types of Variables One general classification is according to types of …
Introduction to integer programming - MIT OpenCourseWare
Integer Programming is a combinatorial optimization problem. Every instance of a combinatorial optimization problem has data, a method for determining which solutions are feasible, and an …
Integer Programming Formulation 1 Integer Programming Introduction
However, for real problems this approach will take practically inflnite amount of time. The solution procedures for IP’s are still under development. Two approaches are common: Branch and …
Linear Programming Notes X: Integer Programming
Integer programming problems are typically much harder to solve than linear programming problems and there are no fundamental theoretical results like duality or computational …
The Lagrangian Relaxation Method for Solving Integer Programming Problems
Solving Integer Programming Problems Marshall L. Fisher University of Pennsylvania, Philadelphia, Pennsylvania One of the most computationally useful ideas of the 1970s is the observation that …
Integer programming formulations - MIT OpenCourseWare
Write Nooz’s problem as an integer program. Modeling logical constraints that include only two binary variables. Step 1. Graph the feasible region as restricted to the two variables. Step 2. Add …
INTEGER LINEAR PROGRAMMING - INTRODUCTION - University …
GLPK integer solver • GLPK has a very good integer solver. • Uses branch-and-bound + Gomory cut techniques • We will examine these techniques soon. • In this lecture, • Show how to solve …
Integer programming formulation examples - wmich.edu
formulate their problem as an integer program. Hint: first formulate the problem allowing non-linear constraints and then attempt to make all the constraints linear.
