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Maximizing subject to constraints, that is, making use of scarce resources, is the central theme of economics. But students of economics are often taught the mathematics of optimization as a branch of mathematics, and its economics application follow separately.This book is aimed for undergraduate students in economics, engineering, operations research, or other disciplines dealing with a branch of optimization theory: linear and integer programming. It supports a variety of teaching and learning and integrates the use of spreadsheets with instructions for Microsoft Excel.
Book Synopsis Linear and Integer Programming: with Excel Examples by : Fernando A. Boeira
Download or read book Linear and Integer Programming: with Excel Examples written by Fernando A. Boeira and published by . This book was released on 2015-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximizing subject to constraints, that is, making use of scarce resources, is the central theme of economics. But students of economics are often taught the mathematics of optimization as a branch of mathematics, and its economics application follow separately.This book is aimed for undergraduate students in economics, engineering, operations research, or other disciplines dealing with a branch of optimization theory: linear and integer programming. It supports a variety of teaching and learning and integrates the use of spreadsheets with instructions for Microsoft Excel.
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.
Book Synopsis Applied Integer Programming by : Der-San Chen
Download or read book Applied Integer Programming written by Der-San Chen and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis An Introduction to Linear Programming and Game Theory by : Paul R. Thie
Download or read book An Introduction to Linear Programming and Game Theory written by Paul R. Thie and published by John Wiley & Sons. This book was released on 2011-09-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
"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."
Book Synopsis Linear and Integer Programming by : Gerard Sierksma
Download or read book Linear and Integer Programming written by Gerard Sierksma and published by CRC Press. This book was released on 2001-11-01 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Since the late 1940s, linear programming models have been used for many different purposes. Airline companies apply these models to optimize their use of planes and staff. NASA has been using them for years to optimize their use of limited resources. Oil companies use them to optimize their refinery operations. Small and medium-sized businesses use linear programming to solve a huge variety of problems, often involving resource allocation. In my study, a typical product-mix problem in a manufacturing system producing two products (each product consists of two sub-assemblies) is solved for ist optimal solution through the use of the latest versions of MATLAB having the command simlp, which is very much like linprog. As analysts, we try to find a good enough solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the product-mix optimization problem and bring the problem into a form ready to call MATLAB’s simlp command. The objective of this study is to find the best product mix that maximizes profit. The graph obtained using MATLAB commands, give the shaded area enclosed by the constraints called the feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profit to find the corner of the feasible region which yield the highest profit. This corner can be found out at the farthest line of equal profit, which still touches the feasible region. The most critical part is the sensitivity analysis, using Excel Solver, and Parametric Analysis, using computer software, which allows us to study the effect on optimal solution due to discrete and continuous change in parameters of the LP model including to identify bottlenecks. We have examined other options like product outsourcing, one-time cost, cross training of one operator, manufacturing of hypothetical third product on under-utilized machines and optimal sequencing of jobs on machines.
Book Synopsis Strategic allocation of resources using linear programming model with parametric analysis: in MATLAB and Excel Solver by : Dinesh Gupta
Download or read book Strategic allocation of resources using linear programming model with parametric analysis: in MATLAB and Excel Solver written by Dinesh Gupta and published by diplom.de. This book was released on 2014-05-01 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the late 1940s, linear programming models have been used for many different purposes. Airline companies apply these models to optimize their use of planes and staff. NASA has been using them for years to optimize their use of limited resources. Oil companies use them to optimize their refinery operations. Small and medium-sized businesses use linear programming to solve a huge variety of problems, often involving resource allocation. In my study, a typical product-mix problem in a manufacturing system producing two products (each product consists of two sub-assemblies) is solved for ist optimal solution through the use of the latest versions of MATLAB having the command simlp, which is very much like linprog. As analysts, we try to find a good enough solution for the decision maker to make a final decision. Our attempt is to give the mathematical description of the product-mix optimization problem and bring the problem into a form ready to call MATLAB’s simlp command. The objective of this study is to find the best product mix that maximizes profit. The graph obtained using MATLAB commands, give the shaded area enclosed by the constraints called the feasible region, which is the set of points satisfying all the constraints. To find the optimal solution we look at the lines of equal profit to find the corner of the feasible region which yield the highest profit. This corner can be found out at the farthest line of equal profit, which still touches the feasible region. The most critical part is the sensitivity analysis, using Excel Solver, and Parametric Analysis, using computer software, which allows us to study the effect on optimal solution due to discrete and continuous change in parameters of the LP model including to identify bottlenecks. We have examined other options like product outsourcing, one-time cost, cross training of one operator, manufacturing of hypothetical third product on under-utilized machines and optimal sequencing of jobs on machines.
This book is primarily intended for undergraduate and postgraduate students of statistics, mathematics, operations research, and engineering. It provides the basic concepts and methods of linear and integer linear programming. The text begins with an introduction containing the mathematical background to the subject matter, and goes on to discuss advancements the field. Formulations of various problems in diverse fields in linear and integer programming formats are also presented here. The book’s presentation of the solution of various numerical problems makes the subject matter and the methods detailed in the text more lucid and easier to comprehend.
Book Synopsis Linear and Integer Programming by : Abdul Bari
Download or read book Linear and Integer Programming written by Abdul Bari and published by Cambridge Scholars Publishing. This book was released on 2019-10-25 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily intended for undergraduate and postgraduate students of statistics, mathematics, operations research, and engineering. It provides the basic concepts and methods of linear and integer linear programming. The text begins with an introduction containing the mathematical background to the subject matter, and goes on to discuss advancements the field. Formulations of various problems in diverse fields in linear and integer programming formats are also presented here. The book’s presentation of the solution of various numerical problems makes the subject matter and the methods detailed in the text more lucid and easier to comprehend.
Reflects the latest applied research and features state-of-the-art software for building and solving spreadsheet optimization models Thoroughly updated to reflect the latest topical and technical advances in the field, Optimization Modeling with Spreadsheets, Second Edition continues to focus on solving real-world optimization problems through the creation of mathematical models and the use of spreadsheets to represent and analyze those models. Developed and extensively classroom-tested by the author, the book features a systematic approach that equips readers with the skills to apply optimization tools effectively without the need to rely on specialized algorithms. This new edition uses the powerful software package Risk Solver Platform (RSP) for optimization, including its Evolutionary Solver, which employs many recently developed ideas for heuristic programming. The author provides expanded coverage of integer programming and discusses linear and nonlinear programming using a systematic approach that emphasizes the use of spreadsheet-based optimization tools. The Second Edition also features: Classifications for the various problem types, providing the reader with a broad framework for building and recognizing optimization models Network models that allow for a more general form of mass balance A systematic introduction to Data Envelopment Analysis (DEA) The identification of qualitative patterns in order to meaningfully interpret linear programming solutions An introduction to stochastic programming and the use of RSP to solve problems of this type Additional examples, exercises, and cases have been included throughout, allowing readers to test their comprehension of the material. In addition, a related website features Microsoft Office® Excel files to accompany the figures and data sets in the book. With its accessible and comprehensive presentation, Optimization Modeling with Spreadsheets, Second Edition is an excellent book for courses on deterministic models, optimization, and spreadsheet modeling at the upper-undergraduate and graduate levels. The book can also serve as a reference for researchers, practitioners, and consultants working in business, engineering, operations research, and management science.
Book Synopsis Optimization Modeling with Spreadsheets by : Kenneth R. Baker
Download or read book Optimization Modeling with Spreadsheets written by Kenneth R. Baker and published by John Wiley & Sons. This book was released on 2012-01-10 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflects the latest applied research and features state-of-the-art software for building and solving spreadsheet optimization models Thoroughly updated to reflect the latest topical and technical advances in the field, Optimization Modeling with Spreadsheets, Second Edition continues to focus on solving real-world optimization problems through the creation of mathematical models and the use of spreadsheets to represent and analyze those models. Developed and extensively classroom-tested by the author, the book features a systematic approach that equips readers with the skills to apply optimization tools effectively without the need to rely on specialized algorithms. This new edition uses the powerful software package Risk Solver Platform (RSP) for optimization, including its Evolutionary Solver, which employs many recently developed ideas for heuristic programming. The author provides expanded coverage of integer programming and discusses linear and nonlinear programming using a systematic approach that emphasizes the use of spreadsheet-based optimization tools. The Second Edition also features: Classifications for the various problem types, providing the reader with a broad framework for building and recognizing optimization models Network models that allow for a more general form of mass balance A systematic introduction to Data Envelopment Analysis (DEA) The identification of qualitative patterns in order to meaningfully interpret linear programming solutions An introduction to stochastic programming and the use of RSP to solve problems of this type Additional examples, exercises, and cases have been included throughout, allowing readers to test their comprehension of the material. In addition, a related website features Microsoft Office® Excel files to accompany the figures and data sets in the book. With its accessible and comprehensive presentation, Optimization Modeling with Spreadsheets, Second Edition is an excellent book for courses on deterministic models, optimization, and spreadsheet modeling at the upper-undergraduate and graduate levels. The book can also serve as a reference for researchers, practitioners, and consultants working in business, engineering, operations research, and management science.
This book presents the state-of-the-art methods in Linear Integer Programming, including some new algorithms and heuristic methods developed by the authors in recent years. Topics as Characteristic equation (CE), application of CE to bi-objective and multi-objective problems, Binary integer problems, Mixed-integer models, Knapsack models, Complexity reduction, Feasible-space reduction, Random search, Connected graph are also treated.
Book Synopsis Linear Integer Programming by : Elias Munapo
Download or read book Linear Integer Programming written by Elias Munapo and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art methods in Linear Integer Programming, including some new algorithms and heuristic methods developed by the authors in recent years. Topics as Characteristic equation (CE), application of CE to bi-objective and multi-objective problems, Binary integer problems, Mixed-integer models, Knapsack models, Complexity reduction, Feasible-space reduction, Random search, Connected graph are also treated.
Book Synopsis Integer Programming by : Harvey M. Salkin
Download or read book Integer Programming written by Harvey M. Salkin and published by Addison Wesley Publishing Company. This book was released on 1975 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
This unique reference/text details the theoretical and practical aspects of linear and integer programming - covering a wide range of subjects, including duality, optimality criteria, sensitivity analysis, and numerous solution techniques for linear programming problems. Requiring only an elementary knowledge of set theory, trigonometry, and calculus, Linear and Integer Programming reflects both the problem-analyzing and problem-solving abilities of linear and integer programming ... presents the more rigorous mathematical material in such a way that it can be easily skipped without disturbing the readability of the text ... contains important pedagogical features such as a user-friendly, IBM-compatible computer software package for solving linear-programming problems, numerous case studies, fully worked examples, helpful end-of-chapter exercises, the answers to selected problems, key literature citations, and over 1375 equations, drawings, and tables ... and more. Linear and Integer programming is a fundamental reference for applied mathematicians, operations researchers, computer scientists, economists, and industrial engineers, as well as an ideal text for upper-level undergraduate and graduate students in this disciplines.
Book Synopsis Linear and Integer Programming by : Gerard Sierksma
Download or read book Linear and Integer Programming written by Gerard Sierksma and published by CRC Press. This book was released on 1996 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique reference/text details the theoretical and practical aspects of linear and integer programming - covering a wide range of subjects, including duality, optimality criteria, sensitivity analysis, and numerous solution techniques for linear programming problems. Requiring only an elementary knowledge of set theory, trigonometry, and calculus, Linear and Integer Programming reflects both the problem-analyzing and problem-solving abilities of linear and integer programming ... presents the more rigorous mathematical material in such a way that it can be easily skipped without disturbing the readability of the text ... contains important pedagogical features such as a user-friendly, IBM-compatible computer software package for solving linear-programming problems, numerous case studies, fully worked examples, helpful end-of-chapter exercises, the answers to selected problems, key literature citations, and over 1375 equations, drawings, and tables ... and more. Linear and Integer programming is a fundamental reference for applied mathematicians, operations researchers, computer scientists, economists, and industrial engineers, as well as an ideal text for upper-level undergraduate and graduate students in this disciplines.
