Author: Marcos Singer Publisher: Routledge ISBN: 1351032127 Category : Business & Economics Languages : en Pages : 400
Book Description
This book takes a unique approach to linear optimization by focusing on the underlying principles and business applications of a topic more often taught from a mathematical and computational perspective. By shifting the perspective away from heavy math, students learn how optimization can be used to drive decision making in real world business settings. The book does not shy away from the theory underlying linear optimization but rather focuses on ensuring students understand the logic without getting caught up in proving theorems. Plenty of examples, applications and case studies are included to help bridge the gap between the theory and the way it plays out in practice. The author has also included several Excel spreadsheets, showing worked-out models of linear optimization that have been used to drive decisions ranging from configuring a police force to purchasing crude oil and media planning. How can the routes and pricing structures of airlines be optimized? How much should be invested in the prevention and punishment of crimes? These are everyday problems that can be solved using linear optimization, and this book shows students just how to do that. It will prove a useful, math-free resource for all students of management science and operations research.
Author: Glenn Hurlbert Publisher: Springer Science & Business Media ISBN: 0387791485 Category : Mathematics Languages : en Pages : 279
Book Description
The Subject A little explanation is in order for our choice of the title Linear Opti- 1 mization (and corresponding terminology) for what has traditionally been called Linear Programming.Theword programming in this context can be confusing and/or misleading to students. Linear programming problems are referred to as optimization problems but the general term linear p- gramming remains. This can cause people unfamiliar with the subject to think that it is about programming in the sense of writing computer code. It isn’t. This workbook is about the beautiful mathematics underlying the ideas of optimizing linear functions subject to linear constraints and the algorithms to solve such problems. In particular, much of what we d- cuss is the mathematics of Simplex Algorithm for solving such problems, developed by George Dantzig in the late 1940s. The word program in linear programming is a historical artifact. When Dantzig ?rstdevelopedthe Simplex Algorithm to solvewhat arenowcalled linear programming problems, his initial model was a class of resource - location problems to be solved for the U.S. Air Force. The decisions about theallocationswerecalled‘Programs’bytheAirForce,andhencetheterm.
Author: Josef Kallrath Publisher: Springer Nature ISBN: 3030732371 Category : Business & Economics Languages : en Pages : 653
Book Description
This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.
Author: Manfred Padberg Publisher: Springer Science & Business Media ISBN: 3662122731 Category : Mathematics Languages : en Pages : 521
Book Description
From the reviews: "Do you know M.Padberg's Linear Optimization and Extensions? [...] Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. Tell your students about it. [...] For those who strive for good exercises and case studies for LP this is an excellent volume." Acta Scientiarum Mathematicarum
Author: Marcos Singer Publisher: Routledge ISBN: 1351032135 Category : Business & Economics Languages : en Pages : 392
Book Description
This book takes a unique approach to linear optimization by focusing on the underlying principles and business applications of a topic more often taught from a mathematical and computational perspective. By shifting the perspective away from heavy math, students learn how optimization can be used to drive decision making in real world business settings. The book does not shy away from the theory underlying linear optimization but rather focuses on ensuring students understand the logic without getting caught up in proving theorems. Plenty of examples, applications and case studies are included to help bridge the gap between the theory and the way it plays out in practice. The author has also included several Excel spreadsheets, showing worked-out models of linear optimization that have been used to drive decisions ranging from configuring a police force to purchasing crude oil and media planning. How can the routes and pricing structures of airlines be optimized? How much should be invested in the prevention and punishment of crimes? These are everyday problems that can be solved using linear optimization, and this book shows students just how to do that. It will prove a useful, math-free resource for all students of management science and operations research.
Author: Richard Kipp Martin Publisher: Springer Science & Business Media ISBN: 1461549752 Category : Business & Economics Languages : en Pages : 739
Book Description
This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.
Author: Miroslav Fiedler Publisher: Springer Science & Business Media ISBN: 0387326987 Category : Mathematics Languages : en Pages : 222
Book Description
Linear programming has attracted the interest of mathematicians since World War II when the first computers were constructed. Early attempts to apply linear programming methods practical problems failed, in part because of the inexactness of the data used to create the models. This book presents a comprehensive treatment of linear optimization with inexact data, summarizing existing results and presenting new ones within a unifying framework.
Author: Robert J Vanderbei Publisher: Springer Science & Business Media ISBN: 1461476305 Category : Business & Economics Languages : en Pages : 420
Book Description
This Fourth Edition introduces the latest theory and applications in optimization. It emphasizes constrained optimization, beginning with a substantial treatment of linear programming and then proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. Readers will discover a host of practical business applications as well as non-business applications. Topics are clearly developed with many numerical examples worked out in detail. Specific examples and concrete algorithms precede more abstract topics. With its focus on solving practical problems, the book features free C programs to implement the major algorithms covered, including the two-phase simplex method, primal-dual simplex method, path-following interior-point method, and homogeneous self-dual methods. In addition, the author provides online JAVA applets that illustrate various pivot rules and variants of the simplex method, both for linear programming and for network flows. These C programs and JAVA tools can be found on the book's website. The website also includes new online instructional tools and exercises.
Author: Cornelis Roos Publisher: Springer Science & Business Media ISBN: 0387263799 Category : Mathematics Languages : en Pages : 501
Book Description
The era of interior point methods (IPMs) was initiated by N. Karmarkar’s 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.
Author: Jiri Matousek Publisher: Springer Science & Business Media ISBN: 3540307176 Category : Mathematics Languages : en Pages : 230
Book Description
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".
Author: Marcos Singer
Author: Glenn Hurlbert
Author: Josef Kallrath
Author: Manfred Padberg
Author: Marcos Singer
Author: Richard Kipp Martin
Author: Miroslav Fiedler
Author: Robert J Vanderbei
Author: Cornelis Roos
Author: Jiri Matousek