Linear Optimization The Simplex Workbook

Hurlbert, Glenn

ISBN 10: 0387791477 / ISBN 13: 9780387791470

Edité par Springer New York, 2009

A propos de cet article

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Détails bibliographiques

• Titre: Linear Optimization The Simplex Workbook
• Éditeur: Springer New York
• Date de parution: 2009
• Langue: anglais
• ISBN à 10 chiffres: 0387791477
• ISBN à 13 chiffres: 9780387791470
• Reliure: Couverture rigide
• État de l'article: Acceptable

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

* Uses the "modified Moore method" approach in which examples and proof opportunities are worked into the text in order to encourage students to develop some of the content through their own examples and arguments while they are reading the text * Concentrates on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them * The material progresses at a gentle and inviting pace * Ample examples and exercises are included This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment allows the use of the "modified Moore method" approach by working examples and proof opportunities into the text in order to encourage students to develop some of the content through their own experiments and arguments while reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them. In particular, the author uses the Simplex Algorithm to motivate these concepts. The text progresses at a gentle and inviting pace. The presentation is driven by numerous examples and illustrations. Ample exercises are provided at the end of each chapter for mastering the material. Opportunities for integrating Maple (or similar) software are included in the book. The author s own WebSim software can be freely downloaded from his website for pedagogical use. The teacher's version of the text contains solutions embedded within the text, rather than in an appendix. It also has extra material and suggestions for the teacher s benefit. Junior/senior level undergraduate students will benefit from the book, as will beginning graduate students. Future secondary school mathematics teachers will also find this book useful.