Linear Programming and Its Applications

ISBN-13: 9783540736707 / Angielski / Twarda / 2007 / 380 str.

H. a. Eiselt; C. -L Sandblom; Horst A. Eiselt

Opis

Based on earlier work by a variety of authors in the 1930s and 1940s, the simplex method for solving linear programming problems was developed in 1947 by the American mathematician George B. Dantzig. Helped by the computer revolution, it has been described by some as the overwhelmingly most significant mathematical development of the last century. Owing to the simplex method, linear programming (or linear optimization, as some would have it) is pervasive in modern society for the planning and control of activities that are constrained by the availability of resources such as manpower, raw materials, budgets, and time. The purpose of this book is to describe the field of linear programming. While we aim to be reasonably complete in our treatment, we have given emphasis to the modeling aspects of the field. Accordingly, a number of applications are provided, where we guide the reader through the interactive process of mathematically modeling a particular practical situation, analyzing the consequences of the model formulated, and then revising the model in light of the results from the analysis.

Recenzje

From the reviews:

"The aim of this book is to focus on the modelling aspects of Linear Programming (LP) ... . the book is a good self-contained resource that introduces readers to the vast area of LP and its applications. This book is suitable for a variety of audiences including undergraduate and postgraduate students, practitioners and scientists who are new or relatively new to LP. ... Overall ... a good introductory book to Linear Programming that combines formal presentations of concepts and techniques with illustrative examples." (D Silva, Journal of the Operational Research Society, Vol. 60, 2009)

"The book intends to present 'a unified treatment of linear programming' ... . the background of the authors, the kind of the presentation, and the choice of the considered applications indicates that it will primarily attract students and researchers who have interest in operations research and in economical problems. ... the main emphasis of the book is on models and applications." (Rembert Reemtsen, Zentralblatt MATH, Vol. 1154, 2009)

Spis treści

Linear Algebra.- Computational Complexity.- Applications.- The Simplex Method.- Duality.- Extensions of the Simplex Method.- Postoptimality Analyses.- Non-Simplex Based Solution Methods.- Problem Reformulations.- Multiobjective Programming.

Blurb

This book presents a unified treatment of linear programming. Without sacrificing mathematical rigor, the main emphasis of the book is on models and applications. The most important classes of problems are surveyed and presented by means of  mathematical formulations, followed by solution methods and a discussion of a variety of "what-if" scenarios. Non-simplex based solution methods and newer developments such as interior point methods are covered along with a variety of approaches that incorporate multiple objectives in the model.