Linear Programming by Ignizio & Cavalier

by James P. Ignizio and Tom M. Cavalier
Prentice Hall International Series in Industrial and Systems Engineering
Prentice Hall, Englewood Cliffs, NJ, 666pp (1994).

ISBN 0-13-183757-5

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In this introductory text on linear programming, a thorough, up-to-date, and comprehensive summary of the philosophies and procedures used in the modeling, solution, and analysis of so-called linear programming problems is provided. The text is for the senior-level college student or for the first-year graduate student having some previous exposure to linear algebra -- and earlier versions (or selected portions) have been used in such courses over the past decade. An associated solutions manual is provided for all exercises and is available to those adopting the text for classroom use.

The text is divided into three parts. Part 1, consisting of Chapters 2 through 8, addresses linear programming in general -- emphasizing the development, presentation, and illustration (via numerous examples) of the fundamentals necessary to model, solve, and analyze linear programs. Although the coverage is relatively traditional, some very unique aspects should be noted. First, coverage is provided in Chapter 7 of recent results with regard to alternative methods to the simplex algorithm, in particular the affine scaling variants of the Karmarkar algorithm. Second, Chapters 8 deals with the use of linear programming in information technology -- particularly as a means to analyze large amounts of data. Topics covered include prediction/forecasting, pattern classification/pattern recognition, clustering analysis, input-output analysis, and even the design and training of neural networks -- all achieved by means of linear programming.

Part 2 addresses integer linear programming, including the network simplex method (Chapter 9), transportation and assignment problems (Chapter 10), and general integer programming methods (Chapter 11). In addition, the very important and all too often neglected area of heuristic programming is addressed in Chapter 12. Further, the coverage of heuristics in that chapter is extended to such currently popular heuristic methods as genetic algorithms, simulated annealing, and various related techniques that are -- as of late -- often associated with the field of artificial intelligence.

Finally, in Part 3, the topic of multiple objective optimization is addressed. This is accomplished by an original, unified approach to both modeling and solution -- the multiplex concept. Topics covered include various multiobjective philosophies, their models, and their solution and analysis via a single algorithm. Discussions and demonstrations are given to how such problems may be solved via conventional linear programming algorithms and software.

The text may be employed in a variety of ways, depending upon the needs/interests of the reader or the purpose of the associated course. For example, a one-term introductory course in linear programming might cover Chapters 1, 2, 3, 4, and 6 (omitting the starred sections) followed by Chapter 10 and selected topics from Chapters 8, 11, and 13. A more advanced course in linear programming might cover Chapter 1 and all of Part 1 (that is, Chapters 2 to 8) with additional topics selected from Chapters 11 and 12. A course emphasizing network and integer models might cover Chapters 1, 3, 4, and 6 (omitting the starred sections) followed by Part 2 (that is, Chapters 9 to 12). A course devoted solely to multiobjective models and methods might cover Chapter 1 and Part 3 (that is, Chapters 13 to 17). Finally, we advocate the use of group projects as a part of any course, and the use of various existing softwares for the solution of a variety of LP models (and the choice of software is left to the reader or course instructor). From experience, a combination of lectures, examples/exercises, projects, and computer implementation has -- we believe -- best served to reinforce the understanding and appreciation of both the power and limitations of the linear programming method.

In this text, the emphasis is to provide a basis for the understanding and appreciation of the truly remarkable power of the linear programming method. As such, emphasis is not placed on the computer implementation of the tools associated with the overall methodology. However, there now exist numerous, inexpensive, commercial linear programming packages that the instructor and/or student may wish to use to accompany the text. Although we certainly advocate such computational support, we would hope that the main emphasis is, and will be, that of the understanding of the fundamental concepts, theory, and solution methods that serve to comprise the linear programming method.

We would like to acknowledge the reviewers selected by Prentice Hall, Professors Wonjang Baek of Mississippi State University and Romesh Saigal of the University of Michigan for taking the time to evaluate the manuscript.

James P. Ignizio
Charlottesville, Virginia

Tom M. Cavalier
University Park, Pennsylvania

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