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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BOOK REVIEW - IIE Transactions 27(6):820, December 1995.
(Reproduced with the permission of Chapman & Hall, 2-6 Boundary Row, London SE1 8HN, UK and Institute of Industrial Engineers, 25 Technology Park - Atlanta, Norcross, GA 30092)

With the large number of linear programming books already in print, one wonders what a new book can add to the existing resources. Therefore the criteria used to evaluate this book were whether it added to the existing literature, how easily it read, how easily could it be used, and how did it integrate the concepts of interior point methods into the general discussion. Based on these criteria the book was a pleasant surprise.

The book consists of three distinct parts. Part I is a classical overview and development of linear programming (LP). The authors do not plow any new ground here and do not attempt anything that is pedagogically daring. However, their writing style and use of examples are very good. In particular, the authors are to be lauded for devoting a whole chapter to the modeling process. This is one of the most important aspects of mathematical programming, yet is often overlooked or given only cursory treatment in most texts. The authors also do a good job of leading the reader through the foundations of the simplex method so that an understanding of the concepts is developed before the nuts and bolts of the method are discussed. This is important since it is the understanding that is desired, not the ability to do the simplex method by hand. Part I also includes a section on alternative methods for LP in which the ellipsoid method, the affine method, and the projective method are discussed. This Chapter was slightly disappointing in that it did not truly integrate concepts with the rest of the chapters. But this is true of every LP book on the market. The authors do make a wise choice in presenting the affine method in detail instead of the projective method but fail to note that the affine method has not, as of yet, been shown to be polynomial. The exercises for this section are somewhat limited as well. Part I concludes with one of the highlights and strengths of this text, which is a chapter on applications of LP. This chapter discusses a variety of different, interesting, and entertaining applications such as pattern classification, cluster analysis, and neural network design. It is well written and gives excellent insight into the flexibility and power of LP.

The second part of the book deals with network and integer models. Again, the authors' presentation is classical in nature, but well done. Part II starts with the introduction of networks and the development of the network simplex method. As before, emphasis is on conceptual understanding, not just computational development. After establishing the network simplex method, the transportation and assignment methods are discussed. These, however, are the only network models presented. A cursory treatment of integer programming is presented next in which the classic concepts of branch and bound and implicit enumeration are presented. Another highlight of the text concludes this part. This is a chapter devoted to heuristic programming. This is an area that has grown considerably over the last decade and deserves more recognition and treatment than it has received in texts thus far. The authors do an excellent job of presenting basic types of heuristics, their usefulness, their applications, and the concept of metaheuristics. The summaries and observations for genetic algorithms, simulated annealing, and tabu search give the reader a good feel for these methods and their limitations.

The third part of this text is probably what sets it apart from other texts. This part deals with multiobjective optimization. It is thorough, yet easily accessible and discusses in detail one of the newer approaches in the field, the multiplex method. All aspects of the method are discussed including duality results and several variants of the method are also presented. In addition, examples and a discussion of modeling and formulation issues are given.

In summary, this is a well written text that can be used in three basic ways. The first is to use Part I of the text as an undergraduate course on LP. The second would be to use Part I and sections of Part II for an advanced course on LP. Lastly, the third would be to use Part III for a course on multiobjective optimization. The highlights of the text are the chapters on modeling, LP applications and heuristic programming, and Part III of the text dealing with the multiplex method. The strengths of the text are its conceptual developments and emphasis on understanding of the material. This is a book that is worth consideration as a class text and that would make a nice library edition.

Cerry M. Klein, Department of Industrial Engineering, University of Missouri, Columbia, MO 65203.

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