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Linear Programming: An Introduction With Applications (Second Edition), by Alan Sultan
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Linear programming is an extremely useful area of applied mathematics and is used on a daily basis by many industries. Most books on linear programming require an in depth knowledge of linear algebra in their exposition, making the subject matter inaccessible to the average reader. This second edition continues the presentation of the subject from a very elementary point of view, using as a foundation just a basic knowledge of high school algebra. The author manages to go into great depth with these minimal prerequisites, and helps the reader understand even some of the most subtle aspects of the subject. This is accomplished by weaving some of the more difficult ideas into informal proofs, with the result that the reader often doesn't even know he or she is reading very difficult material. Some formal proofs are included, and even these are often broken down into small steps to give them clarity. The reader who gets through the whole book will have a strong knowledge of linear programming and also a good basic knowledge of the related areas of game theory, integer programming, goal programming, network analysis, and dynamic programming. This book can be (and has been) used as a primary text for a course in linear programming and related topics. It can also be used for self study by the person who wants to know more about this fascinating and very useful subject. Exercises have been carefully chosen to illustrate a broad range of applications that occur in practice leaving the reader with an appreciation of the wide applicability of this subject to real life problems. Also, solutions to many of the exercises are given, making this an ideal book for the person who is studying this subject independently. A limited number of examination copies are available for instructors who wish to consider this book for adoption. Please contact the author at asultan956@aol.com to receive one.
- Sales Rank: #617800 in Books
- Published on: 2011-07-12
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x 1.49" w x 7.00" l, 2.48 pounds
- Binding: Paperback
- 660 pages
About the Author
Alan Sultan is a professor of mathematics at Queens College of the City University of New York. He has authored and co-authored numerous research and expository articles and is the primary author of the recently published, "The Mathematics That Every Secondary Math Teacher Needs to Know". and "A Primer on Real Analysis." He is also a recipient of the Queens College Presidential Teaching Award, as well the Key Club Award for Excellence in Teaching. His greatest joy is trying to get people to enjoy applied mathematics as much as he does by making it accessible to a wider audience.
Most helpful customer reviews
10 of 10 people found the following review helpful.
Excellent guide to linear programming
By jpmath
A department oversight meant that the book we used to use for linear programming wasn't ordered before the beginning of the semester, so I had the opportunity to choose another book. I went with this one, supplementing it sometimes with Introduction to Linear Optimization (Athena Scientific Series in Optimization and Neural Computation, 6) (which, I learned after receiving it, is a graduate-level textbook). I was somewhat nervous, since I had never heard of the publisher before, but this is in fact a second edition of a book that used to be published by Academic Press, now a subsidiary of Elsevier. I don't regret my decision at all.
In the course of one semester, I was able to cover chapters 1-6 and 10, which include not only geometry and the simplex algorithm (along with a proof of correctness and termination) but duality theory, sensitivity analysis, and the basics of integer programming. This approach is more theoretical than applied, and made for an excellent overview of linear programming. I usually have trouble covering what the textbooks say can be done in one semester, so other instructors should be able to cover a lot more than I did. (On the other hand, I had a small class of smart math majors, so maybe not.)
The book relies heavily on the compact simplex tableau, rather than the extended simplex tableau. I am not sure whether there is any theoretical or pedagogical advantage to one over the other, aside from the fact that the compact tableau is so much shorter. I taught the extended tableau first myself, transitioning to the compact tableau; this text does them in reverse. The explanation of the compact tableau is rigorous nonetheless; the main difference is that, after having accustomed herself to the compact tableau, the student may find the extended tableau more of a sideshow curiosity. I suspect that I will follow the author's approach next time, or perhaps even skip the extended tableau completely.
Many of the proofs look superficially to be done "by example", especially in comparison to texts that present every idea using complicated notation. In fact, most proofs in this book are both rigorous and, more importantly for me, readable by students averse to awful notation. I used them to write more general explanations that the students followed. For the most crucial matter, however, the author has clearly invested time and thought. Chapter 4 provides a well-organized, user-friendly approach to the theory of the simplex algorithm, including correctness, termination, degeneracy, and Bland's rule. It does shirks neither generality nor notation, but argues from the compact tableau, which the author established rigorously at an earlier point in the text. I was quite pleased!
This text can also prove useful to researchers who need to learn a little bit of linear programming for their own projects. I'm in that category, which is one reason I took the class this semester. It has proven invaluable.
As for the book itself: though it is an inexpensive paperback, the paper and the binding held up very well over the semester, surviving a water stain in my bag and abuse from my four year-old daughter's pen. It was printed in the USA, and doesn't look as if it will fall apart anytime soon. I work in a poor part of the country, so this cost/quality benefit is a major consideration; hardback books from many of the big companies fall apart quicker than this!
The author's email appears in the preface, with an invitation for comments. I contacted him several times over the semester with questions, typos, and comments, and he was both responsive and helpful.
The book does not cover computational complexity, interior point methods, or the criss-cross algorithm, so the reader who wants that material should look elsewhere. I'm pretty sure that interior-point methods and the criss-cross algorithm are nonstandard at the undergraduate level, and perhaps complexity is, too, but I care enough about computational complexity that I taught it, using the other text I cited above. The students had no problem following the argument, so Sultan's text does a good job preparing the students for those ideas.
The exercises are fairly easy, though non-trivial. Some contained typographical errors, but Sultan has told me he will correct them in an upcoming edition.
Different texts define a "standard" linear program differently. Sultan defines it this way: "Maximize u subject to Ax=b." If you have a preference for one approach or the other, or if (like me) you want to supplement this book with another, keep that difference in mind.
A final observation. I have struggled for years to get students to read the textbook, even giving reading assignment and quizzes. It never worked in the past, but this semester's students read Sultan's book, told me they sometimes used it as a reference, and came to class with questions about the reading! Alan Sultan has written a book that students read and learn from. I will definitely use this text again, and recommend it highly.
9 of 9 people found the following review helpful.
The best book I've read on how to set-up & solve LP problems
By A Customer
Alan Sultan has done something great! He has taken a complex subject, and made it undestandable to the average person.
I've just started my graduate program in Industrial Engineering, and need a good primer on LP problem function. My background in Comp.Sci. did not prepare me for the study of I.E. I needed a good resource to explain the fundamentals such that they could be quicky and easily comprehended.
Mr. Sultan's text provides a wonderful resource which helps me 'dechiper' my graduate level texts! Way to go, Alan!!
9 of 9 people found the following review helpful.
Excellent first book on LP
By sp
This book (the paperback 2nd edition) provides a very simple and very well written introduction to linear programming; In fact, I cannot imagine anyone
writing a simpler treatment without sacrificing rigor. A college freshman could easily
read this book on his/her own and learn the basic techniques. Calculus is not required...only a background in pre-calculus and
advanced high-school algebra. This book introduces LP by way of the "corner point theorem"
and this method is very effective in teaching the fundamental idea of LP. Beware that this book does not use
Linear Algebra and is based on the simplex tableau. However, this is the preferred approach for the beginner.
The reader interested in taking the next step may consult the following intermediate books that all emphasize linear algebra:
1. Solow, Linear Programming. This is an intermediate book that assumes knowledge of basic linear algebra but still
attempts to review all background material. Interestingly this book also has a generic chapter on how to construct
mathematical proofs. It then goes on to use these methods in the remainder of the text to prove Theorems and Lemmas related to
LP. Overall this book
is absolutely fantastic and not as well know as it should be. (Dover publications is re-releasing this book later in 2014)
2. Bertsimas, Introduction to Linear Optimization. Very nice modern treatment that uses linear algebra and ideas from
convex geometry. Modern interior point methods are also covered. Senior level undergraduate level.
3. Matousek and Gartner, Understanding and Using Linear Programming. Nice modern linear algebra based treatment with also covers modern interior point
methods. The authors actually have a sense of humor and this is a good first book if you have a solid linear algebra background.
4. Hadley, Linear Programming. This oldie but goodie was written in the early 1960's and presents a solid geometric treatment that
covers all the required background linear algebra.
5. Kwon, Introduction to Linear Optimization. This is a new well-written short/compact treatment that emphasizes MATLAB.
After reading Sultan to get the main geometric idea of what is going on, I feel that the best way to
understand LP is by
utilizing linear algebra which all the books listed above do. In my opinion, the matrix
approach takes the mystery out of the simplex tableau.
I should also mention that Gilbert Strang has a nice chapter on LP in his
book Linear Algebra and its Applications, 3rd Edition.
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