Linear Programming: An Introduction With Applications (Second Edition)

This text book served it's purpose perfectly, and was high quality enough to get through the school year in one piece.

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.

I am a retired PhD operations research analyst. I moved in with my daughter and she made me get rid of most of my books. [There was a space constraint on the number of books cases I was allowed.] My mind was going soft so I bought this book as a Christmas gift to myself. Wow, I wish I had this book as my introductory text to linear programming. Alan Sultan is clearly an educator; he writes to inform rather than impress. This book is clearly written with intuitive, easy-to-follow examples followed by proofs that don't break your mind, but are rigorous. The pattern of presentation is: an explanation of the type of problem to be solved; an example of a toy problem with two variables; a couple of more difficult examples; the mathematical proof in an easy to follow expository style; and, how to handle exceptions and special cases. I was taught in an old-school fashion by some of the founders of the field, which at times was difficult. Prof Sultan uses newer techniques that are easier to follow, more intuitive, and get the same results but faster (learning-wise). Dr. John

Wonderful book. There is so much to learn about linear optimization and this math books make you feel like you're in algebra 2 again.

I have no idea why I bought this book. I thought I read this would be a good textbook by which to begin learning optimization modeling and linear programming. I would definitely not rely on it, and if anyone wants to buy it from me for half price then contact me. It's in pristine condition as the professor just used PPT slides.

Really great text book to learn LP. What's even better that it also includes Integer programming, quadratic programming and dynamic programming. Really great book. Wish they published hardcover too.

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." Other books, like the one cited above, define it this way: "Minimize 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.

Good practice

I’ve had this textbook since the start of my semester and I’ve just come across some typos. They mis numbered the exercises.