Linear Programming: 1: Introduction (Springer Series in Operations Research and Financial Engineering) (v. 1) (Hardcover)

~ George B. Dantzig (Author), Mukund N. Thapa (Author) "Since the time it was first proposed by one of the authors (George B. Dantzig) in 1947 as a way for planners to set general..." (more)
Key Phrases: capacitated transportation problem, primal affine method, feasible canonical form, Simplex Method, Simplex Primal, Comprehensive Exam (more...)

Editorial Reviews

Product Description

This book provides a comprehensive introduction to linear programming which encompasses all the major topics students will encounter in courses on the subject. The authors aim to teach both the underlying mathematical foundations and how these ideas are implemented in practice. The book illustrates all the concepts with both worked examples and plenty of exercises. In addition, Windows software is provided with the book so that students can try out numerical methods using the examples and exercises and hone their skills in interpreting the results. As a result, this will make an ideal textbook for all those coming to the subject for the first time. Authors'note: A problem recently found with the software is due to a bug in Formula One, the third party commercial software package that was used for the development of the interface. It occurs when the date currency, etc. format is set to a non-United States version. Please try setting your computer date/currency option to the United States. The new version of Formula One, when ready, will be posted on WWW.

Product Details

• Hardcover: 435 pages
• Publisher: Springer; 1 edition (January 27, 1997)
• Language: English
• ISBN-10: 0387948333
• ISBN-13: 978-0387948331
• Product Dimensions: 9.3 x 7.1 x 1.3 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #1,187,599 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

6 of 6 people found the following review helpful:

5.0 out of 5 stars Clear and concise, March 18, 2008

By	Benjamin I. Triplett (Seattle, WA USA) - See all my reviews (REAL NAME)

I haven't seen this book for over a decade, but I do remember it helping me solve a problem way back when I was still an undergraduate. The summer after my junior year of university I was working at a steel foundry and they asked me to write a program for them that would solve their steel mixture problem in an optimal way. Their old software did this, but ran on a 286 PC and was slow and could not be ported to anything newer. I figured "no problem" and thought for sure that all this would involve was computing a few derivatives. A week into the problem, I found I was wrong and was quickly introduced to the world of linear programming.

I freaked out a little, and wasn't sure how to go about solving my problem. Strang mentions LP in his classic linear algebra book, but his exposition is very terse and entirely theoretical... entirely useless to a newbie needing to solve a real problem.

Then I found Dantzig's book. I was saved. I understood exactly what he was talking about and how everything worked. I was able to write a simplex based optimal solver for the steel formulation problem, which is simply the classic mixtures problem. The book also helped me with the optimal update solution for cases in which the chemistry of the first try was out of spec due to errors in estimates of the chemical compositions of the materials used in the initial charge.

My code was probably pure spaghetti, written in VBA no less using MS Access 97, but it worked very well. The old code on the 286 took around 30 seconds or longer to solve the problem, and my code running in VBA on a Pentium II solved the problem instantaneously. I owe my salvaged nerves to this book.