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Название: Linear Programming: 1: Introduction (v. 1)
Авторы: Dantzig G., Thapa M.
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.