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In real-world problems related to finance, business, and management, mathematicians and economists frequently encounter optimization problems. In this classic book, George Dantzig looks at a wealth of examples and develops linear programming methods for their solutions. He begins by introducing the basic theory of linear inequalities and describes the powerful simplex method used to solve them. Treatments of the price concept, the transportation problem, and matrix methods are also given, and key mathematical concepts such as the properties of convex sets and linear vector spaces are covered. ... Read more

Customer Reviews (2)

good to have but not to learn from
I disagree with the other reviewer.This is a textbook on linear programming and its extension written by George Dantzig the inventor of the simplex method.Even though the simplex method is still popular and useful there are other interesting algorithms that were dsicovered in the 1980s and 1990s that have theoretical and in some cases practical value.

In 1974 I was a graduate student in Operations Research ae Stanford and I took the three quarter mathematical programming course sequence.The first two quarters were taught by George Dantzig out of this book.George was a delightful person to talk to and probably a good thesis advisor and his stories about his graduate school days and the early years at RAND are delightful.However his lectures were disorganized and vague.I found it impossible to learn much from them and the book was not much help either as it too was vague, disjointed and not well organized.Better understanding of the basics of linear programming can be gotten from the fine general books on operations research such as the book by Hillier and Lieberman and the one by Wagner.

I do not know what is the best modern book on linear programming is.It should have good coverage of the simplex method and a lot of applications. Leontiff systems and other special structured programming problems that lead to modifications of the simplex method are covered in this book and should also be in the "ideal" linear progamming book.Integer programming and other special cases of problems with linear constraints should also be included along with alternative algorithms to the simplex method.

This book is more valuable for historic purposes, as it was Dantzig's first book and the first account of the simplex method by its inventor.

Review of Dantzig's book
This softbound newly reprinted edition is clear and light; considering the original version I knew back in 1970's was a thick, heavy hardbound.

The book is a compilation of several authors on linear programming, it includes a table explaining the genesis of linear programming and the programming code for computer calculation.

It is a rich and indispensable book for optimization problems.

... Read more

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Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method, interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory.Graduate students in the fields of operations research, industrial engineering, and applied mathematics will find this volume of particular interest. ... Read more

Customer Reviews (1)

interesting book
There is an example of piecewise linear convex problem which Iwas looking for. ... Read more

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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. ... Read more

Customer Reviews (1)

Clear and concise
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. ... Read more

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These two Studies comprise 28 papers dedicated to Professor George B. Dantzig on the occasion of his 70th birthday. They represent virtually every major topic in the field of mathematical programming: linear and nonlinear programming, discrete and continuous programming, conventional and large-scale programming, deterministic and stochastic programming, theory, applications, network optimization, and complementarity. ... Read more

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Chapters: Charles Sanders Peirce, George Dantzig, Herman Hollerith, W. Edwards Deming, Persi Diaconis, George Gallup, Edwin Thompson Jaynes, Richard Threlkeld Cox, Francis Amasa Walker, Nate Silver, Irving Fisher, Joseph Hilbe, E. Morton Jellinek, Frank Luntz, I. J. Good, Shlomo Sawilowsky, Edward Tufte, John Tukey, Walter A. Shewhart, Sewall Wright, Charles P. Neill, Simon Kuznets, Oscar Kempthorne, Wesley Clair Mitchell, Benjamin Peirce, Raymond Pearl, Alfred J. Lotka, Joseph L. Fleiss, Lloyd Shapley, George E. P. Box, Frederick Mosteller, Mir Masoom Ali, David A. Freedman, Paul Halmos, W. Allen Wallis, Abraham Wald, Rensis Likert, Jack Kiefer, Robert Groves, Harold Hotelling, Allyn Abbott Young, Stefan Ralescu, Solomon Kullback, Jerzy Neyman, William Sanders, Louis Israel Dublin, Donald Geman, Bradley Efron, James C. Hickman, Donald Rubin, James Goodnight, Stephen Stigler, Joseph C. G. Kennedy, John Wingate Thornton, David Blackwell, Howard Raiffa, Claude E. Robinson, Robert R. Sokal, Halbert L. Dunn, Jeff Sagarin, Allan Birnbaum, Erich Leo Lehmann, Gertrude Mary Cox, Darrell Huff, William Kruskal, Emmanuel Candès, Herbert Robbins, Gottfried E. Noether, Kenneth Massey, Otis Dudley Duncan, James Robins, Debabrata Basu, Jessica Utts, David Donoho, Emanuel Parzen, Kai Lai Chung, Leslie Kish, Warren Mitofsky, Carroll D. Wright, Thomas M. Cover, Howard B. Myers, Joseph Berkson, Samuel S. Wilks, William Fielding Ogburn, Gene V. Glass, Joseph Kruskal, D. Raghavarao, Churchill Eisenhart, Nan Laird, Walter L. Smith, Frank Wilcoxon, Richard M. Dudley, Leonard Porter Ayres, Acheson J. Duncan, George W. Snedecor, Stephen Fienberg, Jacob Wolfowitz, Leland Wilkinson, Leo Breiman, Harry V. Roberts, James Berger, William Gemmell Cochran, Wayne Fuller, K. C. Sreedharan Pillai, Leonard Jimmie Savage, Arnold Zellner, Quinn Mcnemar, Adrian Raftery, Mike Wissot, Edwin Bidwell Wilson, A. Ross Eckler, Jr., Raghu Raj Bahadur, Seymour Geisser, Larr...More: http://booksllc.net/?id=6117 ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 669 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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Kapitel: Cornelius Lanczos, Gene H. Golub, Friedrich Ludwig Bauer, George Dantzig, Eduard Stiefel, Hans Georg Bock, Roland Bulirsch, Richard Von Mises, Peter Lax, Lewis Fry Richardson, Stanley Osher, James H. Wilkinson, Tassilo Küpper, Ulrich Trottenberg, James Sethian, Olgierd Cecil Zienkiewicz, Heinz Rutishauser, Karl Hessenberg, Volker Strassen, Ivo Babuška, Leonid Witaljewitsch Kantorowitsch, Peter Henrici, Wolfgang Hackbusch, Germund Dahlquist, Ingrid Daubechies, Leonid Gendrichowitsch Chatschijan, Martin Hermann, Arnold Schönhage, Peter Deuflhard, Alfred Louis, Alston Scott Householder, Peter Shor, Nikolai Mitrofanowitsch Krylow, Wolfgang Dahmen, Sergei Konstantinowitsch Godunow, Hermann Heine Goldstine, Götz Alefeld, Walter Gautschi, Ramon E. Moore, Carl Adam Petri, Martin Wilhelm Kutta, Narendra Karmarkar, Uwe Zimmermann, Rudolf Zurmühl, Karl Zeller, Franco Brezzi, Manil Suri, Klaus Glashoff, Wallace Givens, William Kahan, Boris Grigorjewitsch Galjorkin, André-Louis Cholesky, Theodore Hill, John C. Butcher, Douglas Rayner Hartree, Isaac Jacob Schoenberg, Lester Randolph Ford Junior, Werner Romberg, Rupert Klein. Aus Wikipedia. Nicht dargestellt. Auszug: Lewis Fry Richardson, FRS (11 October 1881 - 30 September 1953) was an English mathematician, physicist, meteorologist, psychologist and pacifist who pioneered modern mathematical techniques of weather forecasting, and the application of similar techniques to studying the causes of wars and how to prevent them. He is also noted for his pioneering work on fractals and a method for solving a system of linear equations known as modified Richardson iteration. Lewis Fry Richardson was the youngest of seven children born to Catherine Fry (1838-1919) and David Richardson (1835-1913). They were a prosperous Quaker family, David Richardson running a successful tanning and leather manufacturing business. At age 12 he was sent to a Quaker boarding school, Bootham in York, where h...http://booksllc.net/?l=de ... Read more

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Chapters: Jim Henson, George Dantzig, Robert L. Forward, Valerie Solanas, Sergey Brin, Larry David, Connie Chung, William S. Donaldson, Juan Dixon, William Cameron Mccool, David Simon, Carly Fiorina, List of University of Maryland, College Park People, Robert M. Parker, Jr., Steny Hoyer, Saqib Ali, Stephen A. Kent, Vivek Kundra, Michael D. Griffin, George Pelecanos, Frank J. Tipler, David Orme-Johnson, Jayson Blair, Dominique Dawes, Gordon R. England, James S. Albus, Mark Rutland, David Mills, Joseph Tydings, Curley Byrd, Len Bias, Dianne Wiest, John Berry, Leonard T. Schroeder, Tom Davis, Joe Haldeman, Rosario Ferré, Rose Kushner, Andrew J. Moyer, Taylor Twellman, Dutch Ruppersberger, William Lacy Clay, Jr., Steve Blake, Don Lichterman, Lawrence Babits, Kiran Chetry, Gabe Cazares, Raymond Davis, Jr., Carl Bernstein, John Pappageorge, Andrew Sherman, Millard Tydings, David Banner, Kori Schake, James E. Hill, Colman Mccarthy, Boyd Petersen, Bonnie Bernstein, Andrew Sears, Trudy H. Clark, David Silverman, Dennis Cardoza, Renaldo Nehemiah, Munro Leaf, Joyce Hens Green, Robert C. Bonner, Russ Potts, Judith Resnik, Gale Pollock, Herbert A. Hauptman, Charlie Keller, Daniel Shanks, Kirsten Powers, Óscar Hahn, Desmond Armstrong, Carmine Isacco, Audrey Terras, Parren Mitchell, Don Cusic, James E. Rzepkowski, Elaine Marshall, Victor Ukpolo, Anies Baswedan, Galo Plaza, Marcia Talley, Craig Seymour, Brian O'neill, Paul S. Stull, Aaron Mcgruder, Alexander Butterfield, Howard Behrens, James M. Kelly, Gail H. Bates, Hamid Jafarkhani, Jen Adams, Ronald J. Meyer, Katie O'donnell, Rudi Vis, Kenneth Ulman, Roscoe S. Suddarth, Ed Snider, Ray O. Johnson, Maria Otero, Harry Hughes, Brian Reid, George B. Simler, Justin Ross, Charles Fefferman, David H. Holtzman, Julio Perillán, Matt Rees, Russell Earl Marker, Sam Kouvaris, Robert Zieger, Marina Harrison, Susan King, Sybil Moses, Patrick N. Hogan, Donald R. Delauter, John W. Derr, Paul W. Richards...More: http://booksllc.net/?id=1613271 ... Read more

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Chapters: List of Computer Scientists, George Dantzig, Ajay Kapur, Pranav Mistry, Peter Coad, Allan Alcorn, Helmuth Orthner, Fred W. Glover, Steven M. Lavalle. Source: Wikipedia. Pages: 53. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: This is a list of well-known computer scientists, people who do work in computer science, in particular researchers and authors. Some persons notable as programmers are included here because they work in research as well as program. A few of these people pre-date the invention of the digital computer; they are now regarded as computer scientists because their work can be seen as leading to the invention of the computer. Others are mathematicians whose work falls within what would now be called theoretical computer science, such as complexity theory and algorithmic information theory. ...More: http://booksllc.net/?id=6834 ... Read more

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Chapters: Milton Friedman, Mel Blanc, Frank Sinatra, Jack Kirby, George Dantzig, Marlon Brando, Frank Capra, Burt Lancaster, Cecil B. Demille, Willie Dixon, Henry Fonda, Eve Arden, Clara Bow, Steve Allen, Roy O. Disney, the Amazing Criswell, W. Mark Felt, Lucille Ball, Mary Astor, John Ritter, Harry Caray, Shelley Winters, Mel Tormé, Paul Frees, Stella Adler, Max Fleischer, John Phillips, Eddie Anderson, Janet Leigh, Phil Silvers, William Fawcett, Mel Ferrer, Red Buttons, Klaus Kinski, Mary Brian, Ethel Barrymore, Gene Barry, Brion James, Jeanette Nolan, Elfi Von Dassanowsky, Tom Wilson, Leo Gordon, Tommy Bond, Dale Evans, Michael Blodgett, E. Lynn Harris, William A. Seiter, Artie Ortego, Herschel Burke Gilbert, Gilda Gray, Andy Hallett, Ken Annakin, Billy Barty, Edwina Booth, Mrs. Leslie Carter, David Vanole, Leonard Schrader, Leonard Rosenman, Herbert G. Klein, Johnny Arthur, Richard Deacon, William Boyd, Earl Wild, Peter R. Hunt, Dean Jagger, August Coppola, Harry Carey, Niven Busch, Virginia Christine, Stafford Repp, Helen Forrest, Lillian Disney, George Louis Mcghee, Alan Reed, Jack Arnold, Bill Scott, Allen Funt, Alvy Moore, Stephen Elliott, Edward Dillon, David Brian, Robert Swink, Hardie Albright, Conrad Hilton, Jr., Nelson Gidding, Tim Mcintire, Arthur Franz, Otis Young, Lew Cody, James Burke, Bill Lancaster, Dorothy Vernon, D'urville Martin. Source: Wikipedia. Pages: 600. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: William Mark Felt, Sr. (August 17, 1913 December 18, 2008) was an agent of the United States Federal Bureau of Investigation who retired in 1973 as the Bureau's Associate Director. After denying his involvement with reporters Bob Woodward and Carl Bernstein for 30 years, Felt revealed himself on May 31, 2005, to be the Watergate scandal's whistleblower, "Deep Thro...More: http://booksllc.net/?id=1967935 ... Read more

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George Dantzig is widely regarded as the founder of this subject with his invention of the simplex algorithm in the 1940's. In this second volume, the theory of the items discussed in the first volume is expanded to include such additional advanced topics as variants of the simplex method; interior point methods, GUB, decomposition, integer programming, and game theory. Graduate students in the fields of operations research, industrial engineering and applied mathematics will thus find this volume of particular interest. ... Read more

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Chapters: George Dantzig. Source: Wikipedia. Pages: 180. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: George Bernard Dantzig (November 8, 1914 May 13, 2005) was an American mathematician, and the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford. Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and his work with linear programming, some years after it was initially invented by Soviet economist and mathematician Leonid Kantorovich. Dantzig is the real-life perpetrator of the tale of a student solving an unproven equation after mistaking it for homework (see "Biography" below), often thought to be an urban legend. George Dantzig was born in Portland, Oregon, and with his middle name "Bernard" named after the writer George Bernard Shaw. His father, Tobias Dantzig, was a Baltic German mathematician and his mother the French linguist Anja Ourisson. They had met during their study at the Sorbonne University in Paris, where Tobias studied with Henri Poincaré. They immigrated to the United States and settled in Portland, Oregon. Early in the 1920s the family moved over Baltimore to Washington. Anja Dantzig became a linguist at the Library of Congress, Dantzig senior became a math tutor at the University of Maryland, College Park, and George attended Powell Junior High School and Central High School. At highschool he was already fascinated by geometry, and this interest was further nurtured his father, by challenging him with complex geometry problems. George Dantzig earned bachelor's degrees in mathematics and physics from the University of Maryland in 1936, his master's degree in mathematics from the University of Michigan in 1938. After a two-year period at t...More: http://booksllc.net/?id=13111 ... Read more

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Chapters: George Dantzig, Archibald Hill, Anthony Stafford Beer, Frank Yates, Thomas L. Saaty, Jacques Drèze, Hugh Everett Iii, Russell L. Ackoff, Suresh P. Sethi, Frederick W. Lanchester, Patrick Blackett, Baron Blackett, Alvin E. Roth, Peter Whittle, Alan Pritsker, Conrad Hal Waddington, Robert E. Machol, Jay Wright Forrester, C. West Churchman, George E. Kimball, Anna Nagurney, Warren Weaver, Seymour Melman, R. Tyrrell Rockafellar, Narendra Karmarkar, Richard Karp, Leonid Kantorovich, Soulaymane Kachani, Henk G. Sol, Philip M. Morse, Roger J-b Wets, Barry Richmond, Peter Hammer, David S. Alberts, David B. Weinberger, Arnold Reisman, Merrill M. Flood, Paul Torgersen, Charles F. Goodeve, Michael Maltz, Stephen Warshall, Alfred Blumstein, Arnold Allen, John Little, Dănuţ Marcu, Thomas L. Magnanti, Guillermo Owen, Reuven Rubinstein, Paweł Wojciechowski, Ronald A. Howard, Albert Percival Rowe, John Sterman, Dan Grimaldi, Naum Z. Shor, Peter C. Fishburn, Takeshi Utsumi, David B. Hertz, Daniel Kleitman, J. Michael Harrison, Claude Lemaréchal, Owen Wansbrough-Jones, Paul Gray, Bernard Koopman, Robert J. Weber, Henk Tijms, Herbert Sichel, Stuart Dreyfus, William Gehrlein, Arthur Swersey. Source: Wikipedia. Pages: 291. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Jacques H. Drèze is a Belgian economist noted for his contributions to economic theory, econometrics, and economic policy as well as for his leadership in the economics profession. Drèze was the first President of the European Economic Association in 1986 and was the President of the Econometric Society in 1970. Jacques Drèze is also the father of five sons. One son is the economist, Jean Drèze, who is known for his work on poverty and hunger in India (some of which has been in collaboration with Amartya K. Sen); another son, Xavier...More: http://booksllc.net/?id=23145473 ... Read more

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Chapters: George Dantzig, Daniel Ellsberg, Henry H. Arnold, Zalmay Khalilzad, Arthur C. Brooks, Harry Markowitz, Benjamin Karney, Paul O'neill, Samuel Genensky, Seth Jones, Merrill M. Flood, William Kaufmann, Donald Wills Douglas, Sr., Anthony Russo, William Robert Graham, Michael D. Rich, Kevin N. Lewis, Cheryl Benard, Alain Enthoven, James Thomson, Melvin Dresher. Source: Wikipedia. Pages: 114. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt:General of the Air Force General of the Air Force Henry Harley "Hap" Arnold (June 25, 1886 January 15, 1950) was an American five-star general officer holding the grades of General of the Army and later General of the Air Force. He is the only officer to ever hold a five-star grade in two different U.S. military services. Arnold was an aviation pioneer and the Chief of the United States Army Air Corps (from 1938), the Commanding General of the U.S. Army Air Forces (from 1941 until 1945), and the only five-star General of the Air Force (starting in 1949). Instructed in flying by the Wright Brothers, Arnold was one of the first military pilots worldwide, and the second rated pilot in the history of the United States Air Force. He overcame a fear of flying that resulted from his experiences with early flight, oversaw the expansion of the Air Service during World War I, and became a protégé of Gen. Billy Mitchell, all of which at times nearly ended his aeronautical career. Arnold became a powerful advocate for creation of an independent Air Force and played a key role in the political struggles over it with the hierarchies of the United States Army and United States Navy. He rose to command the Army Air Forces immediately prior to U.S. entry into World War II and directed its expansion into the largest and most powerful Air Force in the world. An advoca...More: http://booksllc.net/?id=206221 ... Read more