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. George Dantzig is properly acclaimed as the "father of linear programming." Linear programming is a ...
The late George B. Dantzig , widely known as the father of linear programming, was a major influence in mathematics, operations research, and economics. As Professor Emeritus at Stanford University, he continued his decades of research on linear programming and related subjects. Dantzig was awarded eight honorary doctorates, the National Medal of Science, and the John von Neumann Theory Prize from the Institute for Operations Research and the Management Sciences. The 24 chapters of this volume highlight the amazing breadth and enduring influence of Dantzig's research. Short, non-technical summaries at the opening of each major section introduce a specific research area and discuss the current significance of Dantzig's work in that field. Among the topics covered are mathematical statistics, the Simplex Method of linear programming, economic modeling, network optimization, and nonlinear programming. The book also includes a complete bibliography of Dantzig's writings.
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.
For example, parallel processors may make it possible to come to better grips with the fundamental problems of planning, scheduling, design, and control of complex systems such as the economy, an industrial enterprise, an energy system, a water-resource system, military models for planning-and-control, decisions about investment, innovation, employment, and health-delivery systems."
Encompassing all the major topics students will encounter in courses on the subject, the authors teach both the underlying mathematical foundations and how these ideas are implemented in practice. They illustrate all the concepts with both worked examples and plenty of exercises, and, in addition, provide software so that students can try out numerical methods and so 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 option . The new version of Formula One, when ready, will be posted on WWW.
Today we know that before 1947 that four isolated papers had been published on special cases of the linear programming problem by Fourier (1824) , de la Vallʹee Poussin (1911) , Kantorovich (1939)  and Hitchcock (1941) . All except Kantorovich's paper proposed as a solution method descent along the outside edges of the polyhedral set which is the way we describe the simplex method today. There is no evidence that these papers had any influence on each other. Evidently the sparked zero interest on the part of other mathematicians and were unknown to me when I first proposed the simplex method. As we shall see the simplex algorithm evolved from a very different geometry, one in which it appeared to be very efficient."
The paper is a review of research done primarily at IIASA. The problem of finding the optimal policy for controlling the spruce budworm -- an insect whose outbreaks from time to time do great damage to the fir forests of New Brunswick, Canada -- represents a rare opportunity to develop and to successfully apply the methodology of optimization. The two interacting populations, the tree and the insect, constitute about the simplest ecosystem of practical importance. A very detailed computer 'simulation' model is used to evaluate and to compare proposed policies regarding when to apply insecticides and when to cut down trees. The model is considered by biologists to be sufficiently representative that its simulation on the computer can be viewed as one way to bring the real world into the 'laboratory'. The effectiveness of different policies can then be determined by trying them out on the simulation model. In this paper the authors discuss how the simulator can be supplemented with optimization methods to determine an optimal policy, in particular how a Markov model is appropriate. (Modified author abstract).