## On the Significance of Solving Linear Programming Problems with Some Integer Variables Econometrica 28 No. 1 pp. 30–44, January 1960 [DANTZIG ON INTEGER PROGRAMMING]

Econometric Society, 1960. 1st Edition. FIRST EDITION IN ORIGINAL PAPER WRAPS OF DANTZIG’S PAPER ON COMPUTATIONAL COMPLEXITY. Dantzig’s work on the use of computational complexity aims to categorize problems by their solution difficulty is considered foundational (New Palgrave Dictionary of Economics).

George Bernard Dantzig (1914-2005) was an American mathematician who made important contributions to operations research, computer science, industrial engineering, economics, and statistics. In the paper offered here, “he [presents] a number of techniques for expressing various types of complex constraints as systems of linear inequalities in which some variables are constrained to be integers. The constraints include dichotomies, k-fold alternatives, selection from many pairs of regions, discrete variable problems, conditional constraints and finding a global minimum of a concave function. In particular, he showed that the fixed charge problem, the traveling salesman problem, the orthogonal Latin square problem and the problem of four-coloring a map could be expressed as mixed integer programs” (Karp, George Dantzig’s Impact on the Theory of Computation).

“Dantzig was one of the three founders of linear programming, a mathematical method used for the optimum allocation of scarce resources among competing activities… Dantzig discovered that many such allocation problems could be formulated as linear computer programs. He also devised an algorithm, known as the simplex method, which allowed these programs to be performed on a large scale and applied to real-world problems” (Origins of Cyberspace, 92).

Note: We separately offer Dantzig’s “Programming of Interdependent Activities I & II – the first published description of his seminal ‘simplex’ method of linear programming. Item #1296

CONDITION & DETAILS: Complete first edition in original wrappers. 4to. 250 x 175mm. Slight sunning at spine, otherwise fine. Clean and bright throughout.

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Price:
$325.00
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