## Programming of Interdependent Activities I [General Discussion] (Wood & Dantzig, pp. 193-200) AND Programming of Interdependent Activities II [Mathematical Model] (Dantzig, pp. 200-212) in Econometrica 17 Nos 3-4, July-October 1949 [ORIGINAL WRAPPERS: 1st DANTZIG PAPERS ON LINEAR PROGRAMMING]

FIRST EDITION IN ORIGINAL PAPER WRAPPERS OF DANTZIG’S FIRST PUBLISHED DESCRIPTION (in two papers) OF HIS ‘SIMPLEX’ METHOD OF LINEAR PROGRAMMING, one of the most important algorithms of the 20th century. Note that while the 1951 publication of a paper by the National Bureau of Standards is sometimes cited as first published description, Dantzig himself cites the paper offered here as "The first formal paper about the new field of linear programming appeared in Econometrica July - October 1949" (Quote from George Dantzig, iiasa, 4).

“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).

Dantzig’s simplex algorithm allowed for the optimization of models of organizational structures specified with a linear objective function and linear inequality constraints. “An algorithm of tremendous power,” the success of the simplex method led to a vast array of specializations and generalizations that have dominated practical operations research for half a century (ibid).

Part I of the paper – the ‘General Discussion’ – “is concerned with improved techniques of program planning, particularly as they apply to the scheduling of activities over time within an organization or economy in which the activities must share in the use of limitedamounts of various commodities. The contemplated use of electronic computers forrapidly computing programs and the assumptions underlying the mathematical model are discussed. The paper is concluded by an illustrative example” (Dantzig & Wood, 1949).

In Part II of the paper – the ‘Mathematical Model’ – “activities (or production processes) are considered as building blocks out of which a technology is constructed. Postulates are developed by which activities may be combined. The main part of the paper is concerned with the discrete type model and the use of a linear maximization function for finding the "optimum" program. The mathematical problem associated with this approach is developed first in general notation and then in terms of a dynamic system of equations expressed in matrix notation” (Dantzig, 1949).

NOTE: We separately offer Dantzig's "On the Significance of Solving Linear Programming Problems With Some Integer Variables" -- his paper on computational complexity. Item #1295

CONDITION & DETAILS: Complete first edition in original wrappers. 4to. 250 x 175mm. Slight sunning at the edges of the front wrap; small crease at upper right that proceeds through .25 of the pages. Internally bright and clean. Near fine.

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Price:
$825.00
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