Simplex algorithm: Difference between revisions

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== History ==

George Dantzig worked on planning methods for the US Army Air Force during World War II using a desk calculator. During 1946 his colleague challenged him to mechanize the planning process in order to enticedistract him into notfrom taking another job. Dantzig formulated the problem as linear inequalities inspired by the work of [[Wassily Leontief]], however, at that time he didn't include an objective as part of his formulation. Without an objective, a vast number of solutions can be feasible, and therefore to find the "best" feasible solution, military-specified "ground rules" must be used that describe how goals can be achieved as opposed to specifying a goal itself. Dantzig's core insight was to realize that most such ground rules can be translated into a linear objective function that needs to be maximized.<ref>{{Cite journal|url = http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA112060|title = Reminiscences about the origins of linear programming|last = |first = |date = April 1982|journal = Operations Research Letter|doi = 10.1016/0167-6377(82)90043-8|pmid = |access-date = |volume = 1|issue = 2 |pages=43–48}}</ref> Development of the simplex method was evolutionary and happened over a period of about a year.<ref>{{Cite journal|url = http://www.phpsimplex.com/en/Dantzig_interview.htm|title = An Interview with George B. Dantzig: The Father of Linear Programming|last = Albers and Reid|first = |date = 1986|journal = College Mathematics Journal|doi = |pmid = |access-date = |pages = 292–314}}</ref>

After Dantzig included an objective function as part of his formulation during mid-1947, the problem was mathematically more tractable. Dantzig realized that one of the unsolved problems that [[George Dantzig#Mathematical statistics|he mistook]] as homework in his professor [[Jerzy Neyman]]'s class (and actually later solved), was applicable to finding an algorithm for linear programs. This problem involved finding the existence of Lagrange multipliers for general linear programs over a continuum of variables, each bounded between zero and one, and satisfying linear constraints expressed in the form of Lebesgue integrals. Dantzig later published his "homework" as a thesis to earn his doctorate. The column geometry used in this thesis gave Dantzig insight that made him believe that the Simplex method would be very efficient.<ref>{{Cite journal|url = http://www.dtic.mil/dtic/tr/fulltext/u2/a182708.pdf|title = Origins of the simplex method|last = Dantzig|first = George|date = May 1987|journal = A history of scientific computing|doi = 10.1145/87252.88081|pmid = |access-date = |isbn = 0-201-50814-1}}</ref>