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A network simplex method. (English) Zbl 0352.90039


MSC:

90C10 Integer programming
90C05 Linear programming
90C35 Programming involving graphs or networks
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References:

[1] G.B. Dantzig, ”Application of the simplex method to a transportation problem”, in: T.C. Koopmans, ed.,Activity analysis of production and allocation (Wiley, New York, 1951). · Zbl 0045.09901
[2] G.B. Dantzig,Linear programming and extensions (Princeton University Press, Princeton, 1963).
[3] G.B. Dantzig, L.R. Ford, Jr., and D.R. Fulkerson, ”A primal-dual algorithm for linear programs”, in: H.W. Kuhn and A.W. Tucker, eds.,Linear inequalities and related systems, Annals of Mathematics Study 38 (Princeton University Press, Princeton, 1956). · Zbl 0072.37701
[4] Jack Edmonds, ”Exponential growth of the simplex method for shortest path problems”, University of Waterloo, (1970) unpublished.
[5] L.R. Ford, Jr. and D.R. Fulkerson,Flows in networks (Princeton University Press, Princeton, 1962). · Zbl 0106.34802
[6] D.R. Fulkerson and G.B. Dantzig, ”Computations of maximal flows in networks”,Naval Research Logistics Quarterly 2 (1955) 277–283.
[7] D. Gale, ”A theorem on flows in networks”,Pacific Journal of Mathematics 7 (1957) 1073–1082. · Zbl 0087.16303
[8] B.J. Gassner, ”Cycling in the transportation problem”,Naval Research Logistics Quarterly 11 (1964) 43–58. · Zbl 0127.36905
[9] Fred Glover, D. Karney, and D. Klingman, ”The augmented predecessor index method for locating stepping-stone paths and assigning dual prices in distribution problems”,Transportation Science 6 (1972) 171–179.
[10] Ellis Johnson, ”Networks and basic solutions”,Operations Research 14 (1966) 619–623.
[11] Alex Orden, ”The transshipment problem”,Management Science 2 (1956) 276–285. · Zbl 0995.90549
[12] Norman Zadeh, ”A bad network problem for the simplex method and other minimum cost flow algorithms”,Mathematical Programming 5 (1973) 255–266. · Zbl 0287.90030
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