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A Treatment of Transportation Problems by Decomposition
A. C. Williams
Journal of the Society for Industrial and Applied Mathematics
Vol. 10, No. 1 (Mar., 1962), pp. 35-48
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2098795
Page Count: 14
You can always find the topics here!Topics: Transportation, Integers, Algorithms, Optimal solutions, Pricing, Mathematical problems, Supply, Marginal costs, Cost functions, Simplex method
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The "decomposition principle" of Dantzig and Wolfe \lbrack1\rbrack is applied to the solution of the Hitchcock transportation problem and to several generalizations of it. Among these generalizations are (i) the transportation problem in which the source availabilities are subject to general linear constraints, and (ii) the case in which the costs are piecewise linear convex functions. The algorithms developed, while they are of quite general applicability to the problems mentioned, are most efficient when the number of sources is small compared to the number of destinations. Our computational experience is, however, limited to the transportation problem without generalization.
Journal of the Society for Industrial and Applied Mathematics © 1962 Society for Industrial and Applied Mathematics