Abstract
In this paper a procedure is described to orient arcs of a graph so as to mimimize the sum of the distances between certain given source-sink pairs. This work is a substantial part of the more general problem of orienting a road network in such a way as to optimize a specified objective subject to the requirement that one can go from any point of the network to any other one. The proposed method, related to the ideas of sequential optimization [1, 2, 3], uses column-generation as well as row-generation.
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References
H.P. Crowder E.L. Johnson and M.W. Padberg, “Solying large-scale zero-one linear programming problems”, T.J. Watson Research Center Report RC 8888, IBM Research (Yorktown Heights, June 1981).
M.W. Padberg and S. Hong, “On the symmetric travelling salesman problem. A computational study”, Mathematical Programming Study 12 (1980) 78–107.
S. Powell, “Row-generation methods”, contributed paper, International Workshop on Advances in Linear Optimization: Algorithms and Software, Pisa, Italy, July 1980.
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© 1986 The Mathematical Programming Society, Inc.
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Johnson, E.L., Pieroni, P. (1986). A linear programming approach to the optimum network orientation problem. In: Gallo, G., Sandi, C. (eds) Netflow at Pisa. Mathematical Programming Studies, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121098
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DOI: https://doi.org/10.1007/BFb0121098
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