Abstract
A perturbation method is introduced which transforms any fixed cost transportation problem F into a degeneracy-free equivalent F′. If a basic optimal solution to F′ is known, an optimal solution to F can be obtained by means of simple rounding.
This is a preview of subscription content, log in via an institution to check access.
References
M.L. Balinski, “Fixed-cost transportation problems”,Naval Research Logistics Quarterly 8 (1961) 41–54.
L. Cooper and C. Drebes, “An approximate solution method for the fixed charge problem”,Naval Research Logistics Quarterly 14 (1967) 101–113.
D. Denzler, “An approximate algorithm for the fixed charge problem”,Naval Research Logistics Quarterly 16 (1969) 411–416.
P. Gray, “Exact solution of the fixed-charge transportation problem”,Operations Research 19 (1971) 1529–1538.
W.M. Hirsch and G.B. Dantzig, “The fixed charge problem”, RAND Corporation Rept. RM-1383 (1954).
W.M. Hirsch and G.B. Dantzig, “The fixed charge problem”,Naval Research Logistics quarterly 15 (1968) 413–424.
H.W. Kuhn and W.J. Baumol, “An approximate algorithm for the fixed-charges transportation problem”,Naval Research Logistics Quarterly 9 (1962) 1–15.
O.L. Mangasarian,Nonlinear programming (McGraw-Hill, New York, 1969).
K.G. Murty, “Solving the fixed charge problem by ranking the extreme points”,Operations Research 16 (1968) 268–279.
M. Simmonnard,Linear programming (Prentice-Hall, Englewood Cliffs, N.J., 1966).
D. Steinberg, “The fixed charge problem”,Naval Research Logistics Quarterly 17 (1970).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ahrens, J.H., Finke, G. Degeneracy in fixed cost transportation problems. Mathematical Programming 8, 369–374 (1975). https://doi.org/10.1007/BF01580452
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01580452