Abstract
The extreme points of any nondegenerate dual transportation polyhedron are characterized by the m-partitions (or n-partitions) of m+n−1. This is used to show that all such polyhedra have exactly the same number of r-dimensional faces, 0≤r≤m+n−2, and to count them.
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References
J. H. Ahrens, “A Conjecture of E. D. Bolker”, Journal of Combinatorial Theory (B) 31 (1981), 1–8.
M. L. Balinski, “On two special classes of itransportation polytopes”, in M. L. Balinski, ed., Pivoting and Extensions (North-Holland, Amsterdam, 1974) pp. 43–58.
M. L. Balinski, “Signature methods for the assignment problem”, to appear in Operations Research.
M. L. Balinski, “Signatures des points extrêmes du polyèdre dual du problème de transport”, Comptes Rendus de l’Académie des Sciences de Paris 296 (1983), Série I, 457–459.
M. L. Balinski, “The Hirsch conjecture for dual transportation polyhedra”, to appear in Mathematics of Operations Research.
M. L. Balinski and A. Russakoff, “On the assignment polytope”, SIAM Review 16 (1974), 516–525.
E. D. Bolker, “Transportation polytopes”, Journal of Combinatorial Theory (B) 13 (1972), 251–262.
V. Klee and C. Witzgall, “Facets and vertices of transportation polytopes”, in: G. B. Dantzig and A. F. Veinott, Jr., eds., Mathematics of the decision sciences, vol. I (American Mathematical Society, Providence, R.I., 1968) pp. 257–282.
Zhu Yeng-Jen, “Maximum number of iterations in the dual algorithm of the Kantorovic-Hitchcock transportation problem in linear programming”, Chinese Mathematics 3 (1963) 307–313. Translation of paper in Acta Mathematica Sinica 12 (1962) 278–283.
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© 1984 The Mathematical Programming Society, Inc.
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Balinski, M.L., Russakoff, A. (1984). Faces of dual transportation polyhedra. In: Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach II. Mathematical Programming Studies, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121004
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DOI: https://doi.org/10.1007/BFb0121004
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