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Polyhedral combinatorics of multi-index axial transportation problems

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  • Kravtsov, M.K.
  • Lukshin, E.V.

Abstract

This paper studies integer points (IP) and integer vertices (IV) of the p-index axial transportation polytope (p-ATP) of order n1ín2í...ínp, n1,n2,...,np[greater-or-equal, slanted]2, p[greater-or-equal, slanted]2, defined by integer vectors, as well as noninteger vertices of the 3-ATP. In particular, for the p-ATP, we establish criteria for the minimum and maximum number of IPs and describe the class of polytopes for which the number of IPs coincides with the number of IVs. For the 3-ATP of order nínín, we prove the theorem on the exponential growth of denominators of fractional components of the polytope vertices. Three conjectures are stated regarding the maximum number of vertices of the p-ATP, the maximum number of IVs, and the structure of the nondegenerate polytopes with the maximum number of IPs.

Suggested Citation

  • Kravtsov, M.K. & Lukshin, E.V., 2008. "Polyhedral combinatorics of multi-index axial transportation problems," European Journal of Operational Research, Elsevier, vol. 189(3), pages 920-938, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:920-938
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    References listed on IDEAS

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