Mass-transshipment problems and ideal metrics

L. G. Hanin, S. T. Rachev

Research output: Contribution to journalArticle

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Abstract

The Monge-Kantorovich mass-transshipment problem is to minimize the total cost ∫R2n c(x,y) db(x,y) over all transshipments b that satisfy the balancing condition b({filled circle}×Rn)-b(Rn×{filled circle})=(P-:Q)({filled circle}); P and Q are viewed as initial and final mass distributions, respectively, and c(x, y) is a cost function. The dual form of the problem was given by Kantorovich and Rubinstein (1958) for P and Q having bounded support, and the general case was considered in Lecture 20 of Dudley (1976). We extend these results studying more general transshipment problems based on higher-order differences. A new class of ideal metrics arises from our version of the Monge-Kantorovich problem, and a dual representation for these metrics is obtained.

Original languageEnglish
Pages (from-to)183-196
Number of pages14
JournalJournal of Computational and Applied Mathematics
Volume56
Issue number1-2
DOIs
StatePublished - Dec 20 1994

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Keywords

  • Mass-transshipment problems
  • Monge-Kantorovich problem
  • Probability metrics

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