### 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}×R^{n})-b(R^{n}×{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 language | English |
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Pages (from-to) | 183-196 |

Number of pages | 14 |

Journal | Journal of Computational and Applied Mathematics |

Volume | 56 |

Issue number | 1-2 |

DOIs | |

State | Published - Dec 20 1994 |

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### Keywords

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

### Cite this

*Journal of Computational and Applied Mathematics*,

*56*(1-2), 183-196. https://doi.org/10.1016/0377-0427(94)90387-5