TY - JOUR

T1 - Mass-transshipment problems and ideal metrics

AU - Hanin, L. G.

AU - Rachev, S. T.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1994/12/20

Y1 - 1994/12/20

N2 - 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.

AB - 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.

KW - Mass-transshipment problems

KW - Monge-Kantorovich problem

KW - Probability metrics

UR - http://www.scopus.com/inward/record.url?scp=1242341614&partnerID=8YFLogxK

U2 - 10.1016/0377-0427(94)90387-5

DO - 10.1016/0377-0427(94)90387-5

M3 - Article

AN - SCOPUS:1242341614

VL - 56

SP - 183

EP - 196

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 1-2

ER -