SOLUTION OF SOME TRANSPORTATION PROBLEMS WITH RELAXED OR ADDITIONAL CONSTRAINTS

The authors consider some modifications of the usual transportation problem by allowing bounds for the admissible supply -- respectively, demand -- distributions. In particular, the case that the marginal distribution function of the supply is bounded below by a df F(sub 1), while the marginal df of the demand is bounded above by a df is considered. For the case that the difference of the marginals is fixed -- this is an extension of the well-known Kantorovich-Rubinstein problem -- the authors obtain new and general explicit results and bounds, even without the assumption that the cost function is of Monge type. The multivariate case is also treated. In the last section, the authors study Monge-Kantorovich problems with constraints of a local type, that is, on the densities of the marginals. In particular, the classical Dobrushin theorem on optimal couplings is extended with respect to total variation.

• Corporate Authors:

  Society for Industrial and Applied Mathematics

  3600 University City, Science Center
  Philadelphia, PA  United States  19104-2688
• Authors:
  • Rachev, S T
  • Ruschendorf, L
• Publication Date: 1994-5

Language

• English

Media Info

• Pagination: p. 673-689
• Serial:
  • SIAM JOURNAL ON CONTROL AND OPTIMIZATION
  • Volume: 32
  • Issue Number: 3
  • Publisher: Society for Industrial and Applied Mathematics

Subject/Index Terms

• TRT Terms: Couplers; Demand; Distributions (Statistics); Marginal costs; Multivariate analysis; Supply
• Uncontrolled Terms: Supply and demand
• Subject Areas: Data and Information Technology; Highways; Planning and Forecasting; Society; I72: Traffic and Transport Planning;

Filing Info

• Accession Number: 00669326
• Record Type: Publication
• Files: TRIS
• Created Date: Nov 4 1994 12:00AM