Asymptotic approach to solving the multi-index axial transportation problem
type: Item
instance of: scholarly article
title: Asymptotic approach to solving the multi-index axial transportation problem
zbMATH Open document ID: 0966.90049
author: M. K. Kravtsov
author: A. P. Krachkovskij
published in: Computational Mathematics and Mathematical Physics
publication date: 2001-08-14T00:00:00Z
review text: The authors give a theoretical foundation to the fact that the plan for a \(p\)-index axial transportation problem (TP) of dimension \(n{_1}\times\ldots\times{n_p}\) constructed by the minimal element method (\(\psi\)-method) is closed to the optimal plan. Namely, it is proved that the objective function has asymptotically equal values on these plans as \(n_1,\ldots,n_p\) tend to infinity. In other words, it is proved that the relative number of \(p\)-index axial TPs among all problems for which the \(\psi\)-method yields an asymptotically optimal plan tends to unity.
Mathematics Subject Classification ID: 90C08
zbMATH DE Number: 1472936
zbMATH Keywords: transportation problem
zbMATH Keywords: linear programming
zbMATH Keywords: multi-index
zbMATH Keywords: axial
zbMATH Keywords: optimal plan
zbMATH Keywords: minimal element method
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1472936