SOLVING INTEGER TRANSPORTATION PROBLEM SPECIAL BRANCH AND BOUND METHOD

Lapshina Marina; Kovalchuk I.

doi:doi:10.12737/19520

SOLVING INTEGER TRANSPORTATION PROBLEM SPECIAL BRANCH AND BOUND METHOD

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SOLVING INTEGER TRANSPORTATION PROBLEM SPECIAL BRANCH AND BOUND METHOD

Journal: MODELING OF SYSTEMS AND PROCESSES Volume 8 № 4 , 2016

Rubrics: TEHNICHESKIE NAUKI

Lapshina Marina ¹

Kovalchuk I.

Author and publication information

Authors:

1. Voronezh State University of Forestry and Technologies named after G.F. Morozov (Department of Computer Science and Information Systems, Professor)

Voronezh, Voronezh, Russian Federation

Type:

Article

DOI:

https://doi.org/10.12737/19520

Pages:

from 44 to 46

Status:

Published

Received:

10.05.2016

Accepted:

10.05.2016

Published:

10.05.2016

Language:

Russian

Keywords:

decomposition, optimal dual variables, integer variables, optimization assessment.

Abstract and keywords

Abstract (English):
The paper deals with the use of special (expanded) branch and bound method, which allows to significantly increase the dimension of the problem, also shows the comparative characteristics of the traditional approach and proposed.

Keywords:
decomposition, optimal dual variables, integer variables, optimization assessment.

Text

Пусть:

$\sum^{%20}_{i,j}c_{i,j}x_{i,j}\rightarrow%20min$ (1)

$\sum^{%20}_j\lambda_{i,j}x_{i,j}\ge%20a_i$ (2)

$\sum^{%20}_j\mu_{i,j}x_{i,j}\ge%20b_j$ (3)

$x_{i,j}\epsilon\left\{0,1\right\}i=1,...,m;j=1,...,n;$ (..)

$c_{i,j},\lambda_{i,j},a_i,b_j\ge0$ (..)

References

1. Lebedev, S. S.Modifikatsiya metoda Vendersa chastichno tselochislennogo lineynogo programmirovaniya [Tekst] / S.S. Lebedev. Ekonomika i matematicheskie metody. - 2014. - T. 30. Vyp. 2,. S.112-118.

2. Zaslavskiy, A. A. Ispol´zovanie spetsial´nogo metoda vetvey i granits dlya resheniya tselochislennoy obobshchennoy transportnoy zadachi [Tekst] / A. A. Zaslavskiy, S. S.Lebedev. Ekonomika i matematicheskie metody. -2005. - T. 31. Vyp. 2. - S.45-52.

3. Lemarechal C. New Variants of Bundle Methods / C. Lemarechal, A. Nemirovskii, Y. Nesterov. Reports de Recherch. Paris: Institut National de Recherch en Informatique et en Automatique. - 2011. - №15. - Pr.120-128.

4. Azaryan, L. L. Reshenie tselochislennykh zadach transportnogo tipa s ispol´zovaniem obobshchennykh mnozhiteley Lagranzha [Tekst] / L. L. Azaryan, S. S. Lebedev, L. M. Mestetskiy. Ekonomika i matematicheskie metody. - 2013. - T. 13. Vyp. 4. - S. 32-38.

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