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Journal of Computer and Systems Sciences International
Published in: Journal of Computer and Systems Sciences International 6/2019

01-11-2019 | COMPUTER METHODS

Decomposition Algorithm for the Linear Three-Index Transportation Problem

Authors: L. P. Wang, A. P. Tizik, V. I. Tsurkov

Published in: Journal of Computer and Systems Sciences International | Issue 6/2019

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Abstract

The method of sequential modification of an objective function, which was earlier used for the classical transportation problem, is extended to the case of three indices. In the iterative process, the problem with three constraints and one binding variable is solved. Then, three independent problems with one constraint in which the coefficients for the binding variable are changed are considered. Using the suggested algorithm, a sequence of pseudosolutions with a monotonic growth of the objective function that converges to the optimum is constructed. The degeneracies are analyzed.
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Literature
1.
E. G. Gol’shtein and D. B. Yudin, Transport-Type Linear Programming Problems (Nauka, Fizmatlit, Moscow, 1969) [in Russian].
2.
L. G. Raskin and I. O. Kirichenko, Multi-Index Linear Programming Problems (Radio, Moscow, 1982) [in Russian].MATH
3.
Yu. A. Krivolapov, “The potential method for solving the three-index transportation problem,” Available from VIMI, No. D08221 (1990).
4.
L. G. Afraimovich, “A heuristic method for solving integer-valued decompositional multiindex problems,” Autom. Remote Control 75, 1357 (2014).MathSciNetCrossRef
5.
A. P. Tizik and V. I. Tsurkov, “Iterative functional modification methodfor solving a transportation problem,” Autom. Remote Control 73, 134 (2012).MathSciNetCrossRef
6.
V. I. Tsurkov, “Decomposition principle for block-separable systems,” Dokl. Akad. Nauk SSSR 246, 17–31 (1979).MATH
7.
A. A. Mironov and V. I. Tsurkov, “Minimax in transportation models with integral constraints: I,” J. Comput. Syst. Sci. Int. 42, 562 (2003).MATH
8.
A. A. Mironov, V. V. Fedorchuk, and V. I. Tsurkov, “Minimax in transportation models with integral constraints: II,” J. Comput. Syst. Sci. Int. 44, 732 (2005).MATH
Metadata
Title
Decomposition Algorithm for the Linear Three-Index Transportation Problem
Authors
L. P. Wang
A. P. Tizik
V. I. Tsurkov
Publication date
01-11-2019
Publisher
Pleiades Publishing
Published in
Journal of Computer and Systems Sciences International / Issue 6/2019
Print ISSN: 1064-2307
Electronic ISSN: 1555-6530
DOI
https://doi.org/10.1134/S1064230719060157

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