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Diskretn. Anal. Issled. Oper., 2012, Volume 19, Number 6, Pages 56–71 (Mi da712)  

This article is cited in 8 scientific papers (total in 8 papers)

The pricing problem. Part 2. The computational complexity

A. V. Plyasunovab, A. A. Paninba

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: For the problem, it is shown that it belongs to the class Log-APX, cannot be approximable with an absolute error limited by a constant, and the corresponding evaluation problem is non-trivial in the class $\Delta^p_2$. Also, two polynomial solvable cases of the problem are provided. Bibliogr. 8.

Keywords: computational complexity, approximability, the bilevel pricing problem, approximate algorithm, approximability class, NP-hard in the strong sense, polynomial hierarchy.

Full text: PDF file (302 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:3, 420–430

Bibliographic databases:

UDC: 519.87+519.854
Received: 01.06.2011
Revised: 04.06.2012

Citation: A. V. Plyasunov, A. A. Panin, “The pricing problem. Part 2. The computational complexity”, Diskretn. Anal. Issled. Oper., 19:6 (2012), 56–71; J. Appl. Industr. Math., 7:3 (2013), 420–430

Citation in format AMSBIB
\Bibitem{PlyPan12}
\by A.~V.~Plyasunov, A.~A.~Panin
\paper The pricing problem. Part~2. The computational complexity
\jour Diskretn. Anal. Issled. Oper.
\yr 2012
\vol 19
\issue 6
\pages 56--71
\mathnet{http://mi.mathnet.ru/da712}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3076914}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 3
\pages 420--430
\crossref{https://doi.org/10.1134/S1990478913030150}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. V. L. Beresnev, A. A. Melnikov, “Branch-and-bound method for the competitive facility location problem with prescribed choice of suppliers”, J. Appl. Industr. Math., 8:2 (2014), 177–189  mathnet  crossref  mathscinet
    2. V. L. Beresnev, “On the competitive facility location problem with a free choice of suppliers”, Autom. Remote Control, 75:4 (2014), 668–676  mathnet  crossref  isi
    3. A. A. Panin, M. G. Pashchenko, A. V. Plyasunov, “Bilevel competitive facility location and pricing problems”, Autom. Remote Control, 75:4 (2014), 715–727  mathnet  crossref  isi
    4. A. A. Panin, A. V. Plyasunov, “On complexity of bilevel problems of location and pricing”, J. Appl. Industr. Math., 8:4 (2014), 574–581  mathnet  crossref  mathscinet
    5. S. M. Lavlinskii, A. A. Panin, A. V. Plyasunov, “A bilevel planning model for public-private partnership”, Autom. Remote Control, 76:11 (2015), 1976–1987  mathnet  crossref  isi  elib  elib
    6. V. L. Beresnev, A. A. Melnikov, “A capacitated competitive facility location problem”, J. Appl. Industr. Math., 10:1 (2016), 61–68  mathnet  crossref  crossref  mathscinet  elib
    7. A. V. Gubareva, A. A. Panin, A. V. Plyasunov, L. V. Som, “On a three-level competitive pricing problem with uniform and mill pricing strategies”, J. Appl. Industr. Math., 13:1 (2019), 54–64  mathnet  crossref  crossref
    8. A. V. Kononov, A. A. Panin, A. V. Plyasunov, “A bilevel competitive location and pricing model with nonuniform split of demand”, J. Appl. Industr. Math., 13:3 (2019), 500–510  mathnet  crossref  crossref
  • Дискретный анализ и исследование операций
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