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Volume 23, No 1, 2016, P. 3550 UDC 519.85
Keywords: bilevel programming, upper bound, competitive facility location. DOI: 10.17377/daio.2016.23.493 Vladimir L. Beresnev ^{1,2} Received 20 May 2015 References[1] V. L. Beresnev, Diskretnye zadachi razmeshcheniya i polinomy ot bulevykh peremennykh (Discrete Location Problems and Polynomials of Boolean Variables), Izd. Inst. Mat., Novosibirsk, 2005.[2] V. L. Beresnev, Local search algorithms for the problem of competitive location of enterprises, Avtom. Telemekh., No. 3, 12–27, 2012. Translated in Autom. Remote Control, 73, No. 3, 425–439, 2012. [3] V. L. Beresnev, On the competitive facility location problem with a free choice of suppliers, Avtom. Telemekh., No. 4, 94–105, 2014. Translated in Autom. Remote Control, 75, No. 4, 668–676, 2014. [4] V. L. Beresnev, E. N. Goncharov, and A. A. Mel’nikov, Local search with a generalized neighborhood in the optimization problem for pseudoBoolean functions, Diskretn. Anal. Issled. Oper., 18, No. 4, 3–16, 2011. Translated in J. Appl. Ind. Math., 6, No. 1, 22–30, 2012. [5] V. L. Beresnev and A. A. Mel’nikov, Approximate algorithms for the competitive facility location problem, Diskretn. Anal. Issled. Oper., 17, No. 6, 3–19, 2010. Translated in J. Appl. Ind. Math., 5, No. 2, 180–190, 2011. [6] V. L. Beresnev and A. A. Mel’nikov, The branchandbound algorithm for a competitive facility location problem with the prescribed choice of suppliers, Diskretn. Anal. Issled. Oper., 21, No. 2, 3–23, 2014. Translated in J. Appl. Ind. Math., 8, No. 2, 177–189, 2014. [7] A. V. Kononov, Yu. A. Kochetov, and A. V. Plyasunov, Competitive facility location models, Zh. Vychisl. Mat. Mat. Fiz., 49, No. 6, 1037–1054, 2009. Translated in Comput. Math. Math. Phys., 49, No. 6, 994–1009, 2009. [8] A. A. Mel’nikov, Randomized local search for the discrete competitive facility location problem, Avtom. Telemekh., No. 4, 134–152, 2014. Translated in Autom. Remote Control, 75, No. 4, 700–714, 2014. [9] A. V. Plyasunov and A. A. Panin, The pricing problem. Part I: Exact and approximate algorithms, Diskretn. Anal. Issled. Oper., 19, No. 5, 83–100, 2012. Translated in J. Appl. Ind. Math., 7, No. 2, 241251, 2013. [10] A. V. Plyasunov and A. A. Panin, The pricing problem. Part II: Computational complexity, Diskretn. Anal. Issled. Oper., 19, No. 6, 56–71, 2012. Translated in J. Appl. Ind. Math., 7, No. 3, 420430, 2013. [11] V. L. Beresnev, Branchandbound algorithm for a competitive facility location problem, Comput. Oper. Res., 40, No. 8, 2062–2070, 2013. [12] S. Dempe, Foundations of Bilevel Programming, Kluwer Acad. Publ., Dordrecht, 2002. [13] P. L. Hammer and S. Rudeanu, PseudoBoolean programming, Oper. Res., 17, No. 2, 233–261, 1969. [14] J. Krarup and P. M. Pruzan, The simple plant location problem: Survey and synthesis, Eur. J. Oper. Res., 12, No. 1, 36–81, 1983. [15] H. von Stackelberg, The Theory of the Market Economy, Hedge, London, 1952. 

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