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English version: Journal of Applied and Industrial Mathematics, 2017, 11:4, 472480 

Volume 24, No 4, 2017, P. 521 UDC 519.85
Keywords: competitive facility location, bilevel programming, upper bound. DOI: 10.17377/daio.2017.24.578 Vladimir L. Beresnev ^{1,2} Received 2 May 2017 References[1] V. L. Beresnev, On the competitive facility location problem with a free choice of suppliers, Avtom. Telemekh., No. 4, 94–105, 2014 [Russian]. Translated in Autom. Remote Control, 75, No. 4, 668–676, 2014.[2] V. L. Beresnev and A. A. Mel’nikov, A capacitated competitive facility location problem, Diskretn. Anal. Issled. Oper., 23, No. 1, 35–50, 2016 [Russian]. Translated in J. Appl. Ind. Math., 10, No. 1, 61–68, 2016. [3] A. A. Mel’nikov, Randomized local search for the discrete competitive facility location problem, Avtom. Telemekh., No. 4, 134–152, 2014 [Russian]. Translated in Autom. Remote Control, 75, No. 4, 700–714, 2014. [4] M. G. Ashtiani, Competitive location: A stateofart review, Int. J. Ind. Eng. Comput., 7, No. 1, 1–18, 2016. [5] V. L. Beresnev, Branchandbound algorithm for a competitive facility location problem, Comput. Oper. Res., 40, No. 8, 2062–2070, 2013. [6] I. A. Davydov, Yu. A. Kochetov, and E. Carrizosa, A local search heuristic for the ($rp$)centroid problem in the plane, Comput. Oper. Res., 52, Pt. B, 334–340, 2014. [7] S. Dempe, Foundations of Bilevel Programming, Kluwer Acad. Publ., Dordrecht, 2002. [8] T. Drezner, Z. Drezner, and P. Kalczynski, A leaderfollower model for discrete competitive facility location, Comput. Oper. Res., 64, 51–59, 2015. [9] H. A. Eiselt and G. Laporte, Sequential location problems, Eur. J. Oper. Res., 96, No. 2, 217–231, 1996. [10] A. Jakubovskis, Strategic facility location, capacity acquisition, and technology choice decisions under demand uncertainty: Robust vs. nonrobust optimization approaches, Eur. J. Oper. Res., 260, No. 3, [11] A. Karakitsiou, Modeling Discrete Competitive Facility Location, Springer, Cham, 2015 (SpringerBriefs in Optimization). [12] H. von Stackelberg, The Theory of the Market Economy, Oxf. Univ. Press, Oxford, 1952. [13] Y. Zhang, L. V. Snyder, T. K. Ralphs, and Z. Xue, The competitive facility location problem under disruption risks, Transp. Res., Part E, 93, 453–473, 201 

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