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 Diskretn. Anal. Issled. Oper., 2009, Volume 16, Issue 2, Pages 21–41 (Mi da566)

A branch and bound method for the facility location problem with customer preferences

I. L. Vasiliev, K. B. Klimentova

Institute of System Dynamics and Control Theory SB RAS, Irkutsk, Russia

Abstract: The article is focused on computational study of the bilevel facility location problem with customer's preferences taken into account. Different integer linear programming formulations are considered. The cutting plane method is implemented for the new family of valid inequalities which are based on relation with the problem for a pair of matrices. The optimal solution of the problem is searched by two variants of branch and bound method using the cutting plane method implemented. The upper bounds for these exact methods are found by Simulated Annealing method. The computational experience illustrates the effectiveness of the proposed methods in comparison with the known approaches. Pic. 1, tabl. 7, bibl. 15.

Keywords: bilevel facility location problem, cutting plane method, local search, branch and bound method.

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English version:
Journal of Applied and Industrial Mathematics, 2010, 4:3, 441–454

Bibliographic databases:

UDC: 519.854.2
Revised: 04.02.2009

Citation: I. L. Vasiliev, K. B. Klimentova, “A branch and bound method for the facility location problem with customer preferences”, Diskretn. Anal. Issled. Oper., 16:2 (2009), 21–41; J. Appl. Industr. Math., 4:3 (2010), 441–454

Citation in format AMSBIB
\Bibitem{VasKli09} \by I.~L.~Vasiliev, K.~B.~Klimentova \paper A branch and bound method for the facility location problem with customer preferences \jour Diskretn. Anal. Issled. Oper. \yr 2009 \vol 16 \issue 2 \pages 21--41 \mathnet{http://mi.mathnet.ru/da566} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2574307} \zmath{https://zbmath.org/?q=an:1249.90080} \transl \jour J. Appl. Industr. Math. \yr 2010 \vol 4 \issue 3 \pages 441--454 \crossref{https://doi.org/10.1134/S1990478910030178} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77956112361} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Gruzdeva T.V., Klimentova K.B., “Metod otsechenii dlya neravenstv klik v zadache razmescheniya s predpochteniyami klientov”, Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie, 2011, no. 4, 31–39
2. Vasilyev I., Klimentova X., Boccia M., “Polyhedral Study of Simple Plant Location Problem with Order”, Oper. Res. Lett., 41:2 (2013), 153–158
3. 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
4. A. A. Mel'nikov, “Computational complexity of the discrete competitive facility location problem”, J. Appl. Industr. Math., 8:4 (2014), 557–567
5. Camacho-Vallejo J.-F., Eduardo Cordero-Franco A., Gonzalez-Ramirez R.G., “Solving the Bilevel Facility Location Problem Under Preferences by a Stackelberg-Evolutionary Algorithm”, Math. Probl. Eng., 2014, 430243
6. Camacho-Vallejo J.-F., Mar-Ortiz J., Lopez-Ramos F., Pedraza Rodriguez R., “a Genetic Algorithm For the Bi-Level Topological Design of Local Area Networks”, PLoS One, 10:6 (2015), e0128067
7. Moatari-Kazerouni A., Chinniah Yu., Agard B., “Integrating Occupational Health and Safety in Facility Layout Planning, Part i: Methodology”, Int. J. Prod. Res., 53:11 (2015), 3243–3259
8. Kalashnikov V.V., Dempe S., Perez-Valdes G.A., Kalashnykova N.I., Camacho-Vallejo J.-F., “Bilevel Programming and Applications”, Math. Probl. Eng., 2015, 310301
9. I. L. Vasilyev, P. Avella, M. Boccia, “A branch and cut heuristic for a runway scheduling problem”, Autom. Remote Control, 77:11 (2016), 1985–1993
10. Casas-Ramirez M.-S., Camacho-Vallejo J.-F., “Solving the P-Median Bilevel Problem With Order Through a Hybrid Heuristic”, Appl. Soft. Comput., 60 (2017), 73–86
11. Diaz J.A., Luna D.E., Camacho-Vallejo J.-F., Casas-Ramirez M.-S., “Grasp and Hybrid Grasp Tabu Heuristics to Solve a Maximal Covering Location Problem With Customer Preference Ordering”, Expert Syst. Appl., 82 (2017), 67–76
12. Casas-Ramirez M.-S., Camacho-Vallejo J.-F., Martinez-Salazar I.-A., “Approximating Solutions to a Bilevel Capacitated Facility Location Problem With Customer'S Patronization Toward a List of Preferences”, Appl. Math. Comput., 319 (2018), 369–386
13. Casas-Ramirez M.-S., Camacho-Vallejo J.-F., “Analyzing Valid Bounds For a Facility Location Bilevel Problem With Capacities”, Int. J. Comb. Optim. Probl. Inform., 10:2 (2019), 8–16
14. Caramia M., Giordani S., “Location of Differentiated Waste Collection Centers With User Cooperation: a Bilevel Optimization Approach”, Optim. Lett., 14:1 (2020), 85–99
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