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Diskretn. Anal. Issled. Oper.:

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Diskretn. Anal. Issled. Oper., 2008, Volume 15, Number 4, Pages 3–24 (Mi da537)  

This article is cited in 16 scientific papers (total in 16 papers)

Upper bounds for goal functions of discrete competitive facility location problems

V. L. Beresnev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: The facility location problems in the presence of competition are considered, when two competitive firms open facilities sequentially and each client selects one of the open facilities according to his preferences and profits either the first firm (Leader) or the second (Follower). The problem is to find a facility location for the Leader which maximizes its profits with the optimal reaction of the Follower taken into account. The formulations which differ in the Follower's goal function are considered. The models are formulated as bilevel linear integer programming problems and equivalent formulations of these problems are presented in the form of the bilevel pseudo-Boolean programming. A polynomial time algorithm for the problems is presented in the case, where facilities and clients are points of a path. A method of construction of an upper bound for optimal values of the Leader's profit is proposed. The corresponding algorithm consists in construction of an auxiliary pseudo-Boolean function and computing an optimal solution yielding minimal value of this function. Computational results illustrate the good performance of the upper bound for the test examples of the problem on a path. Table 1, illustr. 1, bibl. 15.

Keywords: bilevel programming problem, upper bound, optimal solution, pseudo-Boolean function.

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English version:
Journal of Applied and Industrial Mathematics, 2009, 3:4, 419–432

Bibliographic databases:

UDC: 519.87
Received: 19.03.2008

Citation: V. L. Beresnev, “Upper bounds for goal functions of discrete competitive facility location problems”, Diskretn. Anal. Issled. Oper., 15:4 (2008), 3–24; J. Appl. Industr. Math., 3:4 (2009), 419–432

Citation in format AMSBIB
\by V.~L.~Beresnev
\paper Upper bounds for goal functions of discrete competitive facility location problems
\jour Diskretn. Anal. Issled. Oper.
\yr 2008
\vol 15
\issue 4
\pages 3--24
\jour J. Appl. Industr. Math.
\yr 2009
\vol 3
\issue 4
\pages 419--432

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    This publication is cited in the following articles:
    1. J. Appl. Industr. Math., 4:2 (2010), 147–157  mathnet  crossref  mathscinet
    2. V. L. Beresnev, A. A. Melnikov, “Priblizhennye algoritmy dlya zadachi konkurentnogo razmescheniya predpriyatii”, Diskretn. analiz i issled. oper., 17:6 (2010), 3–19  mathnet  mathscinet  zmath
    3. V. L. Beresnev, E. N. Goncharov, A. A. Mel'nikov, “Local search over generalized neighborhood for an optimization problem of pseudo-Boolean functions”, J. Appl. Industr. Math., 6:1 (2012), 22–30  mathnet  crossref  mathscinet  zmath
    4. A. V. Naumov, I. M. Bobylev, “On the two-stage problem of linear stochastic programming with quantile criterion and discrete distribution of the random parameters”, Autom. Remote Control, 73:2 (2012), 265–275  mathnet  crossref  isi
    5. V. L. Beresnev, “Local search algorithms for the problem of competitive location of enterprises”, Autom. Remote Control, 73:3 (2012), 425–439  mathnet  crossref  isi
    6. Beresnev V., “Branch-and-Bound Algorithm for a Competitive Facility Location Problem”, Comput. Oper. Res., 40:8 (2013), 2062–2070  crossref  mathscinet  zmath  isi  elib  scopus
    7. S. V. Ivanov, “Bilevel stochastic linear programming problems with quantile criterion”, Autom. Remote Control, 75:1 (2014), 107–118  mathnet  crossref  isi
    8. 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
    9. A. A. Mel'nikov, “Computational complexity of the discrete competitive facility location problem”, J. Appl. Industr. Math., 8:4 (2014), 557–567  mathnet  crossref  mathscinet
    10. Rahmani A., MirHassani S.A., “Lagrangean Relaxation-Based Algorithm For Bi-Level Problems”, Optim. Method Softw., 30:1 (2015), 1–14  crossref  mathscinet  zmath  isi  elib  scopus
    11. MirHassani S.A., Raeisi S., Rahmani A., “Quantum Binary Particle Swarm Optimization-Based Algorithm For Solving a Class of Bi-Level Competitive Facility Location Problems”, Optim. Method Softw., 30:4 (2015), 756–768  crossref  mathscinet  zmath  isi  elib  scopus
    12. S. V. Ivanov, M. V. Morozova, “Stochastic problem of competitive location of facilities with quantile criterion”, Autom. Remote Control, 77:3 (2016), 451–461  mathnet  crossref  isi  elib
    13. Karakitsiou A., Migdalas A., “Locating Facilities in a Competitive Environment”, Optim. Lett., 11:5 (2017), 929–945  crossref  mathscinet  zmath  isi  scopus
    14. Aras N., Kucukaydin H., “Bilevel Models on the Competitive Facility Location Problem”, Spatial Interaction Models: Facility Location Using Game Theory, Springer Optimization and Its Applications, 118, eds. Mallozzi L., DAmato E., Pardalos P., Springer, 2017, 1–19  crossref  mathscinet  zmath  isi  scopus
    15. Rahmani A., Yousefikhoshbakht M., “An Effective Branch-and-Cut Algorithm in Order to Solve the Mixed Integer Bi-Level Programming”, Int. J. Prod. Manag. Engineering, 5:1 (2017), 1–10  crossref  isi
    16. Nasiri M.M., Mahmoodian V., Rahbari A., Farahmand Sh., “A Modified Genetic Algorithm For the Capacitated Competitive Facility Location Problem With the Partial Demand Satisfaction”, Comput. Ind. Eng., 124 (2018), 435–448  crossref  isi  scopus
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