Competitive Facility Location Under Cross-Nested Logit Customer Choice Model: Hardness and Exact Approaches

Published Online:https://doi.org/10.1287/ijoc.2025.1150

References

  • Aboolian R, Berman O, Krass D (2007) Competitive facility location model with concave demand. Eur. J. Oper. Res. 181(2):598–619.CrossrefGoogle Scholar
  • Aouad A, Farias V, Levi R, Segev D (2018) The approximability of assortment optimization under ranking preferences. Oper. Res. 66(6):1661–1669.LinkGoogle Scholar
  • Beine MA, Bierlaire M, Docquier F (2021) New York, Abu Dhabi, London or stay at home? Using a cross-nested logit model to identify complex substitution patterns in migration. IZA Discussion Paper No. 14090, Institute of Labor Economics, Luxembourg.Google Scholar
  • Ben-Akiva M (1973) The structure of travel demand models, Unpublished PhD thesis, Massachusetts Institute of Technology, Cambridge.Google Scholar
  • Ben-Akiva M, Bierlaire M (1999) Discrete choice methods and their applications to short term travel decisions. Handbook of Transportation Science (Springer US, Boston), 5–33.CrossrefGoogle Scholar
  • Benati S, Hansen P (2002) The maximum capture problem with random utilities: Problem formulation and algorithms. Eur. J. Oper. Res. 143(3):518–530.CrossrefGoogle Scholar
  • Bierlaire M (2006) A theoretical analysis of the cross-nested logit model. Ann. Oper. Res. 144:287–300.CrossrefGoogle Scholar
  • Daly A, Bierlaire M (2006) A general and operational representation of generalised extreme value models. Transportation Res. Part B Methodological 40(4):285–305.CrossrefGoogle Scholar
  • Dam TT, Ta TA, Mai T (2022) Submodularity and local search approaches for maximum capture problems under generalized extreme value models. Eur. J. Oper. Res. 300(3):953–965.CrossrefGoogle Scholar
  • Dam TT, Ta TA, Mai T (2023) Robust maximum capture facility location under random utility maximization models. Eur. J. Oper. Res. 310(3):1128–1150.CrossrefGoogle Scholar
  • Ding C, Mishra S, Lin Y, Xie B (2015) Cross-nested joint model of travel mode and departure time choice for urban commuting trips: Case study in Maryland–Washington, DC region. J. Urban Planning Development 141(4).CrossrefGoogle Scholar
  • Duran MA, Grossmann IE (1986) An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Math. Programming 36:307–339.CrossrefGoogle Scholar
  • Fosgerau M, McFadden D, Bierlaire M (2013) Choice probability generating functions. J. Choice Model. 8:1–18.CrossrefGoogle Scholar
  • Freire A, Moreno E, Yushimito W (2016) A branch-and-bound algorithm for the maximum capture problem with random utilities. Eur. J. Oper. Res. 252(1):204–212.CrossrefGoogle Scholar
  • Haase K (2009) Discrete location planning (March 1), http://hdl.handle.net/2123/19420.Google Scholar
  • Haase K, Müller S (2014) A comparison of linear reformulations for multinomial logit choice probabilities in facility location models. Eur. J. Oper. Res. 232(3):689–691.CrossrefGoogle Scholar
  • Hasse K (2009) Discrete Location Planning (Institute of Transport and Logistics Studies, Sydney).Google Scholar
  • Lamontagne S, Carvalho M, Frejinger E, Gendron B, Anjos MF, Atallah R (2023) Optimising electric vehicle charging station placement using advanced discrete choice models. INFORMS J. Comput. 35(5):1195–1213.LinkGoogle Scholar
  • Le C, Mai T (2024) Constrained assortment optimization under the cross-nested logit model. Production Oper. Management 33(10):2073–2090.CrossrefGoogle Scholar
  • Le BL, Mai T, Ta TA, Ha MH, Vu DM (2026) Competitive facility location under cross-nested logit customer choice model: Hardness and exact approaches. https://doi.org/10.1287/ijoc.2025.1150.cd, https://github.com/INFORMSJoC/2025.1150.Google Scholar
  • Legault R, Frejinger E (2024) A model-free approach for solving choice-based competitive facility location problems using simulation and submodularity. INFORMS J. Comput. 37(3):603–622.LinkGoogle Scholar
  • Ljubić I, Moreno E (2018) Outer approximation and submodular cuts for maximum capture facility location problems with random utilities. Eur. J. Oper. Res. 266(1):46–56.CrossrefGoogle Scholar
  • Mai T (2016) A method of integrating correlation structures for a generalized recursive route choice model. Transportation Res. Part B Methodological 93:146–161.CrossrefGoogle Scholar
  • Mai T, Lodi A (2020) A multicut outer-approximation approach for competitive facility location under random utilities. Eur. J. Oper. Res. 284(3):874–881.CrossrefGoogle Scholar
  • Mai T, Frejinger E, Fosgerau M, Bastin F (2017) A dynamic programming approach for quickly estimating large network-based MEV models. Transportation Res. Part B Methodological 98:179–197.CrossrefGoogle Scholar
  • McFadden D (1978) Modelling the choice of residential location. Transportation Res. Record 673:72–77.Google Scholar
  • McFadden D (2001) Economic choices. Amer. Econom. Rev. 91(3):351–378.CrossrefGoogle Scholar
  • McFadden D, Train K (2000) Mixed MNL models for discrete response. J. Appl. Econometrics 15(5):447–470.CrossrefGoogle Scholar
  • Méndez-Vogel G, Marianov V, Lüer-Villagra A (2023) The follower competitive facility location problem under the nested logit choice rule. Eur. J. Oper. Res. 310(2):834–846.CrossrefGoogle Scholar
  • Rusmevichientong P, Shmoys D, Tong C, Topaloglu H (2014) Assortment optimization under the multinomial logit model with random choice parameters. Production Oper. Management 23(11):2023–2039.CrossrefGoogle Scholar
  • Şen A, Atamtürk A, Kaminsky P (2018) A conic integer programming approach to constrained assortment optimization under the mixed multinomial logit model. Oper. Res. 66(4):994–1003.LinkGoogle Scholar
  • Small KA (1987) A discrete choice model for ordered alternatives. Econometrica 55(2):409–424.CrossrefGoogle Scholar
  • Train KE (2009) Discrete Choice Methods with Simulation (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Vovsha P (1997) Application of cross-nested logit model to mode choice in Tel Aviv, Israel, metropolitan area. Transportation Res. Record 1607(1):6–15.CrossrefGoogle Scholar
  • Vovsha P, Bekhor S (1998) Link-nested logit model of route choice: Overcoming route overlapping problem. Transportation Res. Record 1645(1):133–142.CrossrefGoogle Scholar
  • Yang L, Zheng G, Zhu X (2013) Cross-nested logit model for the joint choice of residential location, travel mode, and departure time. Habitat Internat. 38:157–166.CrossrefGoogle Scholar
  • Zhang Y, Berman O, Verter V (2012) The impact of client choice on preventive healthcare facility network design. OR Spectrum 34:349–370.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.