Solution of asymmetric discrete competitive facility location problems using ranking of candidate locations


We address a discrete competitive facility location problem with an asymmetric objective function and a binary customer choice rule. Both an integer linear programming formulation and a heuristic optimization algorithm based on ranking of candidate locations are designed to solve the problem. The proposed population-based heuristic algorithm is specially adapted for the discrete facility location problems by using their features such as geographical distances and the maximal possible utility of candidate locations, which can be evaluated in advance. The performance of the proposed algorithm was experimentally investigated by solving different instances of the model with real data of municipalities in Spain.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  1. Atta S, Sinha Mahapatra PR, Mukhopadhyay A (2019) Multi-objective uncapacitated facility location problem with customers’ preferences: pareto-based and weighted sum GA-based approaches. Soft Comput.

    Article  Google Scholar 

  2. Chan KY, Aydin ME, Fogarty TC (2006) Main effect fine-tuning of the mutation operator and the neighbourhood function for uncapacitated facility location problems. Soft Comput 10(11):1075–1090.

    Article  Google Scholar 

  3. Church R, ReVelle C (1974) The maximal covering location problem. Papers Region Sci Assoc 32(1):101–118

    Article  Google Scholar 

  4. Drezner T, Drezner Z (2004) Finding the optimal solution to the Huff based competitive location model. Comput Manag Sci 1(2):193–208

    MATH  Article  Google Scholar 

  5. Farahani RZ, Rezapour S, Drezner T, Fallah S (2014) Competitive supply chain network design: an overview of classifications, models, solution techniques and applications. Omega 45:92–118

    Article  Google Scholar 

  6. Fernandes D, Rocha C, Aloise D, Ribeiro G, Santos E, Silva A (2014) A simple and effective genetic algorithm for the two-stage capacitated facility location problem. Comput Ind Eng 75:200–208

    Article  Google Scholar 

  7. Fernández P, Pelegrín B, Lančinskas A, Žilinskas J (2017) New heuristic algorithms for discrete competitive location problems with binary and partially binary customer behavior. Comput Oper Res 79:12–18

    MathSciNet  MATH  Article  Google Scholar 

  8. FICO Xpress Mosel: Fair Isaac Corporation (2014)

  9. Francis RL, Lowe TJ, Tamir A (2002) Demand point aggregation for location models. In: Drezner Z, Hamacher H (eds) Facility location: application and theory. Springer, Berlin, pp 207–232

    Google Scholar 

  10. Friesz T, Miller T, Tobin R (1998) Competitive networks facility location models: a survey. Papers Region Sci 65:47–57

    Article  Google Scholar 

  11. Hakimi L (1995) Location with spatial interactions: vompetitive locations and games. In: Drezner Z (ed) Facility location: a survey of applications and methods. Springer, Berlin, pp 367–386

    Google Scholar 

  12. Hendrix E, Lančinskas A (2015) On benchmarking stochastic global optimization algorithms. Informatica 26(4):649–662

    MathSciNet  MATH  Article  Google Scholar 

  13. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann Arbor

    Google Scholar 

  14. Huff DL (1964) Defining and estimating a trade area. J Market 28:34–38

    Article  Google Scholar 

  15. Lančinskas A, Fernández P, Pelegín B, Žilinskas J (2017) Improving solution of discrete competitive facility location problems. Optim Lett 11(2):259–270

    MathSciNet  MATH  Article  Google Scholar 

  16. Onwubolu G, Mutingi M (2001) A genetic algorithm approach to cellular manufacturing systems. Comput Ind Eng 39(1):125–144

    MATH  Article  Google Scholar 

  17. Peeters PH, Plastria F (1998) Discretization results for the Huff and Pareto-Huff competitive location models on networks. TOP 6:247–260

    MathSciNet  MATH  Article  Google Scholar 

  18. Peng X, Xia X, Zhu R, Lin L, Gao H, He P (2018) A comparative performance analysis of evolutionary algorithms on k-median and facility location problems. Soft Comput 22(23):7787–7796.

    MATH  Article  Google Scholar 

  19. Plastria F (2001) Static competitive facility location: an overview of optimisation approaches. Eur J Oper Res 129(3):461–470

    MathSciNet  MATH  Article  Google Scholar 

  20. Reeves C, Rowe J (2002) Genetic algorithms: principles and perspectives: a guide to GA theory. Kluwer Academic Publishers, Kluwer

    Google Scholar 

  21. ReVelle C, Eiselt H, Daskin M (2008) A bibliography for some fundamental problem categories in discrete location science. Eur J Oper Res 184(3):817–848

    MathSciNet  MATH  Article  Google Scholar 

  22. Serra D, Colomé R (2001) Consumer choice and optimal locations models: formulations and heuristics. Papers Region Sci 80(4):439–464

    Article  Google Scholar 

  23. Serra D, ReVelle C (1995) Competitive location in discrete space. In: Drezner Z (ed) Facility Location: A Survey of Applications and Methods. Springer, Berlin, pp 367–386

    Google Scholar 

  24. Suárez-Vega R, Santos-Penate DR, Dorta-Gonzalez P (2004) Discretization and resolution of the (\(r|{X}_p\))-medianoid problem involving quality criteria. TOP 12(1):111–133

    MathSciNet  MATH  Google Scholar 

  25. Suárez-Vega R, Santos-Penate DR, Dorta-González P (2007) The follower location problem with attraction thresholds. Papers Region Sci 86(1):123–137

    MATH  Article  Google Scholar 

  26. Watanabe M, Ida K, Gen M (2005) A genetic algorithm with modified crossover operator and search area adaptation for the job-shop scheduling problem. Comput Ind Eng 48(4):743–752

    Article  Google Scholar 

Download references


This research is funded by the European Social Fund under the No. 09.3.3-LMT-K-712 “Development of Competences of Scientists, other Researchers and Students through Practical Research Activities” measure. This research is funded by the Ministry of Economy and Competitiveness of Spain under the research Project MTM2015-70260-P, and by the Fundación Séneca (The Agency of Science and Technology of the Region of Murcia) under the research Project 19241/PI/14.

Author information



Corresponding author

Correspondence to Algirdas Lančinskas.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Communicated by Yaroslav D. Sergeyev.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lančinskas, A., Žilinskas, J., Fernández, P. et al. Solution of asymmetric discrete competitive facility location problems using ranking of candidate locations. Soft Comput (2020).

Download citation


  • Asymmetric facility location
  • Binary choice rule
  • Combinatorial optimization
  • Random search
  • Population-based heuristic algorithms