Advertisement

Discrete Competitive Facility Location by Ranking Candidate Locations

  • Algirdas LančinskasEmail author
  • Pascual Fernández
  • Blas Pelegrín
  • Julius Žilinskas
Chapter
  • 20 Downloads
Part of the Studies in Computational Intelligence book series (SCI, volume 869)

Abstract

Competitive facility location is a strategic decision for firms providing goods or services and competing for the market share in a geographical area. There are different facility location models and solution procedures proposed in the literature which vary on their ingredients, such as location space, customer behavior, objective function(s), etc. In this paper we focus on two discrete competitive facility location problems: a single objective discrete facility location problem for an entering firm and a bi-objective discrete facility location problem for firm expansion. Two random search algorithms for discrete facility location based on ranking of candidate locations are described and the results of their performance investigation are discussed. It is shown that the ranking of candidate locations is a suitable strategy for discrete facility location as the algorithms are able to determine the optimal solution for different instances of the facility location problem or approximate the optimal solution with a reasonable accuracy.

Keywords

Facility location Combinatorial optimization Multi-objective optimization Random search algorithms 

Notes

Acknowledgements

This research has been supported by Fundación Séneca (The Agency of Science and Technology of the Region of Murcia, Spain) under the research project 20817/PI/18. This article is based upon work from COST Action CA15140 “Improving Applicability of Nature-Inspired Optimisation by Joining Theory and Practice (ImAppNIO)” supported by COST (European Cooperation in Science and Technology).

References

  1. Aboolian R, Berman O, Krass D (2008) Optimizing pricing and location decisions for competitive service facilities charging uniform price. J Oper Res Soc 59(11):1506–1519CrossRefGoogle Scholar
  2. Ashtiani M (2016) Competitive location: a state-of-art review. Int J Ind Eng Comput 7(1):1–18Google Scholar
  3. Balinski M (1965) Integer programming: methods, uses and computation. Manage Sci 24:253–313MathSciNetCrossRefGoogle Scholar
  4. Chinchuluun A, Pardalos PM (2007) A survey of recent developments in multiobjective optimization. Ann Oper Res 154(1):29–50MathSciNetCrossRefGoogle Scholar
  5. Chinchuluun A, Pardalos PM, Migdalas A, Pitsoulis L (eds) (2008) Pareto optimality, game theory and equilibria. In: Springer optimization and its applications, vol 17. Springer, New YorkGoogle Scholar
  6. Christaller W (1950) Das grundgerust der raumlichen ordnung in europa : Die systeme der europaischen zentralen orte. Frankfurter Geographische Hefte 24:96SGoogle Scholar
  7. Davis L (1991) Handbook of genetic algorithms. Van Nostrand Reinhold, VNR computer libraryGoogle Scholar
  8. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRefGoogle Scholar
  9. Doerner KF, Gutjahr WJ, Nolz PC (2009) Multi-criteria location planning for public facilities in tsunami-prone coastal areas. OR Spectrum 31(3):651–678MathSciNetCrossRefGoogle Scholar
  10. Drezner T (2014) A review of competitive facility location in the plane. Logistics Res 7(1):114MathSciNetCrossRefGoogle Scholar
  11. Drezner T, Drezner Z (2004) Finding the optimal solution to the huff based competitive location model. Comput Manage Sci 1(2):193–208CrossRefGoogle Scholar
  12. Eiselt HA, Marianov V, Drezner T (2015) Competitive location models. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer International Publishing, Cham, pp 365–398Google Scholar
  13. Farahani RZ, SteadieSeifi M, Asgari N (2010) Multiple criteria facility location problems: a survey. Appl Math Model 34(7):1689–1709MathSciNetCrossRefGoogle Scholar
  14. 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 79:12–18MathSciNetCrossRefGoogle Scholar
  15. FICO Xpress Mosel (2014) Fair Isaac CorporationGoogle Scholar
  16. Fischer K (2011) Central places: the theories of von Thünen, Christaller, and Lösch. In: Eiselt HA, Marianov V (eds) Found Location Anal. Springer, US, pp 471–505CrossRefGoogle Scholar
  17. Francis R, Lowe T, Tamir A (2002) Demand point aggregation for location models. In: Drezner Z, Hamacher H (eds) Facility Location Appl Theor. Springer, Berlin Heidelberg, pp 207–232CrossRefGoogle Scholar
  18. Ghosh A, Craig C (1991) FRANSYS: a franchise distribution system location model. J Retail 64(4):466–495Google Scholar
  19. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning, 1st edn. Addison-Wesley Longman Publishing Co., Inc, Boston, MA, USAGoogle Scholar
  20. Hakimi L (1995) Location with spatial interactions: competitive locations and games. In: Drezner Z (ed) Facility location: a survey of applications and methods. Springer, New York, pp 367–386Google Scholar
  21. Hakimi SL (1964) Optimum locations of switching centers and the absolute centers and medians of a graph. Oper Res 12(3):450–459CrossRefGoogle Scholar
  22. Hakimi SL (1965) Optimal distribution of switching centers in a communication network and some related theoretic graph problems. Oper Res 13:462–475CrossRefGoogle Scholar
  23. Hendrix E, Lančinskas A (2015) On benchmarking stochastic global optimization algorithms. Informatica 26(4):649–662MathSciNetCrossRefGoogle Scholar
  24. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, MichiganGoogle Scholar
  25. Huff D (1964) Defining and estimating a trade area. J Mark 28:34–38CrossRefGoogle Scholar
  26. Jaramillo JH, Bhadury J, Batta R (2002) On the use of genetic algorithms to solve location problems. Comput Oper Res 29(6):761–779MathSciNetCrossRefGoogle Scholar
  27. Lančinskas A, Fernández P, Pelegrín B, Žilinskas J (2016) Solution of discrete competitive facility location problem for firm expansion. Informatica 27(2):451–462CrossRefGoogle Scholar
  28. Lančinskas A, Fernández P, Pelegrín B, Žilinskas J (2017) Improving solution of discrete competitive facility location problems. Optim Lett 11(2):259–270MathSciNetCrossRefGoogle Scholar
  29. Liao SH, Hsieh CL (2009) A capacitated inventory-location model: formulation, solution approach and preliminary computational results. In: Chien BC, Hong TP, Chen SM, Ali M (eds) Next-generation applied intelligence. Springer, Berlin Heidelberg, pp 323–332CrossRefGoogle Scholar
  30. Lösch A (1940) Die räumliche Ordnung der Wirtschaft: eine Untersuchung über Standort. Fischer, Wirtschaftsgebiete und internationalen Handel. GGoogle Scholar
  31. Medaglia AL, Villegas JG, Rodríguez-Coca DM (2009) Hybrid biobjective evolutionary algorithms for the design of a hospital waste management network. J Heuristics 15(2):153CrossRefGoogle Scholar
  32. Montibeller G, Franco A (2010) Multi-criteria decision analysis for strategic decision making. In: Applied optimization, vol 103. Springer, Berlin HeidelbergGoogle Scholar
  33. Peeters PH, Plastria F (1998) Discretization results for the Huff and Pareto-Huff competitive location models on networks. TOP 6:247–260MathSciNetCrossRefGoogle Scholar
  34. ReVelle CS, Swain RW (1970) Central facilities location. Geogr Anal 2(1):30–42CrossRefGoogle Scholar
  35. Serra D, Colomé R (2001) Consumer choice and optimal locations models: formulations and heuristics. Pap Reg Sci 80(4):439–464CrossRefGoogle Scholar
  36. Sinnott RW (1984) Virtues of the haversine. Sky Telescope 68:159Google Scholar
  37. Srinivas N, Deb K (1994) Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2:221–248CrossRefGoogle Scholar
  38. 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):111–133MathSciNetCrossRefGoogle Scholar
  39. Suárez-Vega R, Santos-Penate DR, Dorta-González P (2007) The follower location problem with attraction thresholds. Pap Reg Sci 86(1):123–137CrossRefGoogle Scholar
  40. von Thunen JH (1910) Der isolierte Staat in Beziehung auf Landwirtschaft und Nationalokonomie. Verlag von Gustav Fischer, JenaGoogle Scholar
  41. Villegas JG, Palacios F, Medaglia AL (2006) Solution methods for the bi-objective (cost-coverage) unconstrained facility location problem with an illustrative example. Ann Oper Res 147(1):109–141MathSciNetCrossRefGoogle Scholar
  42. Zhou A, Jin Y, Zhang Q, Sendhoff B, Tsang E (2006) Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In: 2006 IEEE international conference on evolutionary computation, pp 892–899Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Algirdas Lančinskas
    • 1
    Email author
  • Pascual Fernández
    • 2
  • Blas Pelegrín
    • 2
  • Julius Žilinskas
    • 1
  1. 1.Institute of Data Science and Digital TechnologiesVilnius UniversityVilniusLithuania
  2. 2.Department of Statistics and Operations ResearchUniversity of Murcia Campus EspinardoMurciaSpain

Personalised recommendations