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Improving solution of discrete competitive facility location problems

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Abstract

We consider discrete competitive facility location problems in this paper. Such problems could be viewed as a search of nodes in a network, composed of candidate and customer demand nodes, which connections correspond to attractiveness between customers and facilities located at the candidate nodes. The number of customers is usually very large. For some models of customer behavior exact solution approaches could be used. However, for other models and/or when the size of problem is too high to solve exactly, heuristic algorithms may be used. The solution of discrete competitive facility location problems using genetic algorithms is considered in this paper. The new strategies for dynamic adjustment of some parameters of genetic algorithm, such as probabilities for the crossover and mutation operations are proposed and applied to improve the canonical genetic algorithm. The algorithm is also specially adopted to solve discrete competitive facility location problems by proposing a strategy for selection of the most promising values of the variables in the mutation procedure. The developed genetic algorithm is demonstrated by solving instances of competitive facility location problems for an entering firm.

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References

  1. Dorigo, M., Gambardella, L.M.: Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans. Evol. Comput. 1(1), 53–66 (1997). doi:10.1109/4235.585892

    Article  Google Scholar 

  2. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, MHS ’95, pp. 39–43 (1995). doi:10.1109/MHS.1995.494215

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

    Article  Google Scholar 

  4. Francis, R.L., Lowe, T.J., Tamir, A.: Demand point aggregation for location models. In: Drezner, Z., Hamacher, H. (eds.) Facility Location: Application and Theory, pp. 207–232. Springer, Berlin (2002)

    Chapter  MATH  Google Scholar 

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

    Article  Google Scholar 

  6. Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977). doi:10.1111/j.1540-5915.1977.tb01074.x

    Article  Google Scholar 

  7. Hakimi, L.: Locations with spatial interactions: competitive locations and games. In: Mirchandani, P.B., Francis, R.L. (eds.) Discrete Location Theory, pp. 439–478. Wiley, New York (1990)

  8. Hakimi, L.: Location with spatial interactions: competitive locations and games. In: Drezner, Z. (ed.) Facility Location: A Survey of Applications and Methods, pp. 367–386. Springer, Berlin (1995)

    Google Scholar 

  9. Holland, J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  10. Huff, D.L.: Defining and estimating a trade area. J. Mark. 28, 34–38 (1964)

    Article  Google Scholar 

  11. Pelegrín, B., Fernández, P., García, M.D.: On tie breaking in competitive location under binary customer behavior. OMEGA Int. J. Manag. Sci. 52, 156–167 (2015)

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. ReVelle, C.S., Eiselt, H.A., Daskin, M.S.: A bibliography for some fundamental problem categories in discrete location science. Eur. J. Oper. Res. 184(3), 248–259 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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

    Chapter  Google Scholar 

  15. Shaikh, A., Salhi, S., Ndiaye, M.: New MAXCAP related problems: formulation and model resolution. Comput. Ind. Eng. 85(3), 817–848 (2015)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  17. Törn, A., Žilinskas, A.: Global Optimization. Springer, New York (1989)

    Book  MATH  Google Scholar 

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Acknowledgments

This research was funded by a grant (No. MIP-051/2014) from the Research Council of Lithuania.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Vilnius University, Akademijos 4, 08663, Vilnius, Lithuania

    Algirdas Lančinskas & Julius Žilinskas

  2. Department of Statistics and Operations Research, University of Murcia, Campus Espinardo, 30071, Murcia, Spain

    Pascual Fernández & Blas Pelegín

Authors
  1. Algirdas Lančinskas
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  2. Pascual Fernández
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  3. Blas Pelegín
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  4. Julius Žilinskas
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Correspondence to Julius Žilinskas.

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Lančinskas, A., Fernández, P., Pelegín, B. et al. Improving solution of discrete competitive facility location problems. Optim Lett 11, 259–270 (2017). https://doi.org/10.1007/s11590-015-0930-3

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  • DOI: https://doi.org/10.1007/s11590-015-0930-3

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