Abstract
This paper studies effective solving techniques for large p-location problems, in which generalized disutility is applied to incorporate stochastic behavior of real service system. The concept of generalized disutility follows the idea that the nearest located service center may be temporarily unavailable at the moment of currently arisen demand and the demand is serviced from a more distant service center with given probability. The more complex approach to the real p-location asks for enormous computational time of exact solving tools and thus evokes the question whether the faster heuristics can compete with the exact approaches in accuracy of results obtained. To answer the question, two heuristics were proposed for the studied problem. The first of them is a common swap local search with the best-admissible strategy and the second is based on the path-relinking method. The both heuristics make use of so called uniformly deployed sets used for preliminary mapping of the feasible solutions to accelerate the performance of the heuristics. As uniformly deployed set construction can be done in two modes, the paper is also focused on finding the most effective combination of the mode and heuristic. A real case study was performed with seven road networks with number of nodes varying from 250 to 660. In addition, ten different families of uniformly deployed sets were generated for each network and mode. The results of the case study confirm that the suggested approaches are able to produce the solutions of the same quality as the exact approaches. Furthermore, the study indicates drawbacks, which can be met in connection with usage of specific combinations of heuristic and the mode of uniformly deployed set construction.
Similar content being viewed by others
References
Avella P, Sassano A, Vasil’ev I (2007) Computational study of large scale p-median problems. Math Program 109:89–114
Bertsimas D, Farias VF, Trichakis N (2011) The price of fairness. Oper Res 59(1):17–31
Brotcorne L, Laporte G, Semet F (2003) Ambulance location and relocation models. Eur J Oper Res 147:451–463
Buzna Ľ, Koháni M, Janáček J (2013) Proportionally Fairer public service systems design. Commun Sci Lett Univ Žilina 15(1):14–18
Chanta S, Mayorga ME, McLay LA (2014) Improving emergency service in rural areas: a bi-objective covering location model for EMS systems. Ann Oper Res 221:133–159
Current J, Daskin M, Schilling D (2002) Discrete network location models, Drezner Z. et al. (ed) Facility location: applications and theory, Springer, pp 81–118
García S, Labbé M, Marín A (2011) Solving large p-median problems with a radius formulation. INFORMS J Comput 23(4):546–556
Gendreau M, Potvin J (2010) Handbook of metaheuristics, Springer, Berlin
Ingolfsson A, Budge S, Erkut E (2008) Optimal ambulance location with random delays and travel times. Health Care Manag Sci 11(3):262–274
Janáček J, Gábrišová L (2017) Collective fairness in emergency system designing. In: SOR´17: proceedings of the 14th international symposium on operational research, Bled, Slovenia, pp 135–140
Janáček J, Kvet M (2016) Min-max optimization and the radial approach to the public service system design with generalized utility. Croatian Oper Res Rev 7(1):49–61
Janáček J, Kvet M (2019a) Usage of uniformly deployed set for p-location min-sum problem with generalized disutility. In: Proceedings of the 15th international symposium on operational research SOR’19, Bled, Slovenia, ISBN 978-961-6165-55-6, pp 494–499
Janáček J, Kvet M (2019b) Uniform deployment of the p-location problem solutions. In: Operations research proceedings 2019, Springer, in print
Jankovič P (2016) Calculating reduction coefficients for optimization of emergency service system using microscopic simulation model. In: 17th International symposium on computational intelligence and informatics, Budapest, Hungary, pp 163–167
Karatas M, Yakıcıa E (2019) An analysis of p-median location problem: effects of backup service level and demand assignment policy. Eur J Oper Res 272(1):207–218
Kvet M (2014) Computational study of radial approach to public service System design with generalized disutility. In: Digital technologies 2014. Žilina, Slovakia, pp 198–208
Kvet M (2015) Exact and heuristic radial approach to fair public service system design. In: Information and digital technologies. Žilina, Slovakia, pp 185–194
Kvet M, Janáček J (2019) Usage of Uniform Deployment for Heuristic Design of Emergency System. Operations Research Proceedings 2019, Springer, in print
Marianov V, Serra D (2002) Location problems in the public sector. In: Drezner Z (ed) Facility location−applications and theory. Springer, Berlin, pp 119–150
Ogryczak W, Sliwinski T (2006) On direct methods for lexicographic min-max optimization. In: Gavrilova M et al (eds) ICCSA 2006, LNCS 3982. Springer, Berlin, pp 802–811
Rybičková A, Burketová A, Mocková D (2016) Solution to the locating—routing problem using a genetic algorithm. In: SmaRTT cities symposiuum prague (SCSP), pp 1–6
Snyder LV, Daskin MS (2005) Reliability models for facility location; the expected failure cost case. Transp Sci 39(3):400–416
Acknowledgements
This work was supported by the research Grants VEGA 1/0342/18 “Optimal dimensioning of service systems”, VEGA 1/0089/19 “Data analysis methods and decisions support tools for service systems supporting electric vehicles” and VEGA 1/0689/19 “Optimal design and economically efficient charging infrastructure deployment for electric buses in public transportation of smart cities”. This work was supported by the Slovak Research and Development Agency under the Contract no. APVV-19-0441. As far as the disclosure of interest is concerned, both authors of the manuscript declare that they have no conflicts to report. We honestly declare that presented results do not contain studies with human or animal subjects.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Janáček, J., Kvet, M. Efficient incrementing heuristics for generalized p-location problems. Cent Eur J Oper Res 29, 989–1000 (2021). https://doi.org/10.1007/s10100-020-00722-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10100-020-00722-5