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Efficient presolving methods for solving maximal covering and partial set covering location problems

Author

Listed:
  • Chen, Liang
  • Chen, Sheng-Jie
  • Chen, Wei-Kun
  • Dai, Yu-Hong
  • Quan, Tao
  • Chen, Juan

Abstract

The maximal covering location problem (MCLP) and the partial set covering location problem (PSCLP) are two fundamental problems in facility location and have widespread applications in practice. The MCLP determines a subset of facilities to open to maximize the demand of covered customers subject to a budget constraint on the cost of open facilities; and the PSCLP aims to minimize the cost of open facilities while requiring a certain amount of customer demand to be covered. Both problems can be modeled as mixed integer programming (MIP) formulations. Due to the intrinsic NP-hardness nature, however, it is a great challenge to solve them to optimality by MIP solvers, especially for large-scale cases. In this paper, we present five customized presolving methods to enhance the capability of employing MIP solvers in solving the two problems. The five presolving methods are designed to reduce the sizes of the problem formulation and the search tree of the branch-and-cut procedure. For planar problems with an extremely huge number of customers under realistic types of facility coverage, we show that the number of customers in the reduced problems can be bounded above by a quadratic polynomial of the number of facilities. By extensive numerical experiments, the five presolving methods are demonstrated to be effective in accelerating the solution process of solving the MCLP and PSCLP. Moreover, they enable to solve problems with billions of customers, which is at least one order of magnitude larger than those that can be tackled by previous approaches.

Suggested Citation

  • Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.
  • Handle: RePEc:eee:ejores:v:311:y:2023:i:1:p:73-87
    DOI: 10.1016/j.ejor.2023.04.044
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    1. Adenso-Díaz, B. & Rodríguez, F., 1997. "A simple search heuristic for the MCLP: Application to the location of ambulance bases in a rural region," Omega, Elsevier, vol. 25(2), pages 181-187, April.
    2. Byrne, Thomas & Kalcsics, Jörg, 2022. "Conditional facility location problems with continuous demand and a polygonal barrier," European Journal of Operational Research, Elsevier, vol. 296(1), pages 22-43.
    3. Manish Bansal & Kiavash Kianfar, 2017. "Planar Maximum Coverage Location Problem with Partial Coverage and Rectangular Demand and Service Zones," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 152-169, February.
    4. Kahr, Michael & Leitner, Markus & Ruthmair, Mario & Sinnl, Markus, 2021. "Benders decomposition for competitive influence maximization in (social) networks," Omega, Elsevier, vol. 100(C).
    5. He, Zhou & Fan, Bo & Cheng, T.C.E. & Wang, Shou-Yang & Tan, Chin-Hon, 2016. "A mean-shift algorithm for large-scale planar maximal covering location problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 65-76.
    6. Brian T. Downs & Jeffrey D. Camm, 1996. "An exact algorithm for the maximal covering problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(3), pages 435-461, April.
    7. Constantine Toregas & Ralph Swain & Charles ReVelle & Lawrence Bergman, 1971. "The Location of Emergency Service Facilities," Operations Research, INFORMS, vol. 19(6), pages 1363-1373, October.
    8. Sourour Elloumi, 2010. "A tighter formulation of the p-median problem," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 69-83, January.
    9. F. Robert Dwyer & James R. Evans, 1981. "A Branch and Bound Algorithm for the List Selection Problem in Direct Mail Advertising," Management Science, INFORMS, vol. 27(6), pages 658-667, June.
    10. Steffen Rebennack & Marcus Oswald & Dirk Oliver Theis & Hanna Seitz & Gerhard Reinelt & Panos M. Pardalos, 2011. "A Branch and Cut solver for the maximum stable set problem," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 434-457, May.
    11. Galvao, Roberto Dieguez & ReVelle, Charles, 1996. "A Lagrangean heuristic for the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 88(1), pages 114-123, January.
    12. Richard Church & Charles R. Velle, 1974. "The Maximal Covering Location Problem," Papers in Regional Science, Wiley Blackwell, vol. 32(1), pages 101-118, January.
    13. Güney, Evren & Leitner, Markus & Ruthmair, Mario & Sinnl, Markus, 2021. "Large-scale influence maximization via maximal covering location," European Journal of Operational Research, Elsevier, vol. 289(1), pages 144-164.
    14. Arana-Jiménez, Manuel & Blanco, Víctor & Fernández, Elena, 2020. "On the fuzzy maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 283(2), pages 692-705.
    15. Patrick Gemander & Wei-Kun Chen & Dieter Weninger & Leona Gottwald & Ambros Gleixner & Alexander Martin, 2020. "Two-row and two-column mixed-integer presolve using hashing-based pairing methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(3), pages 205-240, October.
    16. Karatas, Mumtaz & Eriskin, Levent, 2021. "The minimal covering location and sizing problem in the presence of gradual cooperative coverage," European Journal of Operational Research, Elsevier, vol. 295(3), pages 838-856.
    17. Letchford, Adam N. & Miller, Sebastian J., 2014. "An aggressive reduction scheme for the simple plant location problem," European Journal of Operational Research, Elsevier, vol. 234(3), pages 674-682.
    18. W. David Pisinger & Anders Bo Rasmussen & Rune Sandvik, 2007. "Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 280-290, May.
    19. QIU, Feng & AHMED, Shabbir & DEY, Santanu S & WOLSEY, Laurence A, 2014. "Covering linear programming with violations," LIDAM Reprints CORE 2618, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Feng Qiu & Shabbir Ahmed & Santanu S. Dey & Laurence A. Wolsey, 2014. "Covering Linear Programming with Violations," INFORMS Journal on Computing, INFORMS, vol. 26(3), pages 531-546, August.
    21. Tobias Achterberg & Robert E. Bixby & Zonghao Gu & Edward Rothberg & Dieter Weninger, 2020. "Presolve Reductions in Mixed Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 473-506, April.
    22. Tedeschi, Danilo & Andretta, Marina, 2021. "New exact algorithms for planar maximum covering location by ellipses problems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 114-127.
    23. Cordeau, Jean-François & Furini, Fabio & Ljubić, Ivana, 2019. "Benders decomposition for very large scale partial set covering and maximal covering location problems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 882-896.
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