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Optimal solutions for the continuous p-centre problem and related -neighbour and conditional problems: A relaxation-based algorithm

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  • Becky Callaghan
  • Said Salhi
  • Jack Brimberg

Abstract

This paper aims to solve large continuous p-centre problems optimally by re-examining a recent relaxation-based algorithm. The algorithm is strengthened by adding four mathematically supported enhancements to improve its efficiency. This revised relaxation algorithm yields a massive reduction in computational time enabling for the first time larger data-sets to be solved optimally (e.g., up to 1323 nodes). The enhanced algorithm is also shown to be flexible as it can be easily adapted to optimally solve related practical location problems that are frequently faced by senior management when making strategic decisions. These include the α$ \alpha $-neighbour p-centre problem and the conditional p-centre problem. A scenario analysis using variable α$ \alpha $ is also performed to provide further managerial insights.

Suggested Citation

  • Becky Callaghan & Said Salhi & Jack Brimberg, 2019. "Optimal solutions for the continuous p-centre problem and related -neighbour and conditional problems: A relaxation-based algorithm," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(2), pages 192-211, February.
    • Handle: RePEc:taf:tjorxx:v:70:y:2019:i:2:p:192-211
    DOI: 10.1080/01605682.2017.1421854
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    Cited by:

    1. Sánchez-Oro, J. & López-Sánchez, A.D. & Hernández-Díaz, A.G. & Duarte, A., 2022. "GRASP with strategic oscillation for the α-neighbor p-center problem," European Journal of Operational Research, Elsevier, vol. 303(1), pages 143-158.
    2. Marilène Cherkesly & Claudio Contardo, 2021. "The conditional p-dispersion problem," Journal of Global Optimization, Springer, vol. 81(1), pages 23-83, September.

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