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The ordered median tree of hubs location problem

Author

Listed:
  • Miguel A. Pozo

    (University of Seville)

  • Justo Puerto

    (University of Seville)

  • Antonio M. Rodríguez Chía

    (University of Cádiz)

Abstract

In this paper, we propose the Ordered Median Tree of Hub Location Problem (OMTHL). The OMTHL is a single-allocation hub location problem where p hubs must be placed on a network and connected by a non-directed tree. Each non-hub node is assigned to a single hub and all the flow between origin–destination pairs must cross at least one hub. The objective is to minimize the sum of the ordered weighted averaged collection and distribution costs plus the sum of the interhub flow costs. We present different MILP formulations for the OMTHL based on the properties of the Minimum Spanning Tree Problem, the ordered median optimization and on the different ways of modeling flow within the network. Given that ordered median hub location problems are rather difficult to solve, we have improved the OMTHL solution performance by introducing covering variables in two valid reformulations. In addition, we have developed two pre-processing phases to reduce the size of these formulations. We establish an empirical comparison between these new formulations and we also provide enhancements that together with a proper formulation allow to solve medium-size instances on general random graphs.

Suggested Citation

  • Miguel A. Pozo & Justo Puerto & Antonio M. Rodríguez Chía, 2021. "The ordered median tree of hubs location problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 78-105, April.
    • Handle: RePEc:spr:topjnl:v:29:y:2021:i:1:d:10.1007_s11750-020-00572-z
    DOI: 10.1007/s11750-020-00572-z
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    References listed on IDEAS

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    Cited by:

    1. Ljubić, Ivana & Pozo, Miguel A. & Puerto, Justo & Torrejón, Alberto, 2024. "Benders decomposition for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 317(3), pages 858-874.
    2. Laureano F. Escudero & Juan F. Monge, 2021. "On Multistage Multiscale Stochastic Capacitated Multiple Allocation Hub Network Expansion Planning," Mathematics, MDPI, vol. 9(24), pages 1-39, December.

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