The ordered median tree of hubs location problem

• Miguel A. Pozo ^[1] ; Justo Puerto ^[1] ; Antonio M. Rodríguez Chía ^[2]
  1. [1] Universidad de Sevilla

     Universidad de Sevilla

     Sevilla, España

     
  2. [2] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 29, Nº. 1, 2021, págs. 78-105
• Idioma: inglés
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• Resumen

  • 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.