The ordered median tree of hubs location problem

Miguel A. Pozo (), Justo Puerto () and Antonio M. Rodríguez Chía ()
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Miguel A. Pozo: University of Seville
Justo Puerto: University of Seville
Antonio M. Rodríguez Chía: University of Cádiz

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 29, issue 1, No 5, 78-105

Abstract: 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.

Keywords: Minimum spanning tree; Hub-and-spoke models; Ordered median; 90B80; 90C11 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11750-020-00572-z

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