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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
