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Multi-product Capacitated Single-Allocation Hub Location Problems: Formulations and Inequalities

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Abstract

In this paper we extend the classical capacitated single-allocation hub location problem by considering that multiple products are to be shipped through the network. We propose a unified modeling framework for the situation in which no more than one hub can be located in each node. In particular, we consider the case in which all hubs are dedicated to handling a single-product as well as the case in which all hubs can handle all products. The objective is to minimize the total cost, which includes setup costs for the hubs, setup costs for each product in each hub and flow routing costs. Hubs are assumed to be capacitated. For this problem several models are proposed which are based on existing formulations for the (single-product) capacitated single-allocation hub location problem. Additionally, several classes of inequalities are proposed in order to strengthen the models in terms of the lower bound provided by the linear relaxation. We report results of a set of computational experiments conducted to test the proposed models and their enhancements.

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Acknowledgments

This work was supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the projects PEst-OE/MAT/UI0152 (CIO/FCUL) and PEst-OE/MAT/UIO297 (CMA/FCT/UNL).The authors would like to express their gratitude to the Associate Editor and to the two anonymous reviewers for the constructive criticism, comments and suggestions which helped to improve the paper.

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Authors and Affiliations

  1. Faculdade de Ciências e Tecnologia, Departamento de Matemática - CMA, Universidade Nova Lisboa, 2829-516, Caparica, Portugal

    Isabel Correia

  2. Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany

    Stefan Nickel

  3. Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germany

    Stefan Nickel

  4. DEIO-CIO, Faculdade de Ciências, Universidade de Lisboa, 1716-049, Lisboa, Portugal

    Francisco Saldanha-da-Gama

Authors
  1. Isabel Correia
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  2. Stefan Nickel
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  3. Francisco Saldanha-da-Gama
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Correspondence to Isabel Correia.

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Correia, I., Nickel, S. & Saldanha-da-Gama, F. Multi-product Capacitated Single-Allocation Hub Location Problems: Formulations and Inequalities. Netw Spat Econ 14, 1–25 (2014). https://doi.org/10.1007/s11067-013-9197-3

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