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Robust hub network design problem

Institution:	1. CIRRELT and DIRO, Université de Montréal, Montréal, Canada;2. Dipartimento di Informatica, Università di Pisa, Pisa, Italy;3. Dipartimento di Ingegneria dell’Informazione, Università di Pisa, Pisa, Italy;1. Departamento de Matemática-CMA, Faculdade de Ciências e Tecnologia, Universidade Nova Lisboa, Caparica 2829-516, Portugal;2. Institute of Operations Research, Karlsruhe Institute of Technology (KIT), Department of Logistics and Supply Chain Optimization, Research Center for Information Technology (FZI), Karlsruhe, Germany;3. Universidade de Lisboa, Faculdade de Ciências, Departamento de Estatística e Investigação Operacional e Centro de Matemática, Aplicações Fundamentais e Investigação Operacional, Bloco C6, Piso 4, 1749-016 Lisboa, Portugal;1. Department of Industrial Engineering, TOBB University of Economics and Technology, Ankara, Turkey;2. Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada

Abstract:	This paper presents a robust formulation for the uncapacitated single and multiple allocation hub location problem where demand is uncertain and its distribution is not fully specified. The proposed robust model is formulated as a mixed integer nonlinear program and then transformed into a mixed integer conic quadratic program. An efficient linear relaxation strategy is proposed which is found to deliver the optimal solutions for all the cases considered in this paper. Numerical experiments suggest location of more number of hubs when accounting for demand uncertainty using robust optimization compared to the deterministic setting.

Keywords:	Hub network design Robust optimization Mixed integer conic quadratic programs
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