Exact solution of hub network design problems with profits

•Study hub network design problems with profit-oriented objectives.•Simultaneous optimization of collected profit, setup and transportation costs.•A Lagrangian function is used to efficiently obtain bounds at nodes of the tree.•Numerical results confirm the superiority of our framework over commerci...

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Bibliographic Details
Published in:European journal of operational research 2018-04, Vol.266 (1), p.57-71
Main Authors: Alibeyg, Armaghan, Contreras, Ivan, Fernández, Elena
Format: Article
Language:English
Subjects:
65 Numerical analysis
65K Mathematical programming, optimization and variational techniques
68 Computer science
68M Computer system organization
90 Operations research, mathematical programming
90C Mathematical programming
Anàlisi numèrica
Arquitectura d'ordinadors
Branch-and-bound
Classificació AMS
Computer architecture
Hub location
Hub network design
Investigació operativa
Lagrangian relaxation
Location
Matemàtica aplicada a les ciències
Matemàtiques i estadística
Numerical analysis
Optimització
Programació (Matemàtica)
Programming (Mathematics)
Àrees temàtiques de la UPC
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Summary:•Study hub network design problems with profit-oriented objectives.•Simultaneous optimization of collected profit, setup and transportation costs.•A Lagrangian function is used to efficiently obtain bounds at nodes of the tree.•Numerical results confirm the superiority of our framework over commercial solver. This paper studies hub network design problems with profits. They consider a profit-oriented objective that measure the tradeoff between the revenue due to served commodities and the overall network design and transportation costs. An exact algorithmic framework is proposed for two variants of this class of problems, where a sophisticated Lagrangian function that exploits the structure of the problems is used to efficiently obtain bounds at the nodes of an enumeration tree. In addition, reduction tests and partial enumerations are used to considerably reduce the size of the problems and thus help decrease the computational effort. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed algorithmic framework. The proposed methodology can be used as a tool to solve more complex variants of this class of problems as well as other discrete location and network design problems involving servicing decisions.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2017.09.024