This paper introduces the joint problem of locating hubs on a network and determining transportation prices between the hubs. Two levels of decision makers are present in the problem acting non-cooperatively: hub transportation provider and customers. The objective of the hub transportation provider is to locate hubs and to set the prices (per unit of commodity) of crossing the hub arcs maximizing its prot, whereas the customers aim is to send their commodities, in the cheapest way, having the possibility of using the hub arcs at the price set by the hub transportation provider or using the existing network at a predefined
tariff. The problem is modeled as a nonlinear bilevel programming formulation, which is in turn linearized, and strengthened through variable reductions as well as valid inequalities. The case in which the price of each hub arc is determined by applying a common discount factor to the predefined tariff in the existing network is also studied. Computational results of mixed integer programming models and a metaheuristic on instances adapted from the literature are presented.
Original languageEnglish
Pages (from-to)1035-1047
Number of pages13
JournalEuropean Journal of Operational Research
Issue number3
Early online date30 Nov 2021
Publication statusPublished - 16 Sept 2022

Bibliographical note

Funding Information:
This research has been partially supported by the Bath Institute for Mathematical Innovation, which the authors gratefully acknowledge. The research of the third author is partially funded by project number PID2020-114594GB-C22, supported by Agencia Estatal de Investigacion (AEI) and the European Regional Development’s funds (FEDER). Regional Government of Andalusia: projects FEDER-UCA18-106895, and P18-FR-1422; and Fundación BBVA: project NetmeetData (Ayudas Fundación BBVA a equipos de investigación científica 2019). This research made use of the Balena High Performance Computing (HPC) Service at the University of Bath.


  • Bilevel programming
  • Hub location
  • Pricing

ASJC Scopus subject areas

  • Computer Science(all)
  • Modelling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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