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 Sep 2022


  • 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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