The competitive hub location under the price war

Dimitrije D. Čvokić, Yury A. Kochetov, Aleksandr V. Plyasunov, Aleksandar Savić

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

4 Citations (Scopus)


Two transportation companies want to enter the market and they are aware of each other. The objective for the both of competitors is to maximize their respective profits by finding the best hub and spoke networks and price structures. One company wants to establish r hubs and the other wants to establish p hubs. It is assumed that the customers choose the route by price and the logistic regression based model is used to estimate how the demand is shared. After setting their networks, the competing companies engage in the price war. We propose a new model for finding a Stackelberg strategy that includes a price game, as bi-level nonlinear mixed-integer program, called the (r|p) hub-centroid problem under the price war. It is shown that there is a unique finite Bertrand-Nash price equilibrium. On the basis of this result, we show the solution existence, propose a new equations for the best response pricing, and address the computational complexity of the problem. Finally, we discuss some possible future research directions that concern the solution approach and some other competitive scenarios that involve pricing.

Original languageEnglish
Title of host publicationMathematical Optimization Theory and Operations Research - 18th International Conference, MOTOR 2019, Proceedings
EditorsMichael Khachay, Panos Pardalos, Yury Kochetov
PublisherSpringer-Verlag GmbH and Co. KG
Number of pages14
ISBN (Print)9783030226282
Publication statusPublished - 1 Jan 2019
Event18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019 - Ekaterinburg, Russian Federation
Duration: 8 Jul 201912 Jul 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11548 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference18th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2019
CountryRussian Federation


  • Bertrand price equilibrium
  • Complexity
  • Hub location
  • Logit model
  • Stackelberg strategy


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