Facility location in unfair competition

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2 Citations (Scopus)


We consider a mathematical model belonging to the family of competitive location problems. In the model, there are two competing parties called Leader and Follower, which open their facilities with the goal to capture customers and maximize profit. In our model we assume that Follower is able to open own facilities as well as to close the Leader’s ones. The model can be written as a pessimistic bilevel integer programming problem. We show that the problem of Leader’s profit maximization can be represented as a problem of pseudo–Boolean function maximization. The number of variables the function depends on equals to the number of sites available for opening a facility. We suggest a method of calculation of an upper bound for the optimal value of the function based on strengthening of a bilevel model with valid inequalities and further relaxation of the model by removing the lower–level optimization problem.

Original languageEnglish
Title of host publicationDiscrete Optimization and Operations Research - 9th International Conference, DOOR 2016, Proceedings
EditorsMichael Khachay, Panos Pardalos, Yury Kochetov, Vladimir Beresnev, Evgeni Nurminski
PublisherSpringer-Verlag GmbH and Co. KG
Number of pages11
ISBN (Print)9783319449135
Publication statusPublished - 2016
Event9th International Conference on Discrete Optimization and Operations Research, DOOR 2016 - Vladivostok, Russian Federation
Duration: 19 Sep 201623 Sep 2016

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9869 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Discrete Optimization and Operations Research, DOOR 2016
CountryRussian Federation


  • Competitive location
  • Stackelberg game
  • Upper bound


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