Location, pricing and the problem of Apollonius

Andre Berger, Alexander Grigoriev*, Artem Panin, Andrej Winokurow

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


In Euclidean plane geometry, Apollonius’ problem is to construct a circle in a plane that is tangent to three given circles. We will use a solution to this ancient problem to solve several versions of the following geometric optimization problem. Given is a set of customers located in the plane, each having a demand for a product and a budget. A customer is satisfied if her total, travel and purchase, costs do not exceed the budget. The task is to determine location of production facilities in the plane and one price for the product such that the revenue generated from the satisfied customers is maximized.
Original languageEnglish
Pages (from-to)1797–1805
Number of pages9
JournalOptimization Letters
Issue number8
Publication statusPublished - Dec 2017

JEL classifications

  • c44 - "Operations Research; Statistical Decision Theory"


  • Pricing problem
  • facility location
  • Apollonius’ problem
  • exact algorithm
  • Complexity

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