Location, Pricing and the Problem of Apollonius

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

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic


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 her 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
Title of host publicationDiscrete Optimization and Operations Research
EditorsYury Kochetov, Michael Khachay, Vladimir Beresnev, Evgeni A. Nurminski, Panos M. Pardalos
Place of PublicationSwitzerland
ISBN (Print)978-3-319-44913-5
Publication statusPublished - 10 Sept 2016
Event Discrete Optimization and Operations Research - Vladivostok, Russian Federation
Duration: 19 Sept 201623 Dec 2016
Conference number: 9th

Publication series

SeriesLecture Notes in Computer Science


Conference Discrete Optimization and Operations Research
Abbreviated titleDOOR 2016
Country/TerritoryRussian Federation
Internet address


  • pricing problem
  • facility location
  • Apollonius' problem
  • complexity
  • exact algorithm


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