Location, Pricing and the Problem of Apollonius

Andre Berger, Alexander Grigoriev, Artem Panin, Andrej Winokurow

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

Abstract

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
PublisherSpringer
Pages563-569
Volume9869
ISBN (Print)978-3-319-44913-5
DOIs
Publication statusPublished - 10 Sep 2016
Event Discrete Optimization and Operations Research - Vladivostok, Russian Federation
Duration: 19 Sep 201623 Dec 2016
Conference number: 9th
http://math.nsc.ru/conference/door/2016/

Publication series

SeriesLecture Notes in Computer Science
Volume9869

Conference

Conference Discrete Optimization and Operations Research
Abbreviated titleDOOR 2016
CountryRussian Federation
CityVladivostok
Period19/09/1623/12/16
Internet address

Keywords

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

Cite this

Berger, A., Grigoriev, A., Panin, A., & Winokurow, A. (2016). Location, Pricing and the Problem of Apollonius. In Y. Kochetov, M. Khachay, V. Beresnev, E. A. Nurminski, & P. M. Pardalos (Eds.), Discrete Optimization and Operations Research (Vol. 9869, pp. 563-569). Switzerland: Springer. Lecture Notes in Computer Science, Vol.. 9869 https://doi.org/10.1007/978-3-319-44914-2_44
Berger, Andre ; Grigoriev, Alexander ; Panin, Artem ; Winokurow, Andrej. / Location, Pricing and the Problem of Apollonius. Discrete Optimization and Operations Research. editor / Yury Kochetov ; Michael Khachay ; Vladimir Beresnev ; Evgeni A. Nurminski ; Panos M. Pardalos. Vol. 9869 Switzerland : Springer, 2016. pp. 563-569 (Lecture Notes in Computer Science, Vol. 9869).
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abstract = "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.",
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Berger, A, Grigoriev, A, Panin, A & Winokurow, A 2016, Location, Pricing and the Problem of Apollonius. in Y Kochetov, M Khachay, V Beresnev, EA Nurminski & PM Pardalos (eds), Discrete Optimization and Operations Research. vol. 9869, Springer, Switzerland, Lecture Notes in Computer Science, vol. 9869, pp. 563-569, Discrete Optimization and Operations Research, Vladivostok, Russian Federation, 19/09/16. https://doi.org/10.1007/978-3-319-44914-2_44

Location, Pricing and the Problem of Apollonius. / Berger, Andre; Grigoriev, Alexander; Panin, Artem; Winokurow, Andrej.

Discrete Optimization and Operations Research. ed. / Yury Kochetov; Michael Khachay; Vladimir Beresnev; Evgeni A. Nurminski; Panos M. Pardalos. Vol. 9869 Switzerland : Springer, 2016. p. 563-569 (Lecture Notes in Computer Science, Vol. 9869).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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KW - pricing problem

KW - facility location

KW - Apollonius' problem

KW - complexity

KW - exact algorithm

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Berger A, Grigoriev A, Panin A, Winokurow A. Location, Pricing and the Problem of Apollonius. In Kochetov Y, Khachay M, Beresnev V, Nurminski EA, Pardalos PM, editors, Discrete Optimization and Operations Research. Vol. 9869. Switzerland: Springer. 2016. p. 563-569. (Lecture Notes in Computer Science, Vol. 9869). https://doi.org/10.1007/978-3-319-44914-2_44