Research Output per year

### 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 language | English |
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Title of host publication | Discrete Optimization and Operations Research |

Editors | Yury Kochetov, Michael Khachay, Vladimir Beresnev, Evgeni A. Nurminski, Panos M. Pardalos |

Place of Publication | Switzerland |

Publisher | Springer |

Pages | 563-569 |

Volume | 9869 |

ISBN (Print) | 978-3-319-44913-5 |

DOIs | |

Publication status | Published - 10 Sep 2016 |

Event | Discrete Optimization and Operations Research - Vladivostok, Russian Federation Duration: 19 Sep 2016 → 23 Dec 2016 Conference number: 9th http://math.nsc.ru/conference/door/2016/ |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 9869 |

### Conference

Conference | Discrete Optimization and Operations Research |
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Abbreviated title | DOOR 2016 |

Country | Russian Federation |

City | Vladivostok |

Period | 19/09/16 → 23/12/16 |

Internet address |

### Keywords

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

## Research Output

- 1 Article

## An efficient algorithm for the single facility location problem with polyhedral norms and disk-shaped demand regions

Berger, A., Grigoriev, A. & Winokurow, A., Dec 2017, In : Computational Optimization and Applications. 68, 3, p. 661–669 9 p.Research output: Contribution to journal › Article › Academic › peer-review

Open Access

## 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). Springer. Lecture Notes in Computer Science, Vol.. 9869 https://doi.org/10.1007/978-3-319-44914-2_44