### Abstract

Original language | English |
---|---|

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 |
---|---|

Volume | 9869 |

### Conference

Conference | Discrete Optimization and Operations Research |
---|---|

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

### Cite this

*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

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

TY - CHAP

T1 - Location, Pricing and the Problem of Apollonius

AU - Berger, Andre

AU - Grigoriev, Alexander

AU - Panin, Artem

AU - Winokurow, Andrej

N1 - no data used

PY - 2016/9/10

Y1 - 2016/9/10

N2 - 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.

AB - 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.

KW - pricing problem

KW - facility location

KW - Apollonius' problem

KW - complexity

KW - exact algorithm

U2 - 10.1007/978-3-319-44914-2_44

DO - 10.1007/978-3-319-44914-2_44

M3 - Chapter

SN - 978-3-319-44913-5

VL - 9869

T3 - Lecture Notes in Computer Science

SP - 563

EP - 569

BT - Discrete Optimization and Operations Research

A2 - Kochetov, Yury

A2 - Khachay, Michael

A2 - Beresnev, Vladimir

A2 - Nurminski, Evgeni A.

A2 - Pardalos, Panos M.

PB - Springer

CY - Switzerland

ER -