### Abstract

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

Pages (from-to) | 1797–1805 |

Number of pages | 9 |

Journal | Optimization Letters |

Volume | 11 |

Issue number | 8 |

DOIs | |

Publication status | Published - Dec 2017 |

### Keywords

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

### Cite this

*Optimization Letters*,

*11*(8), 1797–1805. https://doi.org/10.1007/s11590-017-1159-0

}

*Optimization Letters*, vol. 11, no. 8, pp. 1797–1805. https://doi.org/10.1007/s11590-017-1159-0

**Location, pricing and the problem of Apollonius.** / Berger, Andre; Grigoriev, Alexander; Panin, Artem; Winokurow, Andrej.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

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 - 2017/12

Y1 - 2017/12

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 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.

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 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.

KW - Pricing problem

KW - facility location

KW - Apollonius’ problem

KW - exact algorithm

KW - Complexity

U2 - 10.1007/s11590-017-1159-0

DO - 10.1007/s11590-017-1159-0

M3 - Article

VL - 11

SP - 1797

EP - 1805

JO - Optimization Letters

JF - Optimization Letters

SN - 1862-4472

IS - 8

ER -