TY - JOUR

T1 - Location, pricing and the problem of Apollonius

AU - Berger, André

AU - Grigoriev, Alexander

AU - Panin, Artem

AU - Winokurow, Andrej

N1 - Publisher Copyright: © 2017, The Author(s).

PY - 2017/12/1

Y1 - 2017/12/1

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 - Apollonius’ problem

KW - Complexity

KW - Exact algorithm

KW - Facility location

KW - Pricing problem

UR - http://www.scopus.com/inward/record.url?scp=85020729132&partnerID=8YFLogxK

U2 - 10.1007/s11590-017-1159-0

DO - 10.1007/s11590-017-1159-0

M3 - Article

AN - SCOPUS:85020729132

VL - 11

SP - 1797

EP - 1805

JO - Optimization Letters

JF - Optimization Letters

SN - 1862-4472

IS - 8

ER -