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 Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9869 LNCS, pp. 563–569). Springer Verlag. https://doi.org/10.1007/978-3-319-44914-2_44
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