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#### Year of publication

- 2015 (1) (remove)

A new solution approach for solving the 2-facility location problem in the plane with block norms
(2015)

Motivated by the time-dependent location problem over T time-periods introduced in
Maier and Hamacher (2015) we consider the special case of two time-steps, which was shown
to be equivalent to the static 2-facility location problem in the plane. Geometric optimality
conditions are stated for the median objective. When using block norms, these conditions
are used to derive a polygon grid inducing a subdivision of the plane based on normal cones,
yielding a new approach to solve the 2-facility location problem in polynomial time. Combinatorial algorithms for the 2-facility location problem based on geometric properties are
deduced and their complexities are analyzed. These methods differ from others as they are
completely working on geometric objects to derive the optimal solution set.