### Justo Puerto (Universidad de Sevilla, Spain)

#### Location problems with different transportation means and Snell's Law

*Friday 24 November 2017 at 11.00, JCMB 5328*

##### Abstract

In this talk we address the problem of locating a new facility on a
d-dimensional space when the distance measure (lp or polyhedral-norms) is
different at each one of the sides of a given hyperplane H. We relate this
problem with the physical phenomenon of refraction, and extend it to any
finite dimensional space and different distances at each one of the sides of
any hyperplane. An application to this problem is the location of a facility
within or outside an urban area where different distance measures must be
used. We provide a new second order cone programming formulation, based on a
lp-norm representation that allows one to solve, exactly, the problem in any
finite dimensional space with second order cone or semidefinite programming
tools. We also extend the problem to the case where the hyperplane is
considered as a rapid transit media (a different third norm is also
considered over H) that permits the demand to travel faster through H to
reach the new facility. Extensive computational experiments run in Gurobi are
reported in order to show the effectiveness of the approach.

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