2 research outputs found
Continuous Location under Refraction
In this paper we address the problem of locating a new facility on a
-dimensional space when the distance measure (- or polyhedral-norms)
is different at each one of the sides of a given hyperplane . We
relate this problem with the physical phenomenon of refraction, and extends it
to any finite dimension 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 the
-norm representation given in \cite{BPE2014} that allows to solve,
exactly, the problem in any finite dimension space with 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 ) that allows the demand to travel faster through
to reach the new facility. Extensive computational experiments
run in Gurobi are reported in order to show the effectiveness of the approach.Comment: 22 pages, 9 figures, 4 table
On location-allocation problems for dimensional facilities
This paper deals with a bilevel approach of the location-allocation problem
with dimensional facilities. We present a general model that allows us to
consider very general shapes of domains for the dimensional facilities and we
prove the existence of optimal solutions under mild, natural assumptions. To
achieve these results we borrow tools from optimal transport mass theory that
allow us to give explicit solution structure of the considered lower level
problem. We also provide a discretization approach that can approximate, up to
any degree of accuracy, the optimal solution of the original problem. This
discrete approximation can be optimally solved via a mixed-integer linear
program. To address very large instance sizes we also provide a GRASP heuristic
that performs rather well according to our experimental results. The paper also
reports some experiments run on test data.Comment: 34 pages, 6 figue