TY - INPR
A1 - Carrizosa, Emilio
A1 - Hamacher, Horst W.
A1 - Klein, Rolf
A1 - Nickel, Stefan
T1 - Solving nonconvex planar location problems by finite dominating sets
N2 - It is well-known that some of the classical location problems with polyhedral gauges can be solved in polynomial time by finding a finite dominating set, i.e. a finite set of candidates guaranteed to contain at least one optimal location. In this paper it is first established that this result holds for a much larger class of problems than currently considered in the literature. The model for which this result can be proven includes, for instance, location problems with attraction and repulsion, and location-allocation problems. Next, it is shown that the approximation of general gauges by polyhedral ones in the objective function of our general model can be analyzed with regard to the subsequent error in the optimal objective value. For the approximation problem two different approaches are described, the sandwich procedure and the greedy algorithm. Both of these approaches lead - for fixed epsilon - to polynomial approximation algorithms with accuracy epsilon for solving the general model considered in this paper.
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 18
KW - Continuous Location
KW - Polyhedral Gauges
KW - Finite Dominating Sets
KW - Approximation
KW - Sandwich Algorithm
KW - Greedy Algorithm
Y1 - 2000
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/973
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-9407
ER -