Weber s Problem with attraction and repulsion under Polyhedral Gauges
- Given a finite set of points in the plane and a forbidden region R, we want to find a point X not an element of int(R), such that the weighted sum to all given points is minimized. This location problem is a variant of the well-known Weber Problem, where we measure the distance by polyhedral gauges and allow each of the weights to be positive or negative. The unit ball of a polyhedral gauge may be any convex polyhedron containing the origin. This large class of distance functions allows very general (practical) settings - such as asymmetry - to be modeled. Each given point is allowed to have its own gauge and the forbidden region R enables us to include negative information in the model. Additionally the use of negative and positive weights allows to include the level of attraction or dislikeness of a new facility. Polynomial algorithms and structural properties for this global optimization problem (d.c. objective function and a non-convex feasible set) based on combinatorial and geometrical methods are presented.
Verfasser*innenangaben: | Stefan Nickel, Eva Maria Dudenhöffer |
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URN: | urn:nbn:de:hbz:386-kluedo-4893 |
Schriftenreihe (Bandnummer): | Report in Wirtschaftsmathematik (WIMA Report) (5) |
Dokumentart: | Preprint |
Sprache der Veröffentlichung: | Englisch |
Jahr der Fertigstellung: | 1999 |
Jahr der Erstveröffentlichung: | 1999 |
Veröffentlichende Institution: | Technische Universität Kaiserslautern |
Datum der Publikation (Server): | 03.04.2000 |
Freies Schlagwort / Tag: | Location Theory; discretization; geometrical algorithms; global optimization |
Fachbereiche / Organisatorische Einheiten: | Kaiserslautern - Fachbereich Mathematik |
DDC-Sachgruppen: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Lizenz (Deutsch): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |