Weber problems with high-speed lines

• Mark-Christoph Körner ^[1] ; Anita Schöbel ^[1]
  1. [1] Georg-August-University Goettingen, Alemania
• Localización: Top, ISSN-e 1863-8279, ISSN 1134-5764, Vol. 18, Nº. 1, 2010, págs. 223-241
• Idioma: inglés
• Enlaces
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• Resumen

  • The Weber problem consists of finding a facility which minimizes the sum of weighted distances from itself to a finite set of given demand points.

    In this paper we extend the Weber problem in the following way: We allow traveling along given linear curves (lines, line-segments, and rays) with high speed. Leaving and entering such a curve is allowed at all its points, and hence a network structure is continuously integrated in the plane. This extension gives the chance to model real-world situations like highway networks or other traffic infrastructure.

    The extension of the Weber problem leads to a nonconvex problem. This paper presents a geometric approach to solve the extended Weber problem and gives discretization results for polyhedral gauges.