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Linear Facility Location in Three Dimensions—Models and Solution Methods

University of Prince Edward Island, Charlottetown, Prince Edward Island, Canada, and Groupe d'Études et de Recherche en Analyse des Décisions, Montreal, Quebec, Canada
Technical University of Denmark, Lyngby, Denmark
University of Kaiserslautern, Kaiserslautern, Germany
jbrimberg{at}upei.ca
hj{at}imm.dtu.dk
schoebel{at}mathematik.uni-kl.de

We consider the problem of locating a line or a line segment in three-dimensional space, such that the sum of distances from the facility represented by the line (segment) to a given set of points is minimized. An example is planning the drilling of a mine shaft, with access to ore deposits through horizontal tunnels connecting the deposits and the shaft. Various models of the problem are developed and analyzed, and efficient solution methods are given.

Subject classifications: Facilities equipment: linear facility location. Planning; location; continuous: three dimensions.
History: Received January 2000; revision received October 2001; accepted October 2001.

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