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.
Brimberg, J., Juel, H., & Schöbel, A. (2002). Linear facility location in three dimensions - Models and solution methods. Operations Research, 50(6), 1050-1057. https://doi.org/10.1287/opre.50.6.1050.354