An equivalence result for single facility planar location problems with rectilinear distance and barriers
In a plane with a finite set of disjoint solid barriers to travel, distance is measured by a shortest connecting rectilinear-length path not meeting the interior of any barrier. A point is sought minimising a convex nondecreasing function of its distances to a given finite fixed point set. The paper describes how to enlarge the barriers and add new ones without loss of optimality, thereby maximally reducing the feasible region. An actual solution procedure is described in the companion paper [ibid. 111, 111--133 (2002; Zbl 1041.90027)].
scientific article; zbMATH DE number 1904017