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2012 | OriginalPaper | Chapter
The median line problem
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As the last application considered in this text, we treat a facility location problem where we want to find an optimal location for a straight line. To be more precise, we want to locate a line in such a way that the sum of distances between that line and some given demand points is minimized. Although this problem is easy to solve in two dimensions, things become much more complicated in the threedimensional case. Therefore, our aim is to apply the geometric branch-and-bound solution algorithm to the median line problem in the three-dimensional Euclidean space. To this end, after a short introduction and a literature review in Section 9.1, some theoretical results as well as a suitable problem formulation are given in Section 9.2. Furthermore, some bounding operations are suggested in Section 9.3 and numerical results can be found in Section 9.4.