Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Scholz, D. (2012). The median line problem. In: Deterministic Global Optimization. Springer Optimization and Its Applications(), vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1951-8_9
Download citation
DOI: https://doi.org/10.1007/978-1-4614-1951-8_9
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1950-1
Online ISBN: 978-1-4614-1951-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)