Single Facility Location: Circle Covering Problem, Sylvester's Problem










2020 ◽  
pp. 1248-1271
Author(s):  
Seda Tolun ◽  
Halit Alper Tayalı

This chapter focuses on available data analysis and data mining techniques to find the optimal location of the Multicriteria Single Facility Location Problem (MSFLP) at diverse business settings. Solving for the optimal of an MSFLP, there exists numerous multicriteria decision analysis techniques. Mainstream models are mentioned in this chapter, while presenting a general classification of the MSFLP and its framework. Besides, topics from machine learning with respect to decision analysis are covered: Unsupervised Principal Components Analysis ranking (PCA-rank) and supervised Support Vector Machines ranking (SVM-rank). This chapter proposes a data mining perspective for the multicriteria single facility location problem and proposes a new approach to the facility location problem with the combination of the PCA-rank and ranking SVMs.



2009 ◽  
Vol 52 (3) ◽  
pp. 424-434 ◽  
Author(s):  
Horst Martini ◽  
Margarita Spirova

AbstractWe investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by k unit circles. In particular, we study the cases k = 3, k = 4, and k = 7. For k = 3 and k = 4, the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, d-segments, and the monotonicity lemma.









2013 ◽  
Vol 27 (10) ◽  
pp. 2060-2076 ◽  
Author(s):  
K. Y. Chang ◽  
C. M. Su ◽  
G. E. Jan ◽  
C. P. Chen


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