Locating a Central Hunter on the Plane

M. Cera (), J. A. Mesa, F. A. Ortega and F. Plastria
Additional contact information
M. Cera: University of Seville
J. A. Mesa: University of Seville
F. A. Ortega: University of Seville
F. Plastria: Vrije Universiteit

Journal of Optimization Theory and Applications, 2008, vol. 136, issue 2, No 1, 155-166

Abstract: Abstract Protection, surveillance or other types of coverage services of mobile points call for different, asymmetric distance measures than the traditional Euclidean, rectangular or other norms used for fixed points. In this paper, the destinations are mobile points (prey) moving at fixed speeds and directions and the facility (hunter) can capture them using one of two possible strategies: either it is smart, predicting the prey’s movement in order to minimize the time needed to capture it, or it is dumb, following a pursuit curve, by moving at any moment in the direction of the prey. In either case, the hunter location in a plane is sought in order to minimize the maximum time of capture of any prey. An efficient solution algorithm is developed that uses the particular geometry that both versions of this problem possess. In the case of unpredictable movement of prey, a worst-case type solution is proposed, which reduces to the well-known weighted Euclidean minimax location problem.

Keywords: Continuous location; Travel time; Center problem; Hunter distance; Skewed norm; Elliptic gauge; Game theory (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-007-9293-y

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