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Zbl 1146.90465
Zaferanieh, M.; Kakhki, H.Taghizadeh; Brimberg, J.; Wesolowsky, G.O.
A BSSS algorithm for the single facility location problem in two regions with different norms. (English)
[J] Eur. J. Oper. Res. 190, No. 1, 79-89 (2008). ISSN 0377-2217

Summary: Suppose the plane is divided by a straight line into two regions with different norms. We want to find the location of a single new facility such that the sum of the distances from the existing facilities to this point is minimized. This is in fact a non-convex optimization problem. The main difficulty is caused by finding the distances between points on different sides of the boundary line. In this paper we present a closed form solution for finding these distances. We also show that the optimal solution lies in the rectangular hull of the existing points. Based on these findings then, an efficient big square small square (BSSS) procedure is proposed.

MSC 2000:: *90B85 Continuous location
90C26 Nonconvex programming

Keywords: continuous location; single facility; branch and bound; global optimization

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