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A BSSS algorithm for the single facility location problem in two regions with different norms |
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| Authors: | M Zaferanieh H Taghizadeh Kakhki J Brimberg GO Wesolowsky |
| Institution: | 1. Department of Mathematics, Ferdowsi University of Mashhad, Vakil Abad Blvd., Mashhad 91775-1159, Iran;2. Department of Business Administration, Royal Military College of Canada, Kingston, ON, Canada K7K7B4;3. M.G.DeGroote School of Business, McMaster University, Hamilton, ON, Canada L8S4M4 |
| Abstract: | 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. |
| Keywords: | Continuous location Single facility Branch and bound Global optimization |
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