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IMA Journal of Management Mathematics Advance Access originally published online on April 11, 2006
IMA Journal of Management Mathematics 2006 17(4):397-412; doi:10.1093/imaman/dpl008
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Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications 2006

The multifacility maximin planar location problem with facility interaction

S. B. Welch1, S. Salhi**,2 and Z. Drezner3

1 OR Group, Debenhams, London, UK, 2 Centre for Heuristic Optimisation, Kent Business School, University of Kent at Canterbury, UK, 3 Department of Information Systems and Decision Sciences, California State University—Fullerton, Fullerton, USA

** Email: s.salhi{at}kent.ac.uk

Two branch-and-bound algorithms are proposed to optimally solve the maximin formulation for locating p facilities in the plane. Tight upper and lower bounds are constructed and suitable methods of guiding the search developed. To enhance the method, efficient measures for identifying specific squares for subdivision are suggested. The proposed algorithms are evaluated on a set of randomly generated problems of up to five facilities and 120 nodes.

Keywords: location; continuous space; branch and bound

Received March 2005. accepted on 15 December 2005.


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