Coincidence conditions in multifacility location problems with positive and negative weights |
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| Affiliation: | 1. Division of General Surgery, Trauma, and Surgical Critical Care, Yale School of Medicine, Department of Surgery, New Haven, CT, 06520, USA;2. Investigative Medicine Program, Yale School of Medicine, Yale Graduate School of Arts and Sciences, New Haven, CT, 06510, USA;3. Department of Pediatrics, Yale School of Medicine, New Haven, CT, 06510, USA;4. Violence Intervention Program, Yale New Haven Hospital, USA;5. Injury Prevention Center, Connecticut Children''s Medical Center, Hartford, CT, 06106, USA;6. Department of Pediatrics, University of Connecticut School of Medicine, Farmington, CT, 06032, USA;7. Department of Surgery, Saint Francis Hospital & Medical Center, USA;8. Associate Professor of Surgery University of Connecticut School of Medicine & Frank L. Netter Schools of Medicine, USA;9. Department of Surgery, Hartford Healthcare Hartford Hospital, USA;10. Trauma, Burns and Surgical Critical Care, Bridgeport Hospital, USA |
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| Abstract: | In minisum multifacility location problems one has to find locations for some new facilities, such that the weighted sum of distances between the new and a certain number of old facilities with known locations is minimized. In this kind of problem, the optimal locations of clusters of facilities frequently tend to coincide. By testing conditions for coincidence, one has the opportunity to collapse some or even all facilities coinciding at an optimal point into one. In this way, the dimension of the problem and the degree of nondifferentiability is reduced. Several conditions for coincidence have been published recently. In this paper, these conditions are extended and improved with respect to new sufficient coincidence conditions for location problems with attracting and repelling facilities. An example shows that these new conditions detect more coincidences than the conditions which are known so far, even if all facilities involved are attracting ones. |
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