Properties of ordinary and weighted sums of order p used for distance estimation

J. Brimberg; R. F. Love

RAIRO - Operations Research - Recherche Opérationnelle (1995)

  • Volume: 29, Issue: 1, page 59-72
  • ISSN: 0399-0559

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Brimberg, J., and Love, R. F.. "Properties of ordinary and weighted sums of order $p$ used for distance estimation." RAIRO - Operations Research - Recherche Opérationnelle 29.1 (1995): 59-72. <http://eudml.org/doc/105097>.

@article{Brimberg1995,
author = {Brimberg, J., Love, R. F.},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {continuous location theory; Jensen's inequality},
language = {eng},
number = {1},
pages = {59-72},
publisher = {EDP-Sciences},
title = {Properties of ordinary and weighted sums of order $p$ used for distance estimation},
url = {http://eudml.org/doc/105097},
volume = {29},
year = {1995},
}

TY - JOUR
AU - Brimberg, J.
AU - Love, R. F.
TI - Properties of ordinary and weighted sums of order $p$ used for distance estimation
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1995
PB - EDP-Sciences
VL - 29
IS - 1
SP - 59
EP - 72
LA - eng
KW - continuous location theory; Jensen's inequality
UR - http://eudml.org/doc/105097
ER -

References

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  1. 1. E. F. BECKENBACH, An Inequality of Jensen, American Mathematical Monthly, 53, 1946, pp. 501-505. Zbl0060.14904MR18707
  2. 2. E.F. BECKENBACH, R. BELLMAN, Inequalities, Second revised printing, Springer-Verlag, Berlin, 1965. Zbl0206.06802MR192009
  3. 3. J. BRIMBERG, R. F. LOVE, Estimating Travel Distance by the Weighted lp Norm, Naval Research Logistics, 38 1991, pp. 241-259. Zbl0717.90041MR1095935
  4. 4. S. EILON, C. D. T. WATSOM-GANDY, N. CHRISTOFIDES, Distribution Management: Mathematical Modelling and Practical Analysis, Hafner Publishing Company, New York, 1971. 
  5. 5. V. GINSBURGH, P. HANSEN, Procedures for the Reduction of Errors in Road Network Data, Operational Research Quarterly, 25, 1974, pp. 321-322. 
  6. 6. G. H. HARDY, J. E. LITTLEWOOD, G. PÓLYA, Inequalities, 2nd edition, Cambridge University Press, Cambridge, 1952. Zbl0634.26008MR46395JFM60.0169.01
  7. 7. R. KLEIN, Voronoi Diagrams in the Moscow Metric, Institute für Informatik, Universität Freiburg, 1987. 
  8. 8. G. B. KLEINDORFER, G. A. KOCHENBERG, E. T. REUTZEL, Computing Inter-Site Distances for Routing and Scheduling Problems, Operations Research Letters, 1, 1981, pp. 31-33. Zbl0495.90044
  9. 9. P. KOLESAR, W. WALKER, J. HAUSNER, Determining the Relation between Fire Engine Travel Times and Travel Distances in New York City, Operations Research, 23, 1975, pp. 614-627. 
  10. 10. R. F. LOVE, J. G. MORRIS, Modelling Inter-City Road Distances by Mathematical Models, Operational Research Quarterly, 23, 1972, pp. 61-71. Zbl0231.90059
  11. 11. R. F. LOVE, J. G. MORRIS, Mathematical Models of Road Travel Distances, Management Science, 25, 1979, pp. 130-139. Zbl0419.90053
  12. 12. R. F. LOVE, J. G. MORRIS, On Estimating Road Distances by Mathematical Functions, European Journal of Operational Research, 36, 1988, pp. 251-253. 
  13. 13. R. F. LOVE, J. G. MORRIS, G. O. WESOLOWSKY, Facilities Location: Models and Methods, North-Holland, New York, N.Y., 1988. Zbl0685.90036MR1016608
  14. 14. R. F. LOVE, J. H. WALKER, An Empirical Comparison of Block and Round Norms for Modelling Actual Distances, Location Science, to appear. Zbl0926.90056
  15. 15. ROADNET, Roadnet Technologies, 10540 York Rd., Huntvalley, Maryland, 1993. 
  16. 16. TRUCKSTOPS 2-Vehicle Routing System, Micro-Analytics, Suite One, 2045 North 15th Street, Arlington, Virginia, and Suite 201, 1986 Queen Street East, Toronto, Ontario, 1993. 
  17. 17. J. E. WARD, R. E. WENDELL, A New Norm for Measuring Distance Which Yields Linear Location Models, Operations Research, 28, 1980, pp. 836-844. Zbl0443.90029
  18. 18. J. E. WARD, R. E. WENDELL, Using Block Norms for Location Modelling, Operations Research 33, 1985, pp. 1074-1090. Zbl0582.90026MR806920
  19. 19. J. B. WESTWOOD, A Transport Planning Model for Primary Distribution, Interfaces, 8, 1977, pp. 1-10. 

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