Extension of the Weiszfeld procedure to a single facility minisum location model with mixed ℓ p norms

Mathematical Methods of Operations Research

Volumn 70, Issue 2, 2009, Pages 269-283

  Brimberg, Jack ^a   Love, Robert ^c   Mladenović, Nenad ^b,d  

^a ROYAL MILITARY COLLEGE OF CANADA   (Canada)

^b GERAD   (Canada)

^c MCMASTER UNIVERSITY   (Canada)

^d BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

Mixed norms; Weiszfeld procedure

Indexed keywords

COMPUTATIONAL RESULTS; CONTINUOUS SPACES; CONVERGENCE PROPERTIES; FIXED POINTS; ITERATIVE PROCEDURES; MINISUM LOCATION; MIXED NORMS; MIXED-NORM; OPTIMALITY CRITERIA; TRANSPORTATION MODE; WEISZFELD PROCEDURE;

LOCATION;

EID: 70350566233     PISSN: 14322994     EISSN: 14325217     Source Type: Journal    
DOI: 10.1007/s00186-008-0268-z     Document Type: Article

References (13)

1. Brimberg J (1989) Properties of distance functions and minisum location models. Ph.D. Thesis, McMaster University, Hamilton, Canada
2. J Brimberg RF Love 1992 Local convergence in a generalized Fermat-Weber problem Ann Oper Res 40 33 66 0787.90040 10.1007/BF02060469 1213040
3. p distances Oper Res 41 1153 1163 0795.90037 10.1287/opre.41.6.1153 1253706
4. p norm as an empirical distance measure Transport Sci 27 341 349 0800.90632 10.1287/trsc.27.4.341
5. Brimberg J, Love RF (1995) Estimating distances. In: Drezner Z (eds) Facility location: a survey of applications and methods. Springer, New York
6. R Durier C Michelot 1985 Geometrical properties of the Fermat-Weber problem Eur J Oper Res 20 332 343 0564.90013 10.1016/0377-2217(85)90006-2 800909
7. P Hansen J Perreur JF Thisse 1980 Location theory, dominance, and convexity: some further results Oper Res 28 1241 1250 0449.90027 10.1287/opre.28.5.1241
8. H Juel RF Love 1981 Fixed point optimality criteria for the location problem with arbitrary norms J Oper Res Soc 32 891 897 0463.90035 10.1057/jors.1981.183 (Pubitemid 12521965)
9. Love RF, Morris JG, Wesolowsky GO (1988) Facilities location: models and methods. North-Holland, New York
10. A Planchart AP Hurter 1975 An efficient algorithm for the solution of the Weber problem with mixed norms SIAM J Control 13 650 665 0274.90058 10.1137/0313036 378831
11. Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton
12. E Weiszfeld 1937 Sur le point lequel la somme des distances de n points donnés est minimum Tohoku Math J 43 355 386
13. Witzgall CJ (1964) Optimal location of a central facility: mathematical models and concepts. National Bureau of Standards report 8388, US Department of Commerce, Washington DC, USA