On the convergence of the Weiszfeld algorithm for continuous single facility location-allocation problems

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Volumn 16, Issue 2, 2008, Pages 388-406

  Plastria, Frank ^a   Elosmani, Mohamed ^b  

^a VRIJE UNIVERSITEIT BRUSSEL   (Belgium)

^b NATIONAL POLYTECHNIC SCHOOL OF ORAN   (Algeria)

Author keywords

Convergence; Local decrease method; Location allocation; Planar facility location

Indexed keywords

EID: 56249137868     PISSN: 11345764     EISSN: 18638279     Source Type: Journal    
DOI: 10.1007/s11750-008-0056-1     Document Type: Article

References (26)

1. Brimberg J (2003) Further notes on convergence of the Weiszfeld algorithm. Yugosl J Oper Res 13(2):199-206
2. Cánovas L, Cañavate R, Marín A (2002) On the convergence of the Weiszfeld algorithm. Math Program 93(2):327-330
3. Carrizosa E, Rodríguez-Chía AM (1997) Weber problems with alternative transportation systems. Eur J Oper Res 97:87-93
4. Chandrasekaran R, Tamir A (1989) Open questions concerning Weiszfeld's algorithm for the Fermat-Weber location problem. Math Program 44(3):293-295
5. Cooper L (1963) Location-allocation problems. Oper Res 11:331-343
6. Cooper L (1964) Heuristic methods for location-allocation problems. SIAM Rev 6:37-52
7. Dantzig GB (1957) Discrete variable extremum problems. Oper Res 5:266-277
8. Drezner Z, Suzuki A (2004) The big triangle small triangle method for the solution of non-convex facility location problems. Oper Res 52(1):128-135
9. Drezner Z, Klamroth K, Schöbel A, Wesolowsky GO (2003) The Weber problem. In: Drezner Z, Hamacher H (eds) Aacility location: applications and theory. Springer, Berlin, pp 1-36
10. Eilon S, Watson-Gandy CDT, Christofides N (1971) Distribution management. Hafner, New York
11. Francis RL, McGinnis LF, White JA (1992) Facility layout and location: an analytical approach, 2nd edn. Prentice Hall, Englewood Cliffs
12. Gugat M, Pfeiffer B (2007) Weber problems with mixed distances and regional demand. Math Methods Oper Res 66:419-449
13. Hansen P, Peeters D, Thisse J-F (1983) Public facility location models: a selective survey. In: Thisse J-F, Zoller HG (eds) Locational analysis of public facilities. North-Holland, Amsterdam, pp 223-262
14. Hansen P, Peeters D, Richard D, Thisse J-F (1985) The minisum and minimax location problems revisited. Oper Res 33:1251-1265
15. Kaufman L, Plastria F (1988) The Weber problem with supply surplus. Belgian J Oper Res Stat Comput Sci 28:15-31
16. Kuhn HW, Kuenne RE (1962) An efficient algorithm for the numerical solution of the generalized Weber problem in spatial economics. J Reg Sci 4:21-33
17. Kupitz YS, Martini H (1997) Geometric aspects of the generalized Fermat-Torricelli problem. In: Intuitive geometry, Bolyai society, Mathematical studies, vol 6, pp 55-127
18. Martello S, Toth P (1990) Knapsack problems - algorithms and computer implementations. Wiley, Chichester
19. Nickel S, Puerto J (2005) Location theory - a unified approach. Springer, Berlin
20. Okabe A, Boots B, Sugihara K (1992) Spatial tessellations. Concept and applications of Voronoi diagram. Wiley, Chichester
21. Pfeiffer B, Klamroth K (2008) A unified model for Weber problems with continuous and network distances. Comput Oper Res 35(2):312-326
22. Plastria F (1992) GBSSS: The generalized big square small square method for planar single facility location. Eur J Oper Res 62(2):163-174
23. Vardi Y, Zhang C-H (2001) A modified Weiszfeld algorithm for the Fermat-Weber location problem. Math Program 90:559-566
24. Weiszfeld E (2008) On the point for which the sum of the distances to n given points is minimum (translated and annotated by F. Plastria). Ann Oper Res. doi: 10.1007/s10479-008-0352-z
25. Weiszfeld E (1936-1937) Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math J 355-386
26. Wesolowsky G (1993) The Weber problem: History and perspective. Location Sci 1:5-23