A branch-and-price algorithm for the multi-source Weber problem

International Journal of Operational Research

Volumn 2, Issue 2, 2007, Pages 188-207

  Righini, Giovanni ^a   Zaniboni, Luca ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

Branch and bound; Column generation; Location science; Weber problem

Indexed keywords

EID: 34047218329     PISSN: 17457645     EISSN: 17457653     Source Type: Journal    
DOI: 10.1504/IJOR.2007.012460     Document Type: Article

References (20)

1. Aras, N., Ozkisacik, K.C. and Altinel, I.K. (2006) 'Solving the uncapacitated multi-facility Weber problem by vector quantization and self-organizing maps', Journal of the Operational Research Society, Vol. 57, pp.82-93.
2. Barnhardt, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W.P. and Vance, P.H. (1998) 'Branch-and-price: column generation for solving huge integer programs', Operations Research, Vol. 46, pp.316-329.
3. p, norm location-allocation problems, Mathematical Programming 66, pp.283-312.
4. Brimberg, J., Hansen, P., Mladenovic, N. and Taillard, E.D. (2000) 'Improvement and comparison of heuristics for solving the uncapacitated multi-source Weber problem', Operations Research, Vol. 48, pp.444-460.
5. Chen, P., Hansen, P., Jaumard, B. and Tuy, H. (1998) 'Solution of the multisource Weber and conditional Weber problems by d.-c. programming', Operations Research, Vol. 46, pp.548-562.
6. Cooper, L. (1963) 'Location-allocation problems', Operations Research, Vol. 11, pp.331-343.
7. Cooper, L. (1967) 'Solutions of the generalized locational equilibrium models', Journal of Regional Sciences, Vol. 7, pp.1-18.
8. Drezner, Z. (1984) 'The planar two-center and two-median problems', Transportation Science, Vol. 18, pp.351-361.
9. Drezner, Z., Mehrez, A. and Wesolowsky, G.O. (1991) 'The facility location problem with limited distances', Transportation Science, Vol. 25, pp.183-187.
10. du Merle, O., Villeneuve, D., Desrosiers, J. and Hansen, P. (1999) 'Stabilized column generation', Discrete Mathematics, Vol. 194, pp.229-237.
11. Hansen, P., Peeters, D., Richard, D. and Thisse, J-F. (1985) 'The minisum and minimax location problems revisited', Operations Research, Vol. 33, pp.1251-1265.
12. Krau, S. (1997) Extensions du Problème de Weber, PhD dissertation, École Polytechnique de Montréal, Montréal, Canada.
13. Kuenne, R.E. and Soland, R.M. (1972) 'Exact and approximate solutions to the multisource Weber problem', Mathematical Programming, Vol. 3, pp.193-209.
14. Ostresh, L.M. (1978) 'On the convergence of a class of iterative methods for solving the Weber location problem', Operations Research, Vol. 26, pp.597-609.
15. Reinelt, G. (1991) 'TSPLIB - a traveling salesman problem library', ORSA Journal on Computing, Vol. 3, pp.376-384.
16. Rosing, K.E. (1991) 'Towards the solutions of the (generalised) multi-Weber problem', Environment and Planning, Series B 18, pp.347-360.
17. Rosing, K.E. (1992) 'An optimal method for solving the (generalized) multi-Weber problem', European Journal of Operational Research, Vol. 58, pp.414-426.
18. Rousseau, L.M., Gendreau, M. and Feillet, D. (2003) Interior Point Stabilization for Column Generation, Laboratoire d'Informatique d'Avignon, France.
19. Ryan, D.M. and Foster, B.A. (1981) 'An integer programming approach to scheduling', in Wren, A. (Ed.): Computer Scheduling of Public Transport Urban Passenger Vehicle and Crew Scheduling, North Holland, Amsterdam, pp.269-280.
20. Weiszfeld, E. (1937) 'Sur le point lequel la somme des distances de n points données est minimum', Tohoku Math. Journal, Vol. 43, pp.355-386.