Multicriteria planar ordered median problems

Journal of Optimization Theory and Applications

Volumn 126, Issue 3, 2005, Pages 657-683

  Nickel, S ^a   Puerto, J ^b   Rodriguez Chia A M ^c   Weissler, A ^d  

^a SAARLAND UNIVERSITY   (Germany)

^b UNIVERSITY OF SEVILLE   (Spain)

^c UNIVERSITY OF CÁDIZ   (Spain)

^d SAP RESEARCH   (Germany)

Author keywords

Algebraic optimization; Geometrical algorithms; Location theory; Multicriteria optimization

Indexed keywords

LOCATION;

ALGEBRAIC OPTIMIZATION; GEOMETRICAL ALGORITHMS; LOCATION PROBLEMS; LOCATION THEORY; MULTI-CRITERIA; MULTI-CRITERIA OPTIMISATION; MULTICRITERIA PROBLEMS; OBJECTIVE FUNCTIONS; ORDERED MEDIAN PROBLEMS; PARETO SOLUTION;

MULTIOBJECTIVE OPTIMIZATION;

EID: 23844454289     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-005-5502-8     Document Type: Article

References (20)

1. DREZNER, Z., and HAMACHER, H., Facility Location: Applications and Theory, Springer Verlag, Heidelberg, Germany, 2002.
2. HAMACHER, H.W, and NICKEL, S., Multicriteria Planar Location Problems, European Journal of Operational Research, Vol. 94, pp. 66-86, 1996.
3. PUERTO, J., and FERNÁNDEZ, F.R., Multicriteria Minisum Facility Location Problem, Journal of Multicriteria Decision Analysis, Vol. 8, pp. 268-280, 1999.
4. FERNÁNDEZ, F.R., NICKEL, S., PUERTO, J., and RODRÍGUEZ- CHÍA, A.M., Robustness in Pareto Solutions for the Multicriteria Minisum Location Problem, Journal of Multicriteria Decision Analysis, Vol. 4, pp. 191-203, 2001.
5. RODRÍGUEZ-CHÍA, A.M., and PUERTO, J., Geometrical Description of the Weakly Efficient Solution Set for Multicriteria Location Problems, Annals of Operations Research, Vol. 111, pp. 181-196, 2002.
6. PUERTO, J., RODRÍGUEZ-CHÍA, A.M., and FERNÁNDEZ- PALACÍN, F., Ordered Weber Problems with Attraction and Repulsion, Studies in Locational Analysis, Vol. 11, pp. 127-141, 1997.
7. NICKEL, S., and PUERTO, J., A Unified Approach to Network Location Problems, Networks, Vol. 34, pp. 283-290, 1999.
8. PUERTO, J., and FERNÁNDEZ, F.R., Geometrical Properties of the Symmetrical Single-Facility Location Problem, Journal of Nonlinear and Convex Analysis, Vol. 1, pp. 321-342, 2000.
9. RODRÍGUEZ-CHÍA, A.M., NICKEL, S., PUERTO, J., and FERNÁNDEZ, F.R., A Flexible Approach to Location Problems, Mathematical Methods of Operations Research, Vol. 51, pp. 69-90, 2000.
10. WARD, J.E., and WENDELL, R.E., Using Block Norms for Location Modeling, Operations Research, Vol. 33, pp. 1074-1090, 1985.
11. PUERTO, J., and FERNÁNDEZ, F.R., A Convergent Approximation Scheme for the Efficient Set of the Multicriteria Weber Location Problem, TOP, Vol. 6, pp. 195-204, 1998.
12. DURIER, R., and MICHELOT, C., Geometrical Properties of the Fermat-Weber Problem, European Journal of Operational Research, Vol. 20, pp. 332-343, 1985.
13. EHRGOTT, M., Multicriteria Optimization, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, Vol. 491, 2000.
14. WARBURTON, A.R., Quasiconcave Vector Maximization: Connectedness of the Sets of Pareto-Optimal and Weak Pareto-Optimal Alternatives, Journal of Optimization Theory and Applications, Vol. 40, pp. 537-557, 1983.
15. NICKEL, S., Discretization of Planar Location Problems, Phd Thesis, University of Kaiserslautern, Shaker Verlag, Kaiserslautern, Germany, 1995.
16. WEISSLER, A., General Bisectors and Their Application in Planar Location Theory, PhD Thesis, University of Kaiserslautern, Shaker Verlag, Kaiserslautern, Germany, 1999.
17. EDELSBRUNNER, H., Algorithms in Combinatorial Geometry, Springer Verlag, New York, NY, 1987.
18. WHITE, D.J., Optimally and Efficiency, Wiley, Chicester, UK, 1982.
19. HAMACHER, H.W., LABBÉ, M., and NICKEL, S., Multicriteria Network Location Problems with Sum Objectives, Networks, Vol. 33, pp. 79-92, 1999.
20. HAMACHER, H.W., HENNES H., KALCSICS J., and NICKEL, S., LoLA-Library of Location Algorithms, Fraunhofer ITWM, Version 2.1, 2003; see http://www.itwm.fhg.de/opt/projects/lola.