Simpson points in planar problems with locational constraints. The polyhedral-gauge case

Mathematics of Operations Research

Volumn 22, Issue 2, 1997, Pages 291-300

  Carrizosa, Emilio ^a   Conde, Eduardo ^a   Munoz Márquez, Manuel ^b   Puerto, Justo ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITY OF CÁDIZ   (Spain)

Author keywords

Intersection points; Location with voting; Polyhedral gauges; Simpson points; Weak efficiency

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; FINITE ELEMENT METHOD; OPTIMIZATION; PROBLEM SOLVING;

FINITE DOMINATING SET; LOCATIONAL CONSTRAINTS; PLANAR POINTS; POLYHEDRAL GAUGE CASE; SIMPSON POINTS;

MATHEMATICAL MODELS;

EID: 0031147518     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.22.2.291     Document Type: Article

References (20)

1. Brondsted, A. (1983). An Introduction to Convex Polytopes, Springer-Verlag,
2. Carrizosa, E. (1992). Problemas de localizatión multiobjetivo, Unpublished Ph.D. thesis. University of Seville, Seville, Spain.
3. _, E. Conde, M. Muñoz-Márquez, J. Puerto (1993). Condorcet points with the Manhattan metric. Working paper, Prepublicación n. 4 de la Fac. de Matemáticas, University of Seville, Seville, Spain.
4. _, (1997). Simpson points in planar problems with locational constraints. The round-norm case. Math. Oper. Res. 22 276-290.
5. Demange, G. (1983). Spatial models of collective choice. J. F. Thisse and H. G. Zoller, eds., Locational Analysis of Public Facilities, North-Holland, Amsterdam.
6. Durier, R. (1989). Continuous location theory under majority rule. Math. Oper. Res. 14 258-274.
7. _, (1990). On Pareto optima, the Fermat-Weber problem and polyhedral gauges. Math. Programing 47 65-79.
8. _, C. Michelot (1985). Geometrical properties of the Fermat-Weber problem. European J. Oper. Res. 20 332-343.
9. Francis, R. L. (1963). A note on the optimum location of the new machines in existing plant layouts. J. Indust. Engr. 11 57-59.
10. Hakimi, S. L. (1964). Optimum locations of switching centers and absolute centers and medians of a graph. Oper. Res. 12 450-459.
11. _, (1990). Locations with spatial interactions: Competitive locations and games. P. B. Mirchandani and R. L. Francis, eds., Discrete Location Theory. Wiley, New York.
12. Hansen, P., J. F. Thisse (1981). Outcomes of voting and planning. J. Public Economics 16 1-15.
13. Labbé, M. (1985). Outcomes of voting and planning in single facility location problems. European J. Oper. Res. 20 299-313.
14. Love, R. F., J. G. Morris, G. O. Wesolowsky (1988). Facilities Location. Models and Methods, North-Holland, Amsterdam.
15. Lowe, T. J., J. F. Thisse, J. E. Ward, R. E. Wendell (1984). On efficient solutions to multiple objective mathematical programs. Management Sci. 30 1346-1349.
16. Michelot, C. (1993). The mathematics of continuous location. Studies in Locational Analysis 5 59-83.
17. Plastria, F. (1993). Continuous location Anno 1992. A progress report. Studies in Locational Analysis 5 85-127.
18. Rockafellar, R. T. (1970). Convex Analysis, Princeton University Press, New Jersey.
19. Thisse, J. F., J. E. Ward, R. E. Wendell (1984). Some properties of location problems with block and round norms. Oper. Res. 32 1309-1327.
20. Warburton, A. R. (1983). Quasiconcave vector maximization: Connectedness of the sets of Pareto-optimal and weak Pareto-optimal alternatives. J. Optim. Theory Appl. 40 537-557,