Abstract
We relate the simple plant location problem to the vertex packing problem and derive several classes of facets of their associated integer polytopes.
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E. Balas and N. Christofides, “A restricted Lagrangean approach to the travelling salesman problem”, Management Sciences Research Report 439, Carnegie-Mellon University (1979).
E. Balas and M.W. Padberg, “Set partitioning: A survey”,SIAM Review 18 (1976) 710–760.
E. Balas and E. Zemel, “Critical cutsets of graphs and canonical facets of set-packing polytopes”,Mathematics of Operations Research 2 (1977) 15–20.
D.C. Cho, E.L. Johnson, M.W. Padberg and M.R. Rao, “On the uncapacitated plant location problem I: Valid inequalities and facets”,Mathematics of Operations Research, to appear.
D.C. Cho, M.W. Padberg and M.R. Rao, “On the uncapacitated plant location problem II: Facets and Lifting theorems”,Mathematics of Operations Research, to appear.
V. Chvatal, “On certain polytopes associated with graphs”,Journal of Combinatorial Theory B 18 (1975) 138–154.
G. Cornuejols, M.L. Fisher and G.L. Nemhauser, “On the uncapacitated location problem”,Annals of Discrete Mathematics 1 (1977) 163–177.
G. Cornuejols and W.R. Pulleyblank, “The travelling salesman polytope and {0, 2}-matchings”, in: A. Bachem, M. Grötschel and B. Korte, eds.,Bonn workshop on combinatorial optimization, North-Holland Mathematics Studies, Vol. 66 (Annals of Discrete Mathematics 11) (North-Holland, Amsterdam, 1982) to appear.
J. Edmonds, “Paths, trees and flowers”,Canadian Journal of Mathematics 17 (1965) 449–467.
D.R. Fulkerson, “Blocking and anti-blocking pairs of polyhedra”,Mathematical Programming 1 (1971) 168–194.
M: Guignard, “Fractional vertices, cuts and facets of the simple plant location problem”,Mathematical Programming Study 12 (1980) 150–162.
M. Grötschel and M.W. Padberg, “On the symmetric travelling salesman problem I: Inequalities”,Mathematical Programming 16 (1979) 265–280.
J. Krarup and P.M. Pruzan, “Selected families of location problems, Part III”, Institute of Datalogy, University of Copenhagen, Copenhagen (August 1977) revised version to appear.
J.F. Maurras, “Polytopes à sommets dans {0, 1}n”, Thèse d'état, University of Paris VI, Paris (1976).
G.L. Nemhauser and L.E. Trotter, “Properties of vertex packing and independence system polyhedra”,Mathematical Programming 6 (1974) 48–61.
G.L. Nemhauser and L.E. Trotter, “Vertex packings: Structural properties and algorithms”,Mathematical Programming 8 (1975) 232–248.
M.W. Padberg, “On the facial structure of set packing polyhedra”,Mathematical Programming 5 (1973) 199–215.
M.W. Padberg, “On the complexity of set packing polyhedra”,Annals of Discrete Mathematics 1 (1977) 421–434.
M.W. Padberg and S. Hong, “On the symmetric travelling salesman problem: A computational study”,Mathematical Programming Study 12 (1980) 78–107.
W.R. Pulleyblank, “Faces of matching polyhedra”, Ph.D. thesis, University of Waterloo, Waterloo (1973).
L.E. Trotter, “A class of facet producing graphs for vertex packing polyhedra”,Discrete Mathematics 12 (1975) 373–388.
L.A. Wolsey, “Further facet generating procedures for vertex packing polytopes”,Mathematical Programming 11 (1976) 158–163.
E. Zemel, “Lifting the facets of zero–one polytopes”,Mathematical Programming 15 (1978) 268–277.
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This work was supported by NSF Grant ENG 79-02506.
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Cornuejols, G., Thizy, J.M. Some facets of the simple plant location polytope. Mathematical Programming 23, 50–74 (1982). https://doi.org/10.1007/BF01583779
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DOI: https://doi.org/10.1007/BF01583779