• Jaime Gil-Aluja
Part of the Applied Optimization book series (APOP, volume 32)


One of the most frequent problems arising when taking a decision is linked to a type of relation that is known under the name of “assignment”. With the object of establishing the foundations on which to construct a method that is suitable for finding adequate solutions let us first define this concept.


Directed Tree Fuzzy Relation Initial Vertex Finite Capacity Maximum Linkage 
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  1. 1.
    See for example Gil Aluja, J.: Modelos no numéricos de asignacion en la gestion de personal. Proceedings of the II International SIGEF Congress, Santiago de Compostela, November 15–17, 1995, pages 93–120.Google Scholar
  2. 2.
    Kaufmann, A. and Gil Aluja, J.: Introduccion de la teoria de los subconjun¬tos borrosos a la gestiOn de las empresas. Ed. Milladoiro, Santiago de Compostela, 1986, pages 148–150.Google Scholar
  3. 3.
    In this and other later examples we will use a nomenclature in which we will do without the sub-indices, in order to simplify the expressions.Google Scholar
  4. 4.
    Gil Aluja, J.: La gestion interactiva de los recursos humanos en la incerti¬dumbre. Ed. Ceura. Madrid 1996, pages 166–168.Google Scholar
  5. 5.
    Kaufmann, A. and Gil Aluja, J.: “Introduccion de la teoria de los subcon¬juntos borrosos a la gestiOn de las empresas”. Ed. Milladoiro. Santiago de Compostela, 3rd Edition, 1993, pages 157–158.Google Scholar
  6. 6.
    König, D.: “Theorie der endlichen und unendlichen graphen” (1916) later reprinted by Chelsea Publ. C”, New York, 1950. This work was made known by Kuhn, H.W. in an article on “The Hungarian method for the assignment problem”, Naval Research Logistics Quarterly. Vol 2, N” 1–2. March-June 1959, pages 83–98. The algorithm was made known through the multiple editions of the work by Kaufmann, A.: “Méthodes et Modèles de la Recher¬che Opérationelle” Volume I, D.nod, Paris, 1970, pages 65. 72.Google Scholar
  7. 7.
    Kaufmann, A. and Faure, R.: “Invitation à la Recherche Opérationelle” Dunod, Paris, 1963, pages 91–103. In this work mention is made of the ori¬gin of this presentation that is due to M. Yves Malgrange.Google Scholar
  8. 8.
    With this operation the optimum solution of the problem of assignment is not modified.Google Scholar
  9. 9.
    Gil Aluja, J.: La gestion interactiva de los recursos humanos en la incerti¬dumbre. Ed. Ceura. Madrid, 1986, pages 191–195.Google Scholar
  10. 11.
    Little, J.D.G. and others: “An algorithm for the Travelling Salesman problem” J.O.R.S.A. Vol. 11. 1963, pages 972–989.Google Scholar
  11. 10.
    Here what we have is a didactic example in which the figures have been established in an arbitrary fashion.Google Scholar
  12. 12.
    Bartier, P. and Roy, B.: “Une procédure de résolution pour une classe de problèmes pouvant posséder un caractère combinatoire” Bulletin du Centre International de Calcul de Rome, 1965.Google Scholar
  13. 13.
    Kaufmann, A.: “Introduccion a la combinatoria y sus aplicaciones. Ed. C.E.C.S.A., Barcelona, 1971, page 40. The original was published by Du-nod (Paris) under the title oft “Introduction a la Combinatorique en vue des aplications”.Google Scholar
  14. 14.
    For this general exposition we have adopted the nomenclature used by A.Kaufmann in the aforementioned work.Google Scholar
  15. 15.
    See in this respect, for example: Kaufmann, A. and Gil Aluja, J.: Técnicas operativas de gestion para el tratamiento de la incertidumbre. Ed. Hispano Europea, Barcelona 1987, pages 166–168.Google Scholar
  16. 16.
    Lawler, E.L. and Wood, D.E.: Branch and Bound Methods: A Survey, J.O.R.S.A. Vol 14. No. 4 July-August, 1966, pages 699–719.Google Scholar
  17. 17.
    This is the well known Little’s Algorithm, presented in his already mentioned work in co-operation with other members of his groupGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Jaime Gil-Aluja
    • 1
    • 2
  1. 1.Barcelona UniversitySpain
  2. 2.Paris-Dauphine UniversityFrance

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