Abstract
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.
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References
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.
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.
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.
Gil Aluja, J.: La gestion interactiva de los recursos humanos en la incerti¬dumbre. Ed. Ceura. Madrid 1996, pages 166–168.
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.
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.
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.
With this operation the optimum solution of the problem of assignment is not modified.
Gil Aluja, J.: La gestion interactiva de los recursos humanos en la incerti¬dumbre. Ed. Ceura. Madrid, 1986, pages 191–195.
Little, J.D.G. and others: “An algorithm for the Travelling Salesman problem” J.O.R.S.A. Vol. 11. 1963, pages 972–989.
Here what we have is a didactic example in which the figures have been established in an arbitrary fashion.
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.
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”.
For this general exposition we have adopted the nomenclature used by A.Kaufmann in the aforementioned work.
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.
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.
This is the well known Little’s Algorithm, presented in his already mentioned work in co-operation with other members of his group
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Gil-Aluja, J. (1999). Assignments. In: Elements for a Theory of Decision in Uncertainty. Applied Optimization, vol 32. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3011-1_3
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DOI: https://doi.org/10.1007/978-1-4757-3011-1_3
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