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Efficient and Local Efficient Solutions for Assignment Type Problems

Published online by Cambridge University Press:  15 August 2002

Jacques A. Ferland
Affiliation:
Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal Québec Canada H3C 3J7.
Pina Marziliano
Affiliation:
Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, Succursale Centre-Ville, Montréal Québec Canada H3C 3J7.
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Abstract

In this paper, we analyse the multiobjective problem generated by applying a goal programming approach to deal with linear assignment type problem. We specify sufficient conditions for a solution to be efficient for this problem. The notion of efficiency with respect to a neighborhood is also introduced and characterized through sufficient conditions. Unfortunately, these conditions are not necessary in general.

Type
Research Article
Copyright
© EDP Sciences, 2001

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References

D. Costa, Méthodes de résolution constructives, séquentielles et évolutives pour des problèmes d'affectation sous-contraintes, Doctoral dissertation. Mathematics Department, École Polytechnique Fédérale de Lausanne, Switzerland (1995).
J.A. Ferland, Generalized Assignment Type Problems, a Powerful Modeling Scheme, in Practice and Theory of Automated Timetabling II, edited by E. Burke and M. Carter. Springer, Lecture Notes in Comput. Sci. 1408 (1998) 53-77.
Ferland, J.A., Berrada, I., Nabli, I., Ahiot, A., Michelon, P. and Gascon, V., Generalized Assignment-Type Goal Programming Problem and Application to Nurse Scheduling. J. Heuristics 7 (2001) 391-413. CrossRef
Ferland, J.A., Hertz, A. and Lavoie, A., Objected Oriented Methodology For Solving Assignment Type Problems With Neighborhood Search Techniques, An. Oper. Res. 44 (1996) 347-359. CrossRef
Ferland, J.A. and Lavoie, A., Exchanges Procedures For Timetabling Problems. Discrete Appl. Math. 35 (1992) 237-253. CrossRef
Geoffrion, A.M., Proper Efficiency and Theory of Vector Maximization. J. Math. Anal. Appl. 22 (1968) 618-630. CrossRef
Isermann, H., The Relevance of Duality in Multiple Objective Linear Programming. TIMS Studies in the Management Sci. 6 (1977) 241-262.
F.A. Lootsma, Optimization with Multiple Objectives, in Mathematical Programming: Recent Developments and Applications , edited by M. Iri and K. Tanabe (1989) 333-364.
P. Marziliano, Problèmes multicritères avec contraintes d'affectation, Master Thesis. Département d'Informatique et de Rechereche Opérationnelle, Université de Montréal, Canada (1996).
P. Marziliano and J.A. Ferland, A Heuristic Approach for Multiobjective Problems with Assignment Constraints , Publication # 1128. Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Canada (1998).
Mazzola, J.B. and Neebe, A.W., Resource-Constrained Assignment Scheduling. Oper. Res. 34 (1986) 560-572. CrossRef
V. Robert, La confection d'horaires par décomposition en sous-problèmes d'affectation, Doctoral dissertation. Mathematics Department, École Polytechnique Fédérale de Lausanne, Switzerland (1996).
R.E. Steuer, Multiple Criteria Optimization: Theory,Computation and Application. Wiley, New York (1986).
Zionts, S. and Wallenius, J., Interactive Multiple Objective Linear Programming Method, An for a Class of Underlying Nonlinear Utility Functions. Management Sci. 29 (1983) 519-529. CrossRef