Efficient and Local Efficient Solutions for Assignment Type Problems

Jacques A. Ferland; Pina Marziliano

RAIRO - Operations Research (2010)

  • Volume: 35, Issue: 3, page 301-313
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Ferland, Jacques A., and Marziliano, Pina. "Efficient and Local Efficient Solutions for Assignment Type Problems." RAIRO - Operations Research 35.3 (2010): 301-313. <http://eudml.org/doc/197779>.

@article{Ferland2010,
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. },
author = {Ferland, Jacques A., Marziliano, Pina},
journal = {RAIRO - Operations Research},
keywords = {Efficiency; local efficiency; assignment; multiobjective.; efficiency; multiobjective},
language = {eng},
month = {3},
number = {3},
pages = {301-313},
publisher = {EDP Sciences},
title = {Efficient and Local Efficient Solutions for Assignment Type Problems},
url = {http://eudml.org/doc/197779},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Ferland, Jacques A.
AU - Marziliano, Pina
TI - Efficient and Local Efficient Solutions for Assignment Type Problems
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 3
SP - 301
EP - 313
AB - 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.
LA - eng
KW - Efficiency; local efficiency; assignment; multiobjective.; efficiency; multiobjective
UR - http://eudml.org/doc/197779
ER -

References

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  1. 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).  
  2. 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.  
  3. J.A. Ferland, I. Berrada, I. Nabli, A. Ahiot, P. Michelon and V. Gascon, Generalized Assignment-Type Goal Programming Problem and Application to Nurse Scheduling. J. Heuristics7 (2001) 391-413.  Zbl1173.90403
  4. J.A. Ferland, A. Hertz and A. Lavoie, An Objected Oriented Methodology For Solving Assignment Type Problems With Neighborhood Search Techniques. Oper. Res.44 (1996) 347-359.  Zbl0855.90105
  5. J.A. Ferland and A. Lavoie, Exchanges Procedures For Timetabling Problems. Discrete Appl. Math.35 (1992) 237-253.  Zbl0745.90037
  6. A.M. Geoffrion, Proper Efficiency and Theory of Vector Maximization. J. Math. Anal. Appl.22 (1968) 618-630.  Zbl0181.22806
  7. H. Isermann, The Relevance of Duality in Multiple Objective Linear Programming. TIMS Studies in the Management Sci.6 (1977) 241-262.  
  8. F.A. Lootsma, Optimization with Multiple Objectives, in Mathematical Programming: Recent Developments and Applications, edited by M. Iri and K. Tanabe (1989) 333-364.  Zbl0687.90082
  9. P. Marziliano, Problèmes multicritères avec contraintes d'affectation, Master Thesis. Département d'Informatique et de Rechereche Opérationnelle, Université de Montréal, Canada (1996).  
  10. 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).  
  11. J.B. Mazzola and A.W. Neebe, Resource-Constrained Assignment Scheduling. Oper. Res.34 (1986) 560-572.  Zbl0609.90087
  12. V. Robert, La confection d'horaires par décomposition en sous-problèmes d'affectation, Doctoral dissertation. Mathematics Department, École Polytechnique Fédérale de Lausanne, Switzerland (1996).  
  13. R.E. Steuer, Multiple Criteria Optimization: Theory,Computation and Application. Wiley, New York (1986).  Zbl0663.90085
  14. S. Zionts and J. Wallenius, An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions. Management Sci.29 (1983) 519-529.  Zbl0519.90083

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