Efficient and local efficient solutions for assignment type problems

Jacques A. Ferland; Pina Marziliano

RAIRO - Operations Research - Recherche Opérationnelle (2001)

  • 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 - Recherche Opérationnelle 35.3 (2001): 301-313. <http://eudml.org/doc/105248>.

@article{Ferland2001,
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 - Recherche Opérationnelle},
keywords = {efficiency; local efficiency; assignment; multiobjective},
language = {eng},
number = {3},
pages = {301-313},
publisher = {EDP-Sciences},
title = {Efficient and local efficient solutions for assignment type problems},
url = {http://eudml.org/doc/105248},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Ferland, Jacques A.
AU - Marziliano, Pina
TI - Efficient and local efficient solutions for assignment type problems
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2001
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
UR - http://eudml.org/doc/105248
ER -

References

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  1. [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. [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. [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. Heuristics 7 (2001) 391-413. Zbl1173.90403
  4. [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. Zbl0855.90105MR1675652
  5. [5] J.A. Ferland and A. Lavoie, Exchanges Procedures For Timetabling Problems. Discrete Appl. Math. 35 (1992) 237-253. Zbl0745.90037
  6. [6] A.M. Geoffrion, Proper Efficiency and Theory of Vector Maximization. J. Math. Anal. Appl. 22 (1968) 618-630. Zbl0181.22806MR229453
  7. [7] H. Isermann, The Relevance of Duality in Multiple Objective Linear Programming. TIMS Studies in the Management Sci. 6 (1977) 241-262. 
  8. [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. Zbl0687.90082MR1114321
  9. [9] P. Marziliano, Problèmes multicritères avec contraintes d’affectation, Master Thesis. Département d’Informatique et de Rechereche Opérationnelle, Université de Montréal, Canada (1996). 
  10. [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. [11] J.B. Mazzola and A.W. Neebe, Resource-Constrained Assignment Scheduling. Oper. Res. 34 (1986) 560-572. Zbl0609.90087MR874295
  12. [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. [13] R.E. Steuer, Multiple Criteria Optimization: Theory,Computation and Application. Wiley, New York (1986). Zbl0663.90085MR836977
  14. [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. Zbl0519.90083MR706797

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