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.
@article{RO_2001__35_3_301_0, author = {Ferland, Jacques A. and Marziliano, Pina}, title = {Efficient and local efficient solutions for assignment type problems}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {301--313}, publisher = {EDP-Sciences}, volume = {35}, number = {3}, year = {2001}, mrnumber = {1884555}, zbl = {0991.90114}, language = {en}, url = {http://www.numdam.org/item/RO_2001__35_3_301_0/} }
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 SP - 301 EP - 313 VL - 35 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/item/RO_2001__35_3_301_0/ LA - en ID - RO_2001__35_3_301_0 ER -
%0 Journal Article %A Ferland, Jacques A. %A Marziliano, Pina %T Efficient and local efficient solutions for assignment type problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2001 %P 301-313 %V 35 %N 3 %I EDP-Sciences %U http://www.numdam.org/item/RO_2001__35_3_301_0/ %G en %F RO_2001__35_3_301_0
Ferland, Jacques A.; Marziliano, Pina. Efficient and local efficient solutions for assignment type problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 35 (2001) no. 3, pp. 301-313. http://www.numdam.org/item/RO_2001__35_3_301_0/
[1] 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] 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] Generalized Assignment-Type Goal Programming Problem and Application to Nurse Scheduling. J. Heuristics 7 (2001) 391-413. | Zbl
, , , , and ,[4] An Objected Oriented Methodology For Solving Assignment Type Problems With Neighborhood Search Techniques. Oper. Res. 44 (1996) 347-359. | MR | Zbl
, and ,[5] Exchanges Procedures For Timetabling Problems. Discrete Appl. Math. 35 (1992) 237-253. | Zbl
and ,[6] Proper Efficiency and Theory of Vector Maximization. J. Math. Anal. Appl. 22 (1968) 618-630. | MR | Zbl
,[7] The Relevance of Duality in Multiple Objective Linear Programming. TIMS Studies in the Management Sci. 6 (1977) 241-262.
,[8] Optimization with Multiple Objectives, in Mathematical Programming: Recent Developments and Applications, edited by M. Iri and K. Tanabe (1989) 333-364. | MR | Zbl
,[9] Problèmes multicritères avec contraintes d'affectation, Master Thesis. Département d'Informatique et de Rechereche Opérationnelle, Université de Montréal, Canada (1996).
,[10] A Heuristic Approach for Multiobjective Problems with Assignment Constraints, Publication # 1128. Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Canada (1998).
and ,[11] Resource-Constrained Assignment Scheduling. Oper. Res. 34 (1986) 560-572. | MR | Zbl
and ,[12] La confection d'horaires par décomposition en sous-problèmes d'affectation, Doctoral dissertation. Mathematics Department, École Polytechnique Fédérale de Lausanne, Switzerland (1996).
,[13] Multiple Criteria Optimization: Theory,Computation and Application. Wiley, New York (1986). | MR | Zbl
,[14] An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions. Management Sci. 29 (1983) 519-529. | MR | Zbl
and ,