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An Algorithm For Solving Multiple Objective Integer Linear Programming Problem

Published online by Cambridge University Press:  15 July 2003

Moncef Abbas  and
Djamal Chaabane
Moncef Abbas
Affiliation:
Faculté de Mathématiques, Département de Recherche Opérationnelle, BP. 32, El-Alia Bab-Ezzouar, Alger, Algérie; [email protected].
Djamal Chaabane
Affiliation:
Faculté de Mathématiques, Département de Recherche Opérationnelle, BP. 32, El-Alia Bab-Ezzouar, Alger, Algérie; [email protected].
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Abstract

In the present paper a complete procedure for solvingMultiple Objective Integer Linear Programming Problems is presented. The algorithm can be regarded as a corrected form and an alternative to the method that was proposed by Gupta and Malhotra. A numerical illustration is given to show that this latter can miss some efficient solutions. Whereas, the algorithm stated bellow determines all efficient solutions without missing any one.

Keywords

Multiple objective programminginteger linear programming.
Type
Research Article
Information
RAIRO - Operations Research , Volume 36 , Issue 4 , October 2002 , pp. 351 - 364
Copyright
© EDP Sciences, 2002

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References

Abbas, M. and Moulaï, M., Solving Multiple Objective Integer Linear Programming Problem. Ricerca Operativa 29 (1999) 15-39.
Armand, P. and Malivert, C., Determination of the Efficient Set in Multi-Objective Linear Programming. J. Optim. Theory Appl. 70 (1991) 467-489. CrossRef
Armand, P., Finding all maximal efficient faces in multi-Objective linear programming. Math. Programming 61 (1993) 357-375. CrossRef
M.S. Bazaraa and C.M. Shetty, Non linear Programming theory and Algorithms. J. Wiley, New York (1979).
H.P. Benson, Finding an initial Efficient Extreme Point for a Linear Multiple Objective Program. J. Oper. Res. Soc. (1981) 495-498.
Benson, H.P., Existence of Efficient solutions for vector Maximization Problems. J. Optim. Theory Appl. 26 (1978) 569-580. CrossRef
Bitran, G.R., Linear Multiple Objective Programs with zero-one variables. Math. Programming 13 (1977) 121-139. CrossRef
Ecker, J.G. and Kouada, I.A., Finding Efficient Points for Multi-Objective Linear Programs. Math. Programming 8 (1975) 375-377. CrossRef
Ecker, J.G. and Kouada, I.A., Finding All Efficient Extreme Points for Multi-Objective Linear Programs. Math. Programming 14 (1978) 249-261. CrossRef
Gupta, R. and Malhotra, R., Multi-Criteria Integer Linear Programming Problem. Cahiers Centre Études Rech. Opér. 34 (1992) 51-68.
A.T. Hamdy, Integer Programming, Theory, Applications and Computations. Academic Press (1975).
H. Isermann, The Enumeration of the set of all Efficient solutions for a Linear Multiple Objective Program. Oper. Res. Quarterly 28/3 (1977) 711-725.
Klein, D. and Hannan, E., Algorithm, An for the Multiple Objective Integer Linear Programming Problem. Eur. J. Oper. Res. 9 (1982) 378-385. CrossRef
Philip, J., Algorithms for the Vector Maximization Problem. Math. Programming 2 (1972) 207-229. CrossRef
Problems, B. Roy and methods with Multiple Objective functions. Math. Programming 2 (1972) 207-229.
R.E. Steuer, Multiple Criteria Optimization theory, Computation and Applications. Wiley, New York (1985).
Teghem, J. and Kunsh, P.L., Survey, A of Techniques for Finding Efficient Solutions. Asia-Pacific J. Oper. Res. 3 (1986) 95-108.
Ulungu, E.L. and Teghem, J., Multi-Objective Combinatorial Optimization Problem: A Survey. J. Multi-Criteria Decision Anal. 3 (1994) 83-104. CrossRef
Verma, V., Constrained Integer Linear Fractional Programming Problem. Optimization 21 (1990) 749-757. CrossRef
P.L. Yu, Multiple Criteria Decision Making. Plenum, New York (1985).
Zeleny, M. and The, P.L. Yu set of all non-dominated solutions in linear cases and Multi-criteria simplex method. J. Math. Anal. Appl. 49 (1975) 430-468.
Zionts, S., Integer Programming with Multiple Objectives. Ann. Discrete Math. 1 (1977) 551-562. CrossRef