An algorithm for solving multiple objective integer linear programming problem
RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 4, pp. 351-364.

In the present paper a complete procedure for solving Multiple 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.

DOI : 10.1051/ro:2003006
Mots-clés : multiple objective programming, integer linear programming
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Abbas, Moncef; Chaabane, Djamal. An algorithm for solving multiple objective integer linear programming problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 4, pp. 351-364. doi : 10.1051/ro:2003006. http://archive.numdam.org/articles/10.1051/ro:2003006/

[1] M. Abbas and M. Moulaï, Solving Multiple Objective Integer Linear Programming Problem. Ricerca Operativa 29 (1999) 15-39.

[2] P. Armand and C. Malivert, Determination of the Efficient Set in Multi-Objective Linear Programming. J. Optim. Theory Appl. 70 (1991) 467-489. | MR | Zbl

[3] P. Armand, Finding all maximal efficient faces in multi-Objective linear programming. Math. Programming 61 (1993) 357-375. | MR | Zbl

[4] M.S. Bazaraa and C.M. Shetty, Non linear Programming theory and Algorithms. J. Wiley, New York (1979). | MR | Zbl

[5] H.P. Benson, Finding an initial Efficient Extreme Point for a Linear Multiple Objective Program. J. Oper. Res. Soc. (1981) 495-498. | MR | Zbl

[6] H.P. Benson, Existence of Efficient solutions for vector Maximization Problems. J. Optim. Theory Appl. 26 (1978) 569-580. | MR | Zbl

[7] G.R. Bitran, Linear Multiple Objective Programs with zero-one variables. Math. Programming 13 (1977) 121-139. | MR | Zbl

[8] J.G. Ecker and I.A. Kouada, Finding Efficient Points for Multi-Objective Linear Programs. Math. Programming 8 (1975) 375-377. | MR

[9] J.G. Ecker and I.A. Kouada, Finding All Efficient Extreme Points for Multi-Objective Linear Programs. Math. Programming 14 (1978) 249-261. | MR | Zbl

[10] R. Gupta and R. Malhotra, Multi-Criteria Integer Linear Programming Problem. Cahiers Centre Études Rech. Opér. 34 (1992) 51-68. | MR | Zbl

[11] A.T. Hamdy, Integer Programming, Theory, Applications and Computations. Academic Press (1975). | MR | Zbl

[12] 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. | Zbl

[13] D. Klein and E. Hannan, An Algorithm for the Multiple Objective Integer Linear Programming Problem. Eur. J. Oper. Res. 9 (1982) 378-385. | MR | Zbl

[14] J. Philip, Algorithms for the Vector Maximization Problem. Math. Programming 2 (1972) 207-229. | MR | Zbl

[15] B. Roy, Problems and methods with Multiple Objective functions. Math. Programming 2 (1972) 207-229. | MR | Zbl

[16] R.E. Steuer, Multiple Criteria Optimization theory, Computation and Applications. Wiley, New York (1985). | MR | Zbl

[17] J. Teghem and P.L. Kunsh, A Survey of Techniques for Finding Efficient Solutions. Asia-Pacific J. Oper. Res. 3 (1986) 95-108. | Zbl

[18] E.L. Ulungu and J. Teghem, Multi-Objective Combinatorial Optimization Problem: A Survey. J. Multi-Criteria Decision Anal. 3 (1994) 83-104. | Zbl

[19] V. Verma, Constrained Integer Linear Fractional Programming Problem. Optimization 21 (1990) 749-757. | MR | Zbl

[20] P.L. Yu, Multiple Criteria Decision Making. Plenum, New York (1985). | MR | Zbl

[21] M. Zeleny and P.L. Yu, The set of all non-dominated solutions in linear cases and Multi-criteria simplex method. J. Math. Anal. Appl. 49 (1975) 430-468. | MR | Zbl

[22] S. Zionts, Integer Programming with Multiple Objectives. Ann. Discrete Math. 1 (1977) 551-562. | Zbl

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