An Algorithm For Solving Multiple Objective Integer Linear Programming Problem

Moncef Abbas; Djamal Chaabane

RAIRO - Operations Research (2010)

  • Volume: 36, Issue: 4, page 351-364
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Abbas, Moncef, and Chaabane, Djamal. "An Algorithm For Solving Multiple Objective Integer Linear Programming Problem ." RAIRO - Operations Research 36.4 (2010): 351-364. <http://eudml.org/doc/105278>.

@article{Abbas2010,
abstract = { 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. },
author = {Abbas, Moncef, Chaabane, Djamal},
journal = {RAIRO - Operations Research},
keywords = {Multiple objective programming; integer linear programming.; integer linear programming},
language = {eng},
month = {3},
number = {4},
pages = {351-364},
publisher = {EDP Sciences},
title = {An Algorithm For Solving Multiple Objective Integer Linear Programming Problem },
url = {http://eudml.org/doc/105278},
volume = {36},
year = {2010},
}

TY - JOUR
AU - Abbas, Moncef
AU - Chaabane, Djamal
TI - An Algorithm For Solving Multiple Objective Integer Linear Programming Problem
JO - RAIRO - Operations Research
DA - 2010/3//
PB - EDP Sciences
VL - 36
IS - 4
SP - 351
EP - 364
AB - 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.
LA - eng
KW - Multiple objective programming; integer linear programming.; integer linear programming
UR - http://eudml.org/doc/105278
ER -

References

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  2. P. Armand and C. Malivert, Determination of the Efficient Set in Multi-Objective Linear Programming. J. Optim. Theory Appl.70 (1991) 467-489.  Zbl0793.90064
  3. P. Armand, Finding all maximal efficient faces in multi-Objective linear programming. Math. Programming61 (1993) 357-375.  Zbl0795.90054
  4. M.S. Bazaraa and C.M. Shetty, Non linear Programming theory and Algorithms. J. Wiley, New York (1979).  Zbl0476.90035
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  16. R.E. Steuer, Multiple Criteria Optimization theory, Computation and Applications. Wiley, New York (1985).  
  17. J. Teghem and P.L. Kunsh, A Survey of Techniques for Finding Efficient Solutions. Asia-Pacific J. Oper. Res.3 (1986) 95-108.  Zbl0616.90045
  18. E.L. Ulungu and J. Teghem, Multi-Objective Combinatorial Optimization Problem: A Survey. J. Multi-Criteria Decision Anal.3 (1994) 83-104.  Zbl0853.90098
  19. V. Verma, Constrained Integer Linear Fractional Programming Problem. Optimization21 (1990) 749-757.  Zbl0717.90073
  20. P.L. Yu, Multiple Criteria Decision Making. Plenum, New York (1985).  
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  22. S. Zionts, Integer Programming with Multiple Objectives. Ann. Discrete Math.1 (1977) 551-562.  Zbl0363.90082

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