# An Algorithm For Solving Multiple Objective Integer Linear Programming Problem

RAIRO - Operations Research (2010)

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

## Access Full Article

top## Abstract

top## How to cite

topAbbas, 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

top- M. Abbas and M. Moulaï, Solving Multiple Objective Integer Linear Programming Problem. Ricerca Operativa29 (1999) 15-39.
- 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
- P. Armand, Finding all maximal efficient faces in multi-Objective linear programming. Math. Programming61 (1993) 357-375. Zbl0795.90054
- M.S. Bazaraa and C.M. Shetty, Non linear Programming theory and Algorithms. J. Wiley, New York (1979). Zbl0476.90035
- H.P. Benson, Finding an initial Efficient Extreme Point for a Linear Multiple Objective Program. J. Oper. Res. Soc. (1981) 495-498. Zbl0454.90075
- H.P. Benson, Existence of Efficient solutions for vector Maximization Problems. J. Optim. Theory Appl.26 (1978) 569-580. Zbl0373.90085
- G.R. Bitran, Linear Multiple Objective Programs with zero-one variables. Math. Programming13 (1977) 121-139. Zbl0377.90070
- J.G. Ecker and I.A. Kouada, Finding Efficient Points for Multi-Objective Linear Programs. Math. Programming8 (1975) 375-377. Zbl0385.90105
- J.G. Ecker and I.A. Kouada, Finding All Efficient Extreme Points for Multi-Objective Linear Programs. Math. Programming14 (1978) 249-261. Zbl0385.90105
- R. Gupta and R. Malhotra, Multi-Criteria Integer Linear Programming Problem. Cahiers Centre Études Rech. Opér.34 (1992) 51-68. Zbl0774.90070
- A.T. Hamdy, Integer Programming, Theory, Applications and Computations. Academic Press (1975). Zbl0316.90042
- 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. Zbl0372.90086
- D. Klein and E. Hannan, An Algorithm for the Multiple Objective Integer Linear Programming Problem. Eur. J. Oper. Res.9 (1982) 378-385. Zbl0477.90075
- J. Philip, Algorithms for the Vector Maximization Problem. Math. Programming2 (1972) 207-229. Zbl0288.90052
- B. Roy, Problems and methods with Multiple Objective functions. Math. Programming2 (1972) 207-229.
- R.E. Steuer, Multiple Criteria Optimization theory, Computation and Applications. Wiley, New York (1985).
- 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
- E.L. Ulungu and J. Teghem, Multi-Objective Combinatorial Optimization Problem: A Survey. J. Multi-Criteria Decision Anal.3 (1994) 83-104. Zbl0853.90098
- V. Verma, Constrained Integer Linear Fractional Programming Problem. Optimization21 (1990) 749-757. Zbl0717.90073
- P.L. Yu, Multiple Criteria Decision Making. Plenum, New York (1985).
- 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. Zbl0313.65047
- S. Zionts, Integer Programming with Multiple Objectives. Ann. Discrete Math.1 (1977) 551-562. Zbl0363.90082

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.