Linear optimization with multiple equitable criteria

Michael M. Kostreva; Włodzimierz Ogryczak

RAIRO - Operations Research - Recherche Opérationnelle (1999)

  • Volume: 33, Issue: 3, page 275-297
  • ISSN: 0399-0559

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Kostreva, Michael M., and Ogryczak, Włodzimierz. "Linear optimization with multiple equitable criteria." RAIRO - Operations Research - Recherche Opérationnelle 33.3 (1999): 275-297. <http://eudml.org/doc/105192>.

@article{Kostreva1999,
author = {Kostreva, Michael M., Ogryczak, Włodzimierz},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {multiple criteria; linear programming; efficiency; equity},
language = {eng},
number = {3},
pages = {275-297},
publisher = {EDP-Sciences},
title = {Linear optimization with multiple equitable criteria},
url = {http://eudml.org/doc/105192},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Kostreva, Michael M.
AU - Ogryczak, Włodzimierz
TI - Linear optimization with multiple equitable criteria
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 1999
PB - EDP-Sciences
VL - 33
IS - 3
SP - 275
EP - 297
LA - eng
KW - multiple criteria; linear programming; efficiency; equity
UR - http://eudml.org/doc/105192
ER -

References

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  1. 1. R.E. STEUER, Multiple Criteria Optimization - Theory, Computation and Applications, John Wiley and Sons, New York, 1986. Zbl0663.90085MR836977
  2. 2. T. J. STEWART, A Critical Survey on the Status of Multiple Criteria Decision Making Theory and Practice, OMEGA, 1992, 20, p. 569-586. 
  3. 3. D. J. WHITE, A Bibliography on the Applications of Mathematical Programming Multiple-Objective Methods, J. Oper. Res.Soc., 1990, 41, p. 669-691. Zbl0707.90083
  4. 4. T. IBARAKI and N. KATOH, Resource Allocation Problems, Algorithmic Approaches, MIT Press, Cambridge, Massachusetts, 1988. Zbl0786.90067MR937050
  5. 5. J. R. BROWN, The Sharing Problem, Oper. Res., 1979, 27, p. 324-340. Zbl0394.90039MR533838
  6. 6. J. R. BROWN, The Knapsack Sharing Problem, Oper. Res., 1979, 27, p. 341-355. Zbl0394.90065MR533838
  7. 7. R. S. KLEIN, H. LUSS and D. R. SMITH, A Lexicographie Minimax Algorithm for Multiperiod Resource Allocation, Math. Programming, 1992, 55, p. 213-234. Zbl0766.90022MR1167598
  8. 8. W. OGRYCZAK, On the Lexicographie Minimax Approach to Location Problems, European J. Oper. Res., 1997, 100, p. 566-595. Zbl0921.90106
  9. 9. Ph. VINCKE, Multicriteria Decision-Aid, John Wiley and Sons, New York, 1992. 
  10. 10. A. SEN, On Economic Inequality, Clarendon Press, Oxford, 1973. 
  11. 11. W. OGRYCZAK, Equitable Multiple Criteria Programming, Warsaw University, Institute of Informaties, Technical Report TR 96-02 (223), 1996. Zbl0868.90086
  12. 12. V. V. PODINOVSKII, Multi-Criterion Problems with Uniform Equivalent Criteria, U.S.S.R. Comput. Math. and Math. Phys., 1975, 15, p. 47-60. Zbl0382.90086
  13. 13. A. W. MARSHALL and I. OLKIN, Inequalities: Theory of Majorization and Its Applications, Academic Press New York, New York, 1979. Zbl1219.26003MR552278
  14. 14. P. L. YU, Cone Convexity, Cone Extreme Points, and Nondominated Solutions in Decisions Problems with Multiple Objectives, J. Optim. Theor. Appl., 1974, 14, p. 319-377. Zbl0268.90057MR381739
  15. 15. R. R. YAGER, On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making, IEEE Trans. Systems Man Cybern., 1988, 18, p. 183-190. Zbl0637.90057MR931863
  16. 16. J. A.M. POTTERS and S. H. TUS, The Nucleolus of a Matrix Game and Other Nucleoli, Math. Oper. Res., 1992, 17, p. 164-174. Zbl0763.90104MR1148784
  17. 17. E. MARCHI and J. A. OVIEDO, Lexicographie Optimality in the Multiple Objective Linear Programming: the Nucleolar Solution, Eur. J. Oper, Res., 1992, 57, p. 355-359. Zbl0767.90077
  18. 18. D. T. LUC, Theory of Vector Optimization, Springer-Verlag, Berlin, 1989. MR1116766

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