Generalization of the concept of equitable efficiency in multiobjective optimization problems

Document Type : Original Paper

Authors

Department of Mathematics, Vali Asr University of Rafsanjan, Rafsanjan, Iran

Abstract

The main purpose of the paper is to generalize the concept of equitable efficiency‎ ‎by introducing the concept of equitable A-efficiency‎, ‎where A is an arbitrary matrix with non-negative‎ ‎entries‎. ‎Two conditions are provided to ensure that the relation of equitable A-dominance is an equitable rational preference relation‎. ‎Furthermore the structure of equitably A-efficient set is investigated and is proved that the set of equitably A-efficient solutions is contained within the set of efficient‎. ‎Hence to reduce Pareto-optimal solutions‎, ‎we can use equitably A-efficient solutions‎.

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Main Subjects


[1] Lorenz, M.O. (1905). Methods of measuring the concentration of wealth, American Statistical Association, New Series, 70, 209–219.
[2]. Kostreva, M.M. and Ogryczak, W. (1999). Linear optimization with multiple equitable criteria, RAIRO-Operations Research, 33 (3), 275– 297.
[3]. Kostreva, M.M., Ogryczak, W. and Wierzbicki, A. (2004). Equitable aggregations and multiple criteria analysis, European Journal of Operational Research, 158 (2), 362–377.
[4]. Ogryczak, W. (2000). Multiple criteria linear programming model for portfolio selection, Annals of Operations Research, 97, 143–162.
[5]. Ogryczak, W. (2000). Inequality measures and equitable approaches to location problems, European Journal of Operational Research, 122 (2), 374–391.
[6]. Ogryczak, W., Wierzbicki, A. and Milewski, M. (2008). A multi-criteria approach to fair and efficient bandwidth allocation, Omega, 36 (3), 451– 463.
[7]. Ogryczak, W., Luss, H., Pióro Michałand Nace, D. and Tomaszewski, A. (2014). Fair optimization and networks: A survey, Journal of Applied Mathematics, 2014, ID 340913.
Volume 9, Issue 2
September 2019
Pages 171-190
  • Receive Date: 02 August 2018
  • Revise Date: 19 June 2019
  • Accept Date: 27 June 2019
  • First Publish Date: 23 September 2019