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Stability and accuracy functions in multicriteria linear combinatorial optimization problems

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  • Marek Libura
  • Yury Nikulin

Abstract

We consider a vector linear combinatorial optimization problem in which initial coefficients of objective functions are subject to perturbations. For Pareto and lexicographic principles of efficiency we introduce appropriate measures of the quality of a given feasible solution. These measures correspond to so-called stability and accuracy functions defined earlier for scalar optimization problems. Then we study properties of such functions and calculate the maximum norms of perturbations for which an efficient solution preserves the efficiency. Copyright Springer Science + Business Media, LLC 2006

Suggested Citation

  • Marek Libura & Yury Nikulin, 2006. "Stability and accuracy functions in multicriteria linear combinatorial optimization problems," Annals of Operations Research, Springer, vol. 147(1), pages 255-267, October.
    • Handle: RePEc:spr:annopr:v:147:y:2006:i:1:p:255-267:10.1007/s10479-006-0071-2
    DOI: 10.1007/s10479-006-0071-2
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    Citations

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    Cited by:

    1. Nikulin, Y. & Karelkina, O. & Mäkelä, M.M., 2013. "On accuracy, robustness and tolerances in vector Boolean optimization," European Journal of Operational Research, Elsevier, vol. 224(3), pages 449-457.
    2. Evgeny Gurevsky & Olga Battaïa & Alexandre Dolgui, 2012. "Balancing of simple assembly lines under variations of task processing times," Annals of Operations Research, Springer, vol. 201(1), pages 265-286, December.
    3. Nikulin, Yury & Mäkelä, Marko M., 2010. "Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality "from Condorcet to Pareto"," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1497-1505, December.
    4. Korotkov, Vladimir & Wu, Desheng, 2021. "Benchmarking project portfolios using optimality thresholds," Omega, Elsevier, vol. 99(C).
    5. Yury Nikulin, 2009. "Stability and accuracy functions in a coalition game with bans, linear payoffs and antagonistic strategies," Annals of Operations Research, Springer, vol. 172(1), pages 25-35, November.

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