Milan Hladík. Computing the tolerances in multiobjective linear programming. Optim. Methods Softw., 23(5):731–739, 2008.
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We consider a multiobjective linear program and the coefficients of the multiobjective function are supposed to be uncertain. Let $x^*$ be an efficient point. We propose a procedure computing a tolerance for each objective function coefficient such that all these coefficients may simultaneously and independently vary within their tolerances while preserving efficiency of $x^*$. If $x^*$ is a nondegenerate basic solution, then the procedure runs in a polynomial time. Our method is also applicable in interval multiobjective linear programming for checking necessary efficiency of $x^*$ , i.e., whether $x^*$ is efficient for all realisations of interval values.
@article{Hla2008b,
author = "Milan Hlad\'{\i}k",
title = "Computing the tolerances in multiobjective linear programming",
journal = "Optim. Methods Softw.",
fjournal = "Optimization Methods and Software",
volume = "23",
number = "5",
pages = "731-739",
year = "2008",
doi = "10.1080/10556780802264204",
bib2html_dl_html = "http://dx.doi.org/10.1080/10556780802264204",
abstract = "We consider a multiobjective linear program and the coefficients of the multiobjective function are supposed to be uncertain. Let $x^*$ be an efficient point. We propose a procedure computing a tolerance for each objective function coefficient such that all these coefficients may simultaneously and independently vary within their tolerances while preserving efficiency of $x^*$.
If $x^*$ is a nondegenerate basic solution, then the procedure runs in a polynomial time. Our method is also applicable in interval multiobjective linear programming for checking necessary efficiency of $x^*$ , i.e., whether $x^*$ is efficient for all realisations of interval values.",
keywords = "multiobjective linear programming; interval matrix; efficient point; sensitivity analysis; tolerance analysis",
}
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