Milan Hladík. On relation of possibly efficiency and robust counterparts in interval multiobjective linear programming. In Antonio Sforza and Claudio Sterle, editors, Optimization and Decision Science: Methodologies and Applications, Springer Proceedings in Mathematics & Statistics, pp. 335–343, Springer, Cham, 2017.
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We investigate multiobjective linear programming with uncertain cost coefficients. We assume that lower and upper bounds for uncertain values are known, no other assumption on uncertain costs is needed. We focus on the so called possibly efficiency, which is defined as efficiency of at least one realization of interval coefficients. We show many favourable properties including existence, low computational performance of determining possibly efficient solutions, convexity of the dominance cone or connectedness or the efficiency set. In the second part, we discuss robust optimization approach for dealing with uncertain costs. We show that the corresponding robust counterpart is closely related to possible efficiency.
@inCollection{Hla2017e,
author = "Milan Hlad\'{\i}k",
title = "On relation of possibly efficiency and robust counterparts in interval multiobjective linear programming",
editor = "Sforza, Antonio and Sterle, Claudio",
booktitle = "Optimization and Decision Science: {Methodologies} and Applications",
fbooktitle = "Optimization and Decision Science: Methodologies and Applications: ODS, Sorrento, Italy, September 4-7, 2017",
publisher = "Springer",
address = "Cham",
series = "Springer Proceedings in Mathematics \& Statistics",
volume = "217",
pages = "335-343",
year = "2017",
doi = "10.1007/978-3-319-67308-0_34",
isbn = "978-3-319-67308-0",
issn = "2194-1017",
url = "https://link.springer.com/chapter/10.1007/978-3-319-67308-0_34",
bib2html_dl_html = "https://doi.org/10.1007/978-3-319-67308-0_34",
abstract = "We investigate multiobjective linear programming with uncertain cost coefficients. We assume that lower and upper bounds for uncertain values are known, no other assumption on uncertain costs is needed. We focus on the so called possibly efficiency, which is defined as efficiency of at least one realization of interval coefficients. We show many favourable properties including existence, low computational performance of determining possibly efficient solutions, convexity of the dominance cone or connectedness or the efficiency set. In the second part, we discuss robust optimization approach for dealing with uncertain costs. We show that the corresponding robust counterpart is closely related to possible efficiency.",
keywords = "Interval linear programming; Multiobjective linear programming; Robust optimization",
}
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