Milan Hladík. Various approaches to multiobjective linear programming problems with interval costs and interval weights. Cent. Eur. J. Oper. Res., 31(3):713–731, September 2023.
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Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear programming problems, in which two kinds of input entries have the form of interval data. First, we suppose that the objectives entries are interval values, and, second, we suppose that we have an interval estimation of weights of the particular criteria. These two types of interval data naturally lead to various definitions of efficient solutions. We discuss six meaningful concepts of efficient solutions and compare them to each other. For each of them, we attempt to characterize the corresponding kind efficiency and investigate computational complexity of deciding whether a given solution is efficient.
@article{Hla2023b,
author = "Milan Hlad\'{\i}k",
title = "Various approaches to multiobjective linear programming problems with interval costs and interval weights",
journal = "Cent. Eur. J. Oper. Res.",
fjournal = "Central European Journal of Operations Research",
volume = "31",
number = "3",
month = "September",
pages = "713-731",
year = "2023",
doi = "10.1007/s10100-022-00804-6",
issn = "1613-9178",
url = "https://link.springer.com/article/10.1007/s10100-022-00804-6",
bib2html_dl_html = "https://doi.org/10.1007/s10100-022-00804-6",
bib2html_dl_pdf = "https://rdcu.be/dfdnY",
abstract = "Optimization problems are often subject to various kinds of inexactness or inaccuracy of input data. Here, we consider multiobjective linear programming problems, in which two kinds of input entries have the form of interval data. First, we suppose that the objectives entries are interval values, and, second, we suppose that we have an interval estimation of weights of the particular criteria. These two types of interval data naturally lead to various definitions of efficient solutions. We discuss six meaningful concepts of efficient solutions and compare them to each other. For each of them, we attempt to characterize the corresponding kind efficiency and investigate computational complexity of deciding whether a given solution is efficient.",
keywords = "Multiobjective linear programming; Interval analysis; Robust optimization; Weighted scalarization",
}
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