Aida Batamiz, Mehdi Allahdadi, and Milan Hladík. Obtaining efficient solutions of interval multi-objective linear programming problems. Int. J. Fuzzy Syst., 22(3):873–890, 2020.
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n this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and two generalized methods. In the new method, converting IMOLP into an interval linear programming (ILP) and then obtaining its optimal solutions (OSs), ESs of the IMOLP are determined. This method has several advantages: (i) This method is the only method which obtains a solution box for IMOLP models. (ii) The solving process is not time consuming. (iii) The number of ESs is higher than for other methods. (V) The method is applicable for large-scale problems. Also, we generalize the epsilon-constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which do not have any problems such as lengthy and time-consuming and are applicable for large-scale problems. Some examples were solved to show the efficiency of the proposed methods. Finally, by the proposed method, we solve the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank.
@article{BatAll2020a,
author = "Aida Batamiz and Mehdi Allahdadi and Milan Hlad\'{\i}k",
title = "Obtaining efficient solutions of interval multi-objective linear programming problems",
journal = "Int. J. Fuzzy Syst.",
fjournal = "International Journal of Fuzzy Systems",
volume = "22",
number = "3",
pages = "873-890",
year = "2020",
doi = "10.1007/s40815-020-00800-5",
issn = "2199-3211",
url = "http://link.springer.com/article/10.1007/s40815-020-00800-5",
bib2html_dl_html = "https://doi.org/10.1007/s40815-020-00800-5",
bib2html_dl_pdf = "https://rdcu.be/b1Z3L",
abstract = "n this paper, we consider interval multi-objective linear programming (IMOLP) models which are used to deal with uncertainties of real-world problems. So far, a variety of approaches for obtaining efficient solutions (ESs) of these problems have been developed. In this paper, we propose a new and two generalized methods. In the new method, converting IMOLP into an interval linear programming (ILP) and then obtaining its optimal solutions (OSs), ESs of the IMOLP are determined. This method has several advantages: (i) This method is the only method which obtains a solution box for IMOLP models. (ii) The solving process is not time consuming. (iii) The number of ESs is higher than for other methods. (V) The method is applicable for large-scale problems. Also, we generalize the epsilon-constraint and lexicographic methods which are used for obtaining ESs of the multi-objective linear programming (MOLP) models which do not have any problems such as lengthy and time-consuming and are applicable for large-scale problems. Some examples were solved to show the efficiency of the proposed methods. Finally, by the proposed method, we solve the IMOLP model corresponding to the problem of the facilities and non-return funds in a bank.",
keywords = "Efficient solution; Interval multi-objective linear programming; Uncertainty; epsilon-constraint; Lexicographic; Weighted sum",
}
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