Obtaining Efficient Solutions of Interval Multi-objective Linear Programming Problems
In 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 t...
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| Vydané v: | International journal of fuzzy systems Ročník 22; číslo 3; s. 873 - 890 |
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| Jazyk: | English |
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01.04.2020
Springer Nature B.V |
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| ISSN: | 1562-2479, 2199-3211 |
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| Abstract | In 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
ε
-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. |
|---|---|
| AbstractList | In 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 ε-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. In 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 ε -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. |
| Author | Batamiz, Aida Allahdadi, Mehdi Hladík, Milan |
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| Keywords | Interval multi-objective linear programming Uncertainty constraint Weighted sum Lexicographic Efficient solution |
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| References_xml | – reference: RivazSYaghoobiMAHladíkMUsing modified maximum regret for finding a necessarily efficient solution in an interval MOLP problemFuzzy Optim. Decis. Mak.2016153237253353596710.1007/s10700-015-9226-4 – reference: BotteaMSchöbelADominance for multi-objective robust optimization conceptsEur. J. Oper. Res.20192732430440390712010.1016/j.ejor.2018.08.020 – reference: HladíkMHow to determine basis stability in interval linear programmingOptim. Lett.20148375389315292410.1007/s11590-012-0589-y – reference: HladíkMWeak and strong solvability of interval linear systems of equations and inequalitiesLinear Algebra Appl.20134381141564165303452210.1016/j.laa.2013.02.012 – reference: InuiguchiMSakawaMMinimax regret solution to multi objective linear programming problems with interval objective function coefficientsEur. J. Oper. Res.19958652653610.1016/0377-2217(94)00092-Q – reference: DouradoADPLobatoFSAp CavaliniASteffenVFuzzy reliability-based optimization for engineering system designInt. J. Fuzzy Syst.20192151418142910.1007/s40815-019-00655-5 – reference: InuiguchiMKumeYGoal programming approach for solving IMOLP problemsEur. J. Oper. Res.19915234536010.1016/0377-2217(91)90169-V – reference: Mishmast NehiHAshayerinasabHAAllahdadiMSolving methods for interval linear programming problem: a review and an improved methodOper. Res.201810.1007/s12351-018-0383-4 – reference: Razavi HajiaghaSHProgramming with interval multi-objective linear coefficients: a fuzzy set based approachKybernetes2013423482496308915510.1108/03684921311323707 – reference: AllahdadiMNehiHMThe optimal solutions set of the interval linear programming problemsOptim. Lett.201378931911305739710.1007/s11590-012-0530-4 – reference: InuiguchiMSakawaMAn achievement rate approach to linear programming problems with an interval objective functionJ. Oper. Res. Soc.199748253310.1057/palgrave.jors.2600322 – reference: Dechao LiLLeungYWeizhiWMultiobjective interval linear programming in admissible-order vector spaceInf. Sci.201948611910.1016/j.ins.2019.02.012 – reference: HuangGHBaetzBWPatryGGGrey integer programming: an application to waste management planning under uncertaintyEur. J. Oper. Res.19958359462010.1016/0377-2217(94)00093-R – reference: Inuiguchi, M.: Necessary efficiency is partitioned into possible an necessary optimalities, IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 209–214. Edmonton, AB, Canada (2013) – reference: AlefeldGHerzbergerJIntroduction to Interval Computations1983New YorkAcademic Press0552.65041 – reference: AllahdadiMNehiHMAshayerinasabHAJavanmardMImproving the modified interval linear programming method by new techniquesInf. Sci.201633922423610.1016/j.ins.2015.12.037 – reference: AllahdadiMNehiHMThe optimal value bounds of the objective function in the interval linear programming problemChiang Mai. J. Sci.20154225015111349.90600 – reference: RexJRohnJSufficient conditions for regularity and singularity of interval matricesSIAM J. Matrix Anal. Appl.1998202437445165139610.1137/S0895479896310743 – reference: RivazSYaghoobiMAMinimax regret solution to linear programming problems with an interval objective functionEur. J. Oper. Res.2013213625649309285110.1007/s10100-012-0252-9 – reference: SteuerREMultiple criteria optimization: theory, computation and application1989New YorkWiley0742.90068 – reference: HuangGHMooreRDGrey linear programming, its solving approach, and its applicationInt. J. Syst. 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| Title | Obtaining Efficient Solutions of Interval Multi-objective Linear Programming Problems |
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