Solving the fuzzy earliness and tardiness in scheduling problems by using genetic algorithms
The scheduling problems with fuzzy processing times and fuzzy due dates are concerned in this paper. The fuzzy earliness and fuzzy tardiness are proposed based on the concepts of subtraction and maximum of any two fuzzy numbers, which are defined by using the well-known “Extension Principle” in fuzz...
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| Published in | Expert systems with applications Vol. 37; no. 7; pp. 4860 - 4866 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.07.2010
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| Online Access | Get full text |
| ISSN | 0957-4174 1873-6793 |
| DOI | 10.1016/j.eswa.2009.12.029 |
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| Abstract | The scheduling problems with fuzzy processing times and fuzzy due dates are concerned in this paper. The fuzzy earliness and fuzzy tardiness are proposed based on the concepts of subtraction and maximum of any two fuzzy numbers, which are defined by using the well-known “Extension Principle” in fuzzy sets theory. The objective function is taken as the weighted sum of fuzzy earliness and fuzzy tardiness through the concept of addition among fuzzy numbers. In this case, the objective function turns into a fuzzy-valued function. The purpose of this paper is to obtain an optimal schedule that minimizes this fuzzy-valued objective function. The genetic algorithm will be invoked to solve this problem. Two numerical examples are also provided to clarify the discussions in this paper by using the commercial software MATLAB. |
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| AbstractList | The scheduling problems with fuzzy processing times and fuzzy due dates are concerned in this paper. The fuzzy earliness and fuzzy tardiness are proposed based on the concepts of subtraction and maximum of any two fuzzy numbers, which are defined by using the well-known “Extension Principle” in fuzzy sets theory. The objective function is taken as the weighted sum of fuzzy earliness and fuzzy tardiness through the concept of addition among fuzzy numbers. In this case, the objective function turns into a fuzzy-valued function. The purpose of this paper is to obtain an optimal schedule that minimizes this fuzzy-valued objective function. The genetic algorithm will be invoked to solve this problem. Two numerical examples are also provided to clarify the discussions in this paper by using the commercial software MATLAB. |
| Author | Wu, Hsien-Chung |
| Author_xml | – sequence: 1 givenname: Hsien-Chung surname: Wu fullname: Wu, Hsien-Chung email: hcwu@nknucc.nknu.edu.tw organization: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan |
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| Cites_doi | 10.1007/s10700-004-5870-9 10.1016/0377-2217(93)E0228-P 10.1016/0165-0114(92)90372-B 10.1142/S0218488503002466 10.1016/S0019-9958(65)90241-X 10.1111/j.1475-3995.1999.tb00178.x 10.1016/S0377-2217(02)00561-1 10.1016/0925-5273(94)90118-X 10.1016/0165-0114(94)90210-0 10.1016/S0952-1976(01)00011-2 10.1016/S0360-8352(98)00128-4 10.1016/S0377-2217(99)00094-6 10.1016/0165-0114(95)00273-1 10.1016/0305-0548(93)E0014-K 10.1016/S0360-8352(99)00135-7 10.1007/s10700-004-5571-4 10.1287/ijoc.6.2.154 |
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| Keywords | Fuzzy completion time Fuzzy due date Fuzzy processing time Earliness and Tardiness Fuzzy numbers |
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| SubjectTerms | Earliness and Tardiness Fuzzy Fuzzy completion time Fuzzy due date Fuzzy logic Fuzzy numbers Fuzzy processing time Fuzzy set theory Fuzzy systems Mathematical analysis Mathematical models Matlab Scheduling |
| Title | Solving the fuzzy earliness and tardiness in scheduling problems by using genetic algorithms |
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