APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT
The set together with the operation maximum (max) denoted as and addition (+) denoted as is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the ap...
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Universitas Pattimura
2022-06-01
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5177 |
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| author | Andika Ellena Saufika Hakim Maharani Ari Suparwanto |
| author_facet | Andika Ellena Saufika Hakim Maharani Ari Suparwanto |
| author_sort | Andika Ellena Saufika Hakim Maharani |
| collection | DOAJ |
| description | The set together with the operation maximum (max) denoted as and addition (+) denoted as is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the application of max-plus algebra in a serial manufacturing machine with a storage unit is discussed. The results of this are the generalization system max-plus-linear equations on a production system that is, in addition, noted the max-plus-linear time-invariant system. From the max-plus-linear time-invariant system, it can be obtained the equation which is then used to determine the beginning time of a production system so the manufacturing machine work periodically. The eigenvector and eigenvalue of the matrix are then used to find the beginning time and the period time of the manufacturing machine. Furthermore, the time when the product leaves the manufacturing machine with the time while the raw material enters the manufacturing machine is given and vice versa are obtained from the max-plus-linear time-invariant system that is can be formed in the equation . |
| format | Article |
| id | doaj-art-619b03503747477fbb03a6e1cdae3053 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2022-06-01 |
| publisher | Universitas Pattimura |
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| series | Barekeng |
| spelling | doaj-art-619b03503747477fbb03a6e1cdae30532025-08-20T03:36:12ZengUniversitas PattimuraBarekeng1978-72272615-30172022-06-0116252553010.30598/barekengvol16iss2pp525-5305177APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNITAndika Ellena Saufika Hakim Maharani0Ari Suparwanto1Department of Computer Science, Faculty of Engineering, Bumigora UniversityDepartment Mathematics, Faculty of Mathematics and Science, Gadjah Mada UniversityThe set together with the operation maximum (max) denoted as and addition (+) denoted as is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the application of max-plus algebra in a serial manufacturing machine with a storage unit is discussed. The results of this are the generalization system max-plus-linear equations on a production system that is, in addition, noted the max-plus-linear time-invariant system. From the max-plus-linear time-invariant system, it can be obtained the equation which is then used to determine the beginning time of a production system so the manufacturing machine work periodically. The eigenvector and eigenvalue of the matrix are then used to find the beginning time and the period time of the manufacturing machine. Furthermore, the time when the product leaves the manufacturing machine with the time while the raw material enters the manufacturing machine is given and vice versa are obtained from the max-plus-linear time-invariant system that is can be formed in the equation .https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5177max-plus algebradiscrete event systemproduction systemserial manufacturing machinetime-invariant system |
| spellingShingle | Andika Ellena Saufika Hakim Maharani Ari Suparwanto APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT Barekeng max-plus algebra discrete event system production system serial manufacturing machine time-invariant system |
| title | APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT |
| title_full | APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT |
| title_fullStr | APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT |
| title_full_unstemmed | APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT |
| title_short | APPLICATION OF SYSTEM MAX-PLUS LINEAR EQUATIONS ON SERIAL MANUFACTURING MACHINE WITH STORAGE UNIT |
| title_sort | application of system max plus linear equations on serial manufacturing machine with storage unit |
| topic | max-plus algebra discrete event system production system serial manufacturing machine time-invariant system |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/5177 |
| work_keys_str_mv | AT andikaellenasaufikahakimmaharani applicationofsystemmaxpluslinearequationsonserialmanufacturingmachinewithstorageunit AT arisuparwanto applicationofsystemmaxpluslinearequationsonserialmanufacturingmachinewithstorageunit |