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<![CDATA[EIGENVALUES AND EIGENVECTORS OF LATIN SQUARES IN MAX-PLUS ALGEBRA ]]>
<![CDATA[Mufid, Muhammad Syifa’ul]]>;
<![CDATA[-, Subiono]]>
<![CDATA[ Journal of the Indonesian Mathematical Society Volume 20 Number 1 (April 2014) ]]>
Publisher : <![CDATA[IndoMS ]]>
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DOI: 10.22342/jims.20.1.178.37-45
<![CDATA[A Latin square of order n is a square matrix with n different numberssuch that numbers in each column and each row are distinct. Max-plus Algebra isalgebra that uses two operations, ⊕ and ⊗. In this paper, we solve the eigenproblemfor Latin squares in Max-plus Algebra by considering the permutations determinedby the numbers in the Latin squares.DOI : http://dx.doi.org/10.22342/jims.20.1.178.37-45]]>
<![CDATA[Aljabar Maxplus dan Aplikasinya : Model Sistem Antrian ]]>
<![CDATA[Subiono, Subiono]]>
<![CDATA[ Limits: Journal of Mathematics and Its Applications Vol 6, No 1 (2009) ]]>
Publisher : <![CDATA[Institut Teknologi Sepuluh Nopember ]]>
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DOI: 10.12962/j1829605X.v6i1.1431
<![CDATA[Dalam paper ini dibahas pengertian dari aljabar ma-xplus dan beberapa sifat-sifatnya serta diberikan suatu contoh aplikasi dari aljabar maxplus. Selanjutnya dibahas suatu model sistem antrian satu server dalam aljabar maxplus.]]>
<![CDATA[CATATAN TENTANG PERSAMAAN LYAPUNOV DAN PERSAMAAN ALJABAR RICCATI ]]>
<![CDATA[Subiono, Subiono]]>
<![CDATA[ Limits: Journal of Mathematics and Its Applications Vol 4, No 2 (2007) ]]>
Publisher : <![CDATA[Institut Teknologi Sepuluh Nopember ]]>
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DOI: 10.12962/j1829605X.v4i2.1415
<![CDATA[Dalam paper ini dibahas dua bentuk persamaan yang hampir mi-rip yaitu persamaan Lyapunov dan persamaan aljabar Riccati. Selanjutnya diberikan beberapa catatan dari kedua persamaan tersebut yang masing-masing erat kaitannya dengan masalah kontrol optimal âLinier Quadratic Regulatorâ (LQR) sistem linier loop-buka dan sistem linier loop-tutup.]]>
<![CDATA[Using Max-Plus Algebra in The Flow Shop Scheduling ]]>
<![CDATA[Subiono, Subiono]]>
<![CDATA[ IPTEK The Journal for Technology and Science Vol 20, No 3 (2009) ]]>
Publisher : <![CDATA[IPTEK, LPPM, Institut Teknologi Sepuluh Nopember ]]>
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DOI: 10.12962/j20882033.v20i3.105
<![CDATA[In this paper, it is discussed notion of maxplus algebra and their properties. A model of flow shop production system and analyze the dynamical behavior of the system for scheduling problems are derived by means of max-plus algebra. The solutions of these problems are that the optimal sequence of jobs and the regular scheduling are obtained.]]>
<![CDATA[MENENTUKAN STRUKTUR GRUP BERORDER HINGGA DENGAN ORDER 216 DAN 324 ]]>
<![CDATA[HESTY IRNA AULIA]]>;
<![CDATA[Subiono Subiono]]>
<![CDATA[ Jurnal Sains dan Seni ITS Vol 4, No 2 (2015) ]]>
Publisher : <![CDATA[Lembaga Penelitian dan Pengabdian Kepada Masyarakat (LPPM), ITS ]]>
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DOI: 10.12962/j23373520.v4i2.13931
<![CDATA[Pada Tugas Akhir ini dikaji tentang banyaknya struktur dari grup berorder hingga. Langkah awal untuk mengkaji yaitu dengan menjabarkan tentang sifat-sifat dari grup dengan order berhingga. Sebagaimana diketahui bahwa grup sangat dipengaruhi oleh banyaknya anggota (order) didalam grup tersebut. Apabila order dari grup kecil, maka banyak struktur grup dapat dengan mudah untuk diketahui. Sedangkan untuk order yang besar maka akan sulit untuk mengetahui banyaknya struktur grup dengan order berhingga. Kajian ini dilakukan berdasarkan grup simpel, klas isomorpik grup abelian. Adapun hasil yang didapat pada Tugas Akhir ini yaitu tidak ada grup dengan order 216 dan 324 merupakan grup simpel dan untuk grup dengan order 216 memiliki sembilan klas isomorpik sedangkan untuk grup dengan order 324 memiliki sepuluh klas isomorpik.]]>
<![CDATA[EIGENVALUES AND EIGENVECTORS OF LATIN SQUARES IN MAX-PLUS ALGEBRA ]]>
<![CDATA[Muhammad Syifa’ul Mufid]]>;
<![CDATA[Subiono -]]>
<![CDATA[ Journal of the Indonesian Mathematical Society Volume 20 Number 1 (April 2014) ]]>
Publisher : <![CDATA[IndoMS ]]>
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DOI: 10.22342/jims.20.1.178.37-45
<![CDATA[A Latin square of order n is a square matrix with n different numberssuch that numbers in each column and each row are distinct. Max-plus Algebra isalgebra that uses two operations, ⊕ and ⊗. In this paper, we solve the eigenproblemfor Latin squares in Max-plus Algebra by considering the permutations determinedby the numbers in the Latin squares.DOI : http://dx.doi.org/10.22342/jims.20.1.178.37-45]]>
<![CDATA[Penentuan Nilai Awal Iterasi pada Masalah Pendugaan Parameter Regresi Taklinier ]]>
<![CDATA[Mohammad Jamhuri]]>;
<![CDATA[Subiono Subiono]]>
<![CDATA[ Limits: Journal of Mathematics and Its Applications Vol 18, No 2 (2021) ]]>
Publisher : <![CDATA[Institut Teknologi Sepuluh Nopember ]]>
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DOI: 10.12962/limits.v18i2.8297
<![CDATA[Paper ini membahas tentang pendugaan parameter model regresi tak linier menggunakan metode Newton, Gauss-Newton, steepest descent, dan metode homotopi. Metode-metode tersebut tidak senantiasa dapat memberikan hasil sebagaimana yang diharapkan, sebab hasil yang diperoleh sangat bergantung pada nilai awal yang diberikan. Keberhasilan metode-metode tersebut juga tidak ditentukan oleh seberapa dekat nilai awal terhadap solusi yang diharapkan, tetapi lebih kepada berhingga atau tidaknya elemen-eleman matrik Jacobi dari hampiran sistem persamaan tak liniernya. Selanjutnya, nilai awal diperoleh dengan cara membangkitkan bilangan random pada rentang tertentu dan dipilih yang dapat menghasilkan matriks Jacobi dengan elemen-elemen berhingga]]>
<![CDATA[Pembuktian Sifat non-Hausdorff dari Grup Lie GL(n,C) Bertindak pada M(n,C) ]]>
<![CDATA[Rif`an Amrozi]]>;
<![CDATA[Subiono Subiono]]>
<![CDATA[ Limits: Journal of Mathematics and Its Applications Vol 17, No 1 (2020) ]]>
Publisher : <![CDATA[Institut Teknologi Sepuluh Nopember ]]>
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DOI: 10.12962/limits.v17i1.6680
<![CDATA[Pada penelitian ini dibahas grup Lie General Linear GL(n,C) bertindak secara konjugasi pada manifold M(n,C). Himpunan semua orbit dari tindakan grup Lie tersebut dideskripsikan melalui bentuk kanonik Jordan yang merupakan ruangkuasi. Telah diduga jika X dan Y adalah matriks-matriksdi M(n,C) dengan nilai-nilai eigen yang sama tetapi memiliki bentuk kanonik Jordan yang berbeda, maka irisan dari persekitaran orbit dari Y dan persekitaran orbit dari X tidak kosong. Namun, pembuktian lengkap dari dugaan tersebut belum ada. Pada paper ini, diberikan pembuktian formal dugaan tersebut dengan perturbasi matriks, yaitu ruang kuasi yang berbentuk kanonik Jordan tersebut adalah suatu ruang non-Hausdorff.]]>
<![CDATA[Max Plus Algebra and Petri Net Application on Scheduling of Ship Engine Component’s Spare Part Ordering ]]>
<![CDATA[Farah Azizah]]>;
<![CDATA[Subiono Subiono]]>
<![CDATA[ (IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 4, No 1 (2018) ]]>
Publisher : <![CDATA[Institut Teknologi Sepuluh Nopember ]]>
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DOI: 10.12962/j24775401.v4i1.3555
<![CDATA[Shipping company is a company that runs its business by operating the ships or other businesses that are closely related to the ship. A ship has a main engine and some auxiliary engines to support the ship performance. It needs to do maintenance of engines so that the ship can operate properly. This engine maintenance is replacement of the old engine components with the new ones if the running hours of the components are over. Therefore, in the ship, the spare parts must always be available at least one for each engine component. During this time, the company has experienced a difficulty in determining the time of spare part ordering. When the running hours of engine components are over, the spare parts were not yet available. Then, Petri Net and Max Plus Algebra model will be built to schedule the ordering of ship engine component’s spare part based on the ordering flow and the running hours of engine components. The Petri Net based on the Max Plus Algebra obtains maximum time to order the spare part so that it produces the ship engine component’s spare part ordering schedule in running hour form and date. Therefore, spare part of each ship engine component is always available so that the installation can be timely and never be late.]]>
<![CDATA[Scheduling Of The Crystal Sugar Production System in Sugar Factory Using Max-Plus Algebra ]]>
<![CDATA[Desi Indriyani]]>;
<![CDATA[Subiono Subiono]]>
<![CDATA[ (IJCSAM) International Journal of Computing Science and Applied Mathematics Vol 2, No 3 (2016) ]]>
Publisher : <![CDATA[Institut Teknologi Sepuluh Nopember ]]>
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DOI: 10.12962/j24775401.v2i3.2092
<![CDATA[Sugar is the main trading commodity besides as basic human needs and be a source of energy and mostly traded in the form of solid crystals of sucrose or crystal sugar with cane as raw materials. Sugar production process is very complicated because it had to pass through various stages that require considerable time. The number of machines used in production system affects the complexity in the calculation of production scheduling. In addition, if there are errors in analyzing the operating time that is different for each product, it will cause a chaos in the production scheduling. These conditions encourage us to conduct a study on the production flow or flow lines with buffer. The buffer is used on multiple processors as a placeholder for semi-finished material before it is processed in the next processors. Buffers are used in the form of vessels with varying volume. In this study, the max-plus algebra is the method used to obtain crystal sugar production scheduling system in the sugar factory. From the flow lines that have been made then we derive a model of max-plus algebra to obtain a production schedule that starts with the milling process to obtain crystal sugar. Based on the max-plus algebra model, we also obtained sugar output schedule and some kind of waste. In addition, we obtained two periodicities of each processor, that is from milling processor until sulfitation of thick juice processor with periodicity 177.64 minutes and from vacuum pan A processor until mixer D2 processor with periodicity 1592.63 minutes, from these periodicities, we obtain a periodic production schedule for each processor.]]>
