Judul: Analisis pengendalian peserdiaan bahan baku pada perusahaan rokok putih (Studi kasus pada PT. BAT Indonesia , Cirebon)
Abstrak: Sumbangan industri rokok terhadap perekonomian nasional dan penyerapan tenaga kerja sangat besar, sehingga budidaya dan perkembangan industri rokok tidak dihalangi. Industri rokok terdiri dari rokok kretek dan rokok putih. Konsumsi dan produksi rokok putih dewasa ini semakin meningkat. Pada tahun 1991 konsumsi rokok putih meningkat sebesar 20,3% dan produksinya meningkat sebesar 18,6%. PT. BAT Indonesia merupakan produsen rokok putih terbesar di Indonesia. Perusahaan ini nenggunakan tembakau sebagai bahan baku langsung yang berasal dari dalam dan luar negeri. Tembakau impor selalu tersedia di pasar dan harganya lebih mahal jika dibandingkan dengan tembakau domestik.
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Judul: Perencanaan dan pengendalian produksi rokok di PT BAT Indonesia, Cirebon, Jawa Barat
Abstrak: Perencanaan dan pengendalian produksi dalam suatu industri bertujuan untuk mendapatkan tingkat produksi yang optimal, agar produksi dapat berjalan dengan efektif. Pengkajian masalah di PT BAT Indonesia merupakan perencanaan menggunakan pengendalian dan pengendalian produksi jangka pendek dengan metoda pendekatan berencana. Perencanaan dan produksi tersebut dibatasi pada penjadwalan produksi mingguan selama tiga bulan yang diperoleh berdasar- kan prakiraan permintaan di masa mendatang. Dari penentuan tingkat produksi yang optimal akan ditentukan urutan operasi produksi. Berdasarkan hasil prakiraan produksi dengan menggunakan metoda ARIMA, maka model terpilih untuk masing-masing merek adalah sebagai berikut: Ardath SpD1 (3,1,1), Benson&Hedges (2,1,1), Lucky Strike (0,0,0), SE 555 (2,1,1), Ardath Sp (3,1,1), Commodore KS (2,1,1), Mascot (2,1,2), Ardath Mild (3,1,1), Kent (0,0,0), Commodore KS (4,1,1), Escort (2,1,1). Penjadwalan produksi dilakukan dengan menggunakan program dinamis. Program dinamis selalu mempertimbangkan berbagai kemungkinan kombinasi jumlah produksi pada setiap alternatif jumlah penyimpanan atau status tingkat persediaan rokok setiap periode pperencanaan. ....
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Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm