Judul: Analisa sistem antrian penanganan susu segar di Daerah Peternakan Bandung Utara, Jawa Barat
Abstrak: Pertambahan penduduk yang disertai peningkatan pendapatan, taraf hidup, tingkat pendidikan dan kesadaran tentang pentingnya makanan bergizi bagi kesehatan tubuh, juga turut meningkatkan konsumsi susu dalam negeri.
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Judul: Analisis daya saing dan dampak kebijakan pemerintah terhadap komoditas susu sapi lokal di Jawa Barat
Abstrak: Pengembangan usaha sapi perah merupakan salah satu alternatif dalam rangka pemenuhan gizi masyarakat serta pengurangan tingkat ketergantungan nasional terhadap impor susu. Kemampuan pasok susu peternak lokal saat ini baru mencapai 25-30 persen dari kebutuhan susu nasional, kondisi ini menyebabkan Indonesia menjadi negara pengimpor. Kondisi ini dikarenakan usaha ternak sapi perah di Indonesia didominasi oleh skala kecil dengan kepemilikan ternak kurang dari empat ekor (80 persen), empat sampai tujuh ekor (17 persen), dan lebih dari tujuh ekor (tiga persen). Konsekuensi dari keragaan usaha ternak sapi perah kita yang masih sangat kecil, akan menyebabkan ketidakmampuan untuk bersaing dengan produk impor. Hal tersebut menunjukkan bahwa peran kebijakan pemerintah dalam hal perdagangan sangat mempengaruhi dinamika perkembangan peternakan sapi perah di tengah kondisi perdagangan bebas dan persaingan dengan susu impor. Pasar produk susu segar di Indonesia cenderung memiliki struktur pasar oligopsoni dengan Industri Pengolahan Susu (IPS) sebagai konsumen utama, hal tersebut juga didukung bahwa koperasi susu dan peternak memiliki posisi tawar yang lemah dalam memasok dan menentukan harga susu kepada IPS. Lemahnya posisi tawar peternak terhadap IPS yang lebih cenderung untuk menggunakan bahan baku impor merupakan salah satu kendala utama.
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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