Judul: Analisis Biaya Produksi Minyak Kayu Putih Studi Kasus di Pabrik Minyak Kayu Putih RPH Tonjong Perum Perhutani KPH Kuningan Unit III Jawa Barat Dan Banten
Abstrak: Minyak kayu putih (MKP) merupakan produk hasil hutan bukan kayu yang memiliki potensi besar di Indonesia. Pabrik minyak kayu putih (PMKP) Tonjong KPH Kuningan merupakan salah satu perusahaan Perum Perhutani yang memproduksi MKP di Jawa Barat. Produksi MKP yang dihasilkan dari PMKP Tonjong pada tahun 2018 sebesar 7.675 ton dengan penggunaan daun kayu putih sebesar 1 108.09 ton dan harga jual sebesar Rp250 000/kg MKP. Penelitian ini bertujuan untuk menganalisis biaya produksi, break even point (BEP), profitabilitas yang ditunjukan oleh persentase return on investment (ROI) serta menganalisis harga pokok MKP yang diproduksi di PMKP Tonjong Perum Perhutani KPH Kuningan Unit III Jawa Barat dan Banten. Hasil penelitian menunjukkan total biaya produksi pada tahun 2018 sebesar Rp1.52 milyar. Biaya produksi MKP sebesar Rp198 517/kg.Komponen biaya produksi terbesar adalah biaya variabel sebesar Rp957 juta atau sebesar Rp124 765/kg (62.86%). Nilai BEP yang dihasilkan sebesar 4519 kg yang menunjukan bahwa perusahaan mampu memproduksi MKP di atas titik impas. Nilai ROI yang dihasilkan sebesar 29.69% yang menunjukan kemampuan perusahaan dalam memperoleh keuntungan lebih besar daripada investasi dalam bentuk deposito berjangka. Harga pokok MKP pada tahun 2018 sebesar Rp238 220/kg yang menunjukan bahwa pengusahaan MKP di KPH Kuningan menguntungkan.
Keyword: biaya produksi, BEP, harga pokok, minyak kayu putih, ROI.

Judul: Production Cost Analysis of Cajuput Oil Case Study at Cajuput Oil Factory RPH Bentang Timur BKPH Sagaranten KPH Sukabumi
Abstrak: Minyak kayu putih (MKP) merupakan salah satu jenis minyak atsiri yang berasal dari tanaman kayu putih (Melaleuca spp.). Tanaman kayu putih di Indonesia tersebar secara alami terutama di pulau Jawa dan Maluku (Maulidah 2010). Seiring dengan bertambahnya jumlah penduduk di Indonesia, permintaan dari komoditas minyak kayu putih pun terus meningkat (Rimbawanto 2019). Penelitian ini bertujuan untuk menganalisis biaya produksi, Break Event Point (BEP), profabilitas yang ditunjukan oleh presentase Gross Profit Margin (GPM), dan harga pokok MKP di KPH Sukabumi. Hasil penelitian menunjukkan bahwa biaya produksi MKP di Pabrik Minyak Kayu Putih (PMKP) Ciminyak pada tahun 2021 adalah 177.892,62/kg MKP. Nilai Break Event Point (BEP) sebesar 1.243,25 kg yang menunjukan bahwa perusahaan mampu memproduksi MKP di atas titik impas. Keuntungan yang diperoleh sebesar Rp 134.107,38/kg atau GPM sebesar 42,98%. Harga pokok MKP adalah 236.317,84/kg, lebih kecil dari pada realisasi harga jualnya sebesar Rp 312.000/kg., Cajuput oil is a type of essential oil derived from eucalyptus plants (Melaleuca spp.). Cajuput plants in Indonesia are spread naturally, especially on the islands of Java and Maluku (Maulidah 2010). Along with the increasing population in Indonesia, the demand for cajuput oil commodities continues to increase (Forester 2019). This study aims to analyze production costs, Break Event Point (BEP), profability shown by the percentage of Gross Profit Margin (GPM), and base price analysis MKP at KPH Sukabumi. The results showed that the production cost of MKP at the Ciminyak Eucalyptus Oil Plant (PMKP) in 2021 was 177.892,62/kg MKP. The Break Event Point (BEP) value is 1.243,25 kg which indicates that the company is able to produce MKP above breakeven. The profit obtained was Rp 134.107,38/kg or GPM of 42,98%. Base price of MKP is 236.317,84/kg, smaller than the realization of the selling price of IDR 312.000/kg.
Keyword: Base Price, BEP, Cajuput Oil, Production Cost, Profitability

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