Judul: Optimasi Penjadwalan Produksi Sayuran Organik (Studi Kasus di PT Kebun Sayur Segar, Bogor)
Abstrak: PT Kebun Sayur Segar merupakan salah satu produsen sayuran organik terbesar di Jabodetabek. Salah satu permasalahan yang terjadi dalam industri tanaman di perusahaan ini adalah produksi tanaman yang kurang sesuai dengan permintaan pasar. Tujuan penelitian ini adalah melakukan optimasi penjadwalan produksi sayuran organik melalui pemodelan permintaan pasar untuk komoditas caisim, pakchoy, selada, bayam, kangkung dan jagung muda. Pemodelan dilakukan dengan metode statistik deret waktu ARIMA (Autoregressive Integrated Moving Average). Model yang ditetapkan dalam penelitian ini yaitu model ARIMA (1,0,1) untuk caisim, ARIMA (1,0,0) untuk pakchoy, ARIMA (0,0,1) untuk selada, ARIMA (0,1,1) untuk bayam, ARIMA (2,1,3) untuk kangkung dan jagung muda. Model-model tersebut digunakan untuk peramalan sebagai rekomendasi perusahaan dalam merencanakan produksi satu periode tanam ke depan., PT Kebun Sayur Segar is one of the largest producer of organic vegetables in Jabodetabek. One of the problems that occur in the company is unappropriate crop production according to market demand. The purpose of this study is to optimize the production scheduling of organic vegetables through modeling the market demand for commodities caisim, pakchoy, lettuce, spinach, kale and sweet corn. Modeling is done by the statistical method of time series ARIMA (Autoregressive Integrated Moving Average). The models decided in this research are ARIMA (1,0,1) for caisim, ARIMA (1,0,0) for pakchoy, ARIMA (0,0,1) for lettuce, ARIMA (0,1,1) for the spinach, ARIMA (2,1,3) for kale and sweet corn. The models will used in forecasting as company recommendations in planning the production for the next planting period.
Keyword: ARIMA, deret waktu, PT. Kebun Sayur Segar, peramalan, sayuran organik

Judul: Optimize Hydroponic Vegetable Production Plan at PT Sumber Agro Semesta (PT SAS), Tanjung Sari District, Bogor Regency
Abstrak: Perencanaan jadwal tanam sayur hidroponik di PT Sumber Agro Semesta (PT SAS) masih dilakukan secara subjektif oleh PIC hidroponik, yaitu dengan menggunakan prakiraan rata-rata permintaan sayur pada siklus sebelumnya. Perencanaan jadwal tanam belum dilakukan berdasarkan prakiraan permintaan sehingga terjadi perbedaan antara rencana tanam dan permintaan aktual. Kapasitas greenhouse produksi sebesar 38.556 lubang tanam juga belum digunakan secara maksimal sehingga banyak lubang tanam yang tidak terisi. Adapun tujuan dari penelitian ini adalah menentukan prakiraan permintaan, serta menentukan rencana produksi yang optimal berdasarkan prakiraan permintaan dan penggunaan maksimal kapasitas greenhouse. Prakiraan permintaan pada pakcoy, bayam hijau, caisim, kangkung dan kailan dilakukan melalui dua metode, yaitu menggunakan metode ARIMA dan asumsi peningkatan permintaan sebesar 10% dari permintaan aktual yang terakhir. Hasil optimasi dengan teknik linear programming pada kedua kondisi tersebut menghasilkan keuntungan masing-masing sebesar Rp. 71.296.390 untuk hasil optimasi berdasarkan metode ARIMA dan Rp. 70.690.398 untuk hasil optimasi berdasarkan asumsi peningkatan permintaan sebesar 10%. Selain itu, dilakukan pula optimasi produksi berdasarkan penggunaan maksimal kapasitas greenhouse produksi. Sayur yang dioptimasi penjadwalannya adalah pakcoy, bayam hijau, caisim, kangkung, kailan, siomak, pagoda, bayam merah, romain, selada, dan kale. Hasil optimasi dengan teknik linear programming pada kondisi tersebut menghasilkan keuntungan sebesar Rp. 70.904.345 dan total bobot produksi sekitar 1,5 ton., The planning of the hydroponic vegetable planting schedule at PT Sumber Agro Semesta (PT SAS) is still subjectively to hydroponic PIC, using the forecast of the average vegetable demand in the previous cycle. The planting schedule has not been planned based on the demand forecast, so there is a difference between the planting plan and the actual demand. The greenhouse production capacity of 38,556 planting holes has not been used optimally, so many planting holes are not filled. The purpose of this research is to determine the demand forecast and determine the optimal production plan based on the demand forecast and the maximum use of a greenhouse. Forecasting demand for pakcoy, green spinach, caisim, kangkung, and kailan is made through two methods, namely using the ARIMA method and the assumption of an increase in demand by 10% from the last actual demand. Techniques of linear programming in both conditions produce a profit of Rp. 71,296,390 for optimization results based on the ARIMA method and Rp. 70,690,398 for optimization results based on the assumption of a 10% increase in demand. In addition, production optimization is also carried out based on the maximum use of greenhouse production capacity. Vegetables that are optimized for scheduling are pakcoy, green spinach, caisim, kale, kailan, dumplings, pagoda, red spinach, romain, lettuce, and kale. Techniques of linear programming in these conditions generate a profit of Rp. 70,904,345 and a total production weight of about 1.5 tons.
Keyword: ARIMA, demand forecasting, linear programming, production plan

Judul: Hamiltonian formulation for linear waves motion in two layers fluid
Abstrak: The surface wave could be considered as a wave that separates two fluids, namely water and air. Based on this assumption, it is introduced the interfacial wave, a wave between two layers of fluid with different density. The formulation of interfacial waves motion begins with deriving the base equation of irrotational ideal fluid. Furthermore, according to irrotational fluid assumption, the base equation can be stated in velocity potential. In this derivation, the fluids domain is assumed to be restricted by rigid lid boundary conditions, both at the upper and lower limit. Therefore, the interfacial waves motion can be explained in a hamiltonian formulation. In the hamiltonian formulation, total energy is defined as the sum of kinetic and potential energy. The hamiltonian system is obtained from reduction of kinetic energy by using the Dirichlet Neumann Operator. The resulted kinetic energy equation is nonlinear. Therefore, this form is linearized by first part of the Taylor expansion. This linearization gives a dispersion relation of linear wave. Based on this dispersion relation, the phase speed of the linear wave depends on the density ratio of the two layers fluid.
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