Judul: Champignon Product Combination Planning to Optimize Profit Gained by PT X
Abstrak: PT X is an agroindustry which focuses on the champignon commodities. Champignon commodity has a short shelf life, so it must be sold directly to consumers or processed into champignon preserved products. The number of the mushroom demand is uncertain in terms of excess or lack of stock on both fresh mushroom and champignon preserved products. Therefore, it is necessary to calculate the product combination plan that can meet the desired objectives and obtain a satisfying solution. This study uses the goal programming methods in the making of product combination planning. The data needed includes the number of demands and raw materials from January 2017 to December 2019. Other than that, data regarding man hours, production costs, and prices of each type of product are also needed. Historical data of demand and raw materials are used to predict the level of demand and raw materials in the planning period. Based on planning results that has been made for January 2020, the total production of fresh mushroom is 22 584 kg, 250 ml whole champignon is 4 499 items, 900 ml whole champignon is 2 571 items, 250 ml sliced champignon is 4 567 items, 900 ml of sliced champignon is 32 306 items, and canned champignon is 85 items., PT X merupakan perusahaan di bidang agroindustri khususnya pada komoditas jamur kancing. Jamur kancing memiliki umur simpan yang pendek sehingga harus segera dijual ke konsumen atau diproses menjadi produk olahan. Jumlah permintaan jamur tidak pasti, hal ini menyebabkan terjadinya kelebihan atau kekurangan produksi baik pada produk segar maupun olahan. Oleh karena itu, perlu untuk menghitung rencana kombinasi produk yang dapat memenuhi tujuan yang diinginkan dan mendapatkan solusi yang memuaskan. Penelitian ini menggunakan metode goal programming dalam perencanaan produk kombinasi. Data yang dibutuhkan yaitu data permintaan dan ketersediaan bahan baku dari Januari 2017 hingga Desember 2019. Selain itu juga dibutuhkan data kebutuhan bahan baku, jam tenaga kerja, biaya produksi, dan harga setiap produk. Data historis terkait jumlah permintaan dan ketersediaan bahan baku digunakan untuk meramalkan jumlah permintaan dan ketersediaan bahan baku pada periode perencanaan. Berdasarkan hasil perencanaan yang telah dibuat untuk bulan Januari 2020, total jumlah produksi fresh mushroom yaitu 22 584 kg, produk 250 ml whole champignon sebanyak 4 499 item, produk 900 ml whole champignon sebanyak 2 571 item, produk 250 ml sliced champignon sebanyak 4 567 item, produk 900 ml sliced champignon sebanyak 32 306 item, dan produk canned champignon sebanyak 85 item.
Keyword: champignon, goal programming, production planning, product combination

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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