Judul: Aggregate Production Planning of Frozen Potato Frikadel at PT Khatulistiwa Daya Abadi
Abstrak: PT Khatulistiwa Daya Abadi (KDA) merupakan perusahaan manufaktur kategori usaha makanan yang salah satunya memproduksi perkedel kentang beku. Namun, saat ini perusahaan menghadapi permasalahan produksi berupa kesenjangan antara produksi dan permintaan sehingga keuntungan belum maksimal. Tujuan penelitian ini mengkaji proses produksi dan permintaan, menganalisis peramalan permintaan, dan merekomendasikan strategi perencanaan agregat produk perkedel kentang beku. Penelitian ini dilakukan di PT KDA dan bersifat kuantitatif dengan jenis data berupa data primer diperoleh dari wawancara dan observasi, serta data sekunder berasal dari data operasional dan studi literatur dari Juli–September 2022. Metode peramalan terbaik menggunakan time series model dengan melihat nilai MAD, MSE, dan MAPE. Perencanaan agregat dianalisis dengan alternatif strategi chase, level, dan mixed. Hasil penelitian ini menunjukkan bahwa masih ada kesenjangan antara produksi dan permintaan. Metode peramalan permintaan terbaik menggunakan metode trend analysis (MAPE 8%). Strategi perencanaan agregat direkomendasikan menggunakan mixed strategy dengan nilai Rp331.652.172 per Agustus 2022–Juli 2023. Strategi tersebut menggunakan waktu dan tenaga kerja overtime apabila permintaannya tinggi.
Keyword: aggregate planning, demand forecasting, production planning

Judul: Aggregate Planning of Tempe in the Cooperative of  Indonesian Tempe and Tofu Producers Bogor Regency
Abstrak: Koperasi Produsen Tempe dan Tahu Indonesia (KOPTI) Kabupaten Bogor memproduksi tempe sebagai salah satu produk utama koperasi tersebut. Namun, terdapat kendala pengendalian produksi yang dialami oleh KOPTI Kabupaten Bogor. Tujuan penelitian ini yaitu menganalisis perencanaan agregat KOPTI saat ini, memilih metode dan merekomendasikan strategi peramalan dan perencanaan agregat yang optimal. Jenis penelitian adalah kuantitatif dengan jenis data berupa data primer dan data sekunder. Data primer diperoleh dari wawancara langsung dengan mitra dan data sekunder berasal dari studi literatur, dan data KOPTI. Penelitian ini diolah menggunakan metode peramalan Time Series Models dengan melihat nilai MAD (mean absolute deviation), MSE (mean squared error), dan MAPE (mean absolute percent error), serta perencanaan agregat dengan strategi chase, level, dan mixed. Hasil penelitian menunjukkan bahwa permintaan tempe KOPTI fluktuatif, metode peramalan permintaan dan strategi perencanaan agregat terbaik bagi KOPTI yaitu metode Trend Analysis (MAPE 12%) dan strategi chase (Rp270.896.148). Rekomendasi strategi bagi KOPTI yaitu memproduksi tempe 868.124,39 unit per tahun 2022, menggunakan tenaga kerja regular divariasikan berdasarkan jumlah permintaan dan kapasitas produksi, serta menghindari overtime., Cooperative of Indonesian Tempe and Tofu Producers (KOPTI) Bogor Regency produces tempe as one of the main products of the cooperative. However, there are problems on production controls in the KOPTI Bogor Regency. This study aimed to analyze the existing aggregate planning KOPTI, select methods and recommend optimal forecasting and aggregate planning strategies. This type of research is quantitative with the type of data in the form of primary data and secondary data. Primary data derived from direct interviews with partners and secondary data derived from literature studies and KOPTI data. This research is processed using the Time Series Models forecasting method by looking at the values of MAD (mean absolute deviation), MSE (mean squared error), dan MAPE (mean absolute precent error), and aggregate planning with chase, level, and mixed strategies. The results of this research indicate that KOPTI's tempe demand fluctuates, the demand forecasting method and the best aggregate planning strategy for KOPTI are the Trend Analysis method (MAPE 12%) and the chase strategy (Rp270.896.148). The recommended strategy for KOPTI is to produce tempe 868.124,39 unit per year 2022, use a regular workforce that is varied based on the number of requests and production capacity, and avoid overtime.
Keyword: Aggregate planning, control, demand forecasting, optimization

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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