Judul: Scale Up Production Design of Kombucha Cascara KTH Cibulao
Abstrak: Kombucha cascara merupakan produk minuman olahan cascara atau kulit kopi kering yang dapat menjadi solusi untuk mengatasi 2400 kg limbah kulit buah kopi yang dihasilkan Kelompok Tani Hutan Cibulao setiap tahunnya. Kombucha merupakan minuman ringan hasil fermentasi yang tengah meningkat popularitasnya baik secara global maupun nasional karena rasanya yang enak dan potensi kesehatannya. Komersialisasi kombucha cascara di Indonesia dapat menjadi prospek yang menjanjikan dengan perencanaan produksi yang memadai. Kombucha cascara yang dirancang sejak produta sebelumnya membutuhkan perbaikan formula sebelum digandakan skalanya (scale up) untuk keperluan komersialisasi. Penggandaan skala produksi menggunakan acuan produksi skala laboratorium yaitu kombucha cascara dengan basis produksi 9 liter (L) dan lama fermentasi 9 hari yang menghasilkan 27 botol kemasan 250 ml serta cycle time 8,1 jam. Kapasitas produksi scale up menjadi 414 botol kemasan 250 ml per batch produksi yang dihasilkan dari 15 wadah fermentasi 9 L. Setiap bulannya dioperasikan 2 batch produksi dengan total hari produksi per batch selama 11 hari. Sejumlah 20,1 kg starter kombucha yang dihasilkan dari batch produksi genap akan dijual sebanyak 67 pak/bulan untuk mengendalikan kapasitas penyimpanan. Peralatan dan mesin yang digunakan pada titik fokus scale up adalah sterilizer, panci, kompor 2 tungku, mixer, dispenser kaca, rak 5 tingkat, upright chiller, papan infraboard, serta dispenser galon. Standar kegiatan produksi, lokasi kegiatan, dan penanggung jawab setiap kegiatan produksi disusun dalam Standar Operasional Produksi., Kombucha cascara is a beverage made from cascara, dried coffee skin and pulp, offering a solution for 2400 kg of coffee cherry waste produced annually by Kelompok Tani Hutan Cibulao. Kombucha undergoes a fermentation process which resulting in a sweet, sour, and carbonated beverage. Due to its pleasant taste and potential health benefits, kombucha is gaining popularity globally and nationally. The commercialization of kombucha cascara in Indonesia holds promising prospects with proper production process planning. Kombucha cascara, initially designed by previous produta team, requires formula improvement before scaling up for commercial purposes. Scaling up production is based on chosen formula of laboratory scale kombucha production with a production basis of 9 liters (L) and fermentation period of 9 days, yielding in 27 bottles of 250 ml with a cycle time of 8,1 hours. The capacity of production scales up to 414 bottles of 250 ml per production batch, yielded from 15 fermenting vessels of 9 Ls each. Two production batches are operated monthly, with each batch requiring a total of 11 production days. Kombucha starter worth of 20,1 kg from even numbered production batches will be sold for 67 packs every month to control storage capacity. The equipments utilized for focal points of scale up include sterilizer, pot, 2 burner stove, mixer, glass dispenser, 5 tier rack, upright chiller, infraboard panel, and plastic dispenser. Standard of production activity, activity locations, and responsible workers for each production activity are outlined in the Standard Operating Procedure.
Keyword: Kombucha cascara, product reformulation, scale up, mass balance, production equipment, production standardization

Judul: Designing Business Process Model and Production Facility Layout for Kombucha Cascara
Abstrak: Proses bisnis kombucha cascara CasTIN melibatkan tiga process participants: KTH Cibulao sebagai pemasok, CasTIN sebagai produsen, dan konsumen/reseller sebagai pelanggan. Proses pascapanen dan pemasokkan bahan baku dilakukan oleh KTH Cibulao untuk mengolah kulit buah kopi menjadi cascara kering lalu dikemas dan dikirimkan ke pihak CasTIN yang telah melakukan pre- order 14 hari sebelum cascara harus diterima. KTH Cibulao akan mengirimkan 10,53 kg cascara per bulan selama masa panen (Maret-Juli. Produksi kombucha dilakukan dalam dua batch dengan total kebutuhan 4,05 kg cascara per bulan. Agar kualitas produk tetap terjaga, distribusi kombucha cascara ke konsumen dilakukan dalam waktu maksimal 2 hari perjalanan. Proses bisnis ini dimodelkan dengan BPMN untuk memudahkan pelaksanaan, monitoring, dan pengelolaan bisnis. Fasilitas produksi terdiri dari 15 departemen yang menyesuaikan kapasitas produksi yaitu 828 botol per bulan. Kebutuhan luas ruangan dilakukan dengan menghitung luas alat produksi, ruang gerak, dan allowance menghasilkan total kebutuhan luas ruang produksi yaitu 56,60 m2. Setelah dilakukan penyesuaian tata letak dengan metode Corelap dan mempertimbangkan aliran produksi, aliran keluar masuk barang, dan efisiensi produksi, luas bangunan ruang produksi mendekati perhitungan kebutuhan luas ruangan yaitu 60,04 m2., The business process of CasTIN's cascara kombucha involves three key process participants: KTH Cibulao as the supplier, CasTIN as the manufacturer, and consumers/resellers. KTH Cibulao handles post-harvest processes and supplies cascara by processing coffee fruit skins into dried cascara, which is then packaged and sent to CasTIN after pre-ordering 14 days in advance. KTH Cibulao provides 10.53 kg of cascara per month during the harvest season (March-July), including annual buffer stock. CasTIN conducts production in two batches, requiring a total of 4.05 kg of cascara per month. Distribution to consumers ensures delivery within 2 days to maintain product quality. BPMN is used to model the business process for ease of implementation, monitoring, and management. The production facility consists of 15 departments with a production capacity of 828 bottles per month. Space requirements are calculated based on production equipment, workspace, and allowances, totaling 56.60 m2. After adjusting layout using Corelap method and considering production flow, material flow, and production efficiency, the actual production space approaches the calculated requirement, totaling 60.04 m2.
Keyword: BPMN, Model proses bisnis, Tata letak ruang produksi, Corelap, Kombucha, Cascara

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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