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All Journal Paradikma: Jurnal Pendidikan Matematika Jurnal Cendekia : Jurnal Pendidikan Matematika IKRA-ITH EKONOMIKA JOURNAL OF SCIENCE AND SOCIAL RESEARCH bit-Tech Didaktik : Jurnal Ilmiah PGSD STKIP Subang JUMAT: Jurnal Matematika E-Jurnal Matematika
Nerli Khairani
Universitas Negeri Medan
Computer Science & IT Economics, Econometrics & Finance Education Mathematics Social Sciences Other

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Analisis Optimasi Produksi Jus Buah untuk Memperoleh Keuntungan Maksimum Menggunakan Metode Simpleks pada POM-QM for Windows Windi suryani Wiwi; Gracia Lovian Girsang; Klara Manila laoli; Nerli Khairani
Didaktik : Jurnal Ilmiah PGSD STKIP Subang Vol. 12 No. 02 (2026): Volume 12 Nomor 02, Juni 2026 Published
Publisher : STKIP Subang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36989/didaktik.v12i02.15288

Abstract

Penelitian ini bertujuan untuk menganalisis optimasi produksi jus buah dalam memperoleh keuntungan maksimum menggunakan metode simpleks dengan bantuan POM-QM for Windows. Penelitian ini menggunakan metode kuantitatif dengan pendekatan Linear Programming. Data penelitian diperoleh melalui observasi dan wawancara langsung dengan pemilik usaha jus buah. Data yang dikumpulkan meliputi jumlah bahan baku, jumlah produksi, waktu produksi, dan keuntungan dari setiap jenis jus buah. Analisis data dilakukan dengan menyusun fungsi tujuan dan fungsi kendala ke dalam model linear programming, kemudian diselesaikan menggunakan metode simpleks melalui software POM-QM for Windows. Hasil penelitian menunjukkan bahwa metode simpleks mampu menentukan kombinasi produksi jus buah yang optimal sehingga keuntungan maksimum dapat diperoleh dengan penggunaan bahan baku yang lebih efisien. Selain itu, penggunaan POM-QM for Windows membantu proses perhitungan menjadi lebih cepat, akurat, dan sistematis dibandingkan perhitungan manual.
ANALISIS PERBANDINGAN METODE FUZZY SIMPLEKS DAN KUMAR DALAM OPTIMASI PRODUKSI FULLY FUZZY LINEAR PROGRAMMING NERLI KHAIRANI; RIZAL MUHAIMIN; NAFASA ZAHRI; NAYSLA AURA SIFFA
E-Jurnal Matematika Vol. 15 No. 3 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i03.p519

Abstract

This study discusses a comparative analysis between the fuzzy simplex method and Kumar’s method in solving production optimization problems based on Fully Fuzzy Linear Programming (FFLP). Production optimization problems in real conditions often involve uncertainty in production costs, resource availability, and market demand fluctuations. Therefore, the FFLP approach is applied because all model parameters, including objective functions, constraints, and decision variables, are represented using trapezoidal fuzzy numbers to better describe uncertainty. This research employed a quantitative comparative approach using simulation data with two decision variables. The optimization model was solved using the fuzzy simplex method and Kumar’s method with the Liou–Wang ranking function. The results showed that both methods produced identical optimal solutions, including the same optimal decision variable values, fuzzy profit values, and number of iterations required to reach optimality. However, Kumar’s method provided a simpler pivot selection process through the use of ranking functions, while the fuzzy simplex method was more effective in maintaining the integrity of fuzzy data throughout the iteration process. Based on the comparative analysis, both methods were proven effective for solving FFLP problems, although they differ in computational complexity and operational procedures.
OPTIMALISASI KEUNTUNGAN USAHA TAHU TEMPE DI KOTA MEDAN MENGGUNAKAN METODE GRAFIK PROGRAM LINIER DENGAN SOFTWARE AUTOGRAPH (STUDI KASUS UMKM PAK SAFWAN) Nerli Khairani; Petra Putri Sarinah Pandiangan; Grace Amelia Purba; Rizka Nabila Damanik; Endang Lyfia Saragih
JOURNAL OF SCIENCE AND SOCIAL RESEARCH Vol. 9 No. 3 (2026): June 2026
Publisher : Smart Education

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.54314/jssr.v9i3.6275

Abstract

Abstract: This study aims to optimize the profit of Mr. Muhammad Safwan's tofu and tempeh business in Medan City using a linear programming graphical method assisted by Autograph software. The type of research used is quantitative with a case study approach. Data were obtained through direct interviews, observations, and documentation in May 2026. The results of the study indicate that the actual condition of the business produces 48 tofu trays and 1,000 tempeh pieces per day using 546 kg of soybeans from a total availability of 600 kg, and generates a net profit of Rp1,585,800 per day. Based on the formulation of the objective function to maximize gross profit Z' = 9,600x₁ + 2,345x₂ and the main constraint 2x₁ + 0.45x₂ ≤ 600, the optimal solution obtained by the graphical method is at point B (0; 1,333.33), which is producing 1,333 tempeh pieces per day without producing tofu. The maximum gross profit reached Rp3,126,665 per day, and after deducting fixed costs of Rp1,220,000, the maximum net profit was Rp1,906,665 per day. Thus, the potential profit increase was Rp321,533 per day, or approximately 20.27% compared to the actual situation. This study demonstrates that the linear programming graphical method with the assistance of Autograph software is effective in solving profit optimization problems in MSMEs involving two decision variables. Keywords: Profit Optimization, Linear Programming, Graphical Method, Autograph, Tofu and Tempeh MSMEs Abstrak: Penelitian ini bertujuan untuk mengoptimalkan keuntungan usaha tahu tempe milik Bapak Muhammad Safwan di Kota Medan dengan menggunakan metode grafik program linier berbantuan software Autograph. Jenis penelitian yang digunakan adalah kuantitatif dengan pendekatan studi kasus. Data diperoleh melalui wawancara langsung, observasi, dan dokumentasi pada bulan Mei 2026. Hasil penelitian menunjukkan bahwa kondisi aktual usaha memproduksi 48 loyang tahu dan 1.000 pcs tempe per hari dengan penggunaan kedelai 546 kg dari total ketersediaan 600 kg, serta menghasilkan keuntungan bersih sebesar Rp1.585.800 per hari. Berdasarkan perumusan fungsi tujuan memaksimalkan keuntungan kotor Z' = 9.600x₁ + 2.345x₂ dan kendala utama 2x₁ + 0,45x₂ ≤ 600, solusi optimal yang diperoleh dengan metode grafik adalah pada titik B (0; 1.333,33), yaitu memproduksi 1.333 pcs tempe per hari tanpa memproduksi tahu. Keuntungan kotor maksimum mencapai Rp3.126.665 per hari, dan setelah dikurangi biaya tetap Rp1.220.000, keuntungan bersih maksimum menjadi Rp1.906.665 per hari. Dengan demikian, potensi peningkatan keuntungan sebesar Rp321.533 per hari atau sekitar 20,27% dibandingkan kondisi aktual. Penelitian ini membuktikan bahwa metode grafik program linier dengan bantuan software Autograph efektif untuk menyelesaikan permasalahan optimalisasi keuntungan pada UMKM yang melibatkan dua variabel keputusan. Kata Kunci: Optimalisasi Keuntungan, Program Linier, Metode Grafik, Autograph, UMKM Tahu Tempe
OPTIMALISASI KEUNTUNGAN KEDAI KOPI DENGAN PENDEKATAN METODE GRAFIK BERBASIS APLIKASI AUTOGRAPH Nerli Khairani; Riamonda Singarimbun; Riby Tamara; Farel Al Azmi
JOURNAL OF SCIENCE AND SOCIAL RESEARCH Vol. 9 No. 3 (2026): June 2026
Publisher : Smart Education

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.54314/jssr.v9i3.6300

Abstract

Abstract: This study aims to maximize the production profits of Coffee Milk and Tea Milk in a cafe in Tanah Karo using a graphical linear programming method through the Autograph application. The information used includes production costs, production time per cup, and weekly profits. The constraints encountered were a cost limit of 645,000 per week and a production time of 684 minutes per week. An objective function was created to optimize the profits of both products. Calculations both manually and through Autograph showed that the optimal point was at coordinates (1,1) with the highest profit value reaching 867,000 per week. Therefore, balancing the production proportions between Coffee Milk and Tea Milk is an important factor in achieving maximum profits. Keywords: Autograph; Coffee Shop; Graphical Method; Profit Optimization   Abstrak: Studi ini bertujuan untuk memaksimalkan keuntungan produksi Kopi Susu dan Teh Susu di sebuah kafe yang berada di Tanah Karo dengan menggunakan metode pemrograman linier grafik melalui aplikasi Autograph. Informasi yang digunakan mencakup biaya produksi, durasi pembuatan per gelas, serta keuntungan mingguan. Kendala yang ditemukan adalah batasan biaya sebesar Rp645.000 per minggu dan waktu produksi selama 684 menit per minggu. Fungsi tujuan dibuat untuk mengoptimalkan keuntungan dari kedua produk. Perhitungan baik secara manual maupun melalui Autograph menunjukkan bahwa titik optimal berada pada koordinat (1,1) dengan nilai keuntungan tertinggi mencapai Rp867.000 per minggu. Oleh karena itu, keseimbangan proporsi produksi antara Kopi Susu dan Teh Susu merupakan faktor penting dalam meraih keuntungan maksimal. Kata kunci: Autograph; Kedai Kopi; Metode Grafik; Optimasi Keuntungan
Optimasi Keputusan Produksi untuk Meningkatkan Keuntungan Usaha Minuman Kafe melalui Pendekatan Program Linier Nerli Khairani; Rawiyah; Mey Gracia Sitanggang; Ian Pedrosa manatap Lumban Gaol
JUMAT: Jurnal Matematika Vol. 3 No. 2 (2025): JUMAT, Desember 2025
Publisher : Institut Agama Islam Negeri Fattahul Muluk Papua

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

The coffee shop business is one of the Micro, Small, and Medium Enterprises (MSMEs) sectors that is experiencing rapid growth, but often faces obstacles in optimizing profits due to limited production resources. This study aims to determine the optimal production combination that can maximize the profits of a cafe beverage business through a linear programming approach. This research is a quantitative study with a descriptive-optimization approach conducted at one of the cafe beverage businesses in the period April–May 2026. The research subjects consisted of two decision variables, namely coffee drinks (X₁) and non-coffee drinks (X₂), with five production resource constraints. Data were collected through observation, interviews, and documentation using observation sheets, interview guidelines, and production and sales data. Data analysis was carried out using graphical methods in linear programming to determine the feasible region and optimal solution, and validated using POM-QM software for Windows. The results showed that the optimal solution was obtained at point (40,20), namely 40 units of coffee drinks and 20 units of non-coffee drinks, with a maximum profit of IDR 280,000. In conclusion, the combined production of both products is more optimal than a single product because it maximizes the use of limited resources. The linear programming approach has proven effective as a basis for more rational, efficient, and data-driven production decisions.
Co-Authors Ada Novisari D. Simanungkalit Adrina Fauza Dasrin Pohan Edi Syahputra Edy Surya Elvis Napitupulu Endang Lyfia Saragih Faizah Ibrahim Bakoban Farel Al Azmi Grace Amelia Purba Gracia Lovian Girsang Ian Pedrosa Manatap Lumban Gaol Klara Manila laoli Mas Berlian Nst Maulida Hafni Maulida Hafni Mey Gracia Sitanggang Misbakhul Munir NAFASA ZAHRI NAYSLA AURA SIFFA Nurul Wahida Harahap Petra Putri Sarinah Pandiangan Qisti Hafizhah Lubis Rawiyah Riamonda Singarimbun Riby Tamara RIZAL MUHAIMIN Rizka Nabila Damanik Roseyla Sahdina Pasaribu Sahat Saragih Said . Iskandar Tyesa Junika Sihombing Windi suryani Wiwi Yulia Rinanda Zulfahmi Indra, Zulfahmi