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All Journal Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA) BAREKENG: Jurnal Ilmu Matematika dan Terapan Indonesian Journal of Applied Mathematics Transcendent Journal of Mathematics and Applications
Saputra, T Murdani
Department Of Mathematics, Faculty Of Mathematics And Natural Science, Universitas Syiah Kuala, Indonesia
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Environmental Science Mathematics Mechanical Engineering Medicine & Pharmacology Physics Transportation

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METODE KONJUGAT GRADIEN HIBRID BARU: METODE HS-CD UNTUK MENYELESAIKAN MASALAH OPTIMASI TAK BERKENDALA Saputra, T Murdani; Silalahi, Bib Paruhum; Guritman, Sugi
Jurnal MSA (Matematika dan Statistika serta Aplikasinya) Vol 8 No 1 (2020): Volume 8 Nomor 1
Publisher : Universitas Islam Negeri Alauddin Makassar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24252/msa.v8i1.12294

Abstract

Metode konjugat gradien adalah salah satu metode yang efektif dalam menyelesaikan permasalahan optimasi tak-berkendala dan metode ini juga termasuk salah satu metode iteratif. Pada tulisan ini, peneliti mengusulkan metode konjugat gradien hibrid baru yaitu metode new hybrid 4 yang merupakan gabungan antara metode Hestenes dan Stiefel – Conjugate Descent, dimana metode tersebut diusulkan berdasarkan ide dari metode yang telah diusulkan sebelumnya yaitu metode Polak, Ribiѐre dan Polyak - Fletcher dan Reeves atau metode NH1, metode Hestenes dan Stiefel – Dai dan Yuan atau metode NH2 dan metode Liu dan Storey – Conjugate Descent (NH3). Peneliti mengusulkan metode tersebut dengan menggabungkan antara metode HS dan CD, dimana metode tersebut memiliki kekurangan masing-masing. Dalam penelitian ini, peneliti membandingkan hasil numerik antara metode baru yaitu Metode HS-CD (NH4) dengan metode-metode sebelumnya serta membuktikan bahwa memenuhi sifat konvergen global dan memenuhi kondisi descent setiap iterasinya. Hasil numerik menunjukkan bahwa metode baru adalah sangat efisien dalam menyelesaikan fungsi nonlinear tak-berkendala. Metode tersebut juga terbukti memenuhi sifat konvergen global menggunakan kondisi Wolfe serta memenuhi kondisi descent di setiap iterasinya.
PERBANDINGAN HASIL NUMERIK METODE KONJUGAT GRADIEN HIBRID BARU (LS-DY) DAN METODE HS-CD Saputra, T Murdani; Maulidi, Ikhsan; Radhiah, Radhiah
Jurnal MSA (Matematika dan Statistika serta Aplikasinya) Vol 10 No 1 (2022): VOLUME 10 NOMOR 1 TAHUN 2022
Publisher : Universitas Islam Negeri Alauddin Makassar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24252/msa.v10i1.26901

Abstract

Metode konjugat gradien merupakan suatu metode untuk menyelesaikan sistem persamaan linier pada skala besar, yang mana metode tersebut diperkenalkan oleh Hestenes dan Stiefel untuk menyelesaikan permasalahan tersebut. Metode konjugat gradien merupakan metode iteratif dan juga merupakan salah satu metode yang efektif dalam menyelesaikan optimasi tak berkendala. Dalam tulisan ini, penulis melakukan pengusulan metode konjugat gradien hibrid baru berdasarkan ide dari metode NH1, NH2, NH3 dan NH4. Metode hibrid tersebut diusulkan berdasarkan dari kekurangan dan kelebihan dari metode sebelumnya yaitu metode HS, FR, PRP, CD, LS dan Metode DY. Kekurangan dan kelebihan dari metode-metode tersebut diantaranya proses kinerja komputasi (iterasi) kurang baik dan kekonvergenan global. Berdasarkan dari metode-metode hibrid yang diusulkan tersebut maka penulis mengusulkan metode baru yaitu penggabungan dari metode LS dengan metode DY, dimana metode LS memiliki kelebihan pada kinerja komputasi dan DY kelebihannya pada kekonvergenan globalnya. Metode hibrid baru yang diusulkan tersebut yaitu metode NH5 (LS-DY) dan metode yang diusulkan ini akan di ujikan pada fungsi tak linear orde tinggi. Metode baru menunjukkan bahwa fungsi-fungsi yang diberikan dapat diselesaikan dengan sangat efisien serta perbandingan metode NH5 dengan metode-metode sebelumnya menunjukkan hasil pada proses komputasinya baik dan dapat bersaingKata Kunci: metode konjugat gradien, metode hibrid, knerja komputasi.
Pemrograman Nonlinear Meminimumkan Biaya Pemasangan Keramik Musholla Gapang Sabang dengan Menggunakan Metode Karush Kuhn-Tucker (Studi Kasus: CV. Muerika Teknologi) Saputra, T Murdani; Siti Rusdiana; T. Mohd. Raja Maulana; Intan Syahrini; Mahmudi; Radhiah
Jurnal MSA (Matematika dan Statistika serta Aplikasinya) Vol 11 No 2 (2023): VOLUME 11 NO 2 TAHUN 2023
Publisher : Universitas Islam Negeri Alauddin Makassar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24252/msa.v11i2.37104

Abstract

Musholla merupakan tempat beribadah umat islam. Musholla mengalami perkembangan pesat, baik dalam pembangunan maupun fungsi dan peranannya. Membuat musholla yang nyaman identik dengan bangunan yang luas dan biaya pembangunan yang besar. Namun dengan menggunakan matematika, biaya pembangunan yang cukup besar dapat diminimumkan. Program linier merupakan salah satu metode yang digunakan untuk meminimumkan atau memaksimumkan. Pada penelitian ini yaitu mencari biaya minimum dari pemasangan keramik pada Musholla. Metode yang akan untuk mencari biaya minimumnya yaitu dengan menggunakan metode Karush-Kuhn-Tucker (KKT). Metode KKT merupakan salah satu metode yang digunakan untuk menentukan titik minimum dari suatu fungsi tujuan dan kendala tanpa memperhatikan sifat linier atau nonlinear. Berdasarkan hasil penelitian, biaya minimum pemasangan keramik Musholla Gapang Sabang sebesar Rp. 19.211.800, lebih kecil dari biaya RAB yang ada yaitu sebesar Rp. 22.651.584.
Pengoptimalan Masalah Nonlinier dalam Meminimumkan Biaya Produksi Menggunakan Separable Programming dan Algoritma Genetika Fazilah, Nanda; Saputra, T Murdani; Syahrini, Intan
Indonesian Journal of Applied Mathematics Vol. 4 No. 1 (2024): Indonesian Journal of Applied Mathematics Vol. 4 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v4i1.1781

Abstract

This research aims to form a nonlinear model of the objective function in the case of minimizing production costs and the number of products that must be produced by Lanting Bumbu An-Nisa. The application of the separable programming method is carried out by transforming the nonlinear objective function and constraints to produce a linear objective function and constraints which are then solved by applying the genetic algorithm method. The application of this method produces a solution that producers must produce 250 packages of onion flavored lanting, 750 packages of cheese flavored lanting, 500 packages of sweet and spicy lanting and 500 packages of corn flavored lanting with a production cost of IDR 12,706,037.29 . The nonlinear model formed in this problem was also solved directly using the genetic algorithm method which resulted in the solution that the total production of onion flavored lanting was 533 packages, 507 packages of cheese flavored lanting, 505 packages of sweet and spicy lanting and 455 packages of corn flavored lanting at a cost of the production that must be spent is IDR 11,213,943.55. The application of these two methods results in a difference in production costs of IDR 1,492,093.74. Based on these results, it shows that solving the nonlinear model directly using a genetic algorithm results in production costs that are 11.74% lower than the costs solved using separable programming.
Solusi Numerik Persamaan Good Boussinesq Menggunakan Metode Garis Lubis, Yunika Zultira; Arif, Salmawaty; Saputra, T. Murdani
Transcendent Journal of Mathematics and Applications Vol 3, No 2 (2024)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v3i2.42653

Abstract

The Good Boussinesq equation is a hyperbolic partial differential equation, for which the analytical solution is generally difficult to determine thus necessitating a numerical approach. This study aims to obtain the numerical solution of the Good Boussinesq equation using the method of Lines and to calculate the accuracy of this method in solving the equation. Numerical simulation were also conducted to compare the numerical solution with the analytical solution in the form of a single soliton. Subsequently, a numerical simulation was performed to compare the numerical solution with the analytical solution in the form of a single soliton. The simulation conducted for a single soliton as an analytical solution demonstrates that the numerical solution closely approximates the analytical solution, as indicated by the nearly identical shapes and positions of the resulting wave. This is also indicated by the relatively small Root Mean Square Error (RMSE) of 1.89E-03, which shows that the Method of Lines is quite effective in solving the numerical solution of the Good Boussinesq equation based on the calculation of squared errors.
Kredibilitas Bhlmann Semiparametrik dengan Klaim Berdistribusi Poisson Maulidi, Ikhsan; Iskandar, Taufiq; Zahara, Annisa; Saputra, T Murdani
Transcendent Journal of Mathematics and Applications Vol 2, No 2 (2023)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v2i2.34726

Abstract

One method for calculating premiums based on the policyholder's risk characteristics is to employ the theory of credibility, particularly the semiparametric Bhlmann model. The aim of this research is to estimate the parameters of the Bhlmann credibility model using a semiparametric approach for claim frequencies that follow a Poisson distribution. Additionally, this study compares the semiparametric model, the parametric model, and the nonparametric model for the Bhlmann model. The assumptions made in this study concern claim frequencies following a Poisson distribution. The research results reveal that the semiparametric Bhlmann credibility premium for a Poisson distribution is 0.117992. Furthermore, the comparison between parametric and semiparametric approaches shows that premiums estimated using the semiparametric approach are lower than those estimated using the parametric approach. The difference is approximately 0.0085% for the Negative Binomial distribution and 0.00085% for the two Poisson distributions. However, there is no significant difference in premium values between the semiparametric and nonparametric approaches.
Application of Transportation Methods in Optimizing Transportation Cost for Fleet Product Distribution Radhiah, Radiah; Rusdiana, Siti; Marzuki, Marzuki; Saputra, T. Murdani; Mukhra, Uly Handayani
Transcendent Journal of Mathematics and Applications Vol 2, No 1 (2023)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v2i1.31741

Abstract

Motor vehicle distribution companies which are the source of this research data are located in Banda Aceh and Medan. The vehicles will then be sent to several areas, namely Lhokseumawe, Panton Labu, Meulaboh, Takengon, Subulussalam, Kuta Binjei, Kutacane, Aceh Singkil, Rimo and North Aceh. The problem in the process of sending vehicles is that if the inventory of vehicles in one of the warehouses is empty, then the supply of vehicles is obtained from warehouses that are still available in the warehouse regardless of distance. This paper describes the optimization of transportation costs for Fleet product distribution. Products are distributed from two sources to ten destinations. The cost of sending the vehicle incurred by the company is Rp 152,994,625. By using the Vogel's Approximation Method (VAM) and Modified Distribution Method (MODI), the total cost generated is Rp 142.728.100. Solving transportation problems with the transportation method can minimize and optimize the cost of sending a vehicle of Rp 10.266.525 or 6.71% and it can increase company profits.
Forecasting of Clean Water Usage by Observing Trend Pattern using Time Series Method Mahmudi, Mahmudi; Nurillah, Usmau Lidya; Rusdiana, Siti; Saputra, T Murdani
Transcendent Journal of Mathematics and Applications Vol 2, No 1 (2023)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v2i1.31377

Abstract

Population growth will increase the need for clean water. One of the clean water providers in the city of Banda Aceh is Local Water Supply Utility (PDAM) Tirta Daroy. To anticipate the surge in demand for clean water, PDAM needs to know the need for clean water in the future. One of the steps that can be taken is to do forecasting with the double exponential smoothing and triple exponential smoothing method. The smallest error value can be found using the mean absolute percentage error (MAPE) formula. Based on research, the double exponential smoothing method provides the most accurate forecast data when the parameter value 0.6 with an error of 3.5%. While the triple exponential smoothing method, the most accurate forecast data is obtained when the alpha value is 0.4 with an error of 3.55%.
Application of Path Analysis Method on Student Financial Satisfaction Radhiah, Radhiah; Fitriaa, Siti Nada; Saputra, T Murdani; Ikhwan, Muhammad
Indonesian Journal of Applied Mathematics Vol. 5 No. 1 (2025): Indonesian Journal of Applied Mathematics Vol. 5 No. 1 April Chapter
Publisher : Lembaga Penelitian dan Pengabdian Masyarakat (LPPM), Institut Teknologi Sumatera, Lampung Selatan, Lampung, Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35472/indojam.v5i1.1986

Abstract

THE IMPLEMENTATION OF GEOGRAPHICALLY WEIGHTED REGRESSION (GWR) METHOD ON OPEN UNEMPLOYMENT RATE IN REGENCY/CITY OF SUMATRA ISLAND Yuni, Syarifah Meurah; Saputra, T. Murdani; Fadhilah, Nadya Nur
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp73-86

Abstract

Unemployment is a condition where a person who is included in the labor force but does not have a job and is not actively looking for work. The number of unemployed is measured using the Open Unemployment Rate (OUR) indicator. OUR is obtained by comparing the number of job seekers and the number of labor force. This study aims to obtain a model of OUR in each district / city of Sumatra Island and what factors influence it using the Geographically Weighted Regression (GWR) method and Fixed Gaussian Kernel Function weighting, and describe predictor variables on thematic maps. The GWR method is one of the statistical methods that can prevent the presence of spatial aspects in the data. The parameters estimated by the local regression model vary at each location point and are estimated using the Weighted Least Square (WLS) method. Based on the research results obtained from this study, the GWR models obtained amounted to 154 different local models in each district / city on the island of Sumatra. Variables Labor Force Participation Rate, Population Growth Rate, Population Density and Average Years of Schooling have a significant influence on each location, meanwhile variable Percentage of Poor Population and variable Poverty Line have no influence on any location. These variables are able to explain the OUR by 57.2%, where the remaining 42.8% is explained by other factors that are not explained in the model.
Co-Authors Bib Paruhum Silalahi Fadhilah, Nadya Nur Fazilah, Nanda Fitriaa, Siti Nada Intan Syahrini Lubis, Yunika Zultira MAHMUDI Mahmudi Mahmudi Marzuki Marzuki Maulidi, Ikhsan Muhammad Ikhwan Mukhra, Uly Handayani Nurillah, Usmau Lidya Radhiah Radhiah, Radhiah Radhiah, Radiah Salmawaty Arif Siti Rusdiana Sugi Guritman Syahrini, Intan T. Mohd. Raja Maulana Taufiq Iskandar Yuni, Syarifah Meurah Zahara, Annisa