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All Journal InPrime: Indonesian Journal Of Pure And Applied Mathematics JMT (Jurnal Matematika dan Terapan) Indonesian Journal of Statistics and Its Applications
Agustine, Debby
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Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Mathematics Other

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Graph Representation for the Solutions of Pythagorean Equation over the General Linear Group GL₂ (ℤ₂ ) Mahatma, Yudi; Hadi, Ibnu; Sudarwanto, Sudarwanto; Agustine, Debby
JMT (Jurnal Matematika dan Terapan) Vol. 7 No. 1 (2025): JMT (Jurnal Matematika dan Terapan)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Science, Universitas Negeri Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/jmt.7.1.1

Abstract

In 2023, Hadi et al. found the solvability of the Fermat equation over the general linear group GL2(Zp) for p=2 and p=3. In particular, for Pythagorean equation over GL2(Z2) there are 12 solutions. In this research, we represent the set solutions as a graph and investigate the properties.
Multi-Depot Vehicle Routing with Heterogeneous Vehicles using Nearest Neighbor Combined with Simulated Annealing Agustine, Debby; Naiborhu, Janson; Magdalena, Ikha
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 7 No. 2 (2025)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/ggqnkf48

Abstract

The Vehicle Routing Problem (VRP) is an essential component of contemporary logistics, which becomes more complex as the Multi-Depot Vehicle Routing Problem (MDVRP) and the Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDVRPHF). The main objective of MDVRPHF is to meet all customer demands while minimizing total distribution costs by using vehicles with varying capacities. This paper proposes a metaheuristic framework that first uses the Nearest Neighbor (NN) algorithm to build initial routes and then employs the Simulated Annealing (SA) algorithm to optimize the arrangement of goods within each vehicle, ensuring capacity limits are met. Computational experiments using real-world inspired data, representing 20 items distributed from a Bandung depot to multiple customers with three heterogeneous vehicle types, showed that the proposed hybrid NN–SA method achieved an 18.4% reduction in total distribution cost compared to the NN method alone. These results indicate that this integrated approach offers a practical, computationally efficient solution to the complexities of MDVRPHF, establishing it as a useful tool for logistics planning. Keywords: Multi-Depot Vehicle Routing Problem; Heterogeneous Fleet; Nearest Neighbor; Simulated Annealing; Metaheuristics.   Abstrak Vehicle Routing Problem (VRP) merupakan bagian penting dari logistik kontemporer, yang kompleksitasnya meningkat menjadi Multi-Depot Vehicle Routing Problem (MDVRP) dan Multi-Depot Vehicle Routing Problem with a Heterogeneous Fleet (MDVRPHF). Untuk MDVRPHF, tujuan utamanya adalah memenuhi seluruh permintaan pelanggan sambil meminimalkan biaya distribusi total dengan memanfaatkan kendaraan berkapasitas berbeda. Makalah ini mengusulkan kerangka kerja metaheuristik yang pertama-tama menggunakan algoritma Nearest Neighbor (NN) untuk membentuk rute awal, kemudian algoritma Simulated Annealing (SA) digunakan untuk mengoptimalkan penataan barang di setiap kendaraan agar batas kapasitas terpenuhi. Eksperimen komputasi menggunakan data uji berbasis kondisi nyata yang merepresentasikan distribusi 20 item dari satu depot di Bandung ke beberapa pelanggan dengan tiga jenis kendaraan heterogen. Hasil penelitian menunjukkan bahwa metode hibrida NN–SA ini menghasilkan penurunan biaya distribusi total sebesar 18,4% dibandingkan metode NN murni, yang menunjukkan bahwa pendekatan terpadu ini memberikan solusi praktis dan efisien secara komputasi untuk kompleksitas MDVRPHF. Kata Kunci: Multi-Depot Vehicle Routing Problem; Armada Heterogen; Nearest Neighbor; Simulated Annealing; Metaheuristik. 2020MSC: 90B06, 90C59.
Study of Bagging Application in the Safe-Level Smote Method in Handling Unbalanced Classification: Kajian Penerapan Bagging pada Metode Safe-Level Smote dalam Penanganan Klasifikasi Kelas Tidak Seimbang Meidianingsih, Qorry; Agustine, Debby
Indonesian Journal of Statistics and Applications Vol 5 No 1 (2021)
Publisher : Statistics and Data Science Program Study, SSMI, IPB University, in collaboration with the Forum Pendidikan Tinggi Statistika Indonesia (FORSTAT) and the Ikatan Statistisi Indonesia (ISI)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/ijsa.v5i1p105-116

Abstract

The problems of imbalanced class classification have been found in many real applications. It has potential to make the minority class instances tend to be classified into the majority class. This study examined the performance of bagging method’s application in safe-level SMOTE based on Support Vector Machine classifier. The data used consisted of three types based on the proportion of observations in the majority and minority classes. Each type of data has three variables, two independent variables and one variable dependent. The observations of independent variables were generated based on multivariate normal distribution, while dependent variables are binary. The results showed that the classifier has a high accuracy and sensitivity for all types of data for both in the imbalanced class and the balanced class (obtained by safe-level SMOTE and safe-level SMOTEBagging). Nevertheless, specificity was the main measure in assessing the performance of the classifier because it provides accuracy in classifying the minority class observations. The specificity increased when the number of observations between the two classes were approximately balance due to the implementation of safe-level SMOTE. The best performance of the Support Vector Machine in predicting minority class observations was achieved when bagging were applied in safe-level SMOTE. The specificity rate for all types of data were 77.93 percent, 78.46 percent, and 85.69 percent, respectively.
Co-Authors Ibnu Hadi Janson Naiborhu Magdalena, Ikha Mahatma, Yudi Meidianingsih, Qorry Sudarwanto, Sudarwanto