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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi BAREKENG: Jurnal Ilmu Matematika dan Terapan Eduvest - Journal of Universal Studies Limits: Journal of Mathematics and Its Applications
Herdiana, Ratna
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Aerospace Engineering Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Health Professions Mathematics Mechanical Engineering Neuroscience Physics Social Sciences Transportation

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Elliptical Orbits Mode Application for Approximation of Fuel Volume Change Pratama, Jovian Dian; Herdiana, Ratna; Hariyanto, Susilo
CAUCHY Vol 7, No 2 (2022): CAUCHY: Jurnal Matematika Murni dan Aplikasi (May 2022) (Issue in Progress)
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i2.14407

Abstract

This article discusses the Elliptical Orbits Mode (EOM) as a method of approximating the function of changing the volume of fuel in the Underground Yank (UT). This research was conducted at the 45.507.21 Candirejo Tuntang Pertamina Gas Station. The calculation of the approximation method will be applied to the measuring book data from the Semarang Metrology Regency specifically for the Pertalite (Fuel Product of Pertamina) buried tank, because the calculation of the gas station is not smooth, it is necessary for a smoother data fitting by considering Residual Square Error (RSS) and Mean Square Error (MSE). The result of this research is the application of EOM(θ) measuring book with elliptical height control produces smaller RSS and MSE compared to using COM, EOM, Least Square degree two and three.
TRAFFIC CONGESTION ANALYSIS USING SIR EPIDEMIC MODEL Rafsanjani, Zani Anjani; Herdiana, Ratna; Tjahjana, R Heru; Erlangga, Yogi Ahmad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2471-2478

Abstract

In this work, we propose a mathematical model to represent traffic congestion in the street under some consideration. A congestion problem in a city highway becomes a critical issue since congestion at one point affected congestion propagation on the other points. We focus on the propagation of traffic propagation by adopting the concept of disease spread using the SIR model. We consider that the disease in traffic problems is congestion. Meanwhile, vehicles that enter the highway are susceptible to congestion. In contrast, vehicles free from traffic jams represent individuals free from disease. The SIR model can explain the spread of congestion by looking at the congestion variable as an infected variable. We discuss and analyze the existence and stability of the equilibrium points. The local stability equilibrium point is verified using the Routh-Hurwitz criteria. At the same time, the global stability is analyzed using Lyapunov function. The numerical simulation is provided in the last section to validate the discussion results.
OPTIMIZING BI-OBJECTIVE MULTIPLE TRAVELING SALESMEN ROUTES FOR DISASTER RELIEF LOGISTICS USING GENETIC ALGORITHM Sihombing, Amos Hatoguan; Herdiana, Ratna; Pratama, Jovian Dian
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp2507-2520

Abstract

Handling natural disasters such as floods requires efficient logistics distribution to minimize the negative impact on victims. Distribution route optimization becomes very important in this process. This paper applies a metaheuristic method using Genetic Algorithm to the Bi-objective Multiple Traveling Salesman Problem (BMTSP) to obtain a solution that minimizes the distance and time to deliver disaster relief logistics. Multiple vehicles are used in this study to represent delivery agents with two main objectives, namely minimizing total distance and travel time. Genetic Algorithm is applied by considering these two main objectives through the process of selection, crossover, mutation, and produces an effective Pareto solution. The results indicate that applying the Genetic Algorithm to the Bi-Objective Multiple Traveling Salesman Problem yields more efficient delivery routes—reducing both distance and time—compared to the Nearest Neighbor Algorithm. The simulation and testing in this study utilize data on distances and travel times among Central Java Regional Disaster Management Agency offices in 19 regencies—including a central depot—located in flood-prone areas of Central Java Province. The scenario involves two vehicles with identical load capacities.
Perbandingan Metode Euler - Estimasi Galat Neural Network dan Metode Runge Kutta Orde 4 dalam Menyelesaikan Persamaan Diferensial Biasa Linear Herdiana, Ratna; Alfiani, Clarine
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3467

Abstract

Linear ordinary differential equations are a type of differential equation that is generally easy to solve analytically when the function on a partial integral has a simple form. However, when the function is a difficult function, it requires other methods such as numerical methods and methods adapted from neural networks because analytical methods can only be used when the problem has a simple geometric interpretation. This study involves the Euler method followed by error estimation using neural networks and the Runge-Kutta Orde-4 method as a comparison. The comparison was carried out by solving four equations which were then analyzed for the results and errors in each method based on the graphs generated and the MAPE criteria. The results of the study based on graphs show that the error generated by the method with error estimation using neural networks is more stable than the 4th Order Runge-Kutta method. In addition, based on the results of calculations with the MAPE criteria, the error estimation method using neural networks produces a very high level of accuracy in the category, while the 4th Order Runge-Kutta method produces a level of accuracy in two categories, namely the very high and reasonable categories
Geometric Brownian Motion in Analyzing Seasonality of Gold Derivative Prices Germansah, Germansah; Tjahjana, R. H.; Herdiana, Ratna
Eduvest - Journal of Universal Studies Vol. 3 No. 8 (2023): Journal Eduvest - Journal of Universal Studies
Publisher : Green Publisher Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59188/eduvest.v3i8.892

Abstract

Complex financial markets, influenced by complex and interconnected factors, require proper decision making. Gold derivatives, as an increasingly popular trading instrument, have experienced significant growth. However, with high profit potential also comes significant risk. Market analysis, including technical analysis and leveraging seasonality, can be an important tool in reducing risk and making smart decisions. This research aims to assess the effectiveness of the Geometric Brownian Motion (GBM) model in predicting Gold Derivative prices through the application of the Mean Absolute Percentage Error (MAPE) test.In this study, the Brownian Motion Geometric Method and Simple Moving Average are combined to analyze the seasonality of gold derivative prices to provide a view of price movement patterns. The results showed that the Brownian Motion Geometric Method was effective in predicting the price of gold derivatives, with a low error rate. In addition, seasonality analysis reveals monthly price movement patterns that can be a guide for traders and investors. This research provides valuable insights for decision making in gold derivatives trading in dynamic and complex financial markets.
Co-Authors Alfiani, Clarine Erlangga, Yogi Ahmad Germansah, Germansah Pratama, Jovian Dian Rafsanjani, Zani Anjani Sihombing, Amos Hatoguan susilo hariyanto Tjahjana, R Heru Tjahjana, R. H.