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Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Published by Universitas Jenderal Soedirman
ISSN : 20851456     EISSN : 25500422     DOI : -
Core Subject : Education,
Mathematics
JMP is a an open access journal which publishes research articles, reviews, case studies, guest edited thematic issues and short communications/letters in all areas of mathematics, applied mathematics, applied commutative algebra and algebraic geometry, mathematical biology, physics and engineering, theoretical bioinformatics, experimental mathematics, theoretical computer science, numerical computation and applications of systems, partial differential and differential equations, integral and integral differential equations and mathematical modeling.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 380 Documents
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MODEL PREDATOR-PREY DENGAN KONTROL OPTIMAL PADA BUDIDAYA BAWANG MERAH Wibowo, Rohman Prasetyo; Adi, Yudi Ari
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 1 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.1.15722

Abstract

Shallot farming creates a predator–prey interaction between leaf miner flies as pests and pesticides as control agents applied by farmers. This article discusses the application of a predator–prey mathematical model to shallot cultivation in Selopamioro Village, Imogiri, Bantul. The interaction between predator and prey is mathematically formulated using the Holling-Tanner response function and analyzed numerically using the fourth-order Runge-Kutta method to examine equilibrium point stability. The model is further developed by introducing optimal control in the form of manual pest removal and reduced insecticide dosage, aiming to improve shallot productivity through more effective pest management. The state and co-state conditions are solved using the Forward–Backward Sweep method based on the fourth-order Runge-Kutta on the Hamiltonian function. Simulation results show that the implementation of control significantly reduces the leaf miner fly population from 997 to 141 individuals and decreases the duration of insecticide application from 39 days to just 10 days
PENCARIAN RUTE OPTIMAL TRAVELING SALESMAN PROBLEM DENGAN ALGORITMA ANT COLONY OPTIMIZATION (ACO) Nuraliya, Aliffia Yasya; Nurshiami, Siti Rahmah; Jajang, Jajang
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 1 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.1.15866

Abstract

The implementation of product distribution requires transportation to deliver products effectively across various locations. Challenges encountered during this process include varying distribution sites, travel distances, time taken for product delivery, transportation costs, and other related factors. To address these challenges, selecting an efficient travel route is crucial. The Traveling Salesman Problem (TSP) serves as a practical application of graph theory in tackling such distribution issues. The Ant Colony Optimization (ACO) algorithm emerges as a viable solution for route optimization, particularly in addressing TSP challenges to derive optimal routes. Results derived from the TSP calculations utilizing ACO, executed through the Matlab R2018a application, employed parameters of
PENERAPAN METODE JACKKNIFE RIDGE REGRESSION UNTUK MENGATASI MULTIKOLINEARITAS (STUDI KASUS: KEMISKINAN DI PROVINSI JAWA TENGAH) Yulinda, Nisa Tri; Supriyanto, Supriyanto; Guswanto, Bambang Hendriya
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 1 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.1.16050

Abstract

Multicollinearity is one of the problems in linear regression that can lead to unstable parameter estimates. This study aims to address multicollinearity issues in multiple linear regression models applied to poverty data in Central Java Province using the Jackknife Ridge Regression method. The data used are secondary data from the Central Java Provincial Statistics Agency for 2022-2023, with the poverty rate as the dependent variable and eight independent variables representing poverty-related factors. This research was conducted using a literature review method and data analysis with R software. The results show that the Jackknife Ridge Regression method successfully mitigates multicollinearity, producing an accurate model. The final model indicates that average years of schooling, life expectancy, labor force participation rate, human development indeks, and regional gross domestic product have a negative effect on the poverty rate. These findings highlight the importance of improving education quality, healthcare, human development, and access to basic infrastructure as key strategies for poverty alleviation in Central Java Province.
PENERAPAN METODE REGRESI ROBUST ESTIMASI-M UNTUK KASUS DATA PDRB PERKAPITA PROVINSI JAWA TENGAH TAHUN 2021 Rizqi, Safina Sabila; Nurhayati, Nunung; Maryani, Sri
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 1 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.1.16165

Abstract

Economic growth and a more even distribution of income are needed to improve social welfare. One of the most important indicators for measuring the economic growth of a region is the growth value of the gross regional domestic product (GRDP). The size of the gross regional domestic product (GRDP) in Central Java can be predicted using a regression model. One of the estimation methods used in linear regression models is the LS method. The use of LS method becomes less appropriate if there is a violation of classical assumptions caused by outliers in the data. The M-estimation robust regression method can be used to solve outliers problem in the data. In this study, the M-estimation robust regression method was applied to the case of district or city GDP per capita data in Central Java Province in 2021. The weighting functions used were the Tukey bisquare weighting function and the Huber weighting function. The adjusted R-squared value and mean squared error (MSE) are used to determine the criteria for the best model. Based on the research results, it can be concluded that robust M-estimation regression with the Huber weighting function is the optimal parameter estimate for determining the best model. This is because the Huber weighting function has a higher adjusted R-squared value than the bisquare Tukey weighting function, and the Huber weighting function has a lower MSE than the bisquare Tukey weighting function
PERBANDINGAN KEAKURATAN METODE MACK CHAIN LADDER DAN BORNHUETTER -FERGUSON DALAM ESTIMASI CADANGAN KLAIM Firdausy, Andini Erika; Oktaviarina, Affiati
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 1 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.1.16200

Abstract

Abstract: Risk is an uncertain event that can cause losses, both financially and non-financially, so insurance is needed as a form of protection. In insurance, claim reserves are an estimate of the funds that a company must prepare to pay claims in the future. This study aims to compare two claim reserve estimation methods, namely Mack Chain Ladder and Bornhuetter-Ferguson, and evaluate their accuracy using Root Mean Square Error (RMSE). The Mack Chain Ladder method uses cumulative triangle run-off data, while the Bornhuetter-Ferguson method combines the loss ratio approach with incremental triangle run-off data. The data used comes from an insurance company in the United States with a claim period of 2013–2022. The estimation results show that the claim reserve with the Mack Chain Ladder method is 1,406,731 million USD with an RMSE value of 199,826, while with the Bornhuetter-Ferguson method it is 1,386,492 million USD with an RMSE value of 83,251. These results indicate that the smaller RMSE value is obtained by using the Bornhuetter-Ferguson method. Keywords: insurance, Bornhuetter-Ferguson, claims reserve, Mack Chain Ladder
DYNAMICAL ANALYSIS OF SVEIR MODEL IN SPREAD OF THE MONKEYPOX DISEASE WITH TIME DELAY Saputro, Isnu Aji; Setyowisnu, Glagah Eskacakra; Sofiyati, Noor; Puspita, Dian
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 2 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.2.17707

Abstract

Monkeypox is an infectious disease whose spread is influenced by various epidemiological factors, one of which is the incubation period. This study developed a mathematical model of Monkeypox, SVEIR, by incorporating a time delay in the transition from an exposed individual to an infectious individual, representing the incubation period. Model analysis shows that the system has two equilibrium points: a disease-free state and an endemic state. Based on the simulation results, a threshold value (tau* ) is obtained, which plays a crucial role in disease control. If the incubation period is below the threshold ( tau<tau*), then R0>1 , and the disease will spread endemically. Conversely, if the incubation period exceeds the threshold (tau>tau* ), then R0<1 , and the disease will disappear from the population
MODEL EXTENDED COX UNTUK MENGATASI NON-PROPORTIONAL HAZARD PADA DATA STUDI KANKER PARU-PARU Arumningtyas, Felinda; Juliza, Melda; Chandra, Novita Eka; Wulandari, Amelia
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 2 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.2.18061

Abstract

Lung cancer is a major cause of cancer-related deaths in Indonesia, making it essential to identify factors influencing patient survival. This study aims to analyze lung cancer patient survival using the Extended Cox Model as an alternative when the Proportional Hazard (PH) assumption is not met. Secondary data from 137 lung cancer patients were analyzed using variables such as type of treatment, treatment history, cancer cell type, Karnofsky score, age, and time of diagnosis. The results showed that only the Karnofsky score was significant in Cox-PH, but the assumption test showed that the cell type and Karnofsky score variables violated PH. Therefore, the analysis was continued with the Extended Cox Model. The final results showed that cell type and Karnofsky score had a significant effect on survival. The Hazard Ratio showed that a certain cell type reduced the risk of death by 22.7%, and an increase of one unit in the Karnofsky score reduced the risk of death by 3.1%. Cancer cell type and Karnofsky score are important factors in the survival of lung cancer patients, and the Extended Cox model has been proven to provide more reliable estimates than Cox-PH when the PH assumption is not being followed.
THE CONSERVATION NUMBERS IN THE PETRI NET MODEL OF THREE-PHASE TRAFFIC LIGHTS WITH THE NORWEGIAN SYSTEM Tristono, Tomi; Cahyono, Setiyo Daru; Triono, Joko; Sidqon, Mochamad; Aji, Seno; Sudarno, Sudarno; Junaedi, Nanang
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 2 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.2.18067

Abstract

The Petri net model can be used to represent the discrete state behavior structure of traffic light signals. The Petri net model is also capable of presenting three-phase traffic light scheduling synchronization. This study aims to examine the three-phase traffic light Petri net model that implements the Norwegian system. The Petri net model must pass validation and verification tests, including the use of several Place-Invariants, its boundedness property, conservation, coverability for all states, and simulation. The study results indicate that the model complies with all Place-Invariants, meets all required properties, and the simulation is also accurate. Place-Invariants in each phase must include a dummy. The three-phase traffic light Petri net model with the Norwegian system has a conservation number that applies to the model as a whole. The conservation number is an extension of Place-Invariant that only applies partially to the model.
ASYMPTOTIC STUDY OF NONLINEAR SPRING OSCILLATION WITH EXTERNAL FORCE USING THE MULTIPLE TIME SCALES METHOD Setyowisnu, Glagah Eskacakra; Muzdalifah, Lilik; Saputro, Isnu Aji
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 2 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.2.18081

Abstract

A nonlinear spring is a type of oscillator that does not follow Hooke's law perfectly. In mathematics, this type of oscillator can be modeled in a nonlinear ordinary differential equation. Of the many discussions on oscillation models, one examines the behavior of the model when disturbed by a parameter with a very small value. In this study, a discussion will be conducted regarding the behavior of the oscillation model with external forces added to the disturbance parameters in the damping and spring stiffness terms. To observe this behavior, one of the techniques in asymptotic analysis called the multiple time scales method is used. The results of this study will show the behavior of the oscillation model with the disturbance parameters caused by the resonance that occurs. To provide a clearer picture, the oscillations that occur are presented in the form of a simulation result graph, containing a comparison between the approximate solution and the numerical solution. Based on the discussion given, it is concluded that the oscillations in the model are strongly influenced by a certain relationship between the natural frequency of the nonlinear spring and the frequency of the external force acting on the model.
PENERAPAN GENERALIZED LINEAR MODEL DALAM MENANGANI OVERDISPERSI PADA DATA PENGANGGURAN DI INDONESIA Sari, Meylita
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 17 No 2 (2025): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2025.17.2.19005

Abstract

Unemployment remains a major problem in Indonesia. In 2023, the open unemployment rate was recorded at 5.32%, or approximately 7.86 million people. Low absorption of productive-age workers and limited job opportunities have led to a potential increase in unemployment in several regions. This situation requires in-depth analysis to reduce the increase in the open unemployment rate. Various socio-economic factors in Indonesia influence the unemployment rate and can be analyzed using the Generalized Linear Model (GLM) framework. Because unemployment data is count data, the approach used is Poisson Regression. This model has the basic assumption of equidispersion, meaning that the variance is equal to the mean. However, observations indicate that the variance is greater than the mean, resulting in overdispersion. To address this, a GLM development with an additional dispersion parameter, namely Poisson Generalized Inverse Gaussian Regression (PGIGR), was used. This model was chosen because it can capture greater data variation and represent factors that influence the unemployment rate. The results of this study indicate that the number of unemployed between provinces in Indonesia is influenced by the variables of Provincial Minimum Wage, GRDP Growth Rate on a Constant Basis, Literacy Rate, and TPAK, with an AIC value of 33,577.45.

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