ZERO: Jurnal Sains, Matematika dan Terapan
Blind-Reviewed Academic Journal ZERO: Jurnal Sains, Matematika dan Terapan Publishing scholarly works in mathematics, statistics, computer science, information systems, applied sciences, mathematical modeling, data science, and interdisciplinary applications ZERO: Jurnal Sains, Matematika dan Terapan is a blind-reviewed academic journal established in 2017 under the Universitas Islam Negeri Sumatera Utara Medan. The journal publishes high-quality scholarly articles in mathematics, statistics, computer science, information systems, and related applications. Submit Manuscript Current Issue Author Guidelines Indexed Journal Information ISSN 2580-5754 Online | 2580-569X Print DOI Prefix 10.30829 by Crossref Publisher Department of Mathematics, Universitas Islam Negeri Sumatera Utara Medan Contact WA: +62 852-7000-9767 Abstracting and Indexing ZERO: Jurnal Sains, Matematika dan Terapan is indexed in several academic databases and indexing platforms, supporting the visibility and accessibility of published articles. SINTA 2 DOAJ Garuda Google Scholar
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Numerical Pricing of European Stock Option Based on Black-Scholes Model Using Crank-Nicolson Method
Accurate option pricing is an important issue in quantitative finance, especially in emerging financial markets, which are generally characterized by price volatility and limited historical data. This research evaluates the numerical performance of the classical Crank–Nicolson finite difference method in determining the price of European call options based on the Black–Scholes model using Indonesian stock market data. The Black–Scholes equation is discretized on a uniform spatial and temporal grid, and the numerical solution is verified by comparison with the Black–Scholes analytical solution as a mathematical reference. The numerical results show that the Crank–Nicolson method produces stable and convergent solutions, with a relative error of less than 1% at a sufficiently fine grid resolution. Furthermore, sensitivity analysis to volatility and temporal convergence tests demonstrate the consistency of the numerical solution's behavior to variations in the model's key parameters. These findings indicate that the Crank–Nicolson method provides a reliable numerical approach for evaluating European option pricing within the classical Black–Scholes framework under the analyzed market conditions.
Copyright (c) 2026 Isnaini Emma Wimala http://creativecommons.org/licenses/by-sa/4.0
Exploring the Metric Chromatic Number of Uniform, Centralized Uniform, and Cycle Uniform Theta Graphs
Metric coloring allows adjacent vertices of a graph to share the same color provided that their associated distance vectors are distinct, leading to the concept of the metric chromatic number. This notion is closely related to problems of vertex distinguishability and resource allocation in network-like structures. In this paper, we present the first exact determination of the metric chromatic number for three families of theta type graphs: uniform theta graphs, centralized uniform theta graphs, and a newly introduced class called the cycle uniform theta graph, obtained by cyclically arranging uniform theta subgraphs. The proposed construction enables an investigation of how cyclic configurations influence metric coloring behavior. Using a constructive metric coloring approach, exact values of the metric chromatic number are obtained. It is shown that the uniform theta graph and the centralized uniform theta graph both satisfy for all positive integers and . For the cycle uniform theta graph , the metric chromatic number equals when and have the same parity or when is odd and is even. In contrast, when is even and is odd. This latter case arises because the longest path in the cyclic structure has odd length, forcing the graph to have chromatic number three. Since the graph is connected and its chromatic number is at most three, this structural constraint directly implies that three colors are also necessary for a valid metric coloring.
Copyright (c) 2026 Raventino Raventino, Fransiskus Fran http://creativecommons.org/licenses/by-sa/4.0
Forecasting Macroeconomic Variables in Indonesia Using the Vector Autoregressive Method
This study aims to analyze the dynamic relationship and predict inflation, the rupiah exchange rate, oil and gas exports, and BI interest rates in Indonesia. The Vector Autoregressive (VAR) method was used with monthly data from January 2015 to September 2025, the best model obtained was VAR (2). The Granger causality test results show that most variables are dominated by their own lag effects. Impulse response analysis shows that shocks are temporary and subside in the medium term. Forecast results for October 2025–September 2026 shows relatively stable inflation in the range of 2.42–2.70%. The rupiah exchange rate is expected to depreciate moderately by around 1.4%. Meanwhile, oil and gas exports declined significantly by 3.9%, and the BI interest rate is expected to fall by 12.8% to 4.14%. These findings indicate that Indonesia's macroeconomic stability is dominated by internal dynamics, so monetary policy focuses on inflation and the exchange rate.
Copyright (c) 2026 Nonong Amalita http://creativecommons.org/licenses/by-sa/4.0
Bayesian Path Modeling Simulation for Stunting Analysis
This research assesses the interaction between sample size, model complexity, error variance, and their collective impact on the execution of Bayesian path modeling within the context of stunting, using Monte Carlo simulation over 100 datasets over 18 different conditions. The results indicate that the sample size positively impacts the stability of the model, but the more intricate the model and the more noise there is in the data, the greater the effect. A 0.3 error variance unpredictedly lowered the RMSE on various complex scenarios (eg. for nonlinear structures, it decreased from 0.222 to 0.079), and low error variance, combined with nonlinear pathways, led to lower CI coverage (<0.85) and lower ESS, indicating there was difficulty recovering the true parameters A unique contribution of the research is that, in Bayesian modeling, sample size is not the only driver of model complexity, noise, and stunting research. This information is beneficial in providing evidence on how to choose priors, structure models, and conclusively derive results for Bayesian causal analysis in the field of public health.
Copyright (c) 2026 Celia Sianipar, Adji Achmad Rinaldo Fernandes, Solimun Solimun, Septi Nafisa Ulluya Zahra http://creativecommons.org/licenses/by-sa/4.0
Numerical Pricing of European Options under Proportional Transaction Costs: A Semi-Discretization Approach to the Nonlinear Barles-Soner Model
The classical Black–Scholes model assumes a frictionless market, which often leads to the undervaluation of option premiums when transaction costs are present. This study prices European call options under proportional transaction costs using the nonlinear Barles–Soner framework and a semi-discretization–based numerical approach. Using historical stock data from PT XYZ (an anonymized Indonesian equity), the results show that transaction costs significantly increase effective volatility and generate systematic deviations from classical Black–Scholes prices. In particular, option premiums increase by IDR 392.33 and IDR 776.66 for transaction cost parameters of 0.015 and 0.030, respectively, compared with the frictionless benchmark. These findings confirm that ignoring transaction costs leads to substantial underpricing and that the proposed framework provides a more realistic and conservative valuation for hedging and risk management in emerging markets.
Copyright (c) 2026 Dwi Maya Firanti Noor http://creativecommons.org/licenses/by-sa/4.0
A Bibliometric Analysis of Mathematics Education Research in Elementary Schools: Trends, Institutions, and Post-Pandemic Learning Integration (2020–2025)
Research on elementary mathematics education in the post pandemic period reflects changes in publication patterns and research topics. This study aims to analyze publication trends, institutional contributions, and forms of learning integration in elementary mathematics education research published between 2020 and 2025. The method employed is a bibliometric analysis of 921 Scopus-indexed articles using RStudio. The analysis covers annual publication trends, institutional productivity, authors’ geographical distribution, keyword-based thematic clusters, and citation patterns. The results show variations in annual publication output, with an increasing trend observed since 2023. Monash University and Universitas Negeri Yogyakarta are identified as the institutions with the highest publication output. Cluster analysis identifies three main thematic groups: student-oriented and numeracy-focused research, studies related to methodological approaches and teacher development, and research concerning pedagogy and curriculum. These findings describe the characteristics and thematic distribution of post pandemic research in elementary mathematics education.
Copyright (c) 2026 Lola Aprianda, Karsoni Berta Dinata http://creativecommons.org/licenses/by-sa/4.0
Comparative Study of Hybrid ARIMA-LSTM and CNN-LSTM for Palm Oil Price Forecasting
The forecasting of highly volatile time series data remains a significant challenge due to complex, non-linear patterns. This study compared the performance of two hybrid frameworks, ARIMA-LSTM and CNN-LSTM, which were designed to integrate the statistical strengths of traditional models with the computational power of deep learning. In these architectures, the ARIMA component was utilized to extract linear trends, while the LSTM and CNN layers were employed to identify and manage non-linear dynamics within the data. Utilizing 384 monthly palm oil price data points (1993-2024) sourced from FRED, the models were evaluated using the Mean Absolute Percentage Error (MAPE) metric. The results demonstrated that the hybrid CNN-LSTM outperformed the ARIMA-LSTM and individual models, achieving a superior MAPE of 6.69%. These findings indicated that the integration of Convolutional Neural Networks (CNN) with Long Short-Term Memory (LSTM) networks was more effective in capturing the complexities of price fluctuations. Practically, the study concluded that accurate forecasting served as a critical tool for market stabilization, thereby supporting broader goals of financial certainty and ecological sustainability.
Copyright (c) 2026 Rizki Alifah Putri, Khairil Anwar Notodiputro, Budi Susetyo http://creativecommons.org/licenses/by-sa/4.0
Integrating Clustering and Hybrid Nonparametric Path Modeling for Waste Management Behavior in Batu City
This study formulates a hybrid nonparametric path analysis utilizing truncated spline-Fourier series integrated with Fuzzy C-Means clustering methodologies to investigate nonlinear behavioral patterns in community-based waste management. The model was utilized on survey data from 210 respondents in Bumiaji District, Batu City, encompassing Environmental Quality, Use of Waste Banks, Use of the 3R Principles, and Economic Benefits from Waste. Two distinct behavioral groups with varying emphasis on Use of Waste Banks and Environmental Quality were identified by the analysis. The hybrid model obtained a high coefficient of determination (0.891) and captures nonlinear relationships more successfully than the traditional linear approach. These results emphasize how crucial nonlinear behavioral dynamics are in influencing waste management behavior/decisions. The proposed framework helps local governments create more focused and efficient waste-management plans by offering a useful and adaptable analytical for understanding community behavior.
Copyright (c) 2026 Moh Zhafran Hidayatulloh, Solimun Solimun, Adji Achmad Rinaldo Fernandes, Anggun Fadhila Rizqia, Fachira Haneinanda Junianto http://creativecommons.org/licenses/by-sa/4.0
Simplex vs. Revised Simplex for Budget Allocation in Madrasah Teacher and Staff Development Programs under MoRA Kudus, Indonesia
This study compared the Simplex and Revised Simplex Methods for allocating the 2025 budget for the madrasah teacher and staff development programs under the Madrasah Education Division of the Ministry of Religious Affairs (MoRA) in Kudus, Indonesia. A quantitative case study design was employed to formulate a weighted linear programming model that identifies the most beneficial combination of programs under fixed budget constraints, with an emphasis on procedural comparison rather than policy impact. Both methods converged to the same optimal solution after four iterations, indicating equivalent computational performance for the small-scale model. The optimal allocation resulted in implementable program frequencies and achieved a maximum total weighted benefit of 129,133.6, primarily by prioritizing cost-free, high-benefit training programs while maintaining compliance with budget limits. Methodologically, the study demonstrates a transferable and reproducible linear programming framework that contributes to applied mathematics by illustrating how Simplex-based techniques can be adapted as transparent decision-support tools for small-scale public-sector budgeting problems. Although the Revised Simplex Method offers theoretical advantages for larger models, empirical differences in this case were minimal due to the model’s scale. The study was limited to a single fiscal year and did not include sensitivity analysis, which should be addressed in future research.
Copyright (c) 2026 Dina Fakhriyana http://creativecommons.org/licenses/by-sa/4.0
A Mixed Integer Linear Programming Based Scheduling Model for Cost Minimization in Sea Tollway Vessel Operations
The Sea Tollway Program plays a critical role in Indonesia’s national logistics system by improving maritime connectivity and reducing regional disparities in goods distribution. However, operational inefficiencies in vessel scheduling and prolonged berthing times continue to limit its effectiveness. This study addresses these challenges by formulating a deterministic Mixed Integer Linear Programming (MILP) based vessel scheduling model with capacity and cargo flow constraints aimed at minimizing time-dependent operational cost and improving berthing time efficiency. A case study is conducted on Sea Tollway Route H-1 using operational data from the first semester of 2025. The optimization model is implemented using the PuLP library and solved with the CBC solver. The results show that the optimized schedules consistently reduce operational costs by approximately 5–8% per voyage and decrease berthing time by about 12–17%, corresponding to an average reduction of two hours per voyage. Statistical significance testing confirms that these improvements are not due to random variation, while sensitivity analysis demonstrates the robustness of the optimized solutions under changes in key operational parameters. Overall, the proposed MILP-based framework provides a mathematically sound and practically applicable decision-support tool for improving vessel scheduling and operational efficiency in Sea Tollway maritime logistics.
Copyright (c) 2026 Jauza Ananda Ayuniar, Yuliani Puji Astuti http://creativecommons.org/licenses/by-sa/4.0
Local Stability Analysis of Leptospirosis SEITR - SI Model with the Influence of Hydroclimatic Rate and Treatment
Leptospirosis is a zoonotic disease whose transmission is influenced by interactions between humans, vectors, and environmental conditions. This study proposes a novel SEITR–SI model that simultaneously integrates treatment dynamics and hydroclimate-dependent transmission within a single analytically tractable framework. Unlike previous SEIR–SI and SIR–SI formulations that either exclude treatment or incorporate hydroclimatic effects through explicit environmental compartments, the proposed model represents hydroclimatic influence implicitly through transmission intensity while preserving mathematical simplicity. The local stability of the disease-free and endemic equilibria is analyzed using the basic reproduction number and the Routh–Hurwitz criterion. The analysis confirms classical threshold behavior governed by , while numerical simulations reveal that increased hydroclimatic transmission intensity elevates endemic infection levels even under higher treatment rates. These findings highlight that treatment alone may be insufficient in hydroclimate-sensitive environments and underscore the importance of integrated control strategies combining medical intervention with environmental and vector management.
Copyright (c) 2026 Ega Ananta Erlangga http://creativecommons.org/licenses/by-sa/4.0
Comparative Analysis of Four Actuarial Cost Methods on Unfunded Actuarial Liability in a Pekanbaru Pension Scheme
Unfunded Actuarial Liability (UAL) is an important indicator in assessing the sustainability of a pension fund program, as it reflects the difference between actuarial liabilities and available assets. This study aims to compare the amount of UAL generated by four pension funding methods, namely Accrued Benefit Cost (ABC), Entry Age Normal (EAN), Unit Credit (UC), and Aggregate Cost Method (AGG). A quantitative actuarial valuation is conducted using administrative data from active civil servants of PT. TASPEN (Persero) Pekanbaru Branch Office in 2025 under uniform actuarial assumptions, including the TASPEN mortality table, interest rates, and salary growth rates. A deterministic sensitivity analysis on the discount rate and salary growth rate was conducted to examine the robustness of unfunded actuarial liability estimates. The results show that the ABC, UC, and EAN methods produce identical aggregate UAL values of approximately Rp. 16.841.220.000, - while the Aggregate Cost Method yields a higher UAL of about Rp.22.173.660.000, - due to collective liability recognition. Furthermore, the EAN and AGG methods exhibit relatively more stable contribution patterns over participants’ service periods, whereas the ABC and UC methods are more sensitive to variations in participants’ age and length of service. These findings indicate that the selection of actuarial cost methods has significant practical implications for pension fund management, particularly in terms of funding stability, contribution planning, and long-term sustainability of pension schemes.
Annisa Hevita Gustina Kumalasari Saefulloh
Copyright (c) 2026 Putri Isnaini Cahyaning Baiti, Nasrullah - -, Annisa Hevita Gustina Kumalasari Saefulloh, Tika Kristin Marbun http://creativecommons.org/licenses/by-sa/4.0
Spatial Heterogeneity of Tuberculosis Incidence Using Geographically Weighted Negative Binomial Regression (GWNBR) in Indonesia
Poisson regression is widely used for count data but relies on the equidispersion assumption, which is often violated in epidemiological data due to overdispersion. Negative Binomial Regression (NBR) addresses this issue by introducing a dispersion parameter. However, both models assume spatial homogeneity of parameters. This study applies Geographically Weighted Negative Binomial Regression (GWNBR) to analyze tuberculosis (TB) cases across 38 provinces in Indonesia in 2024. The response variable is the number of TB cases, with predictors including population density, smoking prevalence (age 15), poverty rate, and number of hospitals. Overdispersion was confirmed (deviance/df = 12,020), justifying the use of NBR. Model comparison shows that GWNBR provides improved fit relative to global models, with lower AIC than the NBR model (716.45 vs 732.29). Spatial heterogeneity was confirmed by the Breusch–Pagan test (BP = 21.011; p 0.01). Provinces exhibit distinct patterns of significant determinants; for example, in West Sumatra, poverty and smoking show strong positive local effects, while in several eastern provinces smoking is not significant. These findings highlight the importance of spatially adaptive TB control policies rather than uniform national strategies.
Copyright (c) 2026 Riry Sriningsih, Mohammad Soleh, Muhammad Subhan, Reni Prima Gusty http://creativecommons.org/licenses/by-sa/4.0
A Conceptual Consortium Blockchain Model to Enhance Integrity and Auditability in Indonesia’s Election Result Recapitulation
Election results recapitulation requires stakeholder participation, data integrity, and auditability. However, electronic systems remain largely centralized and provide limited support for multi-stakeholder involvement, traceable audit trails, and verifiable record integrity. This study formalizes the recapitulation process as a rule-based state-transition model and proposes a consortium Blockchain architecture as a parallel recapitulation channel. Built on Hyperledger Fabric, the network comprises peer nodes representing election officials, supervisors, and witnesses, and is governed by smart contracts with policy-driven endorsement. The model encodes stakeholder roles, cryptographic document binding through IPFS content identifiers and hash verification, and rule-based state validation, with emphasis on arithmetic consistency and plenary time-window constraints. The artifact is evaluated through regulatory compliance mapping and computational testing. The results show that the model enables multiparty verification, preserves auditable transaction history, and maintains verifiable linkage between recapitulation records and supporting documents, while constraining accepted state transitions to defined arithmetic and procedural rules.
Copyright (c) 2026 Muhammad Hadi Pranowo, Yani Nurhadryani, Irman Hermadi http://creativecommons.org/licenses/by-sa/4.0
Family Clustering Based On Y-Chromosome DNA Profile Using Unweighted Pair Group Method with Arithmetic Mean
Indonesia is a diverse nation composed of numerous ethnic groups, each with distinct physical and genetic characteristics. Genetic similarities within ethnic populations can be examined through DNA profiling, particularly by analyzing Short Tandem Repeat loci. In Indonesia, DNA profiling has been widely applied in forensic identification and paternity testing. This study focuses on classifying the Javanese population into sub-tribes based on STR profile similarities using divisive hierarchical clustering. The optimal number of clusters was determined by the smallest Sum of Squared Errors (SSE), with the lowest value of 72583.12and the highest Silhouatte coeffisien value is 0.78, yielding seven sub-tribe clusters. Subsequently, these sub-tribe clusters were further classified into family clusters using Y-chromosome STR (YSTR) data, which traces paternal lineage. The clustering process employed the Unweighted Pair Group Method with Arithmetic Mean, resulting in 21 family clusters. Compared to k-means clustering, divisive clustering produced sub-tribe clusters with more balanced population sizes. The establishment of sub-tribe and family clusters enhances the efficiency of individual identification, as DNA profile matching can be performed at the cluster level rather than across the entire population. This approach provides a more systematic framework for forensic applications and victim identification, particularly in cases involving male individuals where YSTR data is critical.
Copyright (c) 2026 Meira Parma Dewi, Nurtami Soedarsono http://creativecommons.org/licenses/by-sa/4.0
Hierarchical Ensemble Actuarial Method for Motor Claim Reserving under Indonesia’s PSAKBI
This study develops and evaluates a hierarchical ensemble actuarial approach for motor claim reserving under Indonesia’s PSAKBI framework. The method integrates traditional actuarial techniques with modern machine learning models in a structured ensemble design to enhance predictive accuracy, reliability, and transparency. Using motor insurance claim data, the ensemble was compared against conventional single-model reserving practices. Results show that the proposed approach achieves lower prediction error (MSE = 220.3), accurate calibration (94.7% coverage), and more stable reserve estimates across accident years. Beyond statistical performance, the design emphasizes interpretability by tracing predictions to weighted contributions of base models, thereby avoiding black-box behavior. These findings highlight the practical relevance of hybrid ensemble reserving in regulated environments, offering a transparent and robust solution aligned with PSAKBI requirements. The study contributes to the literature by demonstrating how hybrid actuarial ensembles can balance methodological rigor, machine learning flexibility, and regulatory compliance in insurance reserving.
Copyright (c) 2026 Mulawarman - Awaloedin http://creativecommons.org/licenses/by-sa/4.0
Crank-Nicolson Finite Difference Pricing of European Call Options under the Black-Scholes Model
This study aims to determine the price of European call options using the Crank–Nicolson finite difference method in the Black–Scholes model with stock data from XYZ Company for the period January 2025 to December 2025. Annual volatility is calculated based on historical closing price data, while numerical option prices are obtained through the Crank–Nicolson finite difference scheme and compared it with the Black–Scholes analytical solution as a reference. The results show that the Crank–Nicolson method produces a call option price of 596.08, while the Black–Scholes analytical solution gives a value of 612.50. The relative difference between the two methods is 2.68%, which indicates a good level of accuracy for the numerical method used. These findings indicate that the Crank–Nicolson finite difference method is capable of providing a stable and accurate numerical approach to determining the price of European call options. In practical terms, the results of this study contribute to the application of numerical-based option pricing models in emerging markets, particularly in conditions of dynamic volatility, where analytical approaches may have limitations in implementation
Copyright (c) 2026 Robiyatul Adawiyyah http://creativecommons.org/licenses/by-sa/4.0
Mathematical Model of Zakat and Low-Tax Policy Effects on Economic Population
Many Islamic countries implement low-tax policies, but these often fail to reduce inequality and poverty. Zakat has a function to redistribute wealth, but previous studies fail to explore its dynamic interaction with tax systems. This study builds a mathematical model that describes the combined effects of zakat and low-tax policies on economic population dynamics. We develop a system of differential equations that represents wealthy, middle, and poor populations, then analyze it qualitatively by finding equilibrium points and their stability. Analysis reveals a single asymptotically stable equilibrium point, indicating that zakat effectively reduces the wealth gap, even under a low-tax setting. We also established a threshold condition for the middle-to-poor population ratio, guiding policymakers on designing effective poverty interventions. This study lays a theoretical groundwork that incorporates Islamic financial institutions into poverty reduction strategies.
Copyright (c) 2026 Muhammad Subhan http://creativecommons.org/licenses/by-sa/4.0
Comparative Modeling of Pineapple Production Using Gaussian GLM and Random Forest Regression
This study aims to conduct a comparative modelling of pineapple production at PT Great Giant Pineapple (GGP) using Gaussian GLM as parametric statistical approach and Random Forest Regression method as machine learning based on monthly data from 2014 to 2022. Multicollinearity testing and distribution fitting were conducted to validate the Gaussian assumption. For the Random Forest Regression, hyperparameters were optimized by tuning the number of trees (ntree) and the number of predictors at each split (mtry) with model stability evaluated using Out-of-Bag (OOB) error. The Gaussian GLM achieved a MAPE of 8.41% (R² = 0.106) for the GP3 clone and 11.27% (R² = 0.149) for the F180 clone. Random Forest Regression produced a testing MAPE of 9.28% (R² = 0.144) for GP3 and 12.11% (R² = 0.105) for F180. While both models achieved low prediction error based on MAPE, they differed in identifying influential variables and showed limited explanatory power as indicated by low R² values. The Gaussian GLM identifies air pressure as significant for both clones and rainfall for F180 clone, while Random Forest consistently identifies rainfall as the most influential predictor. These findings confirm the complementary strengths of parametric and machine learning approaches in supporting climate-based production planning and risk mitigation.
Copyright (c) 2026 Indah Gumala Andirasdini http://creativecommons.org/licenses/by-sa/4.0
Optimization of Real-Time Object Detection in Viola-Jones Method with Enhanced AdaBoost
Face recognition is a widely used biometric technology in security systems, automated attendance, and surveillance applications. This study proposes an enhanced real-time face detection method by integrating a modified AdaBoost-based feature selection strategy into the Viola–Jones framework. The applied mathematical contribution of this study lies in formulating the optimization process as an empirical risk minimization model with adaptive boosting weight updates to reduce face recognition error. The proposed approach optimizes the weighting of weak classifiers by prioritizing Haar-like features with minimal weighted classification error at each boosting iteration, thereby improving discriminative capability. Experiments were conducted on a camera-based dataset consisting of face and non-face samples under varying illumination and pose conditions. Prior to optimization, the system achieved a precision of 70.04% and a recall of 70.05%. After applying the proposed enhancement, precision increased to 81.04% and recall to 90.02%. These results demonstrate that the modified AdaBoost integration significantly improves detection accuracy while remaining suitable for real-time face detection applications.
Copyright (c) 2026 Sucitra Bina Sarana Sahara, Rizqi Agung Permana, Mely Mailasari http://creativecommons.org/licenses/by-sa/4.0
Geometric Data Augmentation with a Two-Stage Fine-Tuning Strategy for EfficientNetB3-Based Fruit Condition Classification
Accurate fruit condition classification is essential for automated food safety assessment, particularly due to health risks associated with chemical contaminants such as formalin. However, reliable generalization in automated inspection systems remains challenging because limited visual variation in image datasets often leads to overfitting in deep learning models. To address this challenge, this study proposes an EfficientNetB3-based framework that integrates geometric data augmentation with a structured two-stage fine-tuning strategy to improve robustness and training stability. The proposed model achieved 99% test accuracy with consistent cross-dataset performance. The framework also demonstrated stable optimization behavior across training stages, indicating improved generalization capability. From a practical perspective, the proposed approach may support scalable food quality monitoring and automated sorting in agricultural supply chains, as well as preliminary food safety screening in large-scale inspection processes.
Copyright (c) 2026 Hana Sajida Azhurra, Sugiyarto Surono, Aris Thobirin http://creativecommons.org/licenses/by-sa/4.0
Optimization of Retention Levels Using the Pentikäinen Method: A Case Study on Unit-Linked Insurance Product
This study evaluates the adequacy of surplus reinsurance retention for unit-linked insurance products in Indonesia under changing market and regulatory conditions. Using 2024 portfolio statistics of Insurance X, the study applies the Pentikäinen method, which is grounded in ruin theory, to determine model-based retention levels and compare them with the company’s actual retention policy. The analysis incorporates premium income, claim experience, reserve considerations, and security loading assumptions. The results show that the company’s actual retention of IDR 500,000,000 is higher than the retention levels generated by the Pentikäinen model, namely IDR 275,000,000 at 0% loading, IDR 305,000,000 at 10% loading, and IDR 335,000,000 at 20% loading. Simulation results further indicate that lower retention reduces the insurer’s net retained claims and improves financial stability, as reflected in a decline in the loss ratio from 6.75% under the actual retention to 6.12%, 5.95%, and 5.74%, respectively. However, lower retention also increases reinsurance premium cessions, implying a trade-off between risk reduction and cost efficiency. The findings suggest that the retention range of IDR 305,000,000 to IDR 335,000,000 provides a more balanced outcome than both the current retention and the lowest simulated retention. This study contributes to the literature by providing an empirical application of the Pentikäinen method in surplus reinsurance for unit-linked products in Indonesia and offers a more objective basis for retention policy adjustment.
Copyright (c) 2026 Karin Amelia Safitri http://creativecommons.org/licenses/by-sa/4.0
Adaptive Continuous Parameter Optimization of ARIMA using a Hybrid GA–PSO Approach for Time Series Forecasting
Accurate forecasting of financial time series remains challenging due to non-stationarity, complex data patterns, and difficulties in parameter optimization within traditional models. Although ARIMA is widely used, its performance is often limited by static parameter estimation and sensitivity to evolving data structures. Existing metaheuristic-based approaches have attempted to address these issues; however, many lack adaptive mechanisms that account for varying data complexity. This study proposes a Continuous Hybrid ARIMA–Metaheuristic (GA–PSO) framework with adaptive parameter tuning guided by Model Complexity Assessment (MCA). The framework enables continuous optimization of ARIMA parameters, allowing the model to dynamically adapt to changing time-series characteristics. Empirical results demonstrate consistent improvements in forecasting performance compared to the baseline ARIMA model. For instance, in the Gold dataset (300 observations), the model achieved RMSE = 56.96, MAE = 41.86, and MAPE = 1.12%, indicating stable and accurate predictions. Statistical validation using the Diebold–Mariano test further confirms the significance of these improvements. The main contribution lies in the integration of adaptive GA–PSO optimization with complexity-aware tuning, which enhances both forecasting stability and responsiveness. However, the findings also indicate the presence of heteroscedasticity in several cases, suggesting that volatility dynamics are not fully captured by the current framework. This limitation highlights the need for incorporating volatility-aware models, such as ARIMA–GARCH, to better represent time-varying variance and improve forecasting robustness in future research.
Copyright (c) 2026 Fitri Andini Ritonga http://creativecommons.org/licenses/by-sa/4.0
Actuarial Evaluation of Additional Contributions in Early Retirement Programs Using the Spreading Gains and Losses Method
This study examines the actuarial and funding implications of accelerated retirement in a defined benefit pension scheme by integrating the Projected Unit Credit (PUC) method with the Spreading Gains and Losses approach. While both methods are widely applied in pension valuation, limited empirical evidence evaluates their combined implementation under retirement age acceleration scenarios, particularly in Indonesian public sector schemes. This study addresses that gap using secondary administrative employment data of 87 female civil servants obtained from the Investment and One-Stop Integrated Services Office of Lampung Province (Dinas Penanaman Modal dan Pelayanan Terpadu Satu Pintu Provinsi Lampung), grouped into four entry-age cohorts (22–25 years). The analysis compares normal retirement at age 58 with accelerated retirement at age 50, assuming a 5% annual effective interest rate and 8% biennial salary growth. The results indicate that, at valuation age 45, actuarial liabilities increase by approximately 49.8% under retirement at age 50 relative to age 58. The shorter discounting period and earlier benefit payments outweigh the reduced contribution period, resulting in the emergence of Unfunded Actuarial Liability (UAL). The resulting Past Service Liability (PSL) is amortized over five years, requiring additional contributions ranging from IDR 27.06 million to IDR 82.05 million across entry-age groups. These findings highlight the high sensitivity of pension funding to retirement age assumptions and emphasize the importance of actuarial impact assessments prior to policy implementation. However, the deterministic framework and relatively small sample size limit broader generalization of the results.
Copyright (c) 2026 Dwi Mahrani, Miftha Ulya Nazima, Ayu Sofia, Tiara Yulita http://creativecommons.org/licenses/by-sa/4.0
Application of Linear Programming Based Transportation Models to Optimize Natural Disaster Relief Distribution
Disaster relief distribution is a complex logistical problem and requires optimal planning for targeted and efficient distribution. This study aims to apply a linear programming-based transportation model to optimize aid distribution from several warehouses to affected shelters, with clearly defined constraints based on field conditions. The method used is a quantitative approach through simulation supported by empirical data representing post-disaster conditions. The model is formulated in an objective function to minimize total distribution costs with warehouse capacity and shelter requirements constraints. The process solution model is carried out using LINDO (Linear, Interactive, Discrete Optimizer) optimization software to ensure calculation accuracy. The optimization results show a cost reduction from 1,550 to 650 units, or a savings of 58.06% while still satisfying all supply and demand constraints. These findings indicate that the linear programming-based transportation model is effective in increasing aid distribution efficiency and supporting more targeted logistics decision-making.
Copyright (c) 2026 Saddam Husein http://creativecommons.org/licenses/by-sa/4.0
A Hybrid Analytical Hierarchy Process (AHP) and Profile Matching Model for E-Wallet Selection Decisions in Medan City
The development of digital payments in Indonesia has increased the complexity of selecting an e-wallet that aligns with user preferences. This study proposes a hybrid DSS integrating AHP and Profile Matching, enhanced by a proportional transformation of AHP weights into ideal values. Unlike conventional approaches that subjectively determine ideal values, this method ensures consistency between criteria weighting and suitability evaluation, thereby reducing bias and improving ranking stability. Data from 100 students across four universities indicate that security dominates (46%), followed by convenience & access (25%), and features & cost (29%), indicating that risk reduction and trust are key adoption factors, in line with technology acceptance theory. OVO achieved the highest score. The hybrid framework reduces subjective bias in ideal-value assignment and improves ranking stability compared to standalone AHP or Profile Matching applications. These findings provide methodological contributions and practical implications for fintech providers.
Copyright (c) 2026 Rahma Aulia, Ismail Husein, Rima Aprilia http://creativecommons.org/licenses/by-sa/4.0
Comparison of Pure Premiums for Motor Vehicle Insurance Using ZTP-Gamma GLM and Tweedie GLM
The increasing number of motor vehicles has contributed to higher traffic density and a greater risk of accidents, thereby reinforcing the importance of protection through motor vehicle insurance. Therefore, accurately determining the pure premium is essential to maintain risk balance and ensure the sustainability of insurance companies. This study employs Generalized Linear Models, which are an extension of classical linear regression that allow the response variable to follow non-normal distributions, particularly the Zero-Truncated Poisson, Gamma, and Tweedie distributions. Using motor vehicle insurance claim data from 2022 with 386 observations, this research compares two premium modeling approaches, namely the ZTP–Gamma model for estimating claim frequency and claim severity, and the Tweedie GLM for modeling total claims in the calculation of pure premiums for motor vehicle insurance. The analysis shows that the estimated pure premiums for the ZTP–Gamma GLM range from IDR 2,138,532 to IDR 19,939,391, while the estimates for the Tweedie GLM range from IDR 2,153,665 to IDR 20,936,047. The ZTP–Gamma GLM demonstrates better accuracy, with a MAPE value of 23.65% compared to 25.844% for the Tweedie GLM, resulting in an accuracy difference of 2.194%. These findings indicate that the ZTP–Gamma GLM is more effective in producing accurate pure premium estimates.
Copyright (c) 2026 Yushinta Cahya Lestari http://creativecommons.org/licenses/by-sa/4.0
Smart Packaging from Durian Seed Starch for Real-Time Quality Classification using DenseNet-121
This study used smart packaging made from durian seed starch with butterfly pea flower extract and applied the DenseNet121 deep learning model for real-time quality classification. Colorimetric analysis revealed a significant transition from Hue ~92° to Hue ~289° as food quality deteriorated due to pH changes. This study aimed to introduce a non-destructive vision-based classification framework utilizing the DenseNet121 deep learning architecture to demonstrate its effectiveness as a real time food freshness monitor. The dataset was divided into 70% training set, 20% validation set, and 10% test set to ensure robust model development. Performance was evaluated using accuracy, precision, recall, and F1 score. This methodology integrated physicochemical (pH) analysis with the development of a DenseNet121 architecture based Deep Learning model to classify food freshness phases. The results showed that edible films derived from durian seed starch and butterfly pea flower extract were capable of being indicators of food freshness. The dataset consisted of 160 images captured during a 12day experiment, which was expanded using stochastic data augmentation to improve model generalization. Computationally, the model achieved convergence with a training accuracy of 96% with loss 0.14 and achieved an internal testing accuracy of 0.94. Although testing on an external dataset recorded an accuracy of 0.78 due to environmental variability. This study proposes the first integration of durian seed starch based smart packaging with DenseNet121 architecture for automatic freshness classification of lempuk durian, providing a new approach for continuous food quality monitoring. These findings provide a quantitative basis for the application of applied mathematics and computer vision in sustainable food logistics.
Copyright (c) 2026 Putri Nutriastuti http://creativecommons.org/licenses/by-sa/4.0
Spatial Analysis of Indonesia’s 2019 Provincial Voter Turnout Using Geographically Weighted Regression
This study analyzes spatial heterogeneity in voter behavior using the Geographically Weighted Regression (GWR) model, estimated via GWR 4.0 software to ensure reproducibility. Using 2019 provincial-level data, we compare an OLS model against GWR to evaluate the mean voter turnout across Indonesia’s concurrent elections. The GWR model significantly improved estimation performance, evidenced by a reduction in AICc from -140.960 to -146.581 and an increase in Adjusted R² from 36.48% globally to a local range of 65.30%–82.60%. Statistical testing via F-statistic yielded a p-value of 0.0633, significant at the 10% level acceptable given the sample size (n=34). Findings reveal significant spatial non-stationarity: the Gini ratio shows a pervasive positive mobilization effect, while education and infrastructure display region-specific impacts, with infrastructure accessibility strongly influencing turnout in eastern Indonesia. These results underscore the mathematical necessity of incorporating geographic variance into predictive electoral models to capture localized socio-political dynamics.
Copyright (c) 2026 Ernawati Pasaribu, Arya Candra Kusuma, Ega Eugenia Naomi, Firman Emmanuel Declarantius Parulian http://creativecommons.org/licenses/by-sa/4.0
The Mediation Effect of Community Empowerment and Good Governance on Forest Productivity: A GSCA Approach
This study examined how transglobal leadership influenced forest productivity in Indonesia’s community plantation forest program, focusing on the mediating roles of community empowerment and governance. Secondary data from 50 regencies, selected from a population of 127, were analyzed using a Generalized Structural Component Analysis (GSCA) with the mediation testing. The results showed that leadership significantly affected community empowerment and governance, but did not directly influence forest productivity, while both mediating variables had significant positive effects on productivity. The indirect effects accounted for 77.8% of the total effect, indicating that leadership operated primarily through intermediary mechanisms. The model demonstrated satisfactory fit, with FIT = 0.612, AFIT = 0.587, and GFI = 0.93, suggesting adequate explanatory power despite the relatively small sample size. These findings indicated that improvements in forest productivity were achieved through strengthened governance systems and enhanced community capacity, highlighting the importance of integrated institutional and participatory policy interventions.
Copyright (c) 2026 Bambang Hendroyono http://creativecommons.org/licenses/by-sa/4.0
A Decision Support System for Selecting Beneficiaries of the Free Nutritious Meal Program Using Fuzzy Possibilistic C-Means
The Free Nutritious Meal Program (MBG) aims to improve students’ nutritional status, but beneficiary selection is challenged by data uncertainty and overlapping criteria. This study proposes a decision support system based on the Fuzzy Possibilistic C-Means (FPCM) algorithm. The dataset consists of 200 students from Bojonegoro Regency using five indicators: nutritional status, household income, family size, participation in social assistance, and distance to school. The methodology includes data standardization, clustering using Fuzzy C-Means (FCM) and FPCM, and evaluation using Partition Coefficient, Silhouette Score, and Dunn Index. The results classify students into three groups: 52% not eligible, 18.5% moderately eligible representing borderline cases requiring further verification, and 29.5% eligible. FPCM achieves higher cluster clarity with a Partition Coefficient of 0.84 compared to 0.74 in FCM, while other evaluation metrics indicate comparable structural quality between methods. These findings indicate that FPCM provides a more interpretable and robust framework for decision-making under uncertainty.
Copyright (c) 2026 M. Husen Al Farisy, M. Ivan Ariful Fathoni, Anisa Fitri, Nabila Alisa Rohmah, Siti Nur Laili Zuhri http://creativecommons.org/licenses/by-sa/4.0
Nonlinear Ordinal Logistic Regression and Multivariate Adaptive Regression Splines (NORL-MARS) for Prediction of Diabetes Mellitus Risk
Diabetes Mellitus (DM) is a high-risk metabolic disease with increasing prevalence in Indonesia, requiring an effective classification model based on significant risk factors. This study uses Nonparametric Ordinal Logistic Regression based on the Multivariate Adaptive Regression Spline estimator (NOLR-MARS). Unlike conventional parametric ordinal regression, this model does not assume a fixed functional pattern but rather determines the form of the relationship based on data patterns through basis functions, making it more flexible in handling complex predictor variable interactions. Using 664 records from the Non-Alcoholic Fatty Liver Disease (NAFLD) cohort, we explore the relationship between metabolic factors, included age, sex, Body Mass Index (BMI), LDL cholesterol, and hypertension—and DM risk. This NOLR-MARS integration addresses the nonlinear relationship while maintaining the ordinal nature of DM stages, a combination often overlooked in traditional models. Based on Generalized Cross Validation (GCV) selection, the best model achieved 74.92% accuracy for in-sample data and 80.30% for out-sample data. Furthermore, a sensitivity of 70% and a specificity of 92.86% were obtained for stage 2 DM. Factors such as age, BMI, LDL cholesterol, and hypertension significantly influenced DM status. The results showed that the NORL-MARS model had good predictive performance. The novelty of this study lies in the integration of the MARS estimator into an ordinal logistic regression framework for more granular DM risk assessment. Although this model shows potential as a screening tool in high-risk metabolic cohorts, further clinical application requires external validation to ensure broader generalizability.
Copyright (c) 2026 Any Tsalasatul Fitriyah, Maylita Hasyim, Nur Chamidah, Toha Saifudin, Vita Fibriyani http://creativecommons.org/licenses/by-sa/4.0
Transmission Dynamics Model of Scabies in Islamic Boarding Schools
Scabies continues to pose a major public health challenge in densely populated congregate settings such as Islamic boarding schools (pesantren) in Indonesia. This study develops a stage structured - - - compartmental model (Susceptible, Early-stage Infected, Late-stage Infected, Recovered) that explicitly accounts for differences in mite burden, infectivity, and recovery rates between early and late-stage infections. Using qualitative analysis of the nonlinear differential equations, the basic reproduction number ( ) was derived via the Next Generation Matrix method, and stability analysis was performed. Results show that the diseasefree equilibrium is locally and globally asymptotically stable when . Under baseline parameters, , with late-stage infections accounting for approximately 88.3% of total transmission. Due to the model’s assumptions of a closed population and permanent immunity, no biologically meaningful endemic equilibrium exists; once the infection runs its course, the disease eventually dies out as susceptibles are exhausted. Sensitivity analysis highlights that reducing the late-stage transmission rate ( ) and increasing the early-stage recovery rate ( ) are the most effective intervention targets. This model provides a rigorous theoretical framework to guide evidencebased scabies control strategies in high-density residential institutions.
Copyright (c) 2026 David Prasetyo http://creativecommons.org/licenses/by-sa/4.0
Exponent and Scrambling Index of Some Composite Graphs
A connected graphs G is primitive provided there is a positive integer k such that for each pair of vertices u and v in G there exists a uv-walk of length k. The scrambling index of a primitive graph G, , is the smallest positive integer k such that for each two vertices u and v there is a vertex w with the property that there exist a uw-walk and a vw-walk of length k. We discuss the scrambling index of the joint and the corona product of two vertex disjoint graphs. For such graphs, we discuss their primtivity and then we present their scrambling index.
Copyright (c) 2026 Linna Syahputri, Saib Suwilo, Mardiningsih Mardiningsih http://creativecommons.org/licenses/by-sa/4.0
Robustness Evaluation of ANFIS, Hybrid GA-SVM, and SVM under Controlled Time Series Structures
This study evaluates the robustness of ANFIS, hybrid GA-SVM, and SVM under synthetic time-series structures using a factorial simulation framework combined with empirical validation. From a practical perspective, robust coal price forecasting is essential for supporting energy planning, trade management, and policy decision-making under uncertain market conditions. Empirical analysis of Indonesian coal prices reveals nonstationary behaviour, high volatility, and nonlinear dynamics. Forecasting performance is assessed using walk-forward validation, where SVM and hybrid GA-SVM demonstrate comparable accuracy and outperform ANFIS on the empirical dataset. To systematically examine model sensitivity to structural variations, a factorial simulation design is implemented by varying seasonality, volatility, and predictor–response structure across 12 scenarios with 100 replications each. The results indicate that volatility is the most dominant factor affecting forecasting error, with significant interaction effects among structural factors. ANOVA and post hoc analysis further confirm that model performance depends more on data characteristics than on algorithmic complexity. These findings demonstrate that factorial simulation provides a systematic and robust framework for evaluating forecasting models beyond conventional empirical comparisons, while offering deeper insight into the relationship between data structure and model performance.
Copyright (c) 2026 Sri Kustiara Kustiara, Kusman Sadik, Hari Wijayanto http://creativecommons.org/licenses/by-sa/4.0