Bulletin of Applied Mathematics and Mathematics Education

Shopping pattern segmentation: HAC versus K-Means performance analysis

2025-10-06T16:10:09+00:00

Despite widespread use in consumer analytics, clustering techniques remain underutilized for analyzing household basic food commodity consumption patterns, particularly for developing localized retail strategies and targeted food security policies in resource-constrained contexts. This study addresses this practical gap by systematically comparing Hierarchical Agglomerative Clustering (HAC) and K-Means performance on essential consumption patterns across seven commodities: bread, vegetables, fruit, meat, poultry, milk, and wine. Using dual validation metrics, Silhouette Coefficient and Davies-Bouldin Index, we evaluate clustering effectiveness specifically for small-scale household datasets typical of regional food policy environments. HAC demonstrated superior cluster stability (Silhouette score = 0.2936, DBI = 0.8977) compared to K-Means (0.2912, 0.9871), enabling identification of three actionable consumption segments, namely budget-conscious households with economical protein consumption, high spender households with premium patterns across categories, and balanced/selective households preferring bread and wine. These empirically-derived segments provide implementable frameworks for food subsidy targeting, inventory optimization in local retail contexts, and nutrition intervention program design. The findings demonstrate that methodologically rigorous clustering analysis yields policy-relevant household segmentation even with constrained data, offering practical guidance for evidence-based food security interventions where basic commodity consumption directly informs resource allocation decisions.

Optimizing stock allocation and profit in MSMEs: Multiple constraints bounded Knapsack model solved using Grey Wolf Optimizer algorithm

2025-10-16T02:05:26+00:00

Effective inventory management is a determining factor in the probability and sustainability of micro, small, and medium enterprises (MSMEs). Adjusting the ideal stock of each product type that has to be distributed while taking perishable items, storage capacity constraints, and client demand unpredictability into account is a difficulty. Stock allocation must maximize profit while adhering to intricate constraints and particular item number limitations in the multiple-constraints Knapsack problem. This research aims to apply the Grey Wolf Optimizer (GWO) algorithm to the multiple constraints bounded Knapsack problem for optimal stock allocation while increasing profitability for MSMEs by comparing the ideal value of the simplex technique. The population parameter (Npop) and the maximum iteration (Max Iter) were the two parameters used to test the GWO method. According to sensitivity analysis, the GWO algorithm optimization study was less successful in producing the best outcomes. This resulted from a discrepancy between the simplex method's IDR 9,508,000 profit optimization and GWO's IDR 9,440,000. Nonetheless, the GWO method was almost ideal, as indicated by the deviation percentage of 0.7152%. The study highlights the applicability of metaheuristic optimization for MSME management inventory, offering a near-optimal solution with minimal deviation from analytical results. Limitations include the single-case scope and parameter sensitivity of the GWO algorithm.

Classification of weather events in Lahat regency using the K-Nearest Neighbor method

2025-11-27T02:09:59+00:00

Weather event classification in a region is very important for various purposes, such as in the fields of transportation, health, agriculture, and others. Lahat has varying land elevations ranging from 26-106 meters above sea level in the East Merapi sub-district to 341-3032 meters above sea level in the Tanjung Sakti Pumi sub-district. It greatly affects local temperature, rainfall, and atmospheric pressure, which in turn affects the distribution of weather patterns and disasters such as floods. KNN is a prediction method that uses the concept of distance for a number of k nearest observations in determining the similarity between observations. Several metrics can be used for this prediction purpose. This study aims to predict weather events in Lahat Regency using the KNN method with several different distance metrics and then compare them to obtain the performance of the KNN prediction method. The results show that the Euclidean distance metric used in the KNN method has a better performance measurement, followed by the Manhattan and Minkowski metrics. In the Euclidean metric, the accuracy, precision, recall, f1-score, AUC, and MC value are 92.69%, 88.21%, 85.81%, 86.99%, 88.99%, and 76.37%, respectively.

Mathematical Model of Social Media Addiction: An Optimal Control Approach

2025-11-25T05:13:00+00:00

In this study, we developed a deterministic mathematical model to analyze social media addiction, incorporating an optimal control strategy. The basic model captures the dynamics through which individuals become exposed to and eventually addicted to social media platforms. To enhance the model, we introduced two time-dependent control variables: one representing awareness campaigns through advertising and education, and the other representing treatment interventions for individuals suffering from addiction. An optimal control framework was then formulated based on these interventions. By applying Pontryagin’s Minimum Principle, we derived the necessary conditions for optimality and constructed the corresponding optimality system. Numerical simulations of the optimal control problem were conducted using the forward-backward sweep method to assess the effectiveness of the proposed strategies. The results demonstrate that the integrated control strategy—combining public awareness efforts with treatment interventions— substantially reduces the number of individuals exposed to and addicted to social media. Compared to scenarios without intervention, the number of affected individuals was significantly lower. These findings underscore the importance of implementing combined strategies rather than isolated measures. Therefore, this integrated approach is strongly recommended for policymakers and stakeholders as a practical and effective means to mitigate the adverse effects of social media addiction on public health and societal well-being..

Keywords: Social Media Addiction, Mathematical Model, Pontryagin Minimum Principle, Optimal Control.