Shopping pattern segmentation: HAC versus K-Means performance analysis

Nur Arina Hidayati — 2025-10-08

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

Mufarrida Dalilah — 2025-10-29

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.

Bulletin of Applied Mathematics and Mathematics Education

Shopping pattern segmentation: HAC versus K-Means performance analysis

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