Metric Space Based Product Portfolio Optimization for MSMEs Using Genetic Algorithm

Desi Vinsensia, Yulia Utami, Andika Pandu Ramadhan, Nabila Shayka

Abstract

Micro, Small, and Medium Enterprises (MSMEs) face capital allocation challenges across multi-category product portfolios in the digital era, while the classical Mean-Variance Optimization (MVO) model exhibits structural limitations due to normality assumptions, estimation instability on small samples, and its inability to capture more than two risk dimensions. This study developed and validated an MSME product portfolio optimization model based on metric space theory and genetic algorithm, capable of handling multidimensional operational risk and cardinality constraints. A weighted distance function was constructed on a three-dimensional feature space comprising contribution margin (?), sales coefficient of variation (?), and Margin of Safety (MOS). Metric space validity was proved deductively through verification of non-negativity, symmetry, and triangle inequality axioms. The genetic algorithm was designed with a three-step repair operator to satisfy allocation and cardinality constraints. The model was validated using secondary data from 10 product categories over a six-month period (April–September 2025) and benchmarked against Equal Weighting (EW) and MVO strategies. Formal proof and empirical verification on 1,000 data triplets yielded zero axiom violations. The genetic algorithm achieved the highest fitness value (0.71798), outperforming EW by 10.3% and MVO by 18.6%. The optimal portfolio selected four products: paper (28.2%), books (21.8%), measuring tools (29.0%), and electronics (20.9%), geometrically explained by inter-product distances in the distance matrix. The proposed model is mathematically rigorous and computationally superior in the validation case. Although constituting a proof-of-concept on a single secondary dataset, this framework offers potential for development into an MSME capital allocation decision support system

Source: semanticscholar · PDF

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