Metric Space Based Product Portfolio Optimization for MSMEs Using Genetic Algorithm

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

doi:10.47709/cnahpc.v8i3.9259

Authors

Desi Vinsensia Digital Bisnis, STMIK Pelita Nusantara Medan, Indonesia
Yulia Utami Informatic Enggeneering, STMIK Pelita Nusantara Medan, Indonesia
Andika Pandu Ramadhan Digital Bisnis, STMIK Pelita Nusantara Medan, Indonesia
Nabila Shayka Digital Bisnis, STMIK Pelita Nusantara Medan, Indonesia

DOI:

https://doi.org/10.47709/cnahpc.v8i3.9259

Keywords:

Metric space; Genetic algorithm; MSME portfolio; Margin safety; Cardinality constraint

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

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References

[1] Badan Pusat Statisrtik, “Selamat Hari UMKM Nasional,” Badan pusat Statistik.

[2] We are social, “Digital 2024: Indonesia,” Digital 2024: Indonesia. [Online]. Available: https://wearesocial.com/id/blog/2024/01/digital-2024/

[3] B. Lamanauw and I. R. A. Lalowang, “Exploring Strategic Financial Management Techniques in Entrepreneurship: A Detailed Literature Review on Practices That Drive Business Sustainability and Growth,” Atestasi J. Ilm. Akunt., vol. 7, no. 2, pp. 1111–1132, 2024, doi: 10.57178/atestasi.v7i2.900.

[4] C. Mohit Bahal, M. Mittal, R. Kumar Singh, G. Gulyani, and N. Sheoliha, “The Impact of Working Capital Management on Profitability in Small and Medium Enterprises (SMEs),” Adv. Consum. Res., vol. 2(4), no. 4, pp. 4408–4417, 2025, [Online]. Available: https://acr-journal.com/article/the-impact-of-working-capital-management-on-profitability-in-small-and-medium-enterprises-smes--1541/

[5] R. N. Husna, L. Syafina, Y. Samri, J. Nasution, M. O. Safety, and P. Laba, “Analisis bep dan mos sebagai alat perencanaan laba pada umkm di toko berlian pancing,” J. Manaj. Terap. dan Keuang., vol. 13, no. 03, pp. 772–782, 2024.

[6] D. ?lusarczyk and R. ?lepaczuk, “Optimal Markowitz portfolio using returns forecasted with time series and machine learning models,” J. Big Data, vol. 12, no. 1, p. 127, 2025, doi: 10.1186/s40537-025-01164-z.

[7] G. Cornuéjols, Ö. Elç?, and V. Patil, “Addressing estimation errors on expected asset returns through robust portfolio optimization,” Quant. Financ., vol. 26, no. 1, pp. 85–98, Jan. 2026, doi: 10.1080/14697688.2025.2606114.

[8] Y. Du, W. He, and X. Mei, “Portfolio optimization with estimation errors—A robust linear regression approach,” J. Empir. Financ., vol. 82, p. 101619, 2025, doi: https://doi.org/10.1016/j.jempfin.2025.101619.

[9] Y. Liu, “The Efficacy of Advanced Covariance Estimators in Constrained Global Minimum Variance Portfolio Optimization: An Empirical Analysis of the S&P 100,” Adv. Econ. Manag. Polit. Sci., vol. 240, pp. 239-249., 2025, doi: https://doi.org/10.54254/2754-1169/2025.BL29590.

[10] L. R. Goldberg, H. Gurdogan, and A. Kercheval, “Portfolio optimisation via strategy-specific eigenvector shrinkage,” Financ. Stochastics, vol. 29, no. 3, pp. 665–706, 2025, doi: 10.1007/s00780-025-00566-4.

[11] M.-L. Torrente and P. Uberti, “Risk-adjusted geometric diversified portfolios,” Qual. Quant., vol. 58, no. 1, pp. 35–55, 2024, doi: 10.1007/s11135-023-01631-w.

[12] G. Marti, F. Nielsen, M. Bi?kowski, and P. Donnat, “A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets,” 2021, pp. 245–274. doi: 10.1007/978-3-030-65459-7_10.

[13] D. C. Fransisca, Sukono, D. Chaerani, and N. A. Halim, “Robust Portfolio Mean-Variance Optimization for Capital Allocation in Stock Investment Using the Genetic Algorithm: A Systematic Literature Review,” Computation, vol. 12, no. 8. p. 166, 2024. doi: 10.3390/computation12080166.

[14] Y. S. Kristianto et al., “Analisis Komparatif Titik Impas ( BEP ) Penjualan Offline dan Online sebagai Dasar Penentuan Strategi Profitabilitas Pada PD . Sinar Mas Stationery ATK Bekasi,” vol. 3, no. 7, pp. 109–127, 2026.

[15] G. Marti, F. Nielsen, M. Bi?kowski, and P. Donnat, “A Review of Two Decades of Correlations, Hierarchies, Networks and Clustering in Financial Markets BT - Progress in Information Geometry: Theory and Applications,” F. Nielsen, Ed., Cham: Springer International Publishing, 2021, pp. 245–274. doi: 10.1007/978-3-030-65459-7_10.

[16] J. R. Munkres, Topology (2 end ed). Prentice Hall, 2000. [Online]. Available: https://eclass.uoa.gr/modules/document/file.php/MATH707/James R. Munkres Topology Prentice Hall%2C Incorporated%2C 2000 by James R. Munkres %28z-lib.org%29.pdf

[17] S. Katoch, S. S. Chauhan, and V. Kumar, “A review on genetic algorithm: past, present, and future.,” Multimed. Tools Appl., vol. 80, no. 5, pp. 8091–8126, 2021, doi: 10.1007/s11042-020-10139-6.

[18] K.-C. Ying, P. Pourhejazy, and K.-Y. Chen, “Revisiting the evolution of genetic algorithms in scheduling,” Appl. Soft Comput., vol. 201, p. 115602, 2026, doi: https://doi.org/10.1016/j.asoc.2026.115602.

[19] B. Subramanian, A. Paul, J. Kim, and K.-W.-A. Chee, “Metrics Space and Norm: Taxonomy to Distance Metrics,” Sci. Program., vol. 2022, no. 1, p. 1911345, Jan. 2022, doi: https://doi.org/10.1155/2022/1911345.

[20] C. Coello, “Coello, A.C.: Theoretical and Numerical Constraint-Handling Techniques Used with Evolutionary Algorithms: A Survey of the State of the Art. Comput. Methods Appl. Mech. Engrg. 191(11-12), 1245-1287,” Comput. Methods Appl. Mech. Eng., vol. 191, pp. 1245–1287, Jan. 2002, doi: 10.1016/S0045-7825(01)00323-1.

[21] V. Puican Rodriguez, R. LÓPEZ, and W. Vera, “Innovations in Inventory Management to Improve the Profitability of Local SMEs,” F1000Research, vol. 14, p. 853, Nov. 2025, doi: 10.12688/f1000research.168900.3.

[22] M. Kaucic, M. Moradi, and M. Mirzazadeh, “Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures,” Financ. Innov., vol. 5, Dec. 2019, doi: 10.1186/s40854-019-0140-6.