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CLUSTER ANALYSIS OF K-MEANS AND WARD METHOD IN FORMING A ROBUST PORTFOLIO: AN EMPIRICAL STUDY OF JAKARTA ISLAMIC INDEX Zain, Zuva Amalina; Mussafi, Noor Saif Muhammad; Supandi, Epha Diana
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss1pp537-546

Abstract

Building a portfolio is one method of reducing investment risk. Cluster analysis can shorten the time required to choose companies for a portfolio because it makes it easy to put firms in the same category together. To maintain the best state of the portfolio cluster analysis in the case of data containing outliers, K-means, and ward cluster analysis are employed in conjunction with a robust portfolio strategy. K-means clustering is a popular method for grouping data by assigning observations to clusters based on proximity to the cluster’s center meanwhile the Ward method is based on the size of the distance between clusters by minimizing the number of squares. This study seeks to determine the robust portfolio performance comparison outcomes produced by K-Means and Ward clustering utilizing the Sharpe ratio criterion. The Sharpe ratio is one of the most widely used methods to evaluate a portfolio’s risk-adjusted performance. The greater a portfolio's Sharpe ratio, the better its risk-adjusted performance. Stocks included in the Jakarta Islamic Index 70 (JII70) are used in this research. The results of the formation of a robust portfolio on K-Means clustering produce a return rate of 0.01038627 and risk of 0.1066364, while in the Ward cluster, the portfolio profit rate is obtained at 0.01632749 and the risk is 0.1340073. Based on the Sharpe ratio criteria, in this case, the robust portfolio with the Ward cluster is superior to the K-Means cluster because it produces a higher Sharpe value.
Distribution Route Optimization of Zakat Al-Fitr Based on the Branch-and-Bound Algorithm Mussafi, Noor Saif Muhammad
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 1 (2023): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i1.10375

Abstract

The short interval between the collecting and distribution of zakat al-fitr is a recurring issue. As a result, ‘amil does not always pay attention to the ideal route, leading in inefficient transportation expenditures. This study aims to minimize the amount of vehicle mileage that affects fuel consumption. The branch-and-bound algorithm was employed to overcome the distribution route optimization problem by proposing the shortest circuit that traverses each district exactly once and returns to its original district. The procedures involve data collecting, graph analysis, branch-and-bound analysis, MATLAB code development, and the recommendation of the best route. The results indicate that the branch-and-bound algorithm can numerically solve the distribution route optimization corresponding to traveling salesman problem. Furthermore, according to a case study of zakat al-fitr distribution conducted by Eradication of Illiteracy Al Quran (PBHA), the total optimal distance of the computational-based algorithm was 152.9 km, with inter-village routes starting from Sidorejo and then via Sumberarum, Pendoworejo, Gerbosari, Banjaroyo, Banjarasri, Sendangagung, Tuksono, Argodadi, Triwidadi, Jatimulyo, Giripurwo, and ends in Sidorejo.