OPTIMASI PORTOFOLIO MEAN ABSOLUTE DEVIATION MENGGUNAKAN METODE SIMPLEKS DUA FASE PADA JAKARTA ISLAMIC INDEX - Visna Mutiara Rahma; Werry Febrianti; Triyana Muliawati (MATHunesa: Jurnal Ilmiah Matematika, 2026)
Investment is the activity of allocating capital to issuers with the aim of generating profits. Investment in the Islamic capital market is becoming increasingly popular, and to manage risk, investors need to construct an optimal portfolio. This study aims to optimize the portfolio of Sharia-compliant stocks listed in the Jakarta Islamic Index (JII) using the Mean Absolute Deviation (MAD) model. The MAD model is formulated as a linear programming problem and is solved using LINGO software version 15.0 as well as the two-phase simplex method manually. Both approaches produced identical results. Portofolio optimization involving 5 stocks, the investment weights are evenly distributed at 20% among MEDC, BRMS, BRIS, ADRO, and MDKA stocks, with a portfolio risk of 0.02241 and a portfolio return of 0.00102. Portofolio optimization involving 10 stocks, each stock receives a 10% allocation, with a portfolio risk of 0.02085 and a portfolio return of 0.00074. Portofolio optimization involving 15 stocks portfolio assigns 6.7% to most stocks and 6.2% to MEDC, with a portfolio risk of 0.02042 and a portfolio return of 0.00052. The best performance, with a Sharpe index of 0.04569, is achieved in the five-stock portfolio. The results demonstrate the effectiveness of the MAD model in optimizing Sharia-compliant stock portfolios.