Analisis Sensitivitas Bobot Kriteria dan Stabilitas Peringkat pada Metode TOPSIS Menggunakan Simulasi Monte Carlo

Abstract

TOPSIS rankings depend on criteria weights, which are often uncertain. This study measures how stable TOPSIS rankings remain when weights vary in a controlled manner. A simulation experiment was conducted on a decision matrix of 100 alternatives with three benefit and two cost criteria generated in Python (fixed seed). A total of 5,000 weight scenarios were drawn from Dirichlet distributions at three levels of uncertainty: narrow and moderate around the base weights, and broad (uniform over the simplex). Stability was measured at the level of the overall order (Spearman and Kendall τ_b), the top ranks, and individual alternatives, and its robustness was tested with 20 dataset replications across three correlation structures and four numbers of alternatives. On the main dataset, mean τ_b fell from 0.894 (narrow) to 0.796 (moderate) and 0.525 (broad), while the top-ten overlap fell from 90.5% to 80.3% and 49.8%. Instability was greatest in the middle ranks, and criteria with high data dispersion were more influential than heavily weighted criteria with low dispersion. Trade-off data consistently reduced stability, while the robustness of the first rank was driven mainly by the preference-score gap between the two leading alternatives. The study contributes a reproducible simulation protocol and an explicit separation of global, top-rank, and per-alternative stability in reporting TOPSIS sensitivity analysis.