Mathematical Modeling and Simulation of Multi-Stage Service Systems with Feedback, Group Service, and Prioritization

This study aims to analyze the mediation effect of land area on the relationship between price and productivity on oil palm farmers’ income in Bangko Pusako District, Rokan Hilir Regency. A quantitative approach using Structural Equation Modeling-Partial Least Squares (SEM-PLS) method was employed to analyze data from 155 oil palm farmers selected through accidental sampling technique. The results show that palm oil prices and productivity do not have significant direct effects on farmers’ income. However, land area proves to have a significant direct effect on farmers’ income (T-statistic = 2.208, p-value = 0.028). Mediation analysis reveals that palm oil prices significantly affect income through land area mediation (T-statistic = 2.112, p-value = 0.035), while productivity does not significantly affect income through land area mediation (T-statistic = 1.611, p-value = 0.108). These findings confirm the important role of economies of scale in oil palm farming, where farmers with large land areas have comparative advantages in utilizing market price fluctuations. This research provides theoretical contributions to the development of farmer income analysis models and practical inputs for formulating more effective and targeted oil palm farmer empowerment policies.