Stochastic scheduling addresses several forms of uncertainty to represent better production environments in the real world.Stochastic scheduling has applications on several areas such as logistics, transportation, production, and healthcare, among others.This paper aims to evaluate the performance of various greedy functions for a GRASP-based approach, under stochastic processing times.Since simulation is used for estimating the objective function, two simulation techniques, Monte Carlo simulation and Common Random Numbers (CRN), are used to compare the performance of different greedy (utility) functions within the GRASP.In order to validate the proposed methodology, the expected total weighted tardiness minimization for a single machine problem was taken as case study.Results showed that both, CRN and Monte Carlo, are not statistically different regarding the expected weighted tardiness results.However, CRN showed a better performance in terms of simulation replications and the confidence interval size for the difference between means.Furthermore, the statistical analysis confirmed that there is a significant difference between greedy functions.