The aim of this paper is to present a simheuristic approach that obtains robust schedules for a multi-objective permutation flow shop problem with stochastic processing times. In fact, this approach minimizes the expected tardiness and standard deviation of tardiness, as a efficiency and a robustness measure for the stated problem. The simheuristic algorithm hybridize the Tabu Search metaheuristic and the Pareto Archived Evolution Strategy algorithm with a Monte Carlo Simulation process. At first, this approach is tested in 540 benchmarked instances for the deterministic case. It uses a zero-standard-deviation strategy to show the competitiveness compared with other implemented tabu search algorithms. Afterwards, two experimental designs are carried out, with the same 540 instances, where two factors of interest are considered, such as the probability distribution and coefficient of variation of processing times. The probability distributions used were the lognormal and uniform distributions, and three coefficients of variation (0.3, 0.4, and 0.5). Results show that both probability distributions and coefficients of variation have a significant effect in the objective functions, showing the importance of an accurate fitting of probability distributions of the parameter under uncertainty. In addition, these results evidence that the usage of deterministic methods in presence of random events are not desirable or recommended. Finally, the simheuristic was implemented to solve the scheduling problem in an optical laboratory showing better results for expected tardiness and standard deviation of tardiness in comparison with company schedules.