## 1 Introduction
Finally, some research approaches consider scheduling under uncertain conditions, and these are generally divided into two approaches: the stochastic approach, in which parameters are modeled with probability distributions (PDs) aiming to minimize the expected value of a selected metric, and the robust approach (RA), in which uncertain parameters are modeled with intervals and the schedule obtained is more stable and less variable. Nonetheless, previous studies have not dealt with a combination of stochastic and robust approaches for solving the flow shop problem. Companies can collect production data in a short time, yielding enough data to accurately estimate the probability distribution of uncertain parameters. Then, we believe that the latter approach leverages the robust schedule as it can be more easily adjusted than other schedules in which uncertainties are modeled with intervals. One of the recent approaches to solve stochastic combinatorial optimization problems is simheuristics. These hybridize a metaheuristic approach with a simulation to obtain solutions for stochastic problems. Simheuristics have been successfully used in vehicle routing problems [11; 12; 13], inventory routing problems [14], facility location problems [15], and scheduling problems [16; 17; 18; 19]. In this sense, this paper attempts to contribute to the literature by proposing a systematic technique for solving the stochastic permutation flow shop problem (SPFSP) considering stochastic processing times and sequence-dependent setup times to optimize multiple criteria. To the best of our knowledge, no previous study has included the simultaneous analysis of a JIT environment with stochastic parameters, quantitative metrics, and qualitative metrics for obtaining robust solutions. Therefore, the current research proposes a multicriteria simheuristic approach to solve an SPFSP, including both quantitative and qualitative objectives, providing robust solutions. On the one hand, for quantitative objectives, the proposed approach addresses the expected earliness/tardiness (E[E/T]) and the standard deviation of earliness/tardiness (SD(E/T)), for estimating the JIT metrics and obtaining several robust schedules. On the other hand, as qualitative metrics, this research considers the expected customer importance of jobs (E[CI]) and the expected product importance (E[PI]), favoring the job priority for the company. Then, this paper considers both customer and product importance as a company might be more interested in delivering high-profitability products regardless of the customer or, conversely, it might be more interested in delivering frequently with high-spending customers rather than sporadic ones. This paper is an extension of a previous conference work [20] that only considered one qualitative criterion and solved a partial set of benchmark instances. This work includes one more qualitative criterion (the maximization of the accomplishment of product importance) and executes more computational experiments by evaluating 180 instances proposed by [21] and analyzing the behavior of Pareto frontiers with more coefficients of variation of processing times and sequence-dependent setup times. The remainder of this paper is organized as follows. Section 2 presents a literature review of the single-objective stochastic FSP (SFSP), robust FSP, and multi-objective SFSP. Section 3 describes the proposed solution for the SPFSP under qualitative and quantitative decision criteria. Section 4 provides the results of the computational experiments that validate the proposed approach. Finally, conclusions and recommendations for future work are presented in Section 5.