## 1 Introduction  
The flow shop problem (FSP) is a largely studied scheduling problem, as it models a wide set of industrial manufacturing environments [1], such as in the chemical, food-processing, automobile, and assembly industries. The purpose of solving the stated problem lies in determining the best processing sequence from n production jobs to process on m machines placed in series, aiming to optimize one or several KPIs such as the flowtime, makespan, earliness, or tardiness. A permutation flow shop scheduling problem (PFSP), which is an extension case of the PSP, considers only permutation schedules, i.e., the processing sequence of the jobs is the same for all m machines. The PFSP is considered an NP-complete problem for three or more machines [2] and an NP-hard problem for one or more machines when minimizing tardiness [3]. Furthermore, this problem augments the complexity when the uncertainty is considered for its resolution. From several approaches, a preliminary approach for tackling the stochastic permutation flow shop problems is elaborating a systematic procedure that includes uncertainties within the scheduling problems [4]. In fact, the scheduling problem and the associated complexity could be as important for designing a proper systematic technique to solve these problems [4]. After analyzing the literature on the FSP and PFSP, four aspects should be highlighted. At first, a set of approaches in the literature considers a single performance indicator as the objective function. The most common approaches are related to the makespan, due date, or just-in-time characteristics. The makespan or the expected makespan indicator, which is an absolute performance indicator, focuses on minimizing the lapsed time from the start to the end of the execution [5; 6]. The due date indicator, which is a relative performance indicator, compares the objective function regarding the expected processing completion. The just-in-time indicator, which is an accuracy performance indicator, indicates the positive or negative deviation occurring from an expected completion time. Certainly, the use of each performance indicator depends on the aim from the scheduling perspective. Second, another set of approaches is focused on single-objective problems rather than multicriteria problems. Certainly, even industrial problems must solve various objectives simultaneously [7], and researchers have focused on optimizing a single objective function rather than multiple ones. This issue can be addressed by considering earliness and tardiness objectives jointly in a JIT environment. Third, most studies consider only quantitative decision criteria. However, researchers have recently become interested in qualitative criteria as this approach might reduce the gap between the theoretical concept of problems and the execution. Some examples are [PERSON] and [PERSON] [8] and [PERSON] et al. [9]. These authors studied a multicriteria job shop, whereas the customers' strategic importance was considered as a qualitative criterion. While [PERSON] and [PERSON] [8] proposed a hybridized genetic algorithm, tabu search, analytic hierarchy process, and fuzzy theory to solve the problem, [PERSON] et al. [9] proposed a hybridization of an ant colony algorithm and an analytic hierarchy process for solving the FSP. Another approach minimized the expected costs of tardiness as a quantitative criterion and strategic customer importance as a qualitative criterion in a stochastic hybrid FSP [10]. The authors employed a GRASP metaheuristic and a Monte Carlo simulation method with a stochastic multicriteria acceptability analysis to handle both qualitative and quantitative criteria.