## 1 Introduction
Currently, the modeling methods for workshop production scheduling can be categorized into four main types: queuing theory models, disjunctive graph models, Petri net models, and mathematical programming models. The core premise of the first three types of modeling approaches is to utilize tools such as graph models to map the workshop's topological structure or the logic of scheduling operations. This allows for the description and evaluation of workshop scheduling based on relevant graph theory analyses. However, these methods primarily focus on describing workshop resources and task information, while the corresponding production scheduling information often involves only simple assignment rules, resulting in significant limitations during practical implementation. In contrast, mathematical programming models represent workshop production factors through model parameters, enabling a more comprehensive description of process- and equipment-related constraints, as well as scheduling optimization objectives. Compared to the aforementioned models, mathematical programming approaches are more adept at capturing the complex process constraints inherent in production environments. Moreover, the parameterized modeling process facilitates the integration of the data characteristics of production parameters into the model. Therefore, this paper adopts mathematical programming methods to model and analyze production systems that incorporate uncertain production parameters. Specifically regarding the FAJSP, [PERSON] et al. provided a comprehensive review of assembly scheduling problems [12]. According to this study, a series of metaheuristic algorithms, represented by tabu search, simulated annealing, genetic algorithms, and particle swarm optimization, are the main methods for solving assembly job shop scheduling problems [13; 14; 15]. [PERSON] et al. [16] studied a two-stage assembly scheduling problem and proposed a discrete particle swarm optimization algorithm. [PERSON] and [PERSON] [17] investigated the assembly job shop scheduling problem with the objective of minimizing makespan and designed a hybrid genetic algorithm and a hybrid particle swarm algorithm. [PERSON] et al. [18] studied a mixed-model assembly shop scheduling problem with batch transfer. They established a mathematical model and designed an enhanced simulated annealingalgorithm to solve the problem. [PERSON] et al. [19] defined the flexible job shop scheduling problem with tree-structure job precedence constraints and designed a shuffled cellular evolutionary gray wolf optimizer. [PERSON] et al. [20] addressed the same problem using a hybrid algorithm. [PERSON] et al. [21] developed a multi-objective optimization algorithm aimed at optimizing both makespan and energy consumption simultaneously. Although the aforementioned studies have proposed effective solutions for various constraints in assembly job shop scheduling problems, research on assembly shop scheduling under uncertain conditions remains very limited. [PERSON] et al. [22] studied a robust scheduling problem involving assembly processes, considering both the product's assembly structure and the uncertainty in processing times. [PERSON] et al. [23] investigated a shop scheduling problem with multi-level assembly structures under processing time uncertainty and designed corresponding surrogate metrics for two different optimization objectives. [PERSON] et al. [3] explored the assembly job shop scheduling problem with uncertain assembly times and developed an adaptive scheduling method based on dual Q-learning. In summary, the flexible job shop scheduling problem with uncertain processing times has not been thoroughly researched to date. Considering the actual production conditions in the workshop, this paper explores the most common and practical interval number representation of processing times. Based on this, we investigate the flexible assembly job shop scheduling problem with uncertain interval processing times. The contributions of this work are included below.