## 1 Introduction  
Current market trends, the variety of consumer demand, the short life cycle of the product, and competitive pressure have pushed companies to tackle the problem of reduction of production costs through better management of available resources. One fundamental tool is represented by the scheduling algorithms for the optimization of production [1]. Scheduling problems are decision-making problems in which the factor of time is of fundamental importance, understood as a (scarce) resource to be allocated in an optimal way [2]. In the context of industrial manufacturing, scheduling consists in determining the sequential allocation of jobs to the machines, which optimizes a certain objective function and respects at the same time the constraints imposed [3]. More specifically, a scheduling problem is uniquely described by three factors: architecture of the production system, process parameters, and any constraints of the function to be optimized. The scheduling problem has been analyzed in numerous studies, which have allowed the development of different models that represent it and different methods to solve it [4]. Several applications can be tracedback to scheduling problems: the regulation of user access to a service, the assignment of operations at workstations during the transformation process of a product, the timing of activities to be carried out within a project complex, the assignment of classrooms to a set of classes, regulation of vehicle accesses at an intersection through traffic light control, the assignment of tracks to railway trains, and the use of tracks and/or gates by planes arriving or departing from an airport. Scheduling problems can be represented through appropriate models [5; 6; 7; 8; 9; 10]. The main scheduling models are (1) single machine, (2) parallel machines, (3) job shop, (4) flexible job shop, (5) flow shop, (6) flexible flow shop, and (7) open shop. The complexity of the models depends on the resources available, the type of constraints present, and the choice of objectives. In Figure 1, the main models used for the scheduling problems are illustrated. An extension of the classical job shop scheduling problem is the flexible job-shop system (FJSS). It is a very important topic in the field of production management and smart manufacturing [11]. FJSS algorithms should be adapted to effectively support the response of available operational technology (OT) within the day-to-day operations of smart companies. However, classical scheduling methods are generally incapable of solving complex problems characterized by a continuous upgrading of the production mode of the manufacturing system [12]. A key aspect to be addressed in this aim is the adoption of a multi-criteria operation selection approach, incorporating the current dynamics of smart FJSS [13]. To face this challenge, this paper proposes a hybrid and innovative model of a dispatching algorithm based on fuzzy AHP (FAHP) and TOPSIS. In particular, FAHP was used to calculate the criteria weights under uncertainty, and TOPSIS was later applied to rank the eligible operations. A case study from the smart apparel industry was employed to validate the effectiveness of the proposed approach. In this case, a FJSS with two objectives (minimize the average lateness and maximize throughput), seven sub-processes, 13 products, and 29 orders was considered. The results evidenced that our approach outperformed the current company's scheduling method by a median lateness of 3.86 days while prioritizing high-throughput products for earlier delivery. Our approach differs from previous work published in the literature that tended to focus solely on the classical approach. Our aim is to propose an integrated approach for the flexible job-shop scheduling problem for smart manufacturing that combines the benefits of each method. The rest of the paper is structured as follows: Section 2 presents a literature review on FJSS and smart manufacturing. The aim of Section 2 is to briefly outline the trends in the topic analyzed.