## 1 Introduction
On the contrary, this is a crucial factor for assembly lines with more than one worker per station to obtain  
Figure 1: Configuration of (**a**) simple, (**b**) two-sided, and (**c**) multi-manned assembly line. an efficient task assignment. Indeed, some tasks assigned to a worker could be delayed if they need to wait for a predecessor task to be completed. Accordingly, the station assembly time cannot be computed by simply summing up the assigned task times, but it requires the solution of a detailed scheduling problem within each station [15]. Addressing these peculiarities of multi-manned assembly lines considerably increases the problem complexity and the simple balancing of workloads among workers is no longer enough. Conversely, proper synchronization of the task assignment to workers is necessary to attain feasible solutions. In addition to the precedence diagram, several other restrictions can force or forbid particular task combinations or certain task assignments to a specific worker in a certain instant [16; 17]. For instance, large products require different mounting positions to be handled by workers. As suggested by [PERSON] and [PERSON] [18], each position enables certain tasks to be assigned and disables some others. Moreover, some tasks could require specific tools or machines to be performed [19]. Hence, a further decision about the equipment types to be allocated to the workstations has to be taken. An efficient task-to-station assignment should consider a maximum number of pieces of equipment installed overall. Workers belonging to the same station could share these pieces of equipment, using them in different moments during the cycle time. Finally, some tasks may require cooperation between two or more workers to be carried out, e.g., windshield installation for cars. This paper tackles the problem of synchronizing assembly lines of large and complex products, e.g., cars, trucks, automatic machines, and white goods. The aim of this research is the development of a methodology suitable for industrial applications able to simultaneously handle all the typical features of these assembly systems. These features are multi-manned workstations, compatibility/incompatibility between mounting positions, equipment sharing, cooperation between workers, and the management of a great number of tasks, i.e., some hundreds. The adopted research methods deal with a detailed analysis of the targeted problem, defining the most relevant features that distinguished real multi-manned assembly lines within an industrial environment. Then, all these relevant features are quantitatively modeled to define a feasible optimization problem since a procedure able to solve this complex multi-manned assembly line synchronization problem (MALSP) is missing in the literature and it is strongly encouraged by industries. First, a mixed-integer programming (MIP) model for this MALSP is presented. Secondly, because this problem is well known as non-polynomial (NP)-hard, a customized meta-heuristic procedure based on a simulated annealing (SA) algorithm is implemented to efficiently solve it. Moreover, the paper presents the assembly dataset of a European luxury sports car manufacturer. This instance involves 665 tasks, and it can probably be considered one of the largest available in the literature, as far as the authors' knowledge. The proposed MIP model is adopted to solve the case study MALSP leveraging the presented SA algorithm. This approach is tested and validated through its successful application to the targeted automotive assembly line. The obtained results demonstrate the procedure efficiency, and the quality of the proposed solutions suggest that it can be a practical reference for companies that tackle the workstation design, the worker and equipment allocation, and the task assignment within multi-manned assembly systems. The remainder of this paper is organized as follows. Section 2 investigates the most relevant contributions to multi-manned assembly line problems by considering the latest trends.