# Analytic Hierarchy Process and Multilayer Network-Based Method for Assembly Line Balancing
## 1 Introduction  
Production line-based assembly lines are still the most widely applied manufacturing systems [1]. Assembly-Line Balancing (ALB) [2] deals with the balanced assignment of tasks to the workstations, resulting in the optimisation of a given objective function without violating precedence constraints [3]. The efficiency of these optimisation tasks is mostly determined by the model of the manufacturing process represented [4]. The concept of Industry 4.0 has already had a significant influence on how production and assembly lines are designed [5] and managed [6]. The requirement of practical design at a high automation level ensures that sensors and equipment can be integrated in a fast, secure, and reliable way. In our research, we study how the interoperability capabilities of Industry 4.0 solutions can be improved and how the efficiency of solution development can be increased. As Internet of Things-based products and processes are rapidly developing in the industry, there is a need for solutions that can support their fast and cost-effective implementation. There is a need for further standardization to achieve more flexible connectivity, interoperability, and fast application-oriented development; furthermore, advanced model-based control and optimisation functions require a better understanding of sensory and process data [7]. Usually, production systems include multiple subsystems and layers of connectivity. Thus, although research-based solutions for classical operations typically use a graph-based representation of problems and flow-based optimisation algorithms, conventional single-layer networks quickly become incapable of representing the complexity and connectivity of all the details of the productionline. With the overlapping data in Industry 4.0 solutions, it should be highlighted that multilayer networks are expected to be the most suitable options for representing modern production lines. The concept of a multilayer network was developed to represent multiple types of relationships [8], and these models have been proven to be applicable to the representation of complex connected systems [9]. Network-based models can also represent how products, resources and operators are connected [10], which is beneficial in terms of solving manufacturing cell formation problems [11]. This work demonstrates how the multilayer network representation of production lines can be utilised in line balancing. In the proposed novel network model, the layers represent the skills of the operators, the tools required for the activities, and the precedence constraints of the activities. At the same time, a multi-objective optimisation algorithm designs the assignment of activities and operators to network layers. The proposed multilayer network approach supports the intuitive formulation of multi-objective line balancing optimisation tasks. Besides the utilisation of operators, the utilisation of the tools and the number of skills of an operator are also taken into account. The main advantage of the proposed network-based representation is that the latter two objectives are directly related to the structural properties of the optimised network. Line balancing is a non-deterministic polynomial-time hard (NP-hard) optimisation problem, which means that the computational complexity of the optimisation problem increases exponentially as the dimensions of the problem increase. This challenge explains why numerous meta heuristic approaches such as simulated annealing (SA) [12; 13], hybrid heuristic optimisation [13; 14], chance-constrained integer programming [15], recursive and dynamic programming [16], as well as tabu search [17] have been utilised in the field of production management. Fuzzy set theory provides a transparent and interpretable framework to represent the uncertainty of information and solve the ALB problem [18; 19].