# Analytic Hierarchy Process and Multilayer Network-Based Method for Assembly Line Balancing
## 5 Conclusions  
We proposed an assembly line balancing algorithm to improve the efficiency of production systems by the multiobjective assignment of tasks to operators. The optimisation of this assignment is based on a multilayer network model that provides information about the activity times, constraints and benefits (objectives) of the assignments, where the layers of the network represent the skills of the operators, the tools required for their activities and the precedence constraints of their activities. The training and equipment costs as well as the precedence of the activities are also taken into account in the activity-operator layer of the network. As these costs and benefits are difficult to evaluate, the analytic hierarchy process (AHP) technique is used to quantify the importance of the criteria. The optimisation problem is solved by a multi-level simulated annealing algorithm (SA) that efficiently handles the precedence constraints thanks to the proposed problem-specific representation. The proposed algorithm was implemented in MATLAB and the applicability of the method demonstrated with an industrial case study of wire harness manufacturing. The results confirm that multilayer network-based representations of optimisation problems in manufacturing seem to be potential promising solutions in the future. The main contribution of the work is that it presents tools that can be used for the efficient representation of expert knowledge that should be utilised in complex production management  
Figure 8: Boxplot of time, skill and equipment-related objectives for different independent runs of the algorithm and with different numbers of operators. Figure 9: Comparison of the operators’ activity times. problems. The proposed multilayer network-based representation of the production line supports the incorporation of advanced (ontology-based) models of production systems and provides an interpretable and flexible representation of all the objectives of the line balancing problem. The AHP-based pairwise comparison of the importance of the nodes, edges and complex paths of this network can be used to evaluate the objectives of the optimisation problems. The integration of the network-based knowledge representation and the AHP-based knowledge extraction makes the application of the proposed methodology attractive in complex optimisation problems. [PERSON], [PERSON] and [PERSON] developed the methodology and software; [PERSON] prepared the original draft; [PERSON] reviewed and edited the manuscript. All authors have read and agreed to the published version of the manuscript. This research was supported from the Higher Educational Institutional Excellence Program 2019 the grant of the Hungarian Ministry for Innovation and Technology (Grant Number: NKFIH-1158-6/2019). [PERSON] was supported by the project 2018-1.3.1-VKE-2018-00048-Development of intelligent Industry 4.0 solutions of production optimization in existing plants and the UNKP-19-3 New National Excellence Program of the Ministry of Human Capacities. The authors are grateful for the valuable comments and suggestions offered by the anonymous reviewers. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: