**László Nagy, Tamás Ruppert and János Abonyi \***

MTA-PE "Lendület" Complex Systems Monitoring Research Group, University of Pannonia, P.O. Box 158, H-8200 Veszprém, Hungary; laszlo.nagy@fmt.uni-pannon.hu (L.N.); ruppert@abonyilab.com (T.R.)

**\*** Correspondence: janos@abonyilab.com

Received: 30 April 2020; Accepted: 2 June 2020; Published: 5 June 2020

**Abstract:** Assembly line balancing improves the efficiency of production systems by the optimal assignment of tasks to operators. The optimisation of this assignment requires models that provide information about the activity times, constraints and costs of the assignments. A multilayer network-based representation of the assembly line-balancing problem is proposed, in which 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 activity–operator network layer is designed by a multi-objective optimisation algorithm in which the training and equipment costs as well as the precedence of the activities are also taken into account. As these costs 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. The efficiency of the method is demonstrated by a case study from wire harness manufacturing.

**Keywords:** assembly-line balancing; multi-objective optimization; simulated annealing; multilayer network
