Balancing Assembly Line with Moving Workers and Worker-Dependent Task Times Using Linear Programming Formulation

This study addresses the moving heterogeneous worker assembly line balancing problem, a new variant of the classical problem that simultaneously considers worker-dependent task times and worker mobility between stations. In this setting, the processing time of each task differs according to the skills and efficiency of the assigned worker, while workers are allowed to move within a limited range to perform tasks at different stations. These features make the problem more realistic but also substantially more complex, as precedence relations, heterogeneous workloads, cycle time restrictions, and worker movements must all be satisfied simultaneously. To capture these interrelated aspects, mixed integer linear programming is proposed, which can provide exact solutions for small-sized instances. A dataset based on well-known precedence diagrams is generated to evaluate model performance across varying levels of task time variability and worker–station configurations. The results show that the formulation optimally solves small-sized instances, whereas medium and large instances remain computationally demanding, with increasing gaps and longer solving times. The findings further reveal that adding an extra workstation can improve efficiency, especially in larger-sized problem instances. Overall, this study contributes to assembly line literature with a novel mathematical model that integrates worker heterogeneity and mobility, highlighting future research opportunities for heuristic and metaheuristic approaches.