An exact method with decomposition techniques and combinatorial Benders' cuts for the type-2 multi-manned assembly line balancing problem

Multi-manned assembly lines are widely applied to manufacturing industries that produce large-size products and are concerned with high levels of productivity. Such lines are commonly found in automotive industries, where different tasks are simultaneously performed by more than one worker on the same product in multi-operated stations, giving rise to a class of balancing problem that aims to minimize the line's cycle time. This clear practical application had made the type-2 multi-manned assembly line balancing problem to be explored in the past. However, only few small-size instances could be solved by preceding exact solution approaches, whereas large and real-life cases still lack optimality proofs since they were tackled by heuristics. In this work, a new Mixed-Integer Linear Programming model is presented and its modeling decisions discussed. Moreover, an innovative exact solution procedure employing a combination of decomposition techniques and combinatorial Benders' cuts is presented to solve large and real-life instances optimally. Tests on an extended literature dataset and a real-life assembly plant case study have demonstrated that the proposed algorithm outperforms previously developed methods in terms of solution quality by an ample margin in efficiency gains. Synergies between the algorithm’s components are also revealed. Finally, the proposed exact method has been able to yield 60 optimal results out of a 108-instance dataset, with the remaining 48 solutions presenting a small integer gap (less than 2%).