Sequence-dependent time- and cost-oriented assembly line balancing problems: a combinatorial Benders' decomposition approach

This article deals with the cost-oriented assembly line balancing problem with sequence-dependent set-up times. To this end, a mixed-integer linear programming (MILP) model is proposed for time- and cost-oriented assembly line balancing problems with sequence-dependent set-up times between tasks. The problem is computationally intractable; therefore, a Benders' decomposition algorithm is developed to solve it. The proposed decomposition yields a master problem that addresses the issue of assigning assembly tasks to workstations, as well as a set of subproblems that deal with sequencing tasks within each workstation owing to sequence-dependent set-up times. The algorithm is tested on a set of randomly generated test problems and numerically compared with a MILP formulation of the problem solved using a commercial optimizer. The computational results demonstrate that the proposed Benders' decomposition approach outperforms the MILP model. The contribution of this article lies in the new models proposed and the decomposition-based exact algorithm developed.

Automated summary

This research focuses on the cost-oriented assembly line balancing problem with sequence-dependent set-up times, proposing a mixed-integer linear programming model and a Benders' decomposition algorithm solution. Computational results show that the algorithm outperforms the traditional MILP model, performing better in task assignment and sequencing.