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.

本文涉及具有顺序相关设置时间的面向成本的装配线平衡问题。为此，针对时间和成本导向的装配线平衡问题，提出了一种混合整数线性规划 (MILP) 模型，该问题具有与任务之间的顺序相关的设置时间。这个问题在计算上是棘手的；因此，开发了 Benders 分解算法来解决它。所提出的分解产生了一个主要问题，该问题解决了将装配任务分配给工作站的问题，以及一组子问题，这些子问题处理每个工作站内由于依赖于序列的设置时间的排序任务。该算法在一组随机生成的测试问题上进行测试，并与使用商业优化器解决的问题的 MILP 公式进行数值比较。计算结果表明，所提出的 Benders 分解方法优于 MILP 模型。本文的贡献在于提出的新模型和开发的基于分解的精确算法。