The Reconfigurable Transfer Line Balancing Problem (RTLB) is considered in this paper. This problem is quite recent and motivated by the growing need of reconfigurability in the new industry 4.0 context. The problem consists into allocating a set of operations necessary to machine a single part to different workstations placed into a serial line. Each workstation can contain multiple machines operating in parallel and the tasks allocated to a workstation should be sequenced since sequence-dependent setup times between operations are needed to perform tool changes. Besides, precedence constraints, inclusion, exclusion and accessibility constraints between operations are considered. In this article we propose an efficient matheuristic of type Balance First, Sequence Last (BFSL). This method is a two-step heuristic with a constructive phase and an improvement phase. It contains several components from exact methods (linear programming, constraint generation and dynamic programming) and metaheuristics (simulated annealing). In addition, we show that the constructive algorithm approximates the optimal solution when the setup times are bounded by the processing times and give an approximation ratio. The obtained results show the effectiveness of the proposed approach. The matheuristic clearly outperforms a genetic algorithm from literature on quite large benchmark instances.

本文考虑了可重配置传输线平衡问题（RTLB）。这个问题是最近才出现的，并且是由于在新的工业4.0环境中对可重配置性的需求日益增长所致。问题在于将一组用于加工单个零件的必要操作分配给置于串行线路中的不同工作站。每个工作站可以包含并行运行的多台机器，并且分配给工作站的任务应按顺序排列，因为在操作之间需要依赖于顺序的设置时间来执行工具更换。此外，还考虑了操作之间的优先约束，包含，排除和可访问性约束。在本文中，我们提出了“余额优先”，“序列最后”（BFSL）类型的有效数学模型。该方法是一个分为两个阶段的启发式方法，具有建设性阶段和改进阶段。它包含来自精确方法（线性规划，约束生成和动态规划）和元启发法（模拟退火）的多个组件。此外，我们表明，当建立时间受处​​理时间限制并给出近似比率时，构造算法会逼近最佳解决方案。获得的结果表明了该方法的有效性。在相当大的基准实例上，该数学方法明显优于文献中的遗传算法。我们表明，当建立时间受处​​理时间限制时，构造算法会逼近最佳解决方案，并给出一个近似比率。获得的结果表明了该方法的有效性。在相当大的基准实例上，该数学方法明显优于文献中的遗传算法。我们表明，当建立时间受处​​理时间限制时，构造算法会逼近最佳解决方案，并给出一个近似比率。获得的结果表明了该方法的有效性。在相当大的基准实例上，该数学方法明显优于文献中的遗传算法。