In the automotive industry, the sequence of vehicles to be produced is determined ahead of the production day. However, there are some vehicles, failed vehicles, that cannot be produced due to some reasons such as material shortage or paint failure. These vehicles are pulled out of the sequence, and the vehicles in the succeeding positions are moved forward, potentially resulting in challenges for logistics or other scheduling concerns. This paper proposes a two-stage stochastic program for the mixed-model sequencing (MMS) problem with stochastic product failures, and provides improvements to the second-stage problem. To tackle the exponential number of scenarios, we employ the sample average approximation approach and two solution methodologies. On one hand, we develop an L-shaped decomposition-based algorithm, where the computational experiments show its superiority over solving the deterministic equivalent formulation with an off-the-shelf solver. Moreover, we provide a tabu search algorithm in addition to a greedy heuristic to tackle case study instances inspired by our car manufacturer partner. Numerical experiments show that the proposed solution methodologies generate high quality solutions by utilizing a sample of scenarios. Particularly, a robust sequence that is generated by considering car failures can decrease the expected work overload by more than 20\% for both small- and large-sized instances.

翻译：在汽车工业中，待生产车辆的序列在生产日之前就已确定。然而，由于材料短缺或油漆故障等原因，部分车辆（即故障车辆）无法生产。这些车辆被移出序列，后续位置的车辆则向前移动，这可能导致物流或其他调度方面的挑战。本文针对带有随机产品故障的混合模型排序（MMS）问题，提出了一种两阶段随机规划方法，并对第二阶段问题进行了改进。为应对指数级数量的场景，我们采用了样本平均近似方法及两种求解方法。一方面，我们开发了一种基于L形分解的算法，计算实验表明，该算法优于使用现成求解器求解确定性等价模型的方法。此外，我们提供了一种禁忌搜索算法以及一种贪婪启发式算法，以处理来自我们汽车制造商合作伙伴的案例研究实例。数值实验表明，所提出的求解方法通过利用场景样本生成了高质量的解。特别是，通过考虑车辆故障生成的鲁棒序列，可将小规模和大规模实例的预期工作超载量降低20%以上。