This paper introduces the maximum length car sequencing problem to support the assembly operations of a multinational automotive company. We propose an integer linear programming (ILP) formulation to schedule the maximum number of cars without violating the so-called option constraints. In addition, we present valid combinatorial lower and upper bounds, which can be calculated in less than 0.01 s, as well as binary and iterative search algorithms to solve the problem when good primal bounds are not readily available. To quickly obtain high-quality solutions, we devise an effective iterated local search algorithm, and we use the heuristic solutions as warm start to further enhance the performance of the exact methods. Computational results demonstrate that relatively low gaps were achieved for benchmark instances within a time limit of ten minutes. We also conducted an instance space analysis to identify the features that make the problem more difficult to solve. Moreover, the instances reflecting the company’s needs could be solved to optimality in less than a second. Finally, simulations with real-world demands, divided into shifts, were conducted over a period of four months. In this case, we use the proposed ILP model in all shifts except the last one of each month, for which we employ an alternative ILP model to sequence the unscheduled cars, adjusting the pace of the assembly line in an optimal fashion. The results pointed out that the latter was necessary in only one of the months.

中文翻译：

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最大长度小车排序问题

本文介绍了支持跨国汽车公司装配业务的最大长度汽车排序问题。我们提出了一种整数线性规划（ILP）公式来在不违反所谓的选项约束的情况下调度最大数量的汽车。此外，我们还提出了有效的组合下限和上限，可以在不到 0.01 秒的时间内计算出来，以及二分和迭代搜索算法来解决当良好的原始边界不易获得时的问题。为了快速获得高质量的解决方案，我们设计了一种有效的迭代局部搜索算法，并使用启发式解决方案作为热启动来进一步提高精确方法的性能。计算结果表明，基准实例在十分钟的时间限制内实现了相对较低的差距。我们还进行了实例空间分析，以确定使问题更难以解决的特征。此外，反映公司需求的实例可以在不到一秒的时间内得到最优解决。最后，对现实世界的需求进行了为期四个月的模拟，分为轮班。在这种情况下，我们在除每个月最后一个班次之外的所有班次中都使用建议的 ILP 模型，为此我们采用替代的 ILP 模型对计划外的汽车进行排序，以最佳方式调整装配线的节奏。结果指出，后者仅在其中一个月内是必要的。