We study the scheduling of production in a multi-item, failure-prone machine with setup times, with the objective of minimising long-run average inventory and backlog costs. We make two contributions to this problem, which has received significantly less attention compared to the standard stochastic economic lot scheduling problem (with random demand and production times). First, we adapt and implement a variety of existing scheduling policies and compare their performance through a set of numerical experiments spanning a wide range of operating conditions. This analysis allows us to identify important shortcomings of the policies, including their poor performance when items have widely different priorities (as dictated by the product of their cost and production rate parameters). Second, we leverage these insights to develop and analyse a new, easy-to-implement policy. This policy tightly controls the surplus of the highest-priority items using fixed base-stock levels and, for all other items, it determines their run lengths dynamically in such a way that long production runs become decreasingly likely with decreasing item priority. Our experiments show that our new policy greatly outperforms the benchmarking policies over a large and important set of operating regimes, comprising high-utilisation systems where the machine cycles through all items at a frequency comparable to or greater than the frequency of failure events.

我们研究了具有设置时间的多项目、容易发生故障的机器中的生产调度，目的是最大限度地减少长期平均库存和积压成本。我们对这个问题做了两个贡献，与标准的随机经济批次调度问题（随机需求和生产时间）相比，该问题受到的关注要少得多。首先，我们调整并实施了各种现有的调度策略，并通过一组跨越各种操作条件的数值实验来比较它们的性能。这种分析使我们能够识别政策的重要缺点，包括当项目具有广泛不同的优先级（由其成本和生产率参数的乘积决定）时它们的性能不佳。其次，我们利用这些见解来开发和分析一个新的、易于实施的政策。该政策使用固定的基本库存水平严格控制最高优先级项目的盈余，并且对于所有其他项目，它动态地确定它们的运行长度，使得长时间生产运行的可能性随着项目优先级的降低而降低。我们的实验表明，我们的新策略在一组大型且重要的操作机制中大大优于基准测试策略，包括高利用率系统，其中机器以与故障事件频率相当或更高的频率循环遍历所有项目。它以这样一种方式动态地确定它们的运行长度，即随着项目优先级的降低，长时间生产运行的可能性变得越来越小。我们的实验表明，我们的新策略在一组大型且重要的操作机制中大大优于基准测试策略，包括高利用率系统，其中机器以与故障事件频率相当或更高的频率循环遍历所有项目。它以这样一种方式动态地确定它们的运行长度，即随着项目优先级的降低，长时间生产运行的可能性变得越来越小。我们的实验表明，我们的新策略在一组大型且重要的操作机制中大大优于基准测试策略，包括高利用率系统，其中机器以与故障事件频率相当或更高的频率循环遍历所有项目。