发表机构
Warwick Business School, University of Warwick; School of Management, Fudan University（华威商学院，华威大学; 管理学院，复旦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对可编程材料生产中的调度问题，提出多操作模式与尾时间模型，证明两种模式即致计算困难，但特定场景仍可高效求解。
AI 中文摘要
本研究探讨了一个受可编程材料（如先进液晶显示器）生产启发的调度挑战。在这些系统中，产品的最终质量只有在无资源的成熟期（称为“尾”）结束后才能达到，在此期间机器可用于处理其他作业。每个作业可以在几种操作模式之一中执行，每种模式决定了机器处理时间和后续尾持续时间的特定组合。主要任务是同时为每个作业选择最佳模式并确定其处理顺序。我们针对几个关键性能目标分析该模型，包括完成所有作业所需的总时间、完成时间的同步性（最早和最晚完成产品之间的差距）以及总加权完成时间。我们的发现提供了这些问题计算复杂性的详细分类。我们证明，虽然每个作业仅有一种模式的传统版本可以使用标准规则简单求解，但仅引入两种模式就使得针对大多数目标寻找最优解在计算上变得困难。当可用模式数量较多时，复杂性显著增加。然而，我们也确定了仍然可以有效求解的特定场景，例如当处理顺序已经确定或当目标是最小化平均完成时间时。这些结果为优化涉及强制冷却或成熟阶段的复杂制造和化学过程提供了理论清晰性和实用策略。
英文摘要
This study explores a scheduling challenge inspired by the production of programmable materials, such as advanced liquid crystal displays. In these systems, the final quality of a product is reached only after a resource-free maturation period, known as a "tail", during which the machine is available for processing other jobs. Each job can be executed in one of several operational modes, with each mode determining a specific combination of machine processing time and subsequent tail duration. The primary task is to simultaneously choose the best mode for every job and determine their processing order. We analyze this model across several key performance goals, including the total time required to finish all jobs, the synchronization of completion times (the gap between the earliest and latest finished products), and the total weighted completion time. Our findings provide a detailed classification of the computational complexity of these problems. We demonstrate that while traditional versions with only one mode per job are simple to solve using standard rules, the introduction of just two modes makes finding optimal solutions for most of these goals computationally difficult. When the number of available modes is large, the complexity increases significantly. However, we also identify specific scenarios that remain efficiently solvable, such as when the processing order is already determined or when the goal is to minimize the average completion time. These results offer theoretical clarity and practical strategies for optimizing complex manufacturing and chemical processes involving forced cooling or maturation stages.
Comments27 pages
