高多样性柔性作业车间：从精确循环流体可达性到结构引导的有限时域调度
High-Multiplicity Flexible Job Shops: From Exact Recurrent Fluid Attainment to Structure-Guided Finite-Horizon Scheduling
浏览论文内容
中文总结 AI 辅助
针对高多样性柔性作业车间调度问题，研究实现最优流体分配的精确离散调度构造，开发TCTR方法，在676个实例上平均差距1.54%，优于对比算法。
中文摘要 AI 辅助
高多样性柔性作业车间包含少量作业类型的大量副本，必须在备选机器上进行调度。流体松弛法可提供可扩展的工作量下界，但其分数机器分配无法定义单个作业的可行调度。我们表明，经过适当的有限缩放后，最优流体分配可通过可行的重复离散调度精确实现。该构造将流体分配缩放为整数工序数量，将所得工序置于不重叠的机器区间中，重复此排列，并将跨重复的工序链接为单个作业而不移动任何区间，从而在保持机器可行性的同时强制执行作业优先级。对于具有相同作业类型构成的不断增长的有限实例，即使额外作业数量固定，最优制造期与流体下界之间的差距仍受常数约束；因此相对差距随实例规模增大而消失。受此重复结构引导，我们开发了基于作业类型的循环模板重放（TCTR），其使用大小不随作业副本数量增长的优化模型搜索作业类型模板，并在整个实例上重放所选模板。在676个多副本扩展的公共柔性作业车间实例上，TCTR在所有情况下均可行，且与流体下界的平均差距为1.54%，而基于作业索引的自适应大邻域搜索的平均差距为5.32%，混合遗传算法的平均差距为6.18%。
英文摘要
High-multiplicity flexible job shops involve many copies of a small set of job types that must be scheduled on alternative machines. Fluid relaxations provide scalable workload lower bounds, but their fractional machine allocations do not define feasible schedules for individual jobs. We show that, after a suitable finite scaling, an optimal fluid allocation can be realized exactly by a feasible repeating discrete schedule. The construction scales the fluid allocation to integer operation counts, places the resulting operations in nonoverlapping machine intervals, repeats this arrangement, and links operations across repetitions into individual jobs without moving any interval, thereby enforcing job precedence while preserving machine feasibility. For growing finite instances with the same job-type composition, even with a fixed number of extra jobs, the gap between the optimal makespan and the fluid lower bound remains bounded by a constant; hence the relative gap vanishes as the instance grows. Guided by this repeated structure, we develop type-based cyclic template replay (TCTR), which searches job-type templates using an optimization model whose size does not grow with the number of job copies and replays the selected template on the full instance. On 676 multiplicity-expanded public flexible-job-shop instances, TCTR is feasible in every case and achieves a 1.54% mean gap to the fluid lower bound, compared with 5.32% for a job-indexed adaptive large-neighborhood search and 6.18% for a hybrid genetic algorithm.
