BOLT: Multi-Bottleneck Bound-Guided Learning for Flexible Job-Shop Scheduling with Time Lags and Resource-Coupled Transport

Flexible job-shop scheduling becomes resource-coupled when a scarce vehicle fleet moves jobs between stations, because the schedule sets the transport waits. BOLT (bound-oriented learning for transport-coupled scheduling) builds a lower bound from chain, machine-capacity, and fleet-capacity relaxations.

当稀缺的车队在工位间搬运工件时，柔性作业车间调度便产生了资源耦合，因为调度方案决定了运输等待时间。BOLT（面向边界的运输耦合调度学习）通过链式、机器容量和车队容量松弛构建了一个下界。

The bound equals the makespan at termination, so its per-step changes form a reward that sums to a constant minus the makespan. Because it never exceeds the attainable makespan, each candidate’s bound increase is a proven rise of the makespan floor, which the policy reads as a price.

该边界在终止时等于完工时间，因此其每一步的变化构成了一个奖励，其总和等于一个常数减去完工时间。由于它永远不会超过可达到的完工时间，每个候选方案的边界增加都被证明是完工时间下限的提升，策略将其解读为一种代价。

The root bound certifies a completed schedule’s suboptimality gap without a solver. On industry-motivated 10-module prefabricated-construction instances, explicit transport coupling outperforms a transport-penalty policy in every tested cell where loaded moves occupy at least 66% of fleet time and in none at or below 56%.

根边界无需求解器即可证明已完成调度方案的次优差距。在工业驱动的10模块预制建筑实例中，在负载移动占用至少66%车队时间的每个测试单元中，显式运输耦合的表现均优于运输惩罚策略；而在占用率低于或等于56%的单元中，则无一表现更优。

Across five zero-shot 50- and 80-module production batches, BOLT outperforms the best dispatching-rule pair on four and the penalty policy on the three with long moves. In the three-vehicle 80-module batch, its mean makespan is 13.0% below the best pair and 4.2% below an hour-budget constraint-programming solver whose proven gap averages 34%.

在五个零样本的50模块和80模块生产批次中，BOLT在四个批次中优于最佳调度规则对，并在三个长距离移动批次中优于惩罚策略。在三车80模块批次中，其平均完工时间比最佳规则对低13.0%，比平均证明差距为34%的一小时预算约束规划求解器低4.2%。

BOLT decides in 2.3-5.9 ms per event on one processor core and re-plans a disruption in seconds.

BOLT在单处理器核心上每个事件的决策时间为2.3-5.9毫秒，并能在几秒钟内重新规划中断情况。