The Oven Scheduling Problem (OSP) is an NP-hard real-world parallel batch scheduling problem arising in the semiconductor industry. The objective of the problem is to schedule a set of jobs on ovens while minimizing several factors, namely total oven runtime, job tardiness, and setup costs. At the same time, it must adhere to various constraints such as oven eligibility and availability, job release dates, setup times between batches, and oven capacity limitations. The key to obtaining efficient schedules is to process compatible jobs simultaneously in batches. In this paper, we develop theoretical, problem-specific lower bounds for the OSP that can be computed very quickly. We thoroughly examine these lower bounds, evaluating their quality and exploring their integration into existing solution methods. Specifically, we investigate their contribution to exact methods and a metaheuristic local search approach using simulated annealing. Moreover, these problem-specific lower bounds enable us to assess the solution quality for large instances for which exact methods often fail to provide tight lower bounds.

翻译：烤箱调度问题（OSP）是半导体工业中一个NP难的实际并行批调度问题。该问题的目标是在满足多个约束条件（如烤箱适用性与可用性、工件释放时间、批次间准备时间以及烤箱容量限制）的同时，调度一组工件至烤箱，以最小化总烤箱运行时间、工件延迟及设置成本。获得高效调度的关键在于将兼容工件以批次形式同时处理。本文针对OSP建立了可快速计算的理论性、问题特异性下界。我们系统分析了这些下界，评估其质量并探索其与现有求解方法的融合途径。具体而言，我们研究了其在精确方法及采用模拟退火的元启发式局部搜索方法中的贡献。此外，这些问题特异性下界使我们能够评估大规模实例的求解质量——对于这类实例，精确方法往往无法提供紧致下界。