New Fitness Evaluation for a Single Machine Scheduling Problem with an Overtime Option

Watcharapan Sukkerd, Jakkrit Latthawanichphan, W. Songserm, T. Wuttipornpun
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Abstract

This research studies a single machine scheduling problem with overtime option. The objective is to minimise the total penalty cost (TPC), which is the sum of tardiness, earliness, and overtime costs. A new fitness evaluation heuristic (FEH) capable of minimising TPC is developed. Since FEH works well only when the sequence of jobs is known, it is then integrated into the fitness evaluation step of a variable neighbourhood search (VNS-FEH) to determine the optimal sequence of jobs that obtains the minimum TPC. Effectiveness of the proposed VNS-FEH is evaluated by using real data from three industrial case studies consisting of five job sizes (5, 10, 20, 50, 100) for each, resulting in 270 experiments. The best common parameter setting (BCS) of VNS-FEH applicable for all of the case studies is determined. The results show that TPC obtained from VNS-FEH with its BCS is deviated on average from the best TPC of 0.02%. Moreover, it is better than the bound obtained from the mathematical model with the relative percentage improvement (RPI) of 37.22%.
带超时选项的单机调度问题的新适应度评价
研究了具有加班选项的单机调度问题。目标是最小化总惩罚成本(TPC),它是延迟、提前和加班成本的总和。提出了一种最小化TPC的适应度评价启发式算法。由于FEH算法只有在作业序列已知的情况下才有效,因此将其集成到可变邻域搜索(VNS-FEH)的适应度评估步骤中,以确定获得最小TPC的最优作业序列。通过使用来自三个工业案例研究的真实数据来评估所提出的VNS-FEH的有效性,这些案例研究包括五个作业规模(5、10、20、50、100),共进行了270次实验。确定了适用于所有案例研究的VNS-FEH的最佳公共参数设置(BCS)。结果表明,采用其BCS的VNS-FEH得到的TPC与最佳TPC平均偏差为0.02%。相对改进百分比(RPI)为37.22%,优于数学模型得到的边界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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