We study a scheduling problem with linear deterioration of job processing times. We consider parallel identical machines. The objective is minimum total load, i.e., minimum total processing times on all the machines. We propose a simple heuristic of a greedy type for this NP-hard problem. A lower bound based on the geometric mean of the job deterioration factors is also introduced. The greedy heuristic is shown to guarantee an optimal solution for small size problems, and our numerical tests indicate that in general it produces very close-to-optimal schedules.

中文翻译：

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最大限度地减少线性恶化的并行机上的总负载

我们研究工作处理时间线性恶化的调度问题。我们考虑并行的相同机器。目标是最小的总负载，即所有机器上的总处理时间最少。对于这个NP难题，我们提出了一种贪婪类型的简单启发式方法。还介绍了基于工作恶化因素的几何平均值的下限。贪婪的启发式方法可以确保为解决小型问题提供最佳解决方案，而我们的数值测试表明，总体而言，它产生了非常接近最优的进度表。