具有逐步退化作业的并行机器调度以最小化总(加权)完成时间

Cuixia Miao, Fanyu Kong, Juan Zou, Ran Ma, Yujia Huo
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引用次数: 0

摘要

本文研究了具有阶跃退化作业的并行机器调度问题。如果每个作业的开始时间超过给定的恶化日期,则每个作业的实际处理时间作为阶跃函数恶化。我们重点讨论了常见的工作恶化日期的情况。对于总完工时间的最小化问题,我们首先证明了该问题在强意义上是np困难的。然后给出了任意最优调度的一个性质。进一步证明了共同正常处理时间或共同处罚的两种特殊情况是多项式可解的。针对总加权完成时间的最小化问题,分析了np -硬度问题,提出了一种常见正常处理时间和常见处罚情况下的多项式时间优化算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Parallel-Machine Scheduling with Step-Deteriorating Jobs to Minimize the Total (Weighted) Completion Time
In this paper, we consider the parallel-machine scheduling with step-deteriorating jobs. The actual processing time of each job deteriorates as a step function if its starting time is beyond a given deteriorating date. We focus on the case of the common job deteriorating date. For the minimization problem of total completion time, we first show that the problem is NP-hard in the strong sense. Then we propose one property of any optimal schedule. Furthermore, we prove that two special cases of common normal processing time or common penalty are polynomially solvable. For the minimization problem of total weighted completion time, we analyze the NP-hardness and present a polynomial time optimal algorithm for the case of common normal processing time and common penalty.
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