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Stochastic single machine scheduling with proportional job weights to minimize deviations of completion times from a common due date

机译：具有比例作业权重的随机单机计划，以最大程度地减少完成时间与常见到期日的偏差

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摘要

Deterministic single machine scheduling to minimize total weighted absolute deviations of job completion times from a common due date (abbreviated by TWD) is a typical scheduling model in just-in-time manufacturing environment, and it is NP-hard. However, LPT (largest processing time) job schedule is optimal for the case where jobs' weights are proportional to their processing times. In this paper, we consider the stochastic counterpart of the TWD problem with proportional weights, where the processing times are arbitrary positive random variables, while the common due date is an exponentially distributed random variable. The optimal solution of the problem is derived. Moreover, the case where the machine is subject to stochastic breakdowns is also discussed. It is shown that the results can be extended to the situation where the machine is subject to stochastic breakdowns when the counting process describing machine breakdowns is characterized by a Poisson process and the down times are independent identically distributed.
机译：确定性单机调度可以最大程度地减少作业完成时间与常见到期日（由TWD缩写）的总加权绝对偏差，这是即时制造环境中的一种典型调度模型，并且具有NP难性。但是，对于作业权重与处理时间成正比的情况，LPT（最大处理时间）作业计划是最佳的。在本文中，我们考虑具有比例权重的TWD问题的随机对应物，其中处理时间是任意正随机变量，而公共到期日是指数分布的随机变量。得出问题的最佳解决方案。此外，还讨论了机器遭受随机故障的情况。结果表明，当描述机器故障的计数过程以泊松过程为特征并且停机时间独立地均匀分布时，结果可以扩展到机器遭受随机故障的情况。

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