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首页> 外文期刊>IFAC PapersOnLine >On a generalized single machine scheduling problem with time-dependent processing times * * Supported by RFBR grants 13-01-12108, 15-07-07489, 15-07-03141 and DAAD grant A/1400328
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On a generalized single machine scheduling problem with time-dependent processing times * * Supported by RFBR grants 13-01-12108, 15-07-07489, 15-07-03141 and DAAD grant A/1400328

机译:关于具有与时间有关的处理时间的广义单机调度问题, * * 由RFBR支持13- 01-12108、15-07-07489、15-07-03141和DAAD授予A / 1400328

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摘要

In this paper, a generalized formulation of a classical single machine scheduling problem is considered. A set of n jobs characterized by their release dates, deadlines and a start time-dependent processing time function p(t) has to be processed on a single machine. The objective is to find a Pareto-optimal set of schedules with respect to the criteria ? max and makespan, where ? max is a non-decreasing function depending on the completion times of the jobs. We present an approach that allows to find an optimal schedule with respect to different scheduling criteria, such as the minimization of makespan, lateness or weighted lateness, tardiness and weighted tardiness etc. in time polynomially depending on the number of jobs. The complexity of the presented algorithm is O(n 3 max{log n, H , P}), where H and P are the complexity of calculating ? j (t) and p(t) , respectively.
机译:在本文中,考虑了经典单机调度问题的广义表述。以发布日期,截止日期和与开始时间相关的处理时间函数p(t)为特征的一组n个作业必须在单台机器上进行处理。目的是找到关于标准的帕累托最优计划集。 max和makepan,在哪里? max是一个非递减函数,具体取决于作业的完成时间。我们提出了一种方法,该方法可以根据作业数量在时间上多项式地找到关于不同调度标准的最佳调度,例如最小化制造期,迟到或加权迟到,迟到和加权迟到等。该算法的复杂度为O(n 3 max {log n,H,P}),其中H和P为计算的复杂度? j(t)和p(t)。

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