不可再生资源的时间安排:最小化完成时间总和

IF 1.4 4区 工程技术 Q4 ENGINEERING, MANUFACTURING
Kristóf Bérczi, Tamás Király, Simon Omlor
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引用次数: 0

摘要

我们考虑的是不可再生资源的单机调度。在这种情况下,我们会得到一组作业,每个作业都有处理时间、权重和资源需求。在固定的时间点,作业会消耗一定量的资源。我们的目标是将作业非抢占式地分配到机器上的时间段,以便每个作业在开始处理时都有足够的可用资源。我们考虑的目标是加权完成时间之和最小化。本文的主要贡献是为处理时间为 0 的情况提供了一个 PTAS(\(1|rm=1,p_j=0|\sum w_jC_j\))。此外,我们还证明了单位资源需求和权重情况下的强 NP-hardness(\(1|rm=1,a_j=1|sum C_j\)),从而回答了 Györgyi 和 Kis 的一个未决问题。我们还证明了与 "最短处理时间优先 "排序相对应的时间表为后一个问题提供了 3/2 近似值。最后,我们研究了处理时间为 0 而资源到达时间未知的问题变体。我们提出了一个((4+\epsilon))近似计算算法,以及一个((4-\varepsilon))近似性结果,适用于任意\(\varepsilon >0\)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Scheduling with non-renewable resources: minimizing the sum of completion times

Scheduling with non-renewable resources: minimizing the sum of completion times

We consider single-machine scheduling with a non-renewable resource. In this setting, we are given a set of jobs, each characterized by a processing time, a weight, and a resource requirement. At fixed points in time, certain amounts of the resource are made available to be consumed by the jobs. The goal is to assign the jobs non-preemptively to time slots on the machine, so that each job has enough resource available at the start of its processing. The objective that we consider is the minimization of the sum of weighted completion times. The main contribution of the paper is a PTAS for the case of 0 processing times (\(1|rm=1,p_j=0|\sum w_jC_j\)). In addition, we show strong NP-hardness of the case of unit resource requirements and weights (\(1|rm=1,a_j=1|\sum C_j\)), thus answering an open question of Györgyi and Kis. We also prove that the schedule corresponding to the Shortest Processing Time First ordering provides a 3/2-approximation for the latter problem. Finally, we investigate a variant of the problem where processing times are 0 and the resource arrival times are unknown. We present a \((4+\epsilon )\)-approximation algorithm, together with a \((4-\varepsilon )\)-inapproximability result, for any \(\varepsilon >0\).

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来源期刊
Journal of Scheduling
Journal of Scheduling 工程技术-工程:制造
CiteScore
3.80
自引率
10.00%
发文量
49
审稿时长
6-12 weeks
期刊介绍: The Journal of Scheduling provides a recognized global forum for the publication of all forms of scheduling research. First published in June 1998, Journal of Scheduling covers advances in scheduling research, such as the latest techniques, applications, theoretical issues and novel approaches to problems. The journal is of direct relevance to the areas of Computer Science, Discrete Mathematics, Operational Research, Engineering, Management, Artificial Intelligence, Construction, Distribution, Manufacturing, Transport, Aerospace and Retail and Service Industries. These disciplines face complex scheduling needs and all stand to gain from advances in scheduling technology and understanding.
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