Single machine scheduling to minimize maximum earliness/tardiness cost with job rejection

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters Pub Date : 2024-01-05 DOI:10.1007/s11590-023-02086-6

Matan Atsmony, Gur Mosheiov

引用次数: 0

Abstract

We study a single machine due-date assignment problem with a common due-date. The objective function is minimizing the maximum earliness/tardiness cost. The scheduler may process only a subset of the jobs and the remaining jobs are rejected. Job-dependent rejection-costs are considered, and an upper bound on the total permitted rejection cost is assumed. The problem is proved to be NP-Hard. We present and test a pseudo-polynomial dynamic programming solution algorithm. An extension to the setting containing additional due-date cost component is also discussed. An efficient implementation of the algorithm is introduced, and medium size problems (containing hundreds of jobs) are shown to be solved in very reasonable running time. In addition, an intuitive heuristic is introduced, tested numerically, and is shown to produce very small optimality gaps.

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单机调度，最大限度降低工作拒绝的迟到/迟到成本

我们研究的是具有共同到期日的单机到期日分配问题。目标函数是使最大迟到/迟到成本最小化。调度员只能处理一部分作业，其余作业将被拒绝。考虑了与作业相关的拒绝成本，并假设了总允许拒绝成本的上限。该问题被证明为 NP-Hard。我们提出并测试了一种伪多项式动态编程求解算法。我们还讨论了对包含额外到期日成本部分的设置的扩展。我们介绍了该算法的高效实现方法，并证明中等规模的问题（包含数百个作业）可以在非常合理的运行时间内求解。此外，还介绍了一种直观的启发式算法，并对其进行了数值测试，结果表明该算法能产生非常小的最优性差距。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.