Scheduling on identical machines with preemption and setup times

IF 7 2区工程技术 Q1 ENGINEERING, INDUSTRIAL

International Journal of Production Research Pub Date : 2023-11-08 DOI:10.1080/00207543.2023.2276825

Amina Haned, Abida Kerdali, Mourad Boudhar

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Abstract

AbstractIn this paper, we address the problem of scheduling jobs on identical machines for minimising the maximum completion time (makespan). Each job requires a sequence-independent setup time, which represents the time needed to prepare the machines for job execution. Then, we introduce a dynamic programme to solve the case with two machines, and show that this problem admits a fully polynomial time approximation scheme. For the case of m machines, we propose heuristics and an adapted genetic algorithm. Some numerical experiments are done to evaluate the proposed algorithms.Keywords: Schedulingpreemptionsetup timesmakespandynamic programmingFPTAS Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementThe authors confirm that the data supporting the findings of this study are available within the article.Notes1 mod(n,m) is the remainder of the Euclidean division of n by m.Additional informationNotes on contributorsAmina HanedAmina Haned received her PhD in mathematics at the University USTHB of Algiers. She is a lecturer at the Faculty of Economic Sciences, Commercial Sciences and Management Sciences, University Algiers 3. Amina is deeply interested in the fields of optimisation, operational research, and data science, with a particular focus on scheduling and operations optimisation.Abida KerdaliAbida Kerdali received her PhD in National Higher School of Statistics and Applied Economics. She is a Lecturer at the same School in University center of Kola, Algeria. Her research area is operational research, with a focus on economic problems.Mourad BoudharMourad Boudhar received his PhD in mathematics at the University USTHB of Algiers. He is a professor at the Department of Operational Research, University USTHB. His research interests include issues related to operational research and optimisation, with a particular focus on scheduling problems with new constraints as transportation, conflict, recirculation, multi-agents, etc. He has published several research papers in national and international journals and conference proceedings.

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在具有抢占和设置时间的相同机器上进行调度

摘要在本文中，我们讨论了在相同机器上调度作业以最小化最大完成时间(makespan)的问题。每个作业都需要独立于序列的设置时间，该时间表示为作业执行准备机器所需的时间。然后，我们引入一个动态规划来解决双机情况，并证明该问题允许一个完全多项式时间逼近方案。对于m台机器的情况，我们提出了启发式算法和自适应遗传算法。通过数值实验对所提出的算法进行了验证。关键词:调度抢占设置时间制造动态编程fptas披露声明作者未报告潜在的利益冲突。数据可用性声明作者确认在文章中可以获得支持本研究结果的数据。注1 mod(n,m)是n除以m的欧几里得除法的余数。附加信息注:samina Haned在阿尔及尔USTHB大学获得数学博士学位。她是阿尔及尔大学经济科学、商业科学和管理科学学院的讲师。Amina对优化、运筹学和数据科学领域非常感兴趣，尤其关注调度和操作优化。Abida Kerdali博士毕业于国家高等统计与应用经济学院。她是阿尔及利亚科拉大学中心同一所学校的讲师。她的研究领域是运筹学，主要关注经济问题。Mourad Boudhar在阿尔及尔USTHB大学获得数学博士学位。他是USTHB大学运筹学系的教授。他的研究兴趣包括与运筹学和优化相关的问题，特别关注运输、冲突、再循环、多代理等新约束下的调度问题。他在国内和国际期刊和会议论文集上发表了多篇研究论文。

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来源期刊

International Journal of Production Research 管理科学-工程：工业

CiteScore

19.20

自引率

14.10%

发文量

318

审稿时长

6.3 months

期刊介绍： The International Journal of Production Research (IJPR), published since 1961, is a well-established, highly successful and leading journal reporting manufacturing, production and operations management research. IJPR is published 24 times a year and includes papers on innovation management, design of products, manufacturing processes, production and logistics systems. Production economics, the essential behaviour of production resources and systems as well as the complex decision problems that arise in design, management and control of production and logistics systems are considered. IJPR is a journal for researchers and professors in mechanical engineering, industrial and systems engineering, operations research and management science, and business. It is also an informative reference for industrial managers looking to improve the efficiency and effectiveness of their production systems.