{"title":"Scheduling problems on parallel machines with machine-dependent generalized due-dates","authors":"Baruch Mor, Gur Mosheiov, Dvir Shabtay","doi":"10.1007/s10479-025-06468-0","DOIUrl":null,"url":null,"abstract":"<div><p>In scheduling problems with generalized due-dates, the due-dates are position-dependent (and not job-dependent as in classical scheduling). In this paper, we study scheduling problems on parallel machines, and the underlying assumption is that the generalized due-dates are machine-dependent. The following scheduling measures are considered: total tardiness, maximum tardiness, number of tardy jobs, and total late work. We show that all the problems are NP-hard even if all generalized due-dates are identical. We complement this hardness result by showing that all problems are solvable in pseudo-polynomial time and that minimizing total late work is fixed parametrized tractable with respect to the number of different generalized due-dates and processing times in the instance. We also tested the pseudo-polynomial time algorithms, showing they can easily solve instances containing up to 200 jobs.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"347 3","pages":"1455 - 1471"},"PeriodicalIF":4.4000,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06468-0","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
In scheduling problems with generalized due-dates, the due-dates are position-dependent (and not job-dependent as in classical scheduling). In this paper, we study scheduling problems on parallel machines, and the underlying assumption is that the generalized due-dates are machine-dependent. The following scheduling measures are considered: total tardiness, maximum tardiness, number of tardy jobs, and total late work. We show that all the problems are NP-hard even if all generalized due-dates are identical. We complement this hardness result by showing that all problems are solvable in pseudo-polynomial time and that minimizing total late work is fixed parametrized tractable with respect to the number of different generalized due-dates and processing times in the instance. We also tested the pseudo-polynomial time algorithms, showing they can easily solve instances containing up to 200 jobs.
期刊介绍：
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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