4.7 Article

Minimizing total late work on a single machine with generalized due-dates

期刊

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 293, 期 3, 页码 837-846

出版社

ELSEVIER
DOI: 10.1016/j.ejor.2020.12.061

关键词

Scheduling; Single machine; Total late work; Generalized due-dates; Job rejection; Unavailability period

资金

  1. Israel Science Foundation [2505/19]
  2. Charles I. Rosen Chair of Management
  3. Recanati Fund of The School of Business Administration of The Hebrew University

向作者/读者索取更多资源

This study focuses on single machine scheduling problems with generalized due-dates, examining scenarios like job rejection and machine unavailability. The research proves the NP-hardness of these problems and proposes dynamic programming algorithms. It concludes that scheduling problems under certain conditions remain NP-hard.
We study single machine scheduling problems with generalized due-dates. The scheduling measure is minimum total late work. We show that unlike the classical version (assuming job-specific due-dates), this problem has a polynomial time solution. Then, the problem is extended to allow job rejection. First, an upper bound on the total permitted rejection cost is assumed. Then we study the setting whereby the rejection cost is part of the objective function, which becomes minimizing the sum of total late work and rejection cost. We prove that both versions are NP-hard, and introduce pseudo-polynomial dynamic programming solution algorithms. We then consider a setting in which the machine is not available for some period (e.g., due to maintenance). Again, a pseudo-polynomial dynamic programming is introduced for the (NP-hard) problem of minimizing total late work with generalized due-dates and unavailability period. These dynamic programming algorithms are tested numerically, and proved to perform well on problems of various input parameters. Then, the extension to the weighted case, i.e., the problem of minimizing total weighted late work with generalized due-dates is proved to be NP-hard. Finally, we study a slightly different setting, in which the given due-dates are assigned to jobs, but there is no restriction on their order, i.e., the j-th due-date is not necessarily assigned to the j-th job in the sequence. We show that this problem (known as scheduling assignable due-dates) to minimize total late work is NP-hard as well. (C) 2021 Elsevier B.V. All rights reserved.

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