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

Gur Mosheiov, Daniel Oron and Dvir Shabtay

European Journal of Operational Research, 2021, vol. 293, issue 3, 837-846

Abstract: 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.

Keywords: Scheduling; Single machine; Total late work; Generalized due-dates; Job rejection; Unavailability period (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221720311231
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:293:y:2021:i:3:p:837-846

DOI: 10.1016/j.ejor.2020.12.061

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().