TY - JOUR

T1 - Minimizing total late work on a single machine with generalized due-dates

AU - Mosheiov, Gur

AU - Oron, Daniel

AU - Shabtay, Dvir

N1 - Funding Information:
This research was supported by the Israel Science Foundation (grant No. 2505/19 ). The first author was also supported by the Charles I. Rosen Chair of Management, and by The Recanati Fund of The School of Business Administration of The Hebrew University.
Publisher Copyright:
© 2021 Elsevier B.V.

PY - 2021/9/16

Y1 - 2021/9/16

N2 - 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.

AB - 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.

KW - Generalized due-dates

KW - Job rejection

KW - Scheduling

KW - Single machine

KW - Total late work

KW - Unavailability period

UR - http://www.scopus.com/inward/record.url?scp=85099629708&partnerID=8YFLogxK

U2 - 10.1016/j.ejor.2020.12.061

DO - 10.1016/j.ejor.2020.12.061

M3 - Article

AN - SCOPUS:85099629708

VL - 293

SP - 837

EP - 846

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -