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 - 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
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AN - SCOPUS:85099629708
SN - 0377-2217
VL - 293
SP - 837
EP - 846
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 3
ER -