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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.