Abstract
A single machine scheduling problem where the objective is to minimize the variance of job completion times is considered. The model is applicable to many environments where it is desirable to provide jobs, customers or computer files, with approximately the same service. It is shown that the problem can be formulated as a problem of maximizing a zero-one quadratic function which is a submodular function with a special cost structure. It immediately follows from the cost structure that value of the function for a sequence that minimizes total absolute deviation about a common unrestrictive due date is at most 100% smaller than the one for an optimal sequence for the completion time variance problem. The Monge property holds for the costs. Other simple properties of the function are also presented. A pair of dynamic programs for maximizing the function is proposed. The worst case time complexity of the best of the pair is O( n 2spt), where spt is the mean flow time of an SPT-schedule for all jobs except the longest one.
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.