Abstract
This paper addresses a stochastic scheduling problem in which a set of independent jobs are to be processed by a number of identical parallel machines under a common deadline. Each job has a processing time, which is a random variable with an arbitrary distribution. Each machine is subject to stochastic breakdowns, which are characterized by a Poisson process. The deadline is an exponentially distributed random variable. The objective is to minimize the expected costs for earliness and tardiness, where the cost for an early job is a general function of its earliness while the cost for a tardy job is a fixed charge. Optimal policies are derived for cases where there is only a single machine or are multiple machines, the decision-maker can take a static policy or a dynamic policy, and job preemptions are allowed or forbidden. In contrast to their deterministic counterparts, which have been known to be NP-hard and are thus intractable from a computational point of view, we find that optimal solutions for many cases of the stochastic problem can be constructed analytically.
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.