Multitasking Scheduling with Part Jobs Interrupted Assignment

We consider the scheduling problem with part jobs interrupted assignment in the multitasking environment on single machine, which can be found in various application domains, such as Internet services. Motivated by the former operations, we extend the the original model considering that some job are uninterrupted job. We introduce some definitions that is typically used for scheduling in the multitasking environment. Our objective is to minimise weighted tardiness, earliness and common due date, we devise a mixed integer programme. We give some basic lemmas and properties to solve the problem, provide a solution algorithm for a case of the problem. Finally, we conclude the paper and suggest topics for future research.