Just-in-time preemptive one-machine problem with costs of earliness- tardiness, interruption and work in process: A mathematical programming

This paper considers preemption and idle time are allowed in a one-machine scheduling problem with just-in-time (JIT) approach. It incorporates earliness/tardiness penalties, interruption penalties and holding cost of jobs which are waiting to be processed as work-in-process (WIP). Generally in non-preemptive problems, earliness/tardiness penalties are a function of the completion time of the jobs. Then, we introduce a non-linear preemptive scheduling model where the earliness penalty depends on the starting time of a job. The model is linearized by an elaborately-designed procedure to reach the optimum solution. To validate and verify the performance of proposed model, computational results are presented by solving a number of numerical examples.