An integrated model of production scheduling and inspection planning for resumable jobs

We developed a model that integrates the schedule of a sequence of resumable jobs and inspection policy for the processing of n jobs with different processing times in a single-component system, whose failures follow a two-stage process. The assignment of inspections is performed at the beginning of the job; if an inspection detects the system to be in a defective state, preventive replacement is performed, whereas if the system fails, minimal repair is carried out to restore the system to an operational condition in the defective state. Analytical and simulation models are proposed to establish the best sequence of jobs and inspections that minimize the expected total cost. The expected total cost is composed of expected maintenance cost and expected tardiness cost. We present a numerical study that demonstrates the importance of integrating inspection policy with the sequencing of jobs, as such integration can lead to a significant cost reduction. The most interesting insights brought by the model highlight the importance of the effectiveness of maintenance actions (perform actions in smaller time and less cost), as well as the importance of deciding the correct moment to do them, considering the sequence of jobs.