Joint optimization of maintenance and production scheduling

Abstract

Maintenance and production scheduling are interconnected activities which should be planned jointly to minimize their total cost as well as jobs tardiness. Although, the joint optimization of maintenance planning and production scheduling has been addressed extensively in literature, no study has considered production and maintenance optimization based on the concept of delay-time model (DTM). DTM has been effectively utilized in industry for inspection optimization of various systems, such as oil-hydraulic extrusion press, production plant, and industrial vehicles. The DTM considers a two-stage failure process for a system, in which an initial defect will eventually lead to a failure, if left unattended. The elapsed time between a defect occurrence and the failure (in the absence of inspection) is called delay-time, which provides a window of opportunity to inspect the system and fix the defect. In this paper, we consider a single system in a manufacturing plant which is required to process n independent jobs, while a job cannot be preempted for another job. We assume that the system has a single dominant failure mode, and model the system's failure using the DTM concept, in which the time to a defect appearance and the delay time follow certain distributions. The delay time distribution is independent of the time to defect. The system can be completely renewed by preventive replacement before a job to reduce the probability of a defect arrival and its subsequent failure while the job is being processed. An unattended defect may lead to a failure, which causes the system shutdown. The system is then replaced after a failure, and the job is restarted. We assume that the time required for a preventive replacement of the system is shorter than the time required for corrective replacement after a failure. We will jointly optimize preventive maintenance and production scheduling which results in the minimum total expected cost consisting of tardiness penalty and preventive and corrective maintenance costs. More specifically, we will determine the optimal sequence of the jobs as well as the decision on whether or not preventive replacement should be performed before a specific job. We will formulate the objective function and derive analytic expressions to obtain the total expected cost for a given sequence of jobs and a preventive replacement scheme. The application of the proposed model is shown in a case study. The results of the study indicate the optimal job sequence obtained from the joint optimization problem could differ from the case where the optimal sequence is obtained in a standalone scheduling problem. Moreover, the optimal solution depends on the input parameters of the model, most specifically, the job processing times and the distributions of defect arrival and delay time.