Integrated model of production plan and preventive maintenance based on a game-theoretic framework

A joint model for integrating preventive maintenance (PM) with the capacitated lot sizing problem (CLSP) based on a game-theoretic framework has been proposed. Assume the production rate varies from period to period according to total lot size of each production period (PP). An imperfect PM model is established for system running with dynamic production rate, which is performed at scheduled times, and minimal repair (MR) is adopted to restore the system to work without altering hazard rate when failure happens. Considering availability reduction caused by maintenance and effect of production rate on hazard rate function of system, a Stackelberg game theory model is adopted to handle the interactive effect between production plan and PM schedule. The optimal production rate of each PP and PM sequences are obtained simultaneously. An example is studied to validate the model, also the results are discussed.