Joint optimizing the Production Sequence and Maintenance Plan for a Single-Machine Multi-Failure System

In this paper, we consider a single-machine manufacturing system in which data about the status of its critical components are instantly available. We aim to optimize simultaneously the jobs sequence and maintenance actions to minimize the total cost of the considered production system. Since the machine parts are subject to several failures during the production, the maintenance actions are either to imperfect repair or replacement, taking into considerations that parts' imperfect repair do not make these parts as good as new. The manufacturing system's cost includes the machine's parts repair or replacement cost, and the penalty if the jobs completion time exceeds a predefined threshold. We assume that the lifetime of the machine's parts has a Weibull distribution. We study a machine cutting tool and engine among others. We consider that the failure of the cutting tool decreases the product's (job) quality, and this product (job) needs to be restarted processing after the imperfect repair or replacement of the tool. For this part, we consider an age-based threshold; if the tool has failed before the threshold, the maintenance action is imperfect repair; otherwise, the tool is replaced by the new one. One of the model objectives is to find the optimal value of this threshold. If the engine fails during the processing of the job, the maintenance action is imperfect repair. The failures of the engine have no effect on the product quality; thus, the product process resumes after engine imperfect repair. The tool and engine imperfect repairs affect the life distribution parameter (scale parameter of Weibull distribution, $\theta$), but tool replacement makes the tool as good as new and presents a mathematical model with the aim of minimizing the total production cost when the system is subject to these two-failure modes. Since the lifetime of the machine's parts follows a Weibull distribution, we use a Monte Carlo simulation for calculating the jobs' completion time and the system's total cost. Job scheduling and maintenance planning problems are NP-hard problems, so we use a Genetic algorithm (GA) to solve the presented model.