Integrated production and maintenance scheduling for a single degrading machine with deterioration-based failures

Abstract In production lines, several factors contribute to the manufacturing of final products. Among these factors, the production time, machine status, and energy consumption, before and during production, need to be investigated further. In this paper, we present a mathematical model which jointly optimizes production scheduling and maintenance planning in a single-machine production environment. The performance of the machine deteriorates with time, and the machine is subject to stochastic deterioration-based failures. We assume that the transitions between the machine’s deterioration states follow an exponential distribution. We consider that processing times and energy consumption are affected by machine deterioration and failures. The main contribution of the paper is that maintenance and scheduling decisions are made based on the machine’s degradation level (i.e., the machine’s condition). We address the machine’s deterioration as a discrete multi-state degradation process; and model the effects of the machine’s deterioration and failures on the duration of job processing and the machine’s energy consumption. Then, we develop a stochastic mixed-integer programming model that integrates decisions about maintenance and production scheduling. The model generates the optimal maintenance action for each degradation state, as well as the optimal inspection policy and job sequence, with the overall aim being to minimize the total cost, including: inspection costs, repair costs, machine energy consumption costs, and the makespan penalty for exceeding a predetermined threshold. Due to the complexity of the developed model, an effective genetic algorithm (GA) based on the properties of the considered problem is proposed. Finally, through a comparative numerical study, we show that making decisions according to the deterioration level of the machine results in more integrated and cost-effective plans compared to the current method of repairing the machine only once it has reached its failure state.