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This paper addresses the problem of joint production and preventive maintenance (PM) planning of a deteriorating manufacturing system generating greenhouse gas (GHG) emissions. The system is composed of a deteriorating machine, subject to random failures and repairs evolving in a dynamic and stochastic context. The main objective is to develop control policies that minimize the sum of backlog, inventory, maintenance, and emission costs. The stochastic optimal control theory based on the dynamic programming approach is used to obtain the optimality conditions and the optimal control policies, which are determined using numerical methods. Sensitivity analyses are provided to depict and validate the obtained structure of the production and PM policies characterized by multiple thresholds that jointly regulate the production and PM rates with the age, emissions, and inventory levels. Furthermore, we compared the performance of the obtained control policies with that of the most relevant policies found in the literature and showed their superiority by considerable cost savings. Finally, the proposal’s implementation is provided to equip managers of the considered manufacturing system with an effective and robust decision-support tool.
Gharbi et al. (2024) studied this question.