A joint optimization model for production scheduling and preventive maintenance interval

Machine maintenance is performed in production to prevent machine failure in order to maintain production efficiency and reduce failure costs. Due to the importance of maintenance in production, it is necessary to consider an integrated schedule for production and maintenance. Most of the literature on machine scheduling assumes that machines are always available. However, this assumption is unrealistic in many industrial applications. Preventive maintenance (PM) is often performed in a production system to prevent premature machine failure in order to maintain production efficiency. However, this assumption is inappropriate in real industrial cases. Machine maintenance plan is often performed in a production system to prevent premature machine failure in order to maintain production efficiency. Parallel machine layout is very common in modern production systems. Its performance sometime has a key impact on overall productivity. In this paper, a parallel machine scheduling problem with individual maintenance operations is considered. Then, a mathematical model is formulated including scheduling and maintenance operation optimization. The objective is to assign all jobs to machines so that the completion time and the average cost are minimized, jointly. Maintenance is considered in time intervals. To solve the proposed problem, a branch and bound (B&B) algorithm is adapted and proposed. The results show the applicability of the mathematical model in production systems and efficiency of the adapted B&B in comparison with Gams optimization software.