A dynamic optimisation approach for a single machine scheduling problem with machine conditions and maintenance decisions

In modern production systems, considering machine conditions is becoming essential to achieving an overall optimisation of the production schedule. This paper studies a single machine scheduling problem, where the actual processing times of jobs depend on their position in the production sequence and maintenance is considered. Moreover, the machine is subject to an uncertain condition variation. There is a trade-off between rejecting a maintenance action, resulting in longer processing times, and accepting a maintenance action, leading to higher processing efficiency for future jobs. The problem is formulated as a finite-horizon Markov Decision Process. The objective is to minimise the makespan. Optimality properties are analysed, based on which a dynamic optimisation approach is developed. Computational experiments demonstrate the effectiveness of the proposed approach.