A Single Machine Scheduling Problem with Discrete Machine Conditions

In a real workshop, machine condition is an essential constraint to achieve an overall scheduling optimization. This paper studies a single machine scheduling problem with discrete machine conditions constraint and maintenance consideration. The scheduling sequence decides the actual processing time of jobs by the processing position in scheduling sequence. A tradeoff exists between the rejection of maintenance resulting in longer processing time and acceptance of maintenance leading to the delay of future jobs. A finite-horizon Markov decision process models the problem to minimize the makespan. An optimal scheduling decision sequence is developed to deal with the dynamic evolution. Computational experiments are conducted to evaluate the proposed approach.