Single-machine scheduling with deteriorating effects and machine maintenance

In this paper, the single-machine scheduling problems with deteriorating effects and a machine maintenance are studied. In this circumstance, the deterioration rates of the jobs during the machining process are the same which reduces the production efficiency. The actual processing time of the job is a linearly increasing function of the starting time. In this process, the machine only performs a maintenance activity, and the maintenance time is a fixed value. After the maintenance work is completed, the machine will be restored to the initial state, and the deterioration of the job will be start again. The goal is to determine the optimal schedule in order to minimise the maximum completion time (i.e. the makespan) and the sum of job completion times. We prove that both problems are polynomial time solvable, and we also provide the corresponding algorithms.