Scheduling with resource allocation and past-sequence-dependent setup times including maintenance

In this work, scheduling problems with resource allocation and past-sequence-dependent (p-s-d) setup times are considered. Under these settings, the actual job processing times are dependent on the amount of resource allocated and the setup times are proportionate to the length of the already processed jobs. The objective function is a combination of the total completion time and the total resource consumption. In addition, the machine may need maintenance to improve its production efficiency, so the maintenance is also integrated. The optimal job sequence, the optimal amount of resource allocated to each job, and the optimal maintenance position are determined jointly. It is shown that the problem under study is polynomial time solvable.