High-multiplicity scheduling on one machine with forbidden start and completion times

We are interested in a single machine scheduling problem where no task can either start or end on some dates and the input is given using a compact encoding. The aim is to minimize the makespan. We present a polynomial time algorithm for large diversity instances (when the number of different processing times is bigger than the number of forbidden dates). We also show that this problem is fixed parameter tracktable when the number of forbidden dates is fixed, regardless of tasks characteristics.