Here is how I would describe the problem in “Complexity of scheduling jobs on arcs in a network” by user thomas.
Complexity of scheduling maintenance jobs so that the number of maintenance days is minimized
There are three machines in a factory, and every day each machine can process at most one job. For each machine, we are given a list of jobs which have to be processed on that machine. Each job takes one day to complete. Each job j has release date rj and deadline dj, both integers and satisfying rj ≤ dj, meaning that job j must be processed on a day between rj and dj, inclusive.
Imagine that these jobs are maintenance jobs. If any of the machines is processing any of the jobs, the whole factory has to be closed for maintenance on that day. Therefore, we would like to schedule the job