Minimizing maximum lateness of jobs with naturally bounded job data on a single machine in polynomial time

We consider the problem of scheduling jobs with given release times and due dates on a single machine to minimize the maximum job lateness. It is NP-hard and remains such if the maximal job processing time is unrestricted and there is no constant bound on the difference between any job release times. We give a polynomial-time solution of the version in which the maximal job processing time and the differences between the job release times are bounded by a constant, which are restrictions that naturally arise in practice. Our algorithm reveals the inherent structure of the problem and also gives conditions when it is able to find an optimal solution unconditionally.