Preemptive scheduling of jobs with tied parameters on a single processor to minimize the number of late jobs

We have n jobs with release times and due-dates to be scheduled on a single-machine that can handle at most one job at a time. Our objective is to minimize the number of late jobs, ones completed after their due-dates. This problem is known to be solvable in time O(n4). We show that the special case of the problem when job processing times and due-dates are tied so that for each pair of jobs i, j with di > dj , pi ≥ pj , can be solved in time O(n2). This particular setting has real-life applications. Key–Words: scheduling single processor, release date, due date, late job, algorithm