Jackson's Rule for Single-Machine Scheduling: Making a Good Heuristic Better

We consider the scheduling problem in which jobs with release dates and delivery times are to be scheduled on one machine. We present a 4/3-approximation algorithm for the problem with precedence constraints among the jobs, and two polynomial approximation schemes for the problem without precedence constraints. At the core of each of the algorithms presented is Jackson's Rule—a simple but seemingly robust heuristic for the problem.