Single Machine Inserted Idle Time Scheduling with Release Times and Due Dates

The single machine scheduling problem is considered in which each task has a release dates, a processing time and a due date. The objective is to mimimize the maximum lateness. Preemption is not allowed. Scheduling problem 1|rj |Lmax is a NP-hard problem. We define an IIT (inserted idle time) schedule as a feasible schedule in which a processor is kept idle at a time when it could begin processing an operation. We propose an approximate IIT algorithm named ELS/IIT (earliest latest start/ inserted idle time) and branch and bound algorithm, which produces a feasible IIT schedule for a fixed the maximum lateness L. In order to optimize over L we must iterate the scheduling process over possible values of L. New dominance criteria are introduced to curtail the enumeration tree. By this approach it is generally possible to eliminate most of the useless nodes generated at the lowest levels of decision tree.