Scheduling with earliest start and due date constraints

We consider the scheduling of n tasks on a single resource. Each task becomes available for processing at time a i , must be completed by time b i , and requires d i time units for processing. The aim is to find a schedule that minimizes the elapsed time to complete all jobs. We present solution algorithms for this problem when job splitting is permitted and when job splitting is not permitted. Then we consider several scheduling situations which arise in practice where these models may apply.