Series-p Arallel Precedence Constraints

The following two-machine flow-shop scheduling problem is solved. Given jobs are classified into groups, and each machine needs some setup before the first job in a group is started processing. If a job in a group is started its process, all jobs in the group must be finished before a job in another group is processed. Each job may have a specified lag time between machines. Moreover, a series-parallel precedence relation may be specified among groups. Find interand intra-group schedules minimizing the total elapsed times on both machines. The proposed method for this problem is based on a new definition of composite jobs and Sidney's theory about seriesparallel algorithms. The proposed method can also solve a version of the problem where each job has setup times not included in the processing times and a series-parallel precedence relation is specified among jobs in a group.