THREE-MACHINE SCHEDULING PROBLEM WITH PRECEDENCE CONSTRAINTS

This paper deals with a three-machine flow-shop problem in which some of the job sequences are infeasible. It is assumed that jobs are grouped into several disjoint subsets within which a job order is pre-determined. Once the first job in a group has started on a machine, then the entire group must be completed on the machine with-out starting a job which does not belong to the group. It is further assumed that a precedence relation between groups is given such that the processing of the jobs in a group must be completed on each machine before the jobs in another group begin on the machine. It is shown that it suffices to consider only permutation schedules for minimizing the total elapsed time and then some restricted cases are solved.