Scheduling Job Families on a Single Machine

The problem of scheduling n jobs on a single machine is considered, where the jobs are partitioned into several families and a set – up time is necessary between jobs of different families. The objective is to find a lower bound for the problem of minimizing the sum of completion times and the maximum tardiness. This paper uses a decomposition property to find a lower bound in order to incorporated in a branch and bound algorithm for constructing an optimal schedule.