Scheduling 2 job classes on parallel machines

The problem of scheduling n jobs on m parallel machines is considered where the jobs are partitioned into two priority classes. The objective is to minimize the total flowtime subject to the constraint that no job in the lower-priority class precedes any job in the higher-priority class that is assigned to the same machine. Conditions for feasibility are derived and used to develop a polynomially bounded dynamic programming algorithm that finds an optimal schedule.