Scheduling for parallel machines with different efficiencies

This paper concerns a scheduling problem for parallel machines with different machining efficiencies. Each job has a common due date. Neither tardiness nor early shipping are allowed. Therefore, jobs completed early must be stored in the shop until the due date. Under these conditions the actual flow time of each job is measured from the starting time until the due date. The performance measure of schedules is the total actual flow time. An analytical procedure leads to some theorems to determine the assignment of jobs to each machine. An optimal algorithm based on these theorems is presented. A numerical example illustrates the procedure of the algorithm.