The complexity of customer order scheduling problems on parallel machines

This paper considers scheduling problems where a set of jobs (customer order) is shipped at the same time. The objective function is associated with the completion time of the orders. While a machine can process only one job at a time, multiple machines can process simultaneously jobs in an order. We first introduce this relatively new class of the customer order scheduling problems on parallel machines. Then, we establish the complexity of several problems with different types of objectives, job restrictions, and machine environments. For some tractable cases, we propose optimal solution procedures.