This paper uses a formulation of the job shop problem with due dates that allows successive operations on a job to overlap in the schedule. Setup times and multiple transports of sublots are two applications where this formulation can result in technologically feasible schedules. A procedure is described for generating multiple transport schedules. Results from a set of test problems indicate that multiple transport scheduling may sometimes be a very economical way to meet due dates without overtime operations. More generally, the procedure provides for managerial assessment of trade-offs between tardiness, overtime, and the use of multiple transports; as well as combinations of these criteria.