On the complexity of generalized due date scheduling problems

The authors study the recently identified class of generalized due date scheduling problems. These are machine scheduling problems for which due dates are specified according to the position in which a job is completed, rather than the identity of that job. Flexible manufacturing environments and public sector planning problems provide applications. The authors study a wide variety of these problems, with a view to determining their computational complexity. In several instances a problem which is NP-hard under a traditional due date definition admits an efficient algorithm under the new definition. As well as determining the complexity of many generalized due date scheduling problems, including one published open problem, the authors also describe several problems, the complexity of which is still unresolved.