A survey on offline scheduling with rejection

In classical deterministic scheduling problems, it is assumed that all jobs have to be processed. However, in many practical cases, mostly in highly loaded make-to-order production systems, accepting all jobs may cause a delay in the completion of orders which in turn may lead to high inventory and tardiness costs. Thus, in such systems, the firm may wish to reject the processing of some jobs by either outsourcing them or rejecting them altogether. The field of scheduling with rejection provides schemes for coordinated sales and production decisions by grouping them into a single model. Since scheduling problems with rejection are very interesting both from a practical and a theoretical point of view, they have received a great deal of attention from researchers over the last decade. The purpose of this survey is to offer a unified framework for offline scheduling with rejection by presenting an up-to-date survey of the results in this field. Moreover, we highlight the close connection between scheduling with rejection and other fields of research such as scheduling with controllable processing times and scheduling with due date assignment, and include some new results which we obtained for open problems.