Multipurpose machine scheduling with rejection and identical job processing times

We study a set of scheduling problems on a uniform machine setting. We focus on the case of equal processing time jobs with the additional feature of job rejection. Jobs can either be processed on a predefined set of machines or rejected. Rejected jobs incur a rejection penalty and have no effect on the scheduling criterion under consideration. A solution to our problems consists of partitioning the jobs into two subsets, AA and A¯¯¯¯A¯ , which are the set of accepted and the set of rejected jobs, respectively. In addition, jobs in set AA have to be scheduled on the mm machines. We evaluate the quality of a solution by two criteria. The first, F1F1 , can be any regular scheduling criterion, while the latter, F2F2 , is the total rejection cost. We consider two possible types of regular scheduling criteria; the former is a maximization criterion, while the latter is a summation criterion. For each criterion type we consider four different problem variations. We prove that all four variations are solvable in polynomial time for anyany maximization type of a regular scheduling criterion. When the scheduling criterion is of summation type, we show that only one of the four problem variations is solvable in polynomial time. We provide a pseudo-polynomial time algorithms to solve interesting variants of the NPNP -hard problems, as well as a polynomial time algorithm that solves various other special cases.