Multiprocessor Scheduling with Rejection
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This paper re-examines the classical problem of minimizing maximum lateness which is defined as follows: given a collection of njobs with processing times and due dates, in what order should they be processed on a single machine to minimize maximum lateness? The lateness of a job is defined as its completion time minus its due date. This problem can be solved easily by ordering the jobs in non-decreasing due date order. We now consider the following question: which subset of kjobs should we reject to reduce the maximum lateness by the largest amount? While this problem can be solved optimally in polynomial time, we show the following surprising result: there is a fixed permutation of the jobs, such that for all k, if we reject the first kjobs from this permutation, we derive an optimal solution for the problem in which we are allowed to reject kjobs. This allows for an incremental solution in which we can keep incrementally rejecting jobs if we need a solution with lower maximum lateness value. Moreover, we also develop an optimal O(nlogn) time algorithm to find this permutation.