Abstract
We study two single machine scheduling problems with two competing agents and the option of rejecting jobs. We seek to minimize the scheduling criterion of one agent under the condition that the maximum completion time of the second agent does not exceed a given upper-bound. Moreover, we assume that jobs are either scheduled or rejected (incurring job-dependent penalties) subject to an upper bound on the total rejection cost. The scheduling objective for the first agent is either the makespan or the total completion time, while that of the second agent is the makespan. As both problems are known to be NP-hard, we develop efficient pseudo-polynomial dynamic programming algorithms to obtain optimal solutions. The algorithms are shown to efficiently solve medium to large size problems through an extensive numerical study.
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