Abstract
In this paper, we study a robust single-machine scheduling problem under four alternative optimization criteria: minimizing total completion time, minimizing total weighted completion time, minimizing maximum lateness, and minimizing the number of late jobs. We assume that job processing times are subject to uncertainty. Accordingly, we construct three alternative uncertainty sets, each of which defines job processing times that can simultaneously occur. The robust optimization framework assumes that, given a job schedule, a worst-case set of processing times will be realized from among those allowed by the uncertainty set under consideration. For each combination of objective function and uncertainty set, we first analyze the problem of identifying a set of worst-case processing times with respect to a fixed schedule, and then investigate the problem of selecting a schedule whose worst-case objective is minimal.
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Acknowledgments
The authors sincerely appreciate the comments made by two anonymous referees. Dr. Smith gratefully acknowledges the support of the National Science Foundation under Grant CMMI-1100765, the Defense Threat Reduction Agency under Grant HDTRA-10-01-0050, the Air Force Office of Scientific Research under Grant FA9550-12-1-0353, and the Office of Naval Research under Grant N000141310036.
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Tadayon, B., Smith, J.C. Algorithms and Complexity Analysis for Robust Single-Machine Scheduling Problems. J Sched 18, 575–592 (2015). https://doi.org/10.1007/s10951-015-0418-0
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DOI: https://doi.org/10.1007/s10951-015-0418-0