This paper examines the behavior of several single machine scheduling problems when presented with times that are random and potentially dependent. A position-based learning effect model is revisited and optimal schedules are derived under several typical performance measures. A sum-of-processing-time based model is proposed to incorporate the learning effects and deteriorations in one unified framework. Optimal schedules are derived to minimize the maximum lateness or jointly minimize the completion times under the proposed model, and the model is used to solve the optimal issuing problem.
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The author acknowledges valuable comments from the two anonymous reviewers, which greatly improve the presentation of this paper. The author also thanks the support by the Research and Creative Activities Support grant (Grant No. AAC2253) and the startup grant (Grant No. PRJ69VR) from the University of Wisconsin-Milwaukee.
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Wei, W. Single machine scheduling with stochastically dependent times. J Sched 22, 677–689 (2019). https://doi.org/10.1007/s10951-019-00600-2
- Stochastic scheduling
- Completion times
- Maximum lateness
- Expected total cost
- Deteriorations/learning effects