Abstract
A single machine stochastic scheduling problems with the jobs’ processing times are considered the random of uniform distribution and the objective is to find an optimal schedule to minimize the expectation of the weighted numbers of tardy jobs from a common due date. By theoretical analysis, the problem formulation of the expectation of the weighted numbers of tardy jobs can be given. For the two cases (1) the weights of jobs are equal and (2) the weights of jobs are proportional to their processing times, the SEPT (shortest expected processing time first) is optimal. Joint use solution the SEPT and the LEPT (longest expected processing time first) is optimal in the case of the expected processing time is non-proportional to weighty of the jobs. The optimality of the algorithms is proved.
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References
Pinedo, M.: Stochastic scheduling with release dates and due dates. Operations Research 31, 559–572 (1983)
Pinedo, M., Rammouz, E.: A note on stochastic scheduling on a single machine subject to breakdown and repair. Probability in the Engineering and Information Sciences 2, 41–49 (1988)
Frenk, J.B.G.: A general framework for stochastic one-machine scheduling problems with zero release times and no partial ordering. Probability in the Engineering and Informational Sciences 5, 297–315 (1991)
Forst, F.G.: Stochastic sequencing on one machine with earliness and tardiness penalties. Probability in the Engineering and Informational Sciences 7, 291–300 (1993)
Jia, C.: Stochastic single machine with an exponentially distributed due date. Operations Research Letters 28, 199–203 (2001)
Sarin, S.C., Steiner, G., Erel, G.: Sequencing jobs on a single machine with a common due date and stochastic processing times. European Journal of Operational Research 51, 188–198 (1990)
Alidee, B., Dragon, I.: A note on minimizing the weighted sum of tardy and early completion penalties in a single machine: A case of small common due dates. European Journal of Operational Research 96(3), 559–563 (1997)
Li, Y., Zeng, F.: Stochastic single machine scheduling with uniform distributed processing times. Journal of Liaoning Technical University (Natural Science) 27, 469–471 (2008) (in Chinese)
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Li, Y., Chen, R. (2010). Stochastic Single Machine Scheduling to Minimize the Weighted Number of Tardy Jobs. In: Cao, By., Wang, Gj., Guo, Sz., Chen, Sl. (eds) Fuzzy Information and Engineering 2010. Advances in Intelligent and Soft Computing, vol 78. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14880-4_38
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DOI: https://doi.org/10.1007/978-3-642-14880-4_38
Publisher Name: Springer, Berlin, Heidelberg
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