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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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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