Abstract
We consider an uncertain single-machine scheduling problem, in which the processing time of a job can take any real value from a given closed interval. The criterion is to minimize the sum of weighted completion times of the n jobs, a weight being associated with each job. For a job permutation, we study the stability box, which is a subset of the stability region. We derive an O(n logn) algorithm for constructing a job permutation with the largest dimension and volume of a stability box. The efficiency of such a permutation is demonstrated via a simulation on a set of randomly generated instances with 1000 ≤ n ≤ 2000. If several permutations have the largest dimension and volume of a stability box, the developed algorithm selects one of them due to a mid-point heuristic.
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Sotskov, Y.N., Lai, TC., Werner, F. (2013). The Stability Box for Minimizing Total Weighted Flow Time under Uncertain Data. In: Pina, N., Kacprzyk, J., Filipe, J. (eds) Simulation and Modeling Methodologies, Technologies and Applications. Advances in Intelligent Systems and Computing, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34336-0_3
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DOI: https://doi.org/10.1007/978-3-642-34336-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34335-3
Online ISBN: 978-3-642-34336-0
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