Problem F2∥Cmax with forbidden jobs in the first or last position is easy |
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Authors: | Mikhail Y Kovalyov Frank Werner |
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Institution: | 1. Faculty of Economics, Belarus State University, and United Institute of Informatics Problems, National Academy of Sciences of Belarus, Skorini 4, 220050 Minsk, Belarus;2. Faculty of Mathematics, Otto-von-Guericke-University Magdeburg, PSF 4120, 39016 Magdeburg, Germany |
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Abstract: | Saadani et al. N.E.H. Saadani, P. Baptiste, M. Moalla, The simple F2∥Cmax with forbidden tasks in first or last position: A problem more complex that it seems, European Journal of Operational Research 161 (2005) 21–31] studied the classical n-job flow shop scheduling problem F2∥Cmax with an additional constraint that some jobs cannot be placed in the first or last position. There exists an optimal job sequence for this problem, in which at most one job in the first or last position is deferred from its position in Johnson’s S.M. Johnson, Optimal two- and three-stage production schedules with setup times included, Naval Research Logistics Quarterly 1 (1954) 61–68] permutation. The problem was solved in O(n2) time by enumerating all candidate job sequences. We suggest a simple O(n) algorithm for this problem provided that Johnson’s permutation is given. Since Johnson’s permutation can be obtained in O(n log n) time, the problem in Saadani et al. (2005) can be solved in O(n log n) time as well. |
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Keywords: | Scheduling Flow shop Makespan |
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