Summary
We consider the classical flow shop problem with m machines, n jobs and the minimum makespan objective. The problem is treated in stochastic formulation, where all operation processing times are random variables with distribution from a given class F. We present a polynomial time algorithm with absolute performance guarantee C max(S) − L ≤ 1.5(m − 1)p + o(1) that holds with high probability (Frieze, 1998) for n → ∞, where L is a trivial lower bound on the optimum (equal to the maximum machine load) and p is the maximum operation processing time. Class F includes distributions with regularly varying tails. The algorithm presented is based on a new algorithm for the compact vector summation problem and constructs a permutation schedule. The new absolute guarantee is superior to the best-known absolute guarantee for the considered problem (C max(S) − L ≤ (m − 1)(m − 2 + 1/(m − 2))p; Sevastyanov, 1995) that holds for all possible inputs of the flow shop problem.
This research was supported by the Russian Foundation for Basic Research (grant 05-01-00960-a)
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Koryakin, R.A., Sevastyanov, S.V. (2006). The Flow Shop Problem with Random Operation Processing Times. In: Haasis, HD., Kopfer, H., Schönberger, J. (eds) Operations Research Proceedings 2005. Operations Research Proceedings, vol 2005. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-32539-5_109
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DOI: https://doi.org/10.1007/3-540-32539-5_109
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