Abstract
We treat the two-machine flowshop problem with the objective of minimizing the expected makespan when the jobs possess stochastic durations of arbitrary distributions. We make three contributions in this paper: (1) we propose an exact approach with exponential worst-case time complexity. We also propose approximations which are computationally modest in their requirements. Experimental results indicate that our procedure is within less than 1% of the optimum; and (2) we provide a more elementary proof of the bounds on the project completion time based on the concepts of 'control networks'; and (3) we extend the 'reverse search' procedure of Avis and Fukuda [1] to the context of permutation schedules.
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Elmaghraby, S.E., Thoney, K.A. The two-machine stochastic flowshop problem with arbitrary processing time distributions. IIE Transactions 31, 467–477 (1999). https://doi.org/10.1023/A:1007697625481
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DOI: https://doi.org/10.1023/A:1007697625481