The two-machine stochastic flowshop problem with arbitrary processing time distributions

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 ʹcontrol networksʹ; and (3) we extend the ʹreverse searchʹ procedure of Avis and Fukuda [1] to the context of permutation schedules.