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. (2) We also propose approximations which are computationally modest in their requirements. Experimental results indicate that our procedure is within less than 1 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 to the context of permutation schedules.