Scheduling stochastic two-machine flow shop problems to minimize expected makespan

During the past few years, despite tremendous contribution on deterministic flow shop problem, there are only limited number of works dedicated on stochastic cases.This paper examines stochastic scheduling problems in two-machine flow shop environment for expected makespan minimization where processing times of jobs are normally distributed.Since jobs have stochastic processing times, to minimize the expected makespan, the expected sum of the second machine's free times is minimized.In other words, by minimization waiting times for the second machine, it is possible to reach the minimum of the objective function.A mathematical method is proposed which utilizes the properties of the normal distributions.Furthermore, this method can be used as a heuristic method for other distributions, as long as the means and variances are available.The performance of the proposed method is explored using some numerical examples.