On Minimizing the Expected Makespan and Flow Time in Stochastic Flow Shops with Blocking

Consider an m machine flow shop with no intermediate storage between any two successive machines and blocking. The processing time of job j, j = 1, …, n, on each one of the m machines is equal to the random variable X_j and is distributed according to F_j. We assume that the processing times are stochastically ordered in such a way that F₁ ≤_st ⋯ ≤_stF_n. We show that the sequence 1, 3, 5, …, n − 1, n, n − 2, …, 6, 4, 2 when n is even and the sequence 1, 3, 5, …, n − 2, n, n − 1, …, 6, 4, 2 when n is odd minimizes the expected makespan and that the sequence 1, …, n minimizes the expected flow time.