For the stochastic E/T problem, no efficient optimizing algorithm is known. The purpose of this exercise is to prove the proposition that no transitive sorting algorithm can solve the problem optimally. Consider three normally-distributed jobs with (α1 + β1)ϕ(z∗

1) = (α2 + β2)ϕ(z∗

2) = 1, (α3 + β3)ϕ(z∗

3) = 5, σ2 1

= σ2 2

= 1, and σ2 3

= 22. Any transitive sorting rule must sequence identical jobs consecutively, because they have the same values. To prove that no such rule exists, show that the optimal sequence places job 3 between the two identical jobs.