Minimizing Makespan with Bimodal Processing Time Distributions

We consider the problem of scheduling n tasks on two identical parallel processors. Task i has a processing time of one time unit, but might have to undergo processing for a second time unit with probability p_i, i.e., the processing time distributions of the tasks have mass only on one and on two. We are interested in the sequence in which to process these tasks in order to minimize the expected completion time of all tasks. The optimal sequence turns out to be a sequence not well-known in the theory of scheduling.