A Stochastic Scheduling Problem with Intree Precedence Constraints

We consider n jobs to be scheduled on two parallel machines. The jobs are subject to intree precedence constraints, that is, each job, except one which is the root of the tree, has one successor. The job of the root is at level 0 and a job is at level l if its predecessor is at level l − 1. A job can start to be processed only after all its predecessors have finished. Job processing times are independent random variables with those at the same level being identically distributed. The objective is to minimize the expected completion time of the last job. Such a model can be applied to assembly line and computational problems. This paper generalizes a result of Pinedo and Weiss.