Methods for the Evaluation of Permutations as Strategies in Stochastic Scheduling Problems

A collection of stochastic jobs is to be processed by a single machine in a manner which is consistent with a precedence relation on the job set. Costs are incurred as jobs are processed and rewards are earned when they complete. The problem of finding optimal processing strategies is in general very complex. However, algorithms exist which in many cases yield the strategies which are optimal among those which are simply permutations of the job set. In light of this, the question of how well permutations perform as strategies is an important one. We present methods which aim to answer this question. They are based on earlier results by Glazebrook.