We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of...

Most research on single machine scheduling has assumed the linearity of job holding costs, which is arguably not appropriate in some applications. This motivates our study of a model for scheduling $n$ classes of stochastic jobs on a single machine, with the objective of minimizing the total...