Single Machine Scheduling Problem When the Machine Capacity Varies Stochastically

We consider single machine scheduling problems when the machine capacity varies stochastically over time. Suppose that R(t) ≥ 0 processing requirements can be processed per unit of time at time t. First, we treat the general “machine capacity” R(t) and then consider the machine breakdown models where R(t) = 0 or 1. Jobs may arrive according to an arbitrary process. We show that simple priority rules are optimal under some assumptions. Specifically, the cμ rule minimizes the expected weighted total number of jobs if the processing requirements are exponentially distributed. The SEPT rule minimizes the expected total number of jobs if the processing requirements of jobs are stochastically ordered. The SERPT rule also minimizes it if the processing requirements form an ICR family.