Scheduling with random processing times to minimize completion time variance on a single machine subject to stochastic breakdowns

This paper addresses a problem of scheduling n jobs with random processing times on a single machine which is subject to stochastic breakdowns. The objective is to determine a job schedule to minimize the expected completion time variance. The deterministic equivalent of the stochastic scheduling problem is derived when the counting process N(t) related to the machine uptimes is a generalized Poisson process. Two properties of the optimal schedules, such as V-shaped property, are developed.