Scheduling with a class of objective functions on a single machine subjected to stochastic breakdowns

In this paper, a scheduling problem with a class of objective functions on a single machine which is subjected to stochastic breakdowns is discussed. The deterministic equivalent objective function is developed for the condition that the counting process N(t) describing the number of breakdowns is a generalized Poisson process. For the two cases that (1) the processing times are equal and (2) the weights of jobs are proportional to their processing times, several properties of the optimal sequences are established.