Stochastic single machine scheduling with a general objective function

We consider the problem of scheduling n jobs on a single machine which is subject to stochastic breakdowns to minimize the expectation of the linear combination of three functions of job completion times: (i) the weighted sum of the squares, (ii) the square of the weighted mean and (iii) the weighted mean. Many regular and irregular objective functions are the particular cases of this general objective function. The deterministic equivalent objective function of this problem is derived when the counting process N(t) describing the number of the machine breakdowns is a generalized Poisson process. For the two cases: (a) the processing times of the jobs are equal and (b) the weights of the jobs are proportional to their processing times, several properties of the optimal sequences of the problem are developed.