Stochastic scheduling on a single machine subject to multiple breakdowns according to different probabilities

A set of stochastic jobs is to be processed on a single machine which is subject to several types of breakdowns according to different probabilities. After the machine fails, jobs’ processing time, uptime and repair time of the machine may be different from the original period. The authors find the optimal nonpreemptive policies that minimize the following objective functions: (1) the weighted sum of the completion times, (2) the weighted number of late jobs have constant due dates, (3) the weighted number of late jobs having random due dates. These results partly generalize the conclusions obtained by Pinedo and Rammouz and (i) Xie and Zheng (ii).