Stochastic single machine scheduling with earliness and tardiness penalties and proportional weights

The problem of minimizing total weighted deviations of job completion times from a common due date on a single machine is a typical scheduling model in a just-in-time production environment. It is a NP-hard problem. However, the largest processing time job sequence is optimal for the case where job weights are proportional to processing times. In this paper, we consider the stochastic counterpart of this problem with proportional weights. The processing times and the due date are exponentially distributed random variables with arbitrary positive rates. It is shown that the largest expected processing time job sequence is optimal. Moreover, the version where the machine is subject to stochastic breakdowns is also discussed.