Stochastic single machine scheduling with an exponentially distributed due date

In this paper, we consider a single machine scheduling problem with random processing times to minimize the expected total weighted deviations of completion times from a random common due date. The processing times and the due date are exponentially distributed. The optimal schedules are shown to be @L-shaped, i.e., the sequence of w"i@l"i(=w"i/E(p"i),p"i is the processing time of job i) (i=1,2,...,n) has a single local maximum, where w"i and @l"i denote the weight and the processing time rate of job i, respectively. Moreover, the case where the machine is subject to stochastic breakdowns is also discussed.

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