Stochastic single machine scheduling with an exponentially distributed due date

Abstract

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 Λ-shaped, i.e., the sequence of w iλ 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 λ 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.