Single-machine stochastic scheduling with dependent processing times

Abstract

A single machine is available to process a collection of stochastic jobs preemptively. Rewards are received at job completions. We seek policies for machine allocation which maximize the total reward. Application areas point to the need to study such models for resource allocation when job processing requirements are dependent. To this end, models are developed in which the nature of such dependence is derived from various notions of positive and negative dependence in common usage in reliability. Optimal policies for resource allocation of simple structure are obtained for a variety of such models.

On permutation policies for the scheduling of deteriorating stochastic jobs on a single machine

“…An important simplifying assumption in almost all of the work just cited is that the future processing requirement ofajob should always be independent of the nature of any On permutation policies for the scheduling ofdeteriorating stochastic jobs 185 processing received in the past by other jobs. See Glazebrook and Whitaker (1992) for a discussion of some models where this is not the case. Moreover, Browne and Yechiali (1990) introduce a class of non-preemptive linear deterioration models in which the processing requirement of a job grows linearly as it awaits processing.…”