Article ID: | iaor2001692 |
Country: | United States |
Volume: | 47 |
Issue: | 3 |
Start Page Number: | 422 |
End Page Number: | 437 |
Publication Date: | May 1999 |
Journal: | Operations Research |
Authors: | Cai Xiaoqiang, Zhou Sean |
This paper addresses a stochastic scheduling problem in which a set of independent jobs are to be processed by a number of identical parallel machines under a common deadline. Each job has a processing time, which is a random variable with an arbitrary distribution. Each machine is subject to stochastic breakdowns, which are characterized by a Poisson process. The deadline is an exponentially distributed random variable. The objective is to minimize the expected costs for earliness and tardiness, where the cost for an early job is a general function of its earliness while the cost for a tardy job is a fixed charge. Optimal policies are derived for cases where there is only a single machine or there are multiple machines, the decision-maker can take a static policy or a dynamic policy, and job preemptions are allowed or forbidden. In contrast to their deterministic counterparts, which have been known to be NP-hard and are thus intractable from a computational point of view, we find that optimal solutions for many cases of the stochastic problem can be constructed analytically.