Stochastic scheduling on parallel machines subject to random breakdowns to minimize expected costs for earliness and tardy jobs

Stochastic scheduling on parallel machines subject to random breakdowns to minimize expected costs for earliness and tardy jobs

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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: ,
Abstract:

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.

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