Tight performance in Bayesian Scheduling
AbstractWe consider a stochastic scheduling problem which generalizes traditional stochastic scheduling by introducing parameter uncertainty. Two classes of independent jobs have to be processed by a single machine so as to minimize the sum of expected completion times. The processing times of the jobs are assumed to be exponentially distributed with parameters v and µ, depending on the class of the job. We adopt a Bayesian framework in which µ is assumed to be known, whereas the value of v is unknown. However, the scheduler has specifc beliefs about the parameter v. By processing jobs from the corresponding class, the scheduler can update his beliefs about this parameter yielding better future decision making. For the traditional stochastic scheduling variant, in which the parameters are known, the policy that always processes a job with shortest expected processing time (SEPT) is an optimal policy. In this paper, we show that in the Bayesian framework the performance of SEPT is at most a factor 2 away from the performance of an optimal policy. Furthermore, we construct instances with non-degenerately distributed processing times for which this bound is tight. To our knowledge, this latter result is unique within stochastic scheduling. Finally, we remark that SEPT is asymptotically optimal when the number of jobs of one class tends to infinity, given a fixed number of jobs of the second class.
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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 052.
Date of creation: 2010
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operations research and management science;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-12-04 (All new papers)
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- Megow, Nicole & Vredeveld, Tjark, 2006. "Approximation Results for Preemptive Stochastic Online Scheduling," Research Memoranda 053, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization.
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