A Bayesian approach to the triage problem with imperfect classification |
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Authors: | Dong Li Kevin D. Glazebrook |
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Affiliation: | a Avis Europe, Avis House, Park Road, Bracknell, RG12 2EW, UK b Department of Management Science, Lancaster University, LA1 4YX, UK |
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Abstract: | A collection of jobs (or customers, or patients) wait impatiently for service. Each has a random lifetime during which it is available for service. Should this lifetime expire before its service starts then it leaves unserved. Limited resources mean that it is only possible to serve one job at a time. We wish to schedule the jobs for service to maximise the total number served. In support of this objective all jobs are subject to an initial triage, namely an assessment of both their urgency and of their service requirement. This assessment is subject to error. We take a Bayesian approach to the uncertainty generated by error prone triage and discuss the design of heuristic policies for scheduling jobs for service to maximise the Bayes’ return (mean number of jobs served). We identify problem features for which a high price is paid in number of services lost for poor initial triage and for which improvements in initial job assessment yield significant improvements in service outcomes. An analytical upper bound for the cost of imperfect classification is developed for exponentially distributed lifetime cases. |
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Keywords: | Dynamic programming Bayes sequential decision problem Imperfect classification Stochastic scheduling Optimal service policy |
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