A Bayesian approach to the triage problem with imperfect classification

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.

► The analyses in the paper concern the impact of imperfect triage on the service offered to possibly misclassified jobs. ► Each job to be served has a random service time and a random lifetime indicating its availability for service. ► The paper takes a Bayesian approach to the uncertainty generated through the error-prone triage. ► Service policies are developed which come close to maximising the Bayes expected number of jobs served. ► The Cost of Imperfect Classification is developed to study the effect of improving the quality of triage.