A Bayesian approach to the triage problem with imperfect classification

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.

Optimal dynamic resource allocation to prevent defaults

“…Therefore, the optimal policy is given by that policy that minimizes the one-period expected cost. This is well captured by the indices given in (10) and (12). If β = 0, from (10), we have that b = 0, and therefore, ν k,G = 0.…”

“…Theorem 3.2 gives the optimal solution to Problem (3) in terms of the index values given in Equations (9), (10) and (12).…”

“…If ν ≥ ν k,n , then it is optimal not to fund company k if it is in state n ∈ N , where ν k,n are given in (9), (10) and (12).…”

“…For instance, similar models have been used in problems where resources are shared among patients [12], or human resources to maintain machinery [7]. The rest of the paper is organized as follows: the model, and the related optimization problem, are stated in Section 2.…”

Managing urgent care in hospitals

“…Alternative patient pathways and policies assigning non-elective patients to these pathways are also investigated [104]. Finally, patient (time dependent) prioritization rules are also investigated [111,164,173,232], and tools to assist the triage patient categorization that provide further guidelines for patient selection [72].…”