Optimal control of an emergency room triage and
treatment process
Kenneth C. Chong, Shane G.
Henderson and Mark E. Lewis
School of Operations Research
& Information Engineering
Cornell University
Ithaca, NY 14853
We consider the problem of routing
and admission control in a loss system featuring two classes of arriving jobs
(high-priority and low-priority jobs) and two types of servers, in which
decision-making for high-priority jobs is forced, and rewards influence the
desirability of each of the four possible routing decisions. We seek a policy
that maximizes expected long-run reward under both the discounted reward and
long-run average reward criteria, and formulate the problem as a Markov
decision process. When the reward structure favors high-priority jobs, we
demonstrate that there exists an optimal monotone switching curve policy with
slope of at least −1. When the reward structure favors low-priority jobs,
we demonstrate that the value function, in general, lacks structure, which
complicates the search for structure in optimal policies. However, we identify
conditions under which optimal policies can be characterized in greater detail. We also examine the performance of heuristic
policies in a brief numerical study.