Research On Optimal Control Strategy For Assignment Of The Intensive Care Unit

This paper presents an optimal discharge and admission decision rule in a capacityconstrained intensive care unit(ICU),where patients are categorized into a finite number of classes,each potentially corresponding to a particular ailment/health condition of the patient upon admission.There are patients arriving ICU at random times.When there is a new arrival and the new one cannot queue up nor wait for a bed to become available,a current patient in the ICU has to be discharged.Such a demanddriven discharge of a patient will incur a cost that depends on that patient’s type.This cost reflects the impact of demand-driven discharge on the patient as well as the system.These demand-driven discharged patients might also require readmission,which in turn impose an additional load on the capacity-limited ICU resources.The goal of our study is to minimize the total expected cost incurred because of demand-driven discharges over a given horizon.We propose the so-called φ/μ rule to prioritize ICU patients,where c is the total cost associated with a demand-driven discharge,and μ is the reciprocal of length of stay.Hence,φ/μ measures the “imputed” cost per unit time of a demand-driven discharged patient to the system.This μ rule has been proved to be optimal for many service systems,and thus we fill a gap in the literature.When the new arrival’s admission is allowed to refuse treatment,we propose an optimal decision in certain regimes on whether to let the new arrival in the ICU or not by comparing his cost of rejection with the discharge cost of a patient in the ICU with a critical type.Since the patients discharged from the ICU may face increased risk of physiological deterioration and then readmit the ICU,we make further analysis on the optimal decision with patients’ readmissions.Finally,numerical examples are carried out to illustrate the model parameters’ impact on the total expected cost incurred by the rule and a greedy heuristic which developed by Chan et al(2012).The former performs significantly better(close to the optimal cost)than the latter.This paper establishes a finite state space and defines the partial order in this space.We need select an optimal decision sequence to make the total expected cost function minimal,so we propose a two-dimensional approximate dynamic programming algorithm,and the algorithm is converged to the optimal cost function a.s.The monotonicity of the optimal cost function in the state space improve convergence rate,and the algorithm can be widely used in the practical problem.