Intensive care unit discharge policies prior to treatment completion

In this study we explore a model to optimize the Intensive Care Unit (ICU) discharging decisions prior to service completion as a result of capacity-constrained situation under uncertainty. Discharging prior to service completion, which is called demand-driven discharge or premature discharging, increases the chance that a patient to be readmitted to the ICU in the near future. Since readmission imposes an additional load on ICUs, the cost of demand-driven discharge is pertained to the surge of readmission chance and the length of stay (LOS) in the ICU after readmission. Hence, the problem is how to select a current patient in the ICU for demand-driven discharge to accommodate a new critically ill patient. In essence, the problem is formulated as a stochastic dynamic programming model. However, even in the deterministic form i.e. knowing the arrival and treatment times in advance, solving the dynamic programming model is almost unaffordable for a sizable problem. This is illustrated by formulating the problem by an integer programming model. The uncertainties and difficulties in the problem are convincing reasons to use the optimization-simulation approach. Thus, using simulations, we evaluate various scenarios by considering Weibull distribution for the LOS. While it is known that selecting a patient with the lowest readmission risk is optimum under certain conditions and supposing a memory-less distribution for LOS; we remark that when LOS is non-memory-less, considering readmission risk and remaining LOS rather than just readmission risk leads to better results.