Optimal bed-control in an ICU when elective surgery patient´s arrivals are known. A simulation-based optimization approach

Early discharge of patients is frequently used as means to control the ratio of rejected incoming patients due to a full Intensive Care Unit. These patient discharge decisions are discussed in the medical literature but few mathematical works have included them in their models. Recently, pioneering works modeled these decisions and obtained different bed-control policies. The so-called cautious policy was accepted by the physicians as the closest one to their own practice. However, this policy does not emerge when the expected Length-of-Stay shortening is minimized. The purpose of this research is to extend the mathematical model including a representation of the real discharge procedures as well as the knowledge of the near-future elective patient´s arrivals from surgery. Discharge probabilities are modeled by using a logistic function of the number of expected arrivals and the number of occupied beds. To prevent the early discharge of patients not sufficiently recovered the LoS is modeled by using a phase-type distribution with the states representing the health status of the patient. Optimal policies are obtained by a simulation-based optimization methodology. The coefficients of the logistic function are interpreted in terms of odd ratios. Cautious policy is now obtained even when minimizing the expected LoS shortening.