An Intensive Care Unit (ICU) is an important and expensive resource. Modeling patient flow through an ICU is challenging because it requires a stochastic and dynamic model of patient physiology Under the auspices of this award, the investigators will use a detailed data set to build a stochastic and dynamic model of patient physiology with the objective of improving ICU discharge predictions and subsequent flow through the hospital. This is achieved through three tasks: 1) creating a dynamic Transfer Readiness Score and a stochastic model of patient length of stay (LOS) based on patient physiology and transfer delay dynamics; 2) developing an optimization model to make anticipative bed requests using the created dynamic and stochastic score; 3) investigating the routing control problems between the ICUs and downstream units by developing new "score-based" queueing and stochastic network models. The PIs will recruit under-represented undergraduate and graduate students to this project.
The intellectual merit of this project lies in the integration of stochastic and dynamic models of physiology with patient flow management to improve patient outcomes as well as operational efficiency. These tasks will require customization of stochastic modeling and optimization techniques. Task I will introduce a physiologically based stochastic and dynamic transfer readiness score that considers physiology as well as blocking delays. Task II will develop an anticipative bed request scheme to optimize patient transitions from ICUs to the downstream units as well as patient outcomes. Approximation techniques and optimality bounds will be developed for the problem. Task III will create score-based queueing and stochastic network models in which the service distribution is a function of an exogenous stochastic process (patient physiology), thus capturing the high variability of LOS in the ICUs. Score-based routing control policies and algorithms will be developed, where routing decisions are made for patients in treatment (jobs in service) rather than in queue. In addition, a decentralized network optimization will be studied in the context. These models will be used to determine ICU capacity decisions through a two-stage stochastic program, in which the recourse problem captures the underlying queueing network.
