One of the most important decisions a hospitalist makes at the intersection of cost and quality of care is when to discharge a patient from the hospital. Keeping patients longer (shorter) increases (decreases) overcrowding and hospital costs but also decreases (increases) readmission risk. Here a long-run average cost optimization problem for determining on each day who and how many patients to discharge is developed. The authors combined structural properties of the model with an analytical solution for a special cost structure to approximately solve the high-dimensional Markov decision process. This transformed the originally intractable problem into a simple univariate optimization problem that can be solved efficiently yet allowed capture of time nonstationarity and fully heterogeneous inpatient populations, where each patient has a personalized risk trajectory. Moreover, the authors took one step beyond theory and implemented their discharge decision support tool in a partner hospital. For the tool to be properly parametrized and implementable, the authors developed a model to predict readmission risk as a function of length of stay that integrated several statistical methods in a novel manner. The resulting implementation was described as a showcase, demonstrating the tool’s applicability for integration with general hospital data systems and workflows.

The prevailing first-come-first-served approach to outpatient appointment scheduling ignores differing urgency levels, leading to unnecessarily long waits for urgent patients. In data from a partner healthcare organization, we found in some departments that urgent patients were inadvertently waiting longer for an appointment than non-urgent patients. This paper develops a capacity allocation optimization methodology that reserves appointment slots based on urgency in a complicated, integrated care environment where multiple specialties serve multiple types of patients. This optimization reallocates network capacity to limit access delays (indirect waiting times) for initial and downstream appointments differentiated by urgency. We formulate this problem as a queueing network optimization and approximate it via deterministic linear optimization to simultaneously smooth workloads and guarantee access delay targets. In a case study of our industry partner we demonstrate the ability to (1) reduce urgent patient mean access delay by 27% with only a 7% increase in mean access delay for non-urgent patients, and (2) increase throughput by 31% with the same service levels and overtime.

The decision of whether to admit a patient to a critical care unit is a crucial operational problem that has significant influence on both hospital performance and patient outcomes. Hospitals currently lack a methodology to selectively admit patients to these units in a way that patient health risk metrics can be incorporated while considering the congestion that will occur. The hospital is modeled as a complex loss queueing network with a stochastic model of how long risk-stratified patients spend time in particular units and how they transition between units. A Mixed Integer Programming model approximates an optimal admission control policy for the network of units. While enforcing low levels of patient blocking, we optimize a monotonic dual-threshold admission policy. A hospital network including Intermediate Care Units (IMCs) and Intensive Care Units (ICUs) was considered for validation. The optimized model indicated a reduction in the risk levels required for admission, and weekly average admissions to ICUs and IMCs increased by 37% and 12%, respectively, with minimal blocking. Our methodology captures utilization and accessibility in a network model of care pathways while supporting the personalized allocation of scarce care resources to the neediest patients. The interesting benefits of admission thresholds that vary by day of week are studied.

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The U.S. Naval shipbuilding industry faces significant challenges to build ships on-time and within budgeted cost. To achieve greater efficiency and timeliness in shipbuilding, we developed a flexible two-stage queueing model under a CONWIP job release policy to enhance the planning and control of the outfitting process, one of the key processes in shipbuilding. The model is formulated using Markov Decision Processes which can provide (1) the optimal dynamic control policy, and (2) the optimal cost. The numerical results showed that the optimal control policy is a state dependent threshold type policy and very complex to analyze. Therefore, we developed a static model to simplify the dynamic model and used Mean Value Analysis to gain insights. Using both data from the dynamic model and the static model, we developed a regression model to calculate a threshold policy heuristic. Testing reveals that the performance of this heuristic is very close to the optimal.