Healthcare Operations

COVID-19 Hospital Capacity Management using Mathematical Models

We use mathematical optimization to determine optimal strategies to reduce the burden of COVID-19 on hospitals. In particular, we focus on patient transfers. In practice, hospitals, even those in the same region or system, experience very different COVID patient loads, meaning that some may have unused capacity even while COVID overwhelms other hospitals. Patient transfers can balance these uneven loads and ensure that all capacity to care for patients is efficiently used. Patient transfers were used by some hospital systems that were hit particularly hard during the first wave of the pandemic, but these transfers were generally made reactively as hospitals ran out of capacity rather than planned. Optimal coordinated transfers have potential to significantly help hospitals cope with the burden of COVID and ensure that all patients receive the best possible level of care. We aim to demonstrate the benefits of this approach on this website using real-world data.


Many outpatient clinics experience variation in their utilization with surge times and down times. We provide a real-time scheduling algorithm to better schedule the patients and improve utilization, patient wait-time, and staff satisfaction.


For patients who are hospitalized, it is often the case that their clinical care team changes, sometimes entirely, during their stay. An interesting question is to understand whether or not such changes in the care team affect patients’ length-of-stay in hospital.


Primary care is the gateway to the healthcare system for many patients. Although primary care itself only accounts for 5% of healthcare spending, the decisions made in primary care setting influences the subsequent medical care including subspecialty referrals, imaging, medical testing, invasive procedures, and hospitalization. We use optimization and data analytics to improve the level-loading for clinical staff in primary care clinics which in turn improves patient flow, wait time, and patient care.


Operating rooms are one of the main resources in a hospital and any disruption in their workflow can have a cascade effect on the rest of the hospital operations. We use machine-learning, data analytics, and optimization to find a stable schedule to maximize utilization while reducing the risk of operational disruptions.


A microsimulation of every business process that requires energy within a hospital was created to build a model for prioritization of power in order from most to least critical. This is used to inform how power should be adjusted in hospitals during power shortages or power outages. A Monte Carlo simulation is used to adjust this model based on percent occupancy, number of walk-ins, and other variables. This research is especially important for areas that have experienced distress to their power grids or that regularly have limited energy capacity. 


Covid-19 has presented countless challenges globally, one of which is the energy costs of Covid-19 interventions in hospitals. This project aims to better understand these costs and their potential benefits. By applying a de-escalation model to covid-19, researchers can evaluate the impact of High Efficiency Particulate Air (HEPA) filtered patient rooms versus the use of UV-xenon gas decontamination rooms. Modeling the energy demand and costs of these interventions and inputting these costs in a cost minimization function allows evaluation of infection impact. This can inform how funds should be distributed among these interventions. 


We have developed an optimization framework for evaluating cost-effectiveness for built-environment infection control interventions. This is done by mathematically calculating the minimization of both secondary infections and cost for the interventions with differential equations to determine infection transmission, optimization, constraints, and objective functions.    This has been expanded upon by using cost of infection data for Methicillin-resistant Staphylococcus aureus (MRSA), carbapenem-resistant Enterobacteriaceae (CRE), and vancomycin-resistant enterococci (VRE) from 10 hospitals to evaluate two infection control interventions within hospitals. The projected number of infections from the infection de-escalation model are then validated by this data, improving the evaluation of infection control interventions during design or hospital renewal projects. As data input improves, the model becomes more precise and results improve. 


C. difficile infections come from a toxin producing bacteria which causes an antibiotic associated diarrhea. These secondary infections result in high expense and negative patient and family impact. This research aims to build an easy to use tool for infection control teams, applying a mathematical model to prevent infections in hospitals. This will help to ensure a more proactive approach to allocating resources and preventing these infections in hospitals. Retrospective data is applied to a cox-proportional hazards model to quantify risk. Additionally, nonlinear models, cross-validation, and bootstrapping techniques assess the best tool. This research is being conducted in collaboration with Hopkins Hospital Epidemiology and Infection Control group. 

Many outpatient facilities with expensive resources, such as infusion and imaging centers, experience surge in their patient arrival at times and are under-utilization at other times. This pattern results in patient safety concerns, patient and staff dissatisfaction, and limitation in growth, among others. Scheduling practices is found to be one of the main contributors to this problem.

We developed a real-time scheduling framework to address the problem, specifically for infusion clinics. The algorithm assumes no knowledge of future appointments and does not change past appointments. Operational constraints are taken into account, and the algorithm can offer multiple choices to patients.

We generalize this framework to a new scheduling model and analyze its performance through competitive ratio. The resource utilization of the real-time algorithm is compared with an optimal algorithm, which knows the entire future. It can be proved that the competitive ratio of the scheduling algorithm is between 3/2 and 5/3 of an optimal algorithm.

This work was performed with the MIT/MGH Collaboration.

In many healthcare services, care is provided continuously, however, the care providers, e.g., doctors and nurses, work in shifts that are discrete. Hence, hand-offs between care providers is inevitable. Hand-offs are generally thought to effect patient care, although it is often hard to quantify the effects due to reverse causal effects between patients’ duration of stay and the number of hand-off events. We use a natural randomized control experiment, induced by physicians’ schedules, in teaching general medicine teams. We employ statistical tools to show that between the two randomly assigned groups of patients, a subset who experiences hand-off experience a different length of stay compared to the other group.

This work was performed with the MIT/MGH Collaboration.

Primary care is an important piece in the healthcare system that affects the downstream medical care of patients heavily. There are specific challenges in primary care as healthcare shifts from fee-for-service to population health management and medical home, focuses on cost savings and integrates quality measures. We consider the primary care unit at a large academic center that is facing similar challenges. In this work we focus on the imbalance in workload, which is a growing regulatory burden and directly concerns any staff in primary care. It can result in missed opportunities to deliver better patient care or providing a good work-environment for the physicians and the staff. We consider the primary care unit at the large academic center and focus on their challenge in balancing staff time with quality of care through a redesign of their system. We employ optimization models to reschedule providers’ sessions to improve the patient flow, and through that, a more balanced work-level for the support staff. 

This work was performed with the MIT/MGH Collaboration.

Perioperative services are one of the vital components of hospitals and any disruption in their operations can leave a downstream effect in the rest of the hospital. A large body of evidence links inefficiencies in perioperative throughput with adverse clinical outcomes. A regular delay in the operating room (OR), may lead to overcrowding in post-surgical units, and consequently, more overnight patients in the hospital. Conversely, an underutilization of OR is not only a waste of an expensive and high-demand resource, but it also means that other services who have a demand are not able to utilize OR. This mismatch in demand and utilization may, in turn, lead to hold-ups in the OR and cause further downstream utilization. We investigate the utilization of operating rooms by each service. The null hypothesis of this work is that the predicted utilization of the OR, i.e., the current block schedule, matches completely with the actual utilization of the service. We test this hypothesis for different utilization definitions, including physical and operational utilization and reject the null hypothesis. We further analyze why a mismatch may exist and how to optimize the schedule to improve patient flow in the hospital.