Optimal Hospital Capacity Management During Demand Surges

TL;DR

The paper addresses hospital capacity management during demand surges by optimizing two practical decisions: allocating dedicated surge capacity and transferring patients across hospitals. It employs a data-driven workflow that combines facility-level demand forecasting (TiDE with conformalized quantile regression) and a robust MILP optimization framework that accounts for setup times, conversion costs, and transfer constraints over a planning horizon of $2$ to $8$ weeks with daily resolution. Key contributions include the first integrated optimization of dedicated surge capacity with patient transfers, a facility-level robust forecasting-and-optimization pipeline, and real-world validation using COVID-19 data that shows substantial reductions in surge capacity when transfers are feasible (e.g., transferring $32$ patients over $63$ days could reduce surge needs by nearly $90"). The work provides a practical decision-support tool for proactive surge planning, with a flexible model that can adapt to different surge types and hospital-system configurations, potentially enhancing care quality and system resilience.

Abstract

Effective hospital capacity management is pivotal for enhancing patient care quality, operational efficiency, and healthcare system resilience, notably during demand spikes like those seen in the COVID-19 pandemic. However, devising optimal capacity strategies is complicated by fluctuating demand, conflicting objectives, and multifaceted practical constraints. This study presents a data-driven framework to optimize capacity management decisions within hospital systems during surge events. Two key decisions are optimized over a tactical planning horizon: allocating dedicated capacity to surge patients and transferring incoming patients between emergency departments (EDs) of hospitals to better distribute demand. The optimization models are formulated as robust mixed-integer linear programs, enabling efficient computation of optimal decisions that are robust against demand uncertainty. The models incorporate practical constraints and costs, including setup times and costs for adding surge capacity, restrictions on ED patient transfers, and relative costs of different decisions that reflect impacts on care quality and operational efficiency. The methodology is evaluated retrospectively in a hospital system during the height of the COVID-19 pandemic to demonstrate the potential impact of the recommended decisions. The results show that optimally allocating beds and transferring just 32 patients over a 63 day period around the peak, about one transfer every two days, could have reduced the need for surge capacity in the hospital system by nearly 90%. Overall, this work introduces a practical tool to transform capacity management decision-making, enabling proactive planning and the use of data-driven recommendations to improve outcomes.

Figures (9)

• Figure 1: Overview of our framework for optimizing capacity management decisions. The primary component of the framework and the focus of this work is the set of capacity management models (purple). It is data-driven and prospective, so it requires data from the hospital system (green) as well as forecasts of future demand (blue). This data can come from a variety of sources (yellow).
• Figure 2: COVID-19 ICU occupancy of each hospital in the system relative to their baseline capacity. Values under 100% (red line) indicate that the hospital did not require surge capacity, while values above 100% indicate that the hospital must have activated some surge capacity. The dark blue line represents the occupancy of the system as a whole, aggregating all patients and capacity. It peaks at 97% on January 12, 2022.
• Figure 3: Amount of ICU capacity that must be allocated to COVID-19 patients at each hospital over time. Capacity cannot be adjusted by individual beds, only entire units at a time, creating discrete levels. The required capacity also reflects a maximum 95% occupancy rate across each hospital. While H3 requires significantly more capacity allocated than the other hospitals, it can remain at baseline, as seen in \ref{['fig:surge-timeline']} due to also having much more capacity available.
• Figure 4: Optimized "unit" allocations for H1 ((a) and (b)) and H3 ((c) and (d)) using no operational constraints (left) and with practical constraints (right). Each row represents a unit of capacity, and is colored blue for each period of time when it is allocated as dedicated capacity. The shade of blue indicates the number of beds in the "unit". Without constraints, the model sometimes chooses to use units in a higher surge level than necessary despite higher marginal costs because they fit the demand better, resulting in lower total costs. The behavior can be easily adjusted using parameters to introduce priority order, which can help improve logistics at the expense of higher objective function value.
• Figure 5: Total required dedicated capacity in bed-days for COVID-19 ICU patients in our case study under different allocation strategies. Optimal bed-level allocation (top) is the theoretical minimum, assuming individual beds can be allocated as needed. Our models perform optimal unit-level allocation (second bar) as well as optimal unit-level allocation that is constrained by practical considerations (third and fourth bars). We also compare against surge-level allocations (last two bars).