A Two-Stage Operating Room Allocation Framework for Reducing Surgical Waiting Lists in Public Hospitals

In public healthcare systems, the operating room is often the ultimate bottleneck. Efficiently managing these high-intensity resources is a matter of life and death. Delays in elective surgeries can lead to deteriorating patient health and systemic inequity. Researchers have developed various mathematical ways to schedule these rooms. However, applying them in the chaotic reality of a public hospital remains a massive challenge. Real-world factors like last-minute patient cancellations and varying surgical durations complicate every plan.

A new study proposes a two-step way to schedule operating rooms in public hospitals. Instead of trying to schedule every single patient at once, the researchers first decide how much time each medical specialty gets. Only then do they fill those specific slots with patients. This method is significantly faster for computers. It also ensures that no medical specialty is unfairly ignored. Ultimately, this helps reduce waiting times for children in pediatric settings.

The imbalance of specialty-based scheduling

Current approaches to operating-room (OR) scheduling generally fall into two camps. One is manual scheduling based on historical patterns. This is flexible but prone to systematic errors. Specialties often receive a fixed proportion of time regardless of actual patient demand. The second camp involves fully integrated mathematical models. These models use Mixed-Integer Linear Programming (MILP)—a mathematical method for finding the best outcome in a complex system with discrete choices. They attempt to optimize everything at once. They aim to maximize room utilization (the percentage of available time actually used for surgery) and minimize overtime.

However, these integrated models struggle in the high-pressure environment of public hospitals like the Dr. Luis Calvo Mackenna Hospital (HLCM) in Chile. As the number of patients grows, the math becomes too heavy to compute quickly. This makes it impossible to update schedules in response to sudden disruptions. Such disruptions include surgery suspensions or failed patient confirmations. Furthermore, prioritizing sheer "utilization" can create a hidden injustice. The model might favor specialties with shorter, predictable surgeries to keep the rooms busy. Meanwhile, specialties with longer, more complex needs may languish on a growing waiting list. This mismatch is clearly visible in the hospital's historical data. The time offered to certain specialties fails to meet the actual surgical demand .

A decomposed approach to capacity and patients

To resolve this tension between efficiency and fairness, the authors propose a two-stage framework called BlockDist-PatAlloc. The core architectural choice is decomposition. This means breaking a single, massive problem into two smaller, manageable tasks.

1. The Tactical Stage (BlockDist): Instead of looking at individual patients, this stage looks at medical specialties. Using a MILP model, it allocates "blocks" of time (morning or afternoon shifts) to each specialty. The goal is not just to fill time. It is to balance the relationship between the "offered" time and the "demanded" time. To ensure fairness, the model uses a weighting mechanism ($\omega_m$) based on the average waiting time of patients in that specialty. Specialties whose patients have waited the longest are given higher priority in receiving more blocks.
2. The Operational Stage (PatAlloc): Once the blocks are assigned to specialties, the second stage handles the actual people. Using a priority-based greedy heuristic (a fast, rule-of-thumb algorithm), the system assigns patients from the waiting list into the allocated blocks. It respects the hospital's priority rules. In this study, it uses a First-In-First-Out (FIFO) approach. It also accounts for necessary cleaning times between surgeries and the physical limits of the time blocks.

By separating these layers, the hospital gains "operational flexibility." If a patient cancels, the hospital only needs to re-run the second stage to find a replacement. It does not need to re-calculate the entire hospital's weekly specialty distribution.

Efficiency gains and long-term stability

The authors compared their framework against a traditional integrated MILP baseline (MILP-PatAlloc) using 12,054 historical surgical records. The most immediate result is the massive reduction in computational latency. In a single-week scenario, the integrated model took 1,800 seconds to find a solution. The two-stage framework finished in just 1.6 seconds [Table 3]. This is a massive speedup for a system that requires constant updates. This advantage becomes even more dramatic in long-term simulations. Over a 20-week period, the integrated model required 21,600 seconds. The proposed method took only 32 seconds [Table 6].

Crucially, the authors found that higher utilization does not always mean better outcomes. The integrated baseline achieved a higher utilization rate of 98.1%. The proposed framework achieved 90.9% [Table 3]. However, the proposed framework was far more effective at actually clearing the waiting list. In the 20-week simulation, the two-stage approach operated 1,337 patients. The baseline operated only 1,207 patients [Table 6].

The impact on patient experience was profound. The proposed method reduced the final median waiting time from 70 days down to 42 days. This represents a 40% reduction [Table 6]. This improvement is visualized in .

The graph shows that the gap in waiting-time reduction between the two methods actually widens as the simulation progresses. Furthermore, the framework achieved much greater equity. Using a Lorenz curve—a graphical representation used to show inequality—the authors demonstrated that the proposed method achieved a significantly lower Gini coefficient (0.06 vs 0.14). This means the distribution of resources was much closer to the actual needs of each specialty .

Limitations in the clinical model

While the results are compelling, the framework is not a complete digital twin of a hospital. First, the study treats surgery durations as deterministic. This means it assumes they are fixed. The researchers estimated durations based on historical averages for the "principal surgery" performed. In reality, surgery duration is highly stochastic (randomly determined). A patient's specific anatomy or unexpected complications can cause a surgery to run much longer than the average. This could cause a cascade of delays in the afternoon blocks.

Second, the prioritization logic was simplified. Because the researchers lacked historical "urgency scores," they relied on a FIFO (First-In-First-Out) criterion. In a real clinical setting, a patient with a life-threatening condition must jump to the front of the line. While the authors note the model can accommodate custom priority scores, the current evaluation does not test this clinical nuance. Finally, the model does not explicitly account for emergency surgeries. These are the primary disruptors of elective schedules in any functioning hospital.

The verdict: A scalable tool for public health

The evidence suggests that the two-stage BlockDist-PatAlloc framework is a superior choice for public hospitals. These institutions manage large, heterogeneous waiting lists. By shifting the focus from "maximizing room occupancy" to "balancing specialty demand," the authors have identified a way to achieve meaningful reductions in waiting times. This happens without sacrificing the stability of the system.

The trade-off is clear. You accept a slightly lower utilization rate (roughly 84-91% instead of near 100%). In exchange, you get a massive boost in computational speed and operational flexibility. Most importantly, you gain fairness across medical specialties. For a hospital administrator who needs to re-optimize a schedule every Monday morning, speed is essential. A model that runs in seconds rather than half an hour is a vital tool. This research moves us away from the pursuit of "perfect" local efficiency. It moves toward a more robust and equitable management of systemic bottlenecks.

Figures from the paper