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Why would you believe a physicist when they try to advise you on how to optimize your operating room?
What could the study of physical systems possibly contribute to hospital operations?
The answer: networks.
An epidemic spreads through a social network. A blackout cascades across a power grid. Signals propagate through neurons in your brain. Hospital systems coordinate a complex web of patients, staff, and resources. Despite their differences, these systems share a fundamental mathematical structure—they are all complex networks where connections determine behavior.
From Theory to Hospital Corridors
Our journey began when Mor - my now Co-Founder and CEO - stepped into our Complex Network Dynamics Lab with a proposition: "You're researching infrastructure networks. There's no more crucial infrastructure than hospitals."
She was right. Hospitals represent our most critical infrastructure, with lives practically depending on operational efficiency. The insight was transformative: the mathematical tools we had developed for optimizing social, biological, brain and power networks could be repurposed to solve seemingly intractable hospital problems.
The Complexity Challenge
When hospital administrators create operating room schedules, they face staggering complexity. A mid-sized hospital with 50 ORs and 300 staff members being scheduled for two weeks has billions of potential configurations. In fact, quite strikingly, the number of ways to arrange such a schedule exceeds the number of atoms in the universe.
Traditional approaches simply cannot navigate this vast solution space effectively. Human schedulers, no matter how experienced, can only evaluate a tiny fraction of possible configurations. Even conventional algorithms struggle with the interdependencies and constraints of real-world hospital operations. Consequently, there is significant amount of lost opportunity - our existing OR schedules are simply sub-optimal.
The Networks Perspective
By recasting scheduling as a network problem, we can apply specialized algorithms that navigate this vast solution space efficiently.
In OR scheduling, each staff member has preferences and constraints. When two doctors want the same time slot, it creates a conflict. Mathematically, these conflicts form a network where:
- Nodes represent different assignments
- Links represent conflicts between assignments
- The goal is to select as many nodes as possible without selecting conflicting nodes
This transformation isn't just academic—it's the key to unlocking extraordinary improvements in hospital operations.
The Mathematics Behind the Magic
At Opmed, our approach builds on cutting-edge network science concepts. We analyze hospital operations using graph theory fundamentals—studying adjacency matrices, centrality measures, and community detection algorithms.
When we look at patient flow from pre-op to OR to PACU and beyond, we're essentially analyzing a directed, weighted graph. By calculating the network characteristics, we can identify crucial "hubs" or bottlenecks that, when optimized, yield the greatest system-wide improvements.
But network science alone isn't enough. To truly transform healthcare operations, we integrate these network principles with multiple AI technologies. Our machine learning models establish baseline predictions for case durations, while deep learning algorithms capture the complex non-linear patterns in patient data that simple averages miss.
Beyond Scheduling: A Comprehensive Approach to Healthcare Operations
This integrated approach extends to many healthcare challenges:
PACU Flow Optimization
By viewing recovery rooms as network nodes with capacity constraints, we can predict and prevent bottlenecks before they occur. Our algorithms analyze historical data to model how patient volume propagates through the system, ensuring smooth transitions from OR to recovery.
The power comes in combining network analysis with deep learning time-series forecasting. While network science helps us understand the structural relationships between rooms, staff and equipment, our AI models predict exactly when and where bottlenecks will occur based on historical patterns. We then use constraint programming to ensure all solutions satisfy critical PACU staffing and capacity requirements.
Multi-site Planning and Load Balancing
For healthcare systems with multiple facilities, we build network models that optimize case distribution across the entire system. Here, the intersection of multiple AI technologies becomes particularly powerful.
Our deep learning models predict patient volumes and case complexities at each site, while network science algorithms identify the optimal distribution patterns. Constraint programming ensures that all assignments respect practical limitations like travel distances and facility capabilities. The result? A balanced workload that reduces wait times and maximizes resource utilization across the entire healthcare system.
The Future of Healthcare Operations
As healthcare systems face increasing pressure to do more with less, our integrated approach to operational decision-making will become increasingly vital.
The results speak for themselves. As we've seen at Geisinger Health and Mayo Clinic, our approach has saved hundreds of OR hours annually, improved prediction accuracy by over 40%, and helped hospitals achieve significant operational and financial improvements.
Our vision at Opmed goes beyond simply optimizing existing workflows. By applying network science principles alongside advanced AI, we can help hospitals:
- Create more resilient systems that adapt to unexpected changes
- Design more efficient workflows that reduce staff burnout
- Allocate resources more effectively to improve patient access and outcomes
The unlikely connection between blackouts, your brain, and hospital operations reminds us that beneath seemingly disparate complex systems often lies a common mathematical structure. By leveraging these structures and enhancing them with the latest in artificial intelligence, we can transform hospital operations—creating more efficient systems, better working conditions for healthcare professionals, and ultimately, improved patient care.
Prof. Baruch Barzel is Co-Founder and Chief Scientist at Opmed.ai and heads the Complex Network Dynamics Lab at Bar-Ilan University, where his team develops mathematical approaches to optimize complex systems ranging from power grids to social networks and healthcare operations.
