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# Solving The Puzzle of OR Scheduling Optimization with AI

Avi Paz

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Optimizing Operating Room (OR) scheduling is a complex but critical component of hospital operations. It is a puzzle that requires constant attention and fine-tuning to ensure the most efficient use of resources while also providing quality patient care.

Operating rooms are crucial revenue centers for hospitals, contributing up to 70% of a hospital’s revenue and 35–40% of its expenses.a An empty OR suite can cost up to \$1,000 per hour, and even a minute of downtime can be costly. The OR’s efficiency affects the entire hospital. It is the most complex department and a primary source of admissions.

## Why OR Scheduling is Such A Challenge

OR scheduling is a complex process involving multiple factors and stakeholders. It requires coordination between surgeons, anesthesiologists, nurses, and support staff, taking into account various constraints such as equipment availability, patient needs, turnover times necessary to set up and clean up ORs, and surgeon preferences (preference cards).b

In addition to managing logistics, OR scheduling also must balance constantly shifting priorities, including urgent and elective surgeries, as well as the needs of individual patients. This requires constant communication and collaboration between surgeons, anesthesiologists, nurses, and other healthcare professionals involved in each patient’s care.

### Significant Human And Computational Hurdle

The challenge here is daunting for human planners and presents a significant computational hurdle, falling into the ‘NP-hard’ problems category.

The “NP” in “ NP-hard “ is “nondeterministic polynomial time.” To understand this better, it’s helpful to break down the concept:

1. Nondeterministic: This implies that the problem doesn’t have a straightforward, deterministic algorithm that leads to a solution in a predictable manner. Instead, the solution involves dealing with many uncertainties and variables.
2. Polynomial Time: In computational terms, ‘polynomial time’ refers to the rate at which the time to solve a problem increases with the size of the problem. A problem solvable in polynomial time is generally considered efficient and feasible. However, in the case of NP-hard problems, while verifying a given solution is possible in polynomial time, finding the best solution is not.

In simpler terms, for NP-hard problems like OR scheduling, if someone presents a potential schedule, it’s relatively quick and easy to check if that schedule works or not. However, the process of finding the best possible schedule from all available options is extremely time-consuming and becomes exponentially more difficult as the size of the problem increases.

This is largely because of the vast number of possible combinations and scenarios that must be considered. With each added variable, the complexity of the scheduling puzzle grows, making it a quintessential NP-hard problem.c,d

### Exponential Increase in Complexity

As the number of surgeries, surgeons, operating rooms, and other variables increase, the number of possible schedules grows exponentially. This makes it incredibly challenging to find the optimal schedule, especially in large hospitals with high surgery volumes.

To illustrate the complexity of OR scheduling, consider a relatively simple scenario: a hospital with 10 operating rooms (ORs), each capable of handling 8 cases per day. The number of ways to arrange 8 cases is 8 factorial (8!), which equals 40,320.

Therefore, for one OR, there are 40,320 possible ways to schedule the cases. When you consider 10 ORs, the complexity magnifies. Ideally, each OR’s schedule could be decided independently, but in reality, they are often interdependent due to shared resources like staff and equipment. This interdependency further complicates the scheduling. To understand the magnitude, if we naively assume each OR’s schedule is independent (which is not the case but simplifies our calculation), the total permutations would be the permutations for one OR raised to the power of the number of ORs:

##### This results in a staggeringly large number, far beyond the scope of manual computation or simple algorithms. It’s a clear illustration of why OR scheduling is an NP-hard problem and requires sophisticated computational methods to tackle efficiently.

Now, imagine the case for a facility with 20, or even 30–40 ORs. The complexity doesn’t just increase linearly; it skyrockets exponentially, making the task of scheduling akin to solving a colossal multidimensional puzzle.

In conclusion, OR scheduling isn’t just about fitting pieces into a schedule. It’s about managing an enormous number of variables and combinations, all while ensuring optimal patient care and resource utilization. The exponential increase in complexity with each added variable or constraint makes it a perfect example of the challenges faced in healthcare operations.

### Dynamic and Uncertain Nature

OR scheduling is not just about creating a static plan. It needs to accommodate emergencies, last-minute changes, delays, and unpredictable surgery durations. This dynamic nature adds another layer of complexity, as the schedule must be adaptable yet efficient.

### Balancing Multiple Objectives

The optimal schedule must balance a variety of objectives, such as maximizing OR utilization, minimizing patient wait times, aligning with the availability of specialized staff and equipment, and adhering to various health and safety regulations. Balancing these often conflicting objectives adds to the complexity.

### Interdependencies

These variables are not independent. For instance, the availability of a particular surgeon might depend on the availability of specific equipment or support staff.

### Multiple Variables

In OR scheduling, numerous variables exist, such as the length of each surgery, the availability of surgeons, nurses, anesthetists, operating rooms, and equipment. Here are some variables that have a significant impact on the schedule:

• Case Length: Predicting how long each surgery will take is crucial for planning and can affect the entire day’s schedule if not estimated accurately.
• Block Length and Time Management: This involves allocating specific time blocks to surgeons or surgical teams. Efficient block time management is essential to avoid idle ORs or overbooked schedules.
• Nursing Staff Scheduling: Ensuring the right number of nurses, with the appropriate skills, are available for each surgery is vital for patient safety and operational efficiency.
• Anesthesia Coordination: Anesthesia teams must be aligned with the surgery schedules, ensuring their availability throughout each procedure.
• PACU (Post-Anesthesia Care Unit) Management: Efficiently managing the PACU is key for smooth patient flow from surgery to recovery, ensuring space for incoming post-operative patients.e
• SDS (Same-Day Surgery) Logistics: Careful timing is needed for surgeries where patients are discharged on the same day, considering not just the surgery but also the recovery time and discharge processes.
• Equipment Allocation: Proper management of surgical equipment, ensuring it is available, sterilized, and efficiently used across surgeries, is a critical component of OR scheduling.
• Room Allocation: Deciding which room should take each case from a pool of surgeries, considering OR capabilities and specializations, surgeon and team availability, and the need for efficient use of space and time. This includes the readiness of rooms post-cleaning and sterilization.
• Multi-Site Optimization: For healthcare systems with multiple locations, balancing resources like staff and equipment across sites is an additional layer of complexity.

Considering all these factors and their interdependencies, the number of possible scheduling combinations can be vast, especially in a large hospital with multiple ORs. Determining the most efficient schedule from among all these possibilities is where the NP-hard complexity comes in. It’s akin to solving a highly complex puzzle where changing one piece (like the time of surgery) affects the placement and fit of all the other pieces.

## Solving the OR Schedule Puzzle with Opmed.ai

Given the NP-hard nature of the problem, traditional scheduling methods or simple computational algorithms are often inadequate. This has led to the exploration of more advanced solutions, such as machine learning algorithms, artificial intelligence, and sophisticated optimization techniques, which can better handle the complexity and dynamic nature of the problem.

This complexity is why AI, Network Science, and advanced optimization algorithms are needed. These technologies can process and analyze more data and scenarios than a human planner could feasibly consider. They can rapidly assess numerous potential schedules, predict outcomes, and find the most efficient arrangement of resources.

### Revolutionizing Efficiency with Predictive AI

Leveraging historical logistic data (no PHI), our platform accurately forecasts case and block lengths, utilizing scheduling gaps to increase operational capacity. This not only maximizes OR efficiency but also significantly enhances revenue potential.

## Complex Puzzle, Simplified

Opmed.ai tackles the ‘Tetris’ puzzle of OR scheduling by expanding small gaps into larger, usable time slots. This approach is not just about reducing costs; it’s about increasing resource utilization and case volume, thereby improving overall hospital efficiency.

### Advanced Integration for Unparalleled Results

Our platform’s distinct edge lies in its integration of AI, network science, and heuristic optimization algorithms. This powerful combination enables us to efficiently solve the NP-hard problem of resource allocation, analyzing billions of permutations swiftly to optimize operational and revenue outcomes.

### Seamless EHR Integration through Partnerships

A pivotal feature of Opmed.ai is its seamless integration with existing Electronic Health Records (EHR) systems. Our platform integrates seamlessly with these widely-used EHR tools thanks to our partnerships with their companies. This integration ensures that schedule insights and optimizations are directly reflected in the hospital’s existing workflow, enhancing efficiency without disrupting established processes.

### Dynamic Resource Allocation

Beyond predicting surgical durations, Opmed.ai dynamically allocates resources, encompassing staff, equipment, and PACU and SDS logistics. Our focus extends to optimizing post-anesthesia care unit operations, ensuring optimal use of every resource.

### User-Friendly Interface

Despite advances in technology, the role of human planners remains crucial. They provide context, make judgments about priorities, and make adjustments based on real-time situations. The ideal solution often involves a collaboration between human experts who know their hospital the best and the computational power of advanced algorithms.

With an emphasis on functionality and ease of use, Opmed.ai offers an intuitive interface that simplifies complex scheduling tasks and empowers its users to make the best decisions. Hospital administrators and planners can easily navigate its comprehensive suite of tools for effective OR management.

Far from a “black box” approach, our platform provides complete transparency in its decision-making process, allowing users to fully understand the rationale behind schedule recommendations and make informed decisions based on these recommendations.

### Analytics, Validation and Optimization Tools

In addition to predicting surgical durations and allocating resources, Opmed.ai also offers a variety of analytics and optimization tools to further improve OR efficiency. These include real-time monitoring of OR utilization, identification of potential bottlenecks, and scenario planning for optimal resource allocation.

## Join the Revolution in Healthcare Efficiency

Whether it’s streamlining the scheduling process, identifying potential bottlenecks or optimizing resource allocation, Opmed.ai provides a comprehensive and user-friendly solution for all your OR management.

Join the revolution in healthcare efficiency today and see the benefits of Opmed.ai in action at your hospital.

Footnotes

a. Healthcare Financial Management Association, Operating room (OR) can generate up to 70% of a hospital’s margin, December 2020

b. Health Truse Performance Group, The Benefit of Accurate Preference Cards, September 2022

c. Sagnik Saha, Manish Purohit, NP-completeness of the Active Time Scheduling Problem, Dec 2021

#### Avi Paz

Avi Paz, the Co-Founder and Chief Technology Officer at Opmed, is a seasoned technology leader with extensive experience across PayPal, EMC, and Microsoft. His expertise in software development, system architecture, and AI-driven solutions has been pivotal in driving innovation at Opmed. Avi's work focuses on leveraging cutting-edge technology to enhance patient care, showcasing his commitment to operational efficiency and scheduling optimization in the healthcare sector.