Design of Patient Visit Itineraries in Tandem Systems

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Multistage service is common in healthcare. One widely adopted approach to manage patient visits in multistage service is to provide patients with visit itineraries that specify personalized appointment time for each patient at each service stage. Nan Liu discusses how to design such visit itineraries.

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Institution: Boston College

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This video discusses the complexities of appointment scheduling in healthcare, highlighting the challenges faced in managing patient flow through multi-stage service environments. Healthcare appointment scheduling aims to align provider capacity with patient demand, but it becomes complicated due to various stakeholder objectives, such as patients seeking quicker access and providers wanting to optimize resource utilization.

Traditional models have largely focused on single-stage systems, which simplify the process, whereas real-world healthcare often involves multi-stage processes where patients undergo several service stages, resulting in longer wait times and increased anxiety. The development of personalized visit itineraries, which detail appointment times at each service stage, is suggested as a way to enhance patient experience and operational efficiency.

This video introduces a new optimization framework that accounts for patient flow across multiple stages, aiming to minimize waiting and idle times for both patients and providers. This video framework contrasts with traditional models, which may overlook the complexities of multi-stage systems and lead to inefficiencies.

The author details the two solution methods developed to improve computational efficiency for this framework, demonstrating their effectiveness through case studies in specific healthcare settings. The new model shows a cost reduction in operations while enhancing patient experiences by differentiating between types of waiting and provider idling. Future research is proposed to explore more complex healthcare networks and patient flow dynamics, acknowledging the necessity for advanced modeling frameworks to improve healthcare delivery.

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Here are five key points from the video about appointment scheduling in healthcare:

1. **Complexities of Multi-Stage Appointment Scheduling**: Appointment scheduling in healthcare is a complex task due to competing objectives among stakeholders, such as patients wanting quicker access to care while providers aim to maximize resource utilization. This complexity increases in multi-stage systems, where patients undergo several services sequentially, as opposed to single-stage models where patients receive a single service before leaving.

2. **Inefficiencies in Current Models**: Traditional scheduling models usually focus on single-stage systems, which do not adequately address the interdependencies and operational challenges experienced in multi-stage environments. Factors such as patient no-shows, variability in service times, and the need for multiple appointments contribute to inefficiencies when applying single-stage solutions to multi-stage processes.

3. **Development of a New Optimization Framework**: The video describes a new framework for optimizing multi-stage healthcare appointment scheduling, which aims to provide personalized visit itineraries for patients. This framework accounts for various types of patient waiting and provider idling, aiming to minimize waiting times and improve overall service efficiency.

4. **Improved Performance Through Quantification**: The proposed multi-stage model enables precise quantification of system performance, such as patient waiting times and provider idle times, which leads to enhanced operational efficiencies that traditional models cannot achieve. The study highlights the importance of recognizing the dynamics of patient flow in improving systems performance.

5. **Case Study and Cost Reduction**: A case study conducted in an infusion center demonstrated the practical application and benefits of this multi-stage model, achieving a notable 28% cost reduction by enhancing patient experience and provider productivity. The study emphasizes the importance of carefully managing appointments in multi-stage healthcare systems to avoid operational inefficiencies commonly seen with simplistic adjustments based on single-stage models.

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Here are some key quotes extracted from the video:

1. **Complexity of Appointment Scheduling**:
- "Appointment scheduling is a commonly used tool in healthcare to match provider capacity with patient demand."
- "While it may seem straightforward, appointment scheduling is actually a complex task, due to competing objectives among various stakeholders."

2. **Challenges Faced**:
- "Patients may want quicker access to care, but providers want to maximize resource utilization, and delays add to managerial challenges."
- "Numerous environmental factors contribute to these challenges, including patient no-shows, preferences, punctuality, provider lateness, and variability in service times."

3. **Multi-Stage Systems**:
- "Most studies focus on single stage systems where customers are assumed to receive service from only a single stage and then leave."
- "Such a model does not fully capture the complexity of management challenges present in real-world multi-stage service environments."

4. **Patient Experience**:
- "Patients typically go through three stages of services... in orthopedic clinics, a common patient care path would involve an X-ray exam followed by physician consultation."
- "These prolonged, unproductive, and uncomfortable experiences often have significant consequences beyond just mere inconvenience."

5. **Proposed Solution**:
- "One promising approach to managing patient experience in such complex environments is to provide patients with a structured visit itinerary."
- "Our multi-stage model captures patient flow through multiple stages, explicitly quantifying different patients' waiting time at different stages."

6. **Operational Efficiency**:
- "Our model offers a precise quantification of system performances, which the traditional single-stage model cannot provide, and leads to improved operational efficiencies for running multi-stage healthcare systems."
- "A carefully designed patient itinerary, considering different types of patient waiting and provider idling, can improve both patient experience and provider productivity."

7. **Cost Reduction & Performance Improvement**:
- "On average across all the testing scenarios, our model achieved a 28% cost reduction that relied on simple adjustments to single-stage models."
- "This cost reduction is stemming from better patient experiences and improved provider productivity."

8. **Future Directions**:
- "Current practices often rely on simple adjustments to schedules derived from single-stage models and can lead to significant loss of operational efficiency."
- "One particularly important direction for future research is to explore more complex healthcare networks."

These quotes encapsulate the main ideas regarding the complexity of appointment scheduling in healthcare, the challenges faced in multi-stage systems, the proposed solutions to improve patient experience and operational efficiency, and directions for future research.

X-TIMESTAMP-MAP=LOCAL:00:00:00.000,MPEGTS:90000

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Appointment scheduling is a commonly used,

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tool in healthcare to match provider capacity with,

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patient demand.

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Uh, it is something we all experience when,

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booking visits with primary care doctors or dentists.

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Uh, while we may seem straightforward,

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appointment scheduling is actually a complex task, due

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to competing objectives among, various stakeholders.

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For example, you know, patients may want quicker access

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to care, but providers want to maximize, resource

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allocation, utilization, which can often lead

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to, delays.

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Uh, additionally, numerous, environmental factors,

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add to, managerial challenges,

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including patient no-shows, preferences,

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punctuality, provider lateness

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and variability in service times.

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Appointment scheduling has been a classic problem in

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operations management.

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Uh, the area of research I specialize in,

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extensive work has been done on this topic

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dating back to 1950s.

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However, most of these studies focus on,

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single stage systems where customers are assumed

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to receive service from,

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only a single stage and, and then leave.

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Uh, such a model does not fully capture the complexity of,

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management, challenges,

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present in real world multi-stage, service environments.

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Healthcare, multi-stage services are very common for,

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for instance, in an infusion center.

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Uh, patients typically go through three stages of services,

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you know, like block draw, physician exam

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to verify the treatment plan,

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and finally infusion, treatment.

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Uh, as another example, in orthopedic, clinic, a common,

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patient care path would involve a X-ray exam,

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followed by physician consultation.

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Uh, and finally service from an,

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orthopedic, technician.

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A patient who receive care in such,

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tender healthcare systems, often spend, extended hours,

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if not full day in the facility, they might have

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to take a whole day off work

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and have considerable anxieties about their treatments.

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So these prolonged, unproductive

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and uncomfortable experiences often have significant

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consequences beyond just mere inconvenience

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or, irritation.

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So one promising approach

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to managing patient experience in such complex environments

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is to provide patients with a structured,

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visit itinerary, which specifies appointment time

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for each service stage.

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It's like having a travel join. Uh,

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It's like having a travel guide,

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for your healthcare, journey.

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Uh, as, but as mentioned earlier, you know,

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research has primarily focusing on, single stage systems

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and inspired by the need

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to better manage multi-stage systems.

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We develop the first optimization framework,

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to provide personalized visit itineraries

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for patients intended healthcare system.

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In traditional single stage models,

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the process is relatively straightforward.

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You know, patient arrive, they wait,

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they receive care, and then they leave.

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Uh, the manager

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or the planner, determines the number of patients

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to schedule for each appointment slot

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to balance patient waiting,

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provide idle time and overtime.

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Uh, if you think about it,

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if too many patients are scheduled too, too closely,

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wait time increases.

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Uh, in contrast, if too few are scheduled to loosely,

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providers are underutilized.

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So there's a trade off there,

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but the trade off is

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relatively straight, straightforward.

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Uh, however, multi-stage systems are significantly more,

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complex in these systems.

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Patients receive sequential services,

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with each stage requiring a substantial amount of time,

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often with, significant variability.

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Uh, and patient cannot proceed to the next service

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until the current one is completed.

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Uh, and providers cannot begin their work

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until patients arrive, from the previous, stage.

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Uh, and these interdependencies make managing a multi-stage

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system far more complicated.

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Uh, there are two practical ways to apply

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a single stage models to manage a multi-stage.

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First way is you could just tell patients

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the appointment time at the initial stage,

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and then ask them to check in at subsequent stages

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and wait until they can be seen.

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But this is clearly not desirable from patient's perspective

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because they are not well informed about what to expect,

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during their visits.

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The second approach is to first determine,

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patient appointment times based on the bottleneck

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stage among all stages.

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And then the appointment times for proceeding

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or following stages can be

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provided by, you know, subtracting, and adding

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or adding the expected service times in those

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stages respectively.

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Uh, so let me give you example.

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Say if the infusion service in the bottleneck

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and the appointment time is set at 11:15 AM

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the average duration on infusion service,

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let's say is two hours

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and 15 minutes, then the preceding physician appointment may

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be set at 9:00 AM which is two hour and 15 minutes

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before 11:15 AM.

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Uh, so while these two ideas are easy to implement,

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taking advantage

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of existing knowledge on single stage system,

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they rely solely on expected service times to capture

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the interdependencies

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of patient services across multiple stages.

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And this can actually lead to loss of,

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operational in inefficiencies.

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So, and this may actually lead to a loss

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of operational efficiencies.

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Um, in contrast, our multi-stage model,

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captures patient flow through multiple stages,

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explicitly quantifying different patients' waiting time at

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different stages, idle time

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and overtime of different providers at different stages.

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And the objective of our model is to personalize,

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appointment times for each patient at each service stage

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with the objective to minimizing a weighted sum

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of all patients waiting time, all providers idle time

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and over time across all different stages.

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So in essence, our model offers a precise

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quantification of system performances,

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which the traditional single stage model cannot provide, and

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therefore our model is more accurate

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and leads to improved operational efficiencies

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for running multi-stage healthcare systems.

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Traditional, single stage models,

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the objective functions often exhibit something called a

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discrete conve, properties.

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And these properties are very nice

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and useful mathematical properties making the problem

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relatively easy to solve.

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But we show that these nice properties,

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however, do not necessarily hold for multi-stage models.

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Hence, new solution, approaches need to be developed.

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Uh, we actually come up with two exact solution methods.

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Uh, the first approach,

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reformulates the problem using the classic Big M method

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with binary variables.

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And this method, linearize those

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non convex constraints in the problem.

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And the advantage of this reformulation is

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that it can be directly solved

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by off the shelf optimization software packages.

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And this reformulation used quite some binary variables

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and may take some time for solving large scale instances.

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So to improve computational e efficiencies, we came up

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with a second idea, which is

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to move the complicating constraints

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to the objective of the model.

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Uh, and this makes the objective function concave

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and the constraints set comebacks.

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Uh, it turns out that there are efficient ways

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to solve problems with, such a structure,

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in our numerical tests.

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The first reformation takes no more than 500 seconds,

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to find the optimal visit itinerary

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for the most complex instance,

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our second solution method significantly

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reduces computational time, averaging only a quarter

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of the time required

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by the first approach across all testing, instances.

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So this demonstrates that our approaches can be,

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practical for generating visit itineraries In real world

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settings, the computation is efficient

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and can actually be performed, in advance

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because the set of patients who will come for service

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that they are typically decided ahead of time.

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We conducted a case study in the setting of,

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infusion center populated

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by data from the Donna Fiber Cancer Institute.

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Uh, in this particular setting, patients will go

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through two main service, stages, exam rooms

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for physician consultations and infusion beds for treatment.

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So there are 15 exam rooms,

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25 infusion beds accommodating approximately 90

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patients, daily.

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The regular working hours consists of eight hours

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split into 32 slots of 15 minutes each.

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Uh, and to model the service time, we use empirical,

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distributions based on previous studies conducted

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at the same location.

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Uh, so to give you an idea,

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the average time in the exam room is about 1.1 hours

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with a standard deviation of 0.4 hours,

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and the average time on infusion bed is about two point 25

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hours with a standard deviation of 1.4 hours.

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Um, so what we do in our experiments, we, we tested

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our model across various environments where the level

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of administrative support for providers

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and the emphasis on patient experience varied

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on average across all the testing scenarios.

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Uh, our model achieved a 28% cost reduction

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compared to practic, practice approaches

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that rely on simple adjustments to single stage models.

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So to explain the mechanism behind this cost reduction,

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it is crucial to differentiate, two types

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of patient waiting and two types of provider idling.

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And these are unique elements,

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in the multi-stage healthcare system.

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And these are the also the unique elements

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that we introduced in our multi-stage model.

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So the first type of waiting is called regular waiting,

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and it occurs when a patient completes a prior stage,

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and the appointment time

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for the current stage has already passed,

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but the provider is still occupied.

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So patient cannot be served, they have to wait.

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The second type of waiting is called leisure waiting.

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And this happens when the patient finishes a prior stage

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earlier, then the scheduled time for the next stage.

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And leisure waiting is less costly per unit of time

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because it is anticipated, by patients.

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And patients may stretch their legs, get a coffee

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or take a walk for provider idling.

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A recoverable idling happens when a provider

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completes a service, but the next patient's appointment time

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has not yet arrived, allowing the provider to use the time

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for some ancillary tasks, for example,

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making some phone calls or doing some administrative work.

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Uh, in contrast, regular idling occurs when the provider is

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ready, but the patient's not present at the

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patient's, appointment time.

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So recover idling costs less than regular idling per unit

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of time because during regular idling, the provider has

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to stay put waiting for patients who may come anytime.

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Now, our multi-stage model improve systems performance by

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smartly designing patient with itineraries

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to replace patient regular waiting

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with less costly leisure waiting,

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and provide the regular idling

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with less costly recoverable idling.

250
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So simply put, the cost reductions coming from our,

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model is actually stemming from better patient experiences

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and improved provider productivity.

253
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And this is made possible by our model,

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which explicitly captures patient flow dynamics in a

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00:13:44.415 --> 00:13:46.345
multi-stage healthcare system.

256
00:13:46.405 --> 00:13:49.345
Our study highlights the importance of,

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carefully accounting for

258
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interdependencies across service stages when

259
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managing patient appointments.

260
00:13:56.725 --> 00:13:59.715
In multi-stage healthcare systems,

261
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current practices often rely on simple adjustments

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to schedules, derive from single stage models,

263
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and can lead to significant loss of operational efficiency.

264
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A carefully designed patient with itineraries

265
00:14:15.385 --> 00:14:17.545
considering different types of patient waiting

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00:14:17.805 --> 00:14:20.025
and provider idling that I talked about it earlier,

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can improve both patient experience

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and provider productivity.

269
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And, in terms of future research, directions

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our work focus on tandem healthcare system

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where patients are served sequentially at,

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at each stage.

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One particularly important direction

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for future research in my point of view is to explore

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more complex healthcare networks, in these networks.

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Patients may receive a subset

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of services in different orders, leading to more dynamic

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and complex patient flows.

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Uh, managing these flows requires developing new

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modeling frameworks and solution approaches.

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I believe this is a critical area to investigate further

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to improve healthcare delivery in diverse settings.

Challenges and Complexities in Healthcare Appointment Scheduling

00:00:00 - Appointment scheduling is a commonly used, tool in healthcare to match provider capacity with, patient demand. it is something we all experience when, booking visits with primary care doctors or dentists. while we may seem straightforward, appointment scheduling is actually a complex task, due to competing objectives among, various stakeholders. For example, you know, patients may want quicker access to care, but providers want to maximize, resource

00:00:39 - to, delays. additionally, numerous, environmental factors, add to, managerial challenges, including patient no-shows, preferences, punctuality, provider lateness and variability in service times. Appointment scheduling has been a classic problem in operations management. the area of research I specialize in,

00:01:09 - dating back to 1950s. However, most of these studies focus on, single stage systems where customers are assumed to receive service from, only a single stage and, and then leave. such a model does not fully capture the complexity of, management, challenges, present in real world multi-stage, service environments.

Enhancing Patient Experience in Multi-Stage Healthcare Services

00:01:41 - for instance, in an infusion center. patients typically go through three stages of services, you know, like block draw, physician exam to verify the treatment plan, and finally infusion, treatment. as another example, in orthopedic, clinic, a common, patient care path would involve a X-ray exam, followed by physician consultation.

00:02:10 - orthopedic, technician. A patient who receive care in such, tender healthcare systems, often spend, extended hours, if not full day in the facility, they might have to take a whole day off work and have considerable anxieties about their treatments. So these prolonged, unproductive and uncomfortable experiences often have significant consequences beyond just mere inconvenience

00:02:42 - So one promising approach to managing patient experience in such complex environments is to provide patients with a structured, visit itinerary, which specifies appointment time for each service stage. It's like having a travel join. It's like having a travel guide, for your healthcare, journey. as, but as mentioned earlier, you know, research has primarily focusing on, single stage systems

Optimizing Multi-Stage Healthcare Systems: Personalized Patient Itineraries

00:03:12 - to better manage multi-stage systems. We develop the first optimization framework, to provide personalized visit itineraries for patients intended healthcare system. In traditional single stage models, the process is relatively straightforward. You know, patient arrive, they wait, they receive care, and then they leave. the manager or the planner, determines the number of patients to schedule for each appointment slot

00:03:43 - provide idle time and overtime. if you think about it, if too many patients are scheduled too, too closely, wait time increases. in contrast, if too few are scheduled to loosely, providers are underutilized. So there's a trade off there, but the trade off is relatively straight, straightforward. however, multi-stage systems are significantly more, complex in these systems.

00:04:14 - with each stage requiring a substantial amount of time, often with, significant variability. and patient cannot proceed to the next service until the current one is completed. and providers cannot begin their work until patients arrive, from the previous, stage. and these interdependencies make managing a multi-stage system far more complicated.

Optimizing Appointment Scheduling in Multi-Stage Healthcare Systems

00:04:46 - a single stage models to manage a multi-stage. First way is you could just tell patients the appointment time at the initial stage, and then ask them to check in at subsequent stages and wait until they can be seen. But this is clearly not desirable from patient's perspective because they are not well informed about what to expect, during their visits. The second approach is to first determine,

00:05:19 - stage among all stages. And then the appointment times for proceeding or following stages can be provided by, you know, subtracting, and adding or adding the expected service times in those stages respectively. so let me give you example. Say if the infusion service in the bottleneck and the appointment time is set at 11:15 AM the average duration on infusion service,

00:05:50 - and 15 minutes, then the preceding physician appointment may be set at 9:00 AM which is two hour and 15 minutes before 11:15 AM. so while these two ideas are easy to implement, taking advantage of existing knowledge on single stage system, they rely solely on expected service times to capture the interdependencies of patient services across multiple stages.

Enhancing Operational Efficiency in Multi-Stage Healthcare Models

00:06:23 - operational in inefficiencies. So, and this may actually lead to a loss of operational efficiencies. in contrast, our multi-stage model, captures patient flow through multiple stages, explicitly quantifying different patients' waiting time at different stages, idle time and overtime of different providers at different stages.

00:06:58 - appointment times for each patient at each service stage with the objective to minimizing a weighted sum of all patients waiting time, all providers idle time and over time across all different stages. So in essence, our model offers a precise quantification of system performances, which the traditional single stage model cannot provide, and

00:07:26 - and leads to improved operational efficiencies for running multi-stage healthcare systems. Traditional, single stage models, the objective functions often exhibit something called a discrete conve, properties. And these properties are very nice and useful mathematical properties making the problem relatively easy to solve. But we show that these nice properties, however, do not necessarily hold for multi-stage models.

Optimizing Healthcare Appointment Scheduling: Two Solution Methods

00:08:00 - we actually come up with two exact solution methods. the first approach, reformulates the problem using the classic Big M method with binary variables. And this method, linearize those non convex constraints in the problem. And the advantage of this reformulation is that it can be directly solved by off the shelf optimization software packages. And this reformulation used quite some binary variables

00:08:35 - So to improve computational e efficiencies, we came up with a second idea, which is to move the complicating constraints to the objective of the model. and this makes the objective function concave and the constraints set comebacks. it turns out that there are efficient ways to solve problems with, such a structure, in our numerical tests. The first reformation takes no more than 500 seconds,

00:09:06 - for the most complex instance, our second solution method significantly reduces computational time, averaging only a quarter of the time required by the first approach across all testing, instances. So this demonstrates that our approaches can be, practical for generating visit itineraries In real world settings, the computation is efficient and can actually be performed, in advance

Enhancing Patient Flow and Cost Efficiency in Infusion Centers

00:09:39 - that they are typically decided ahead of time. We conducted a case study in the setting of, infusion center populated by data from the Donna Fiber Cancer Institute. in this particular setting, patients will go through two main service, stages, exam rooms for physician consultations and infusion beds for treatment. So there are 15 exam rooms,

00:10:10 - patients, daily. The regular working hours consists of eight hours split into 32 slots of 15 minutes each. and to model the service time, we use empirical, distributions based on previous studies conducted at the same location. so to give you an idea, the average time in the exam room is about 1.1 hours

00:10:40 - and the average time on infusion bed is about two point 25 hours with a standard deviation of 1.4 hours. so what we do in our experiments, we, we tested our model across various environments where the level of administrative support for providers and the emphasis on patient experience varied on average across all the testing scenarios. our model achieved a 28% cost reduction

Optimizing Patient Waiting and Provider Idling in Multi-Stage Healthcare

00:11:14 - that rely on simple adjustments to single stage models. So to explain the mechanism behind this cost reduction, it is crucial to differentiate, two types of patient waiting and two types of provider idling. And these are unique elements, in the multi-stage healthcare system. And these are the also the unique elements that we introduced in our multi-stage model.

00:11:46 - and it occurs when a patient completes a prior stage, and the appointment time for the current stage has already passed, but the provider is still occupied. So patient cannot be served, they have to wait. The second type of waiting is called leisure waiting. And this happens when the patient finishes a prior stage earlier, then the scheduled time for the next stage. And leisure waiting is less costly per unit of time

00:12:18 - And patients may stretch their legs, get a coffee or take a walk for provider idling. A recoverable idling happens when a provider completes a service, but the next patient's appointment time has not yet arrived, allowing the provider to use the time for some ancillary tasks, for example, making some phone calls or doing some administrative work. in contrast, regular idling occurs when the provider is

Optimizing Patient Flow in Multi-Stage Healthcare Systems

00:12:50 - patient's, appointment time. So recover idling costs less than regular idling per unit of time because during regular idling, the provider has to stay put waiting for patients who may come anytime. Now, our multi-stage model improve systems performance by smartly designing patient with itineraries to replace patient regular waiting with less costly leisure waiting,

00:13:22 - with less costly recoverable idling. So simply put, the cost reductions coming from our, model is actually stemming from better patient experiences and improved provider productivity. And this is made possible by our model, which explicitly captures patient flow dynamics in a multi-stage healthcare system. Our study highlights the importance of, carefully accounting for

00:13:55 - managing patient appointments. In multi-stage healthcare systems, current practices often rely on simple adjustments to schedules, derive from single stage models, and can lead to significant loss of operational efficiency. A carefully designed patient with itineraries considering different types of patient waiting and provider idling that I talked about it earlier, can improve both patient experience

Future Research Directions in Healthcare Delivery Models

00:14:26 - And, in terms of future research, directions our work focus on tandem healthcare system where patients are served sequentially at, at each stage. One particularly important direction for future research in my point of view is to explore more complex healthcare networks, in these networks. Patients may receive a subset of services in different orders, leading to more dynamic

00:15:12 - managing these flows requires developing new modeling frameworks and solution approaches. I believe this is a critical area to investigate further to improve healthcare delivery in diverse settings.

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