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M.J. van der Tuin
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Designing Optimized Rheumatology Patient Journeys
Enhancing Capacity Planning and Sustainable Engagement of Rheumatologists
Currently, Rheumatology outpatient clinics face increasing physician workload because patient demand varies over time, rheumatologic diagnoses can be chronic in nature, and the number of active physicians is decreasing. Based on a case study provided by Leiden University Medical Center (LUMC) and in collaboration with Reinier de Graaf Gasthuis Delft (RdGG), this thesis develops a mathematical framework to improve capacity utilization while supporting sustainable employability and timely access to care.
This thesis focuses on the tactical and operational levels of appointment scheduling (AS). Tactical AS addresses medium-term capacity allocation decisions, whereas operational AS focuses on scheduling individual appointments. Therefore, we develop a multi-stage approach in which uncertain factors
such as patient inflow and follow-up patterns are included. These factors are based on historical data provided by LUMC.
At the tactical level, different blueprint AS models are formulated. Tactical blueprint AS refers to the allocation of capacity into time slots across physicians and appointment types. Each model corresponds to a blueprint AS scenario, differentiating between new appointment distributions among physicians,
urgent appointment restrictions, and slot allocation within the blueprint schedules. These models consider hierarchical optimization problems to deal with multiple objectives having different priorities, such as preferred cyclic blueprint schedules, urgent and regular slot allocations, and accessibility for new patients.
Next, at the operational level, the realized blueprint schedules from the tactical level are used for the AS algorithms. We develop a sequential algorithm that traverses our arrival horizon (e.g., one year) day by day and schedules follow-up appointments if necessary. Three operational scheduling approaches are considered: fixed and flexible blueprint scheduling, and open scheduling. Moreover, we evaluate whether reserving future capacity affects timely access to care.
Computational results show that good tactical blueprint scheduling performance does not necessarily match good operational performance, for example, with respect to new appointments scheduled within their target timeframe of four weeks. This emphasizes the importance of evaluating tactical scheduling decisions within a realistic operational setting. Among the blueprint scheduling approaches, semi-flexible blueprint scheduling marginally outperformed fixed blueprint scheduling, while flexible blueprint scheduling performed best in terms of timely access to care. Open scheduling is also a suitable approach, as it offers good access to care. However, these improvements come at the cost of less
predictable physician schedules. Hospitals can decide whether performance improvements outweigh the additional planning effort and implementation costs.
Instead of recommending one optimal scheduling approach, the proposed framework enables hospitals to choose the approach that best fits their organizational setting, priorities, and desired balance between timely access to care and sustainable employability. Finally, we discuss the limitations of this research and suggest directions for future work, such as incorporating patient satisfaction, staff job satisfaction, and the use of AI tools in appointment scheduling (AS). ...
This thesis focuses on the tactical and operational levels of appointment scheduling (AS). Tactical AS addresses medium-term capacity allocation decisions, whereas operational AS focuses on scheduling individual appointments. Therefore, we develop a multi-stage approach in which uncertain factors
such as patient inflow and follow-up patterns are included. These factors are based on historical data provided by LUMC.
At the tactical level, different blueprint AS models are formulated. Tactical blueprint AS refers to the allocation of capacity into time slots across physicians and appointment types. Each model corresponds to a blueprint AS scenario, differentiating between new appointment distributions among physicians,
urgent appointment restrictions, and slot allocation within the blueprint schedules. These models consider hierarchical optimization problems to deal with multiple objectives having different priorities, such as preferred cyclic blueprint schedules, urgent and regular slot allocations, and accessibility for new patients.
Next, at the operational level, the realized blueprint schedules from the tactical level are used for the AS algorithms. We develop a sequential algorithm that traverses our arrival horizon (e.g., one year) day by day and schedules follow-up appointments if necessary. Three operational scheduling approaches are considered: fixed and flexible blueprint scheduling, and open scheduling. Moreover, we evaluate whether reserving future capacity affects timely access to care.
Computational results show that good tactical blueprint scheduling performance does not necessarily match good operational performance, for example, with respect to new appointments scheduled within their target timeframe of four weeks. This emphasizes the importance of evaluating tactical scheduling decisions within a realistic operational setting. Among the blueprint scheduling approaches, semi-flexible blueprint scheduling marginally outperformed fixed blueprint scheduling, while flexible blueprint scheduling performed best in terms of timely access to care. Open scheduling is also a suitable approach, as it offers good access to care. However, these improvements come at the cost of less
predictable physician schedules. Hospitals can decide whether performance improvements outweigh the additional planning effort and implementation costs.
Instead of recommending one optimal scheduling approach, the proposed framework enables hospitals to choose the approach that best fits their organizational setting, priorities, and desired balance between timely access to care and sustainable employability. Finally, we discuss the limitations of this research and suggest directions for future work, such as incorporating patient satisfaction, staff job satisfaction, and the use of AI tools in appointment scheduling (AS). ...
Currently, Rheumatology outpatient clinics face increasing physician workload because patient demand varies over time, rheumatologic diagnoses can be chronic in nature, and the number of active physicians is decreasing. Based on a case study provided by Leiden University Medical Center (LUMC) and in collaboration with Reinier de Graaf Gasthuis Delft (RdGG), this thesis develops a mathematical framework to improve capacity utilization while supporting sustainable employability and timely access to care.
This thesis focuses on the tactical and operational levels of appointment scheduling (AS). Tactical AS addresses medium-term capacity allocation decisions, whereas operational AS focuses on scheduling individual appointments. Therefore, we develop a multi-stage approach in which uncertain factors
such as patient inflow and follow-up patterns are included. These factors are based on historical data provided by LUMC.
At the tactical level, different blueprint AS models are formulated. Tactical blueprint AS refers to the allocation of capacity into time slots across physicians and appointment types. Each model corresponds to a blueprint AS scenario, differentiating between new appointment distributions among physicians,
urgent appointment restrictions, and slot allocation within the blueprint schedules. These models consider hierarchical optimization problems to deal with multiple objectives having different priorities, such as preferred cyclic blueprint schedules, urgent and regular slot allocations, and accessibility for new patients.
Next, at the operational level, the realized blueprint schedules from the tactical level are used for the AS algorithms. We develop a sequential algorithm that traverses our arrival horizon (e.g., one year) day by day and schedules follow-up appointments if necessary. Three operational scheduling approaches are considered: fixed and flexible blueprint scheduling, and open scheduling. Moreover, we evaluate whether reserving future capacity affects timely access to care.
Computational results show that good tactical blueprint scheduling performance does not necessarily match good operational performance, for example, with respect to new appointments scheduled within their target timeframe of four weeks. This emphasizes the importance of evaluating tactical scheduling decisions within a realistic operational setting. Among the blueprint scheduling approaches, semi-flexible blueprint scheduling marginally outperformed fixed blueprint scheduling, while flexible blueprint scheduling performed best in terms of timely access to care. Open scheduling is also a suitable approach, as it offers good access to care. However, these improvements come at the cost of less
predictable physician schedules. Hospitals can decide whether performance improvements outweigh the additional planning effort and implementation costs.
Instead of recommending one optimal scheduling approach, the proposed framework enables hospitals to choose the approach that best fits their organizational setting, priorities, and desired balance between timely access to care and sustainable employability. Finally, we discuss the limitations of this research and suggest directions for future work, such as incorporating patient satisfaction, staff job satisfaction, and the use of AI tools in appointment scheduling (AS).
This thesis focuses on the tactical and operational levels of appointment scheduling (AS). Tactical AS addresses medium-term capacity allocation decisions, whereas operational AS focuses on scheduling individual appointments. Therefore, we develop a multi-stage approach in which uncertain factors
such as patient inflow and follow-up patterns are included. These factors are based on historical data provided by LUMC.
At the tactical level, different blueprint AS models are formulated. Tactical blueprint AS refers to the allocation of capacity into time slots across physicians and appointment types. Each model corresponds to a blueprint AS scenario, differentiating between new appointment distributions among physicians,
urgent appointment restrictions, and slot allocation within the blueprint schedules. These models consider hierarchical optimization problems to deal with multiple objectives having different priorities, such as preferred cyclic blueprint schedules, urgent and regular slot allocations, and accessibility for new patients.
Next, at the operational level, the realized blueprint schedules from the tactical level are used for the AS algorithms. We develop a sequential algorithm that traverses our arrival horizon (e.g., one year) day by day and schedules follow-up appointments if necessary. Three operational scheduling approaches are considered: fixed and flexible blueprint scheduling, and open scheduling. Moreover, we evaluate whether reserving future capacity affects timely access to care.
Computational results show that good tactical blueprint scheduling performance does not necessarily match good operational performance, for example, with respect to new appointments scheduled within their target timeframe of four weeks. This emphasizes the importance of evaluating tactical scheduling decisions within a realistic operational setting. Among the blueprint scheduling approaches, semi-flexible blueprint scheduling marginally outperformed fixed blueprint scheduling, while flexible blueprint scheduling performed best in terms of timely access to care. Open scheduling is also a suitable approach, as it offers good access to care. However, these improvements come at the cost of less
predictable physician schedules. Hospitals can decide whether performance improvements outweigh the additional planning effort and implementation costs.
Instead of recommending one optimal scheduling approach, the proposed framework enables hospitals to choose the approach that best fits their organizational setting, priorities, and desired balance between timely access to care and sustainable employability. Finally, we discuss the limitations of this research and suggest directions for future work, such as incorporating patient satisfaction, staff job satisfaction, and the use of AI tools in appointment scheduling (AS).
Surgery scheduling
Dealing with overtime
Surgical scheduling is a complex task that requires consideration of various factors, including the probability of overtime. In this study, we address the research problem of surgery scheduling while accounting for the likelihood of exceeding scheduled operating room (OR) time. To tackle this problem, we employ integer linear programming (ILP) models to determine the optimal number of surgeries per group, with the objective of maximizing OR utilization while incorporating the probability of overtime as a constraint.
To capture the probabilistic nature of surgery durations, we investigate suitable probability distributions. Existing literature suggests that surgery durations follow a lognormal distribution. However, since the sum of lognormally distributed random variables lacks a closed form solution, we initially assume a normal distribution for analytical convenience. Subsequently, we approximate the lognormal distribution using the Fenton-Wilkinson method to account for its realistic behavior. To incorporate the
lognormalistic behavior and solve the ILP models efficiently, we employ a column based approach. This approach enables us to handle the complexities introduced by the lognormal distribution. Our study utilizes data provided by a hospital in the Netherlands, including information on surgeries, specialties, groups, and the master surgery schedule (MSS). Given the consideration of both normal and lognormal distributions for surgery durations, we assess the goodness of fit using appropriate statistical
tests.
Our results reveal that using averages or expected values yields the highest OR utilizations. However, there is a discussion regarding the validity of this method, as it does not explicitly incorporate the probabilistic overtime constraints. Nevertheless, we observe that all methods include cases which
surpass the predetermined overtime threshold, suggesting that utilizing averages or expected values can be a valid alternative. However, utilizing averages or expected values gives rise to high percentage
of cases surpassing our overtime threshold. So, we suggest to use a method which explicitly uses the probabilistic nature of the surgery durations.
During the examination of our methods, we had to take a minimum number of mandatory scheduled surgeries for each group into account. This means that another dataset, with different mandatory numbers, might lead to different results. Additionally, we noticed that our overtime definition might not be the most optimal, as we still have cases that surpass our overtime threshold. In future research, it would be valuable to include financial and staff factors, which can further enhance the scheduling process.
Overall, this study contributes to the field of surgery scheduling by addressing the probability of overtime and presenting insights into the trade-offs between OR utilization and the inclusion of probabilistic
constraints. Further research can build upon these findings to refine the scheduling approaches and incorporate additional factors for a more comprehensive solution. ...
To capture the probabilistic nature of surgery durations, we investigate suitable probability distributions. Existing literature suggests that surgery durations follow a lognormal distribution. However, since the sum of lognormally distributed random variables lacks a closed form solution, we initially assume a normal distribution for analytical convenience. Subsequently, we approximate the lognormal distribution using the Fenton-Wilkinson method to account for its realistic behavior. To incorporate the
lognormalistic behavior and solve the ILP models efficiently, we employ a column based approach. This approach enables us to handle the complexities introduced by the lognormal distribution. Our study utilizes data provided by a hospital in the Netherlands, including information on surgeries, specialties, groups, and the master surgery schedule (MSS). Given the consideration of both normal and lognormal distributions for surgery durations, we assess the goodness of fit using appropriate statistical
tests.
Our results reveal that using averages or expected values yields the highest OR utilizations. However, there is a discussion regarding the validity of this method, as it does not explicitly incorporate the probabilistic overtime constraints. Nevertheless, we observe that all methods include cases which
surpass the predetermined overtime threshold, suggesting that utilizing averages or expected values can be a valid alternative. However, utilizing averages or expected values gives rise to high percentage
of cases surpassing our overtime threshold. So, we suggest to use a method which explicitly uses the probabilistic nature of the surgery durations.
During the examination of our methods, we had to take a minimum number of mandatory scheduled surgeries for each group into account. This means that another dataset, with different mandatory numbers, might lead to different results. Additionally, we noticed that our overtime definition might not be the most optimal, as we still have cases that surpass our overtime threshold. In future research, it would be valuable to include financial and staff factors, which can further enhance the scheduling process.
Overall, this study contributes to the field of surgery scheduling by addressing the probability of overtime and presenting insights into the trade-offs between OR utilization and the inclusion of probabilistic
constraints. Further research can build upon these findings to refine the scheduling approaches and incorporate additional factors for a more comprehensive solution. ...
Surgical scheduling is a complex task that requires consideration of various factors, including the probability of overtime. In this study, we address the research problem of surgery scheduling while accounting for the likelihood of exceeding scheduled operating room (OR) time. To tackle this problem, we employ integer linear programming (ILP) models to determine the optimal number of surgeries per group, with the objective of maximizing OR utilization while incorporating the probability of overtime as a constraint.
To capture the probabilistic nature of surgery durations, we investigate suitable probability distributions. Existing literature suggests that surgery durations follow a lognormal distribution. However, since the sum of lognormally distributed random variables lacks a closed form solution, we initially assume a normal distribution for analytical convenience. Subsequently, we approximate the lognormal distribution using the Fenton-Wilkinson method to account for its realistic behavior. To incorporate the
lognormalistic behavior and solve the ILP models efficiently, we employ a column based approach. This approach enables us to handle the complexities introduced by the lognormal distribution. Our study utilizes data provided by a hospital in the Netherlands, including information on surgeries, specialties, groups, and the master surgery schedule (MSS). Given the consideration of both normal and lognormal distributions for surgery durations, we assess the goodness of fit using appropriate statistical
tests.
Our results reveal that using averages or expected values yields the highest OR utilizations. However, there is a discussion regarding the validity of this method, as it does not explicitly incorporate the probabilistic overtime constraints. Nevertheless, we observe that all methods include cases which
surpass the predetermined overtime threshold, suggesting that utilizing averages or expected values can be a valid alternative. However, utilizing averages or expected values gives rise to high percentage
of cases surpassing our overtime threshold. So, we suggest to use a method which explicitly uses the probabilistic nature of the surgery durations.
During the examination of our methods, we had to take a minimum number of mandatory scheduled surgeries for each group into account. This means that another dataset, with different mandatory numbers, might lead to different results. Additionally, we noticed that our overtime definition might not be the most optimal, as we still have cases that surpass our overtime threshold. In future research, it would be valuable to include financial and staff factors, which can further enhance the scheduling process.
Overall, this study contributes to the field of surgery scheduling by addressing the probability of overtime and presenting insights into the trade-offs between OR utilization and the inclusion of probabilistic
constraints. Further research can build upon these findings to refine the scheduling approaches and incorporate additional factors for a more comprehensive solution.
To capture the probabilistic nature of surgery durations, we investigate suitable probability distributions. Existing literature suggests that surgery durations follow a lognormal distribution. However, since the sum of lognormally distributed random variables lacks a closed form solution, we initially assume a normal distribution for analytical convenience. Subsequently, we approximate the lognormal distribution using the Fenton-Wilkinson method to account for its realistic behavior. To incorporate the
lognormalistic behavior and solve the ILP models efficiently, we employ a column based approach. This approach enables us to handle the complexities introduced by the lognormal distribution. Our study utilizes data provided by a hospital in the Netherlands, including information on surgeries, specialties, groups, and the master surgery schedule (MSS). Given the consideration of both normal and lognormal distributions for surgery durations, we assess the goodness of fit using appropriate statistical
tests.
Our results reveal that using averages or expected values yields the highest OR utilizations. However, there is a discussion regarding the validity of this method, as it does not explicitly incorporate the probabilistic overtime constraints. Nevertheless, we observe that all methods include cases which
surpass the predetermined overtime threshold, suggesting that utilizing averages or expected values can be a valid alternative. However, utilizing averages or expected values gives rise to high percentage
of cases surpassing our overtime threshold. So, we suggest to use a method which explicitly uses the probabilistic nature of the surgery durations.
During the examination of our methods, we had to take a minimum number of mandatory scheduled surgeries for each group into account. This means that another dataset, with different mandatory numbers, might lead to different results. Additionally, we noticed that our overtime definition might not be the most optimal, as we still have cases that surpass our overtime threshold. In future research, it would be valuable to include financial and staff factors, which can further enhance the scheduling process.
Overall, this study contributes to the field of surgery scheduling by addressing the probability of overtime and presenting insights into the trade-offs between OR utilization and the inclusion of probabilistic
constraints. Further research can build upon these findings to refine the scheduling approaches and incorporate additional factors for a more comprehensive solution.