Scheduling the hospital-wide flow of elective patients

In this paper, we address the problem of planning the patient flow in hospitals subject to scarce medical resources with the objective of maximizing the contribution margin. We assume that we can classify a large enough percentage of elective patients according to their diagnosis-related group (DRG) and clinical pathway. The clinical pathway defines the procedures (such as different types of diagnostic activities and surgery) as well as the sequence in which they have to be applied to the patient. The decision is then on which day each procedure of each patient’s clinical pathway should be done, taking into account the sequence of procedures as well as scarce clinical resources, such that the contribution margin of all patients is maximized. We develop two mixed-integer programs (MIP) for this problem which are embedded in a static and a rolling horizon planning approach. Computational results on real-world data show that employing the MIPs leads to a significant improvement of the contribution margin compared to the contribution margin obtained by employing the planning approach currently practiced. Furthermore, we show that the time between admission and surgery is significantly reduced by applying our models

Flexible hospital-wide elective patient scheduling

In this paper, we build on and extend Gartner and Kolisch (2014)’s hospital-wide patient scheduling problem. Their contribution margin maximizing model decides on the patients' discharge date and therefore the length of stay. Decisions such as the allocation of scarce hospital resources along the clinical pathways are taken. Our extensions which are modeled as a mathematical program include admission decisions and flexible patient-to-specialty assignments to account for multi-morbid patients. Another flexibility extension is that one out of multiple surgical teams can be assigned to each patient. Furthermore, we consider overtime availability of human resources such as residents and nurses. Finally, we include these extensions in the rolling-horizon approach and account for lognormal distributed recovery times and remaining resource capacity for elective patients. Our computational study on real-world instances reveals that, if overtime flexibility is allowed, up to 5% increase in contribution margin can be achieved by reducing length of stay by up to 30%. At the same time, allowing for overtime can reduce waiting times by up to 33%. Our model can be applied in and generalized towards other patient scheduling problems, for example in cancer care where patients may follow defined cancer pathways

Mathematical Modelling and Cluster Analysis in Healthcare Analytics - The Case of Length of Stay Management

Length of Stay (LOS) is an important metric of care quality and efficiency in hospitals that has been studied for decades. Longer stays lead to increased costs and higher burdens on patients, caregivers, clinicians and facilities. Understanding characteristics of LOS outliers is important for developing actionable steps to address LOS reduction. Our study examines clustering of inpatients using key clinical and demographic attributes to identify LOS outliers and investigates the opportunity to reduce their LOS by comparing order sequences with similar non-outliers in the same cluster. Learning from retrospective data, we develop a mathematical model and a two-stage heuristic algorithm. Results indicate that switching orders in homogeneous inpatient sub-populations within the limits of clinical guidelines may be a promising decision support strategy for LOS management. These novel data-driven insights can be offered as suggestions for clinicians to apply new evidence-based, clinical guideline-compliant opportunities for LOS reduction through healthcare analytics

Improving hospital layout planning through clinical pathway mining

Clinical pathways (CPs) are standardized, typically evidence-based health care processes. They define the set and sequence of procedures such as diagnostics, surgical and therapy activities applied to patients. This study examines the value of data-driven CP mining for strategic healthcare management. When assigning specialties to locations within hospitals—for new hospital buildings or reconstruction works—the future CPs should be known to effectively minimize distances traveled by patients. The challenge is to dovetail the prediction of uncertain CPs with hospital layout planning. We approach this problem in three stages: In the first stage, we extend a machine learning algorithm based on probabilistic finite state automata (PFSA) to learn significant CPs from data captured in hospital information systems. In that stage, each significant CP is associated with a transition probability. A unique feature of our approach is that we can generalize the data and include those CPs which have not been observed in the data but which are likely to be followed by future patients according to the pathway probabilities obtained from the PFSA. At the same time, rare and non-significant CPs are filtered out. In the second stage, we present a mathematical model that allows us to perform hospital layout planning decisions based on the CPs, their probabilities and expert knowledge. In the third stage, we evaluate our approach based on different performance measures. Our case study results based on real-world hospital data reveal that using our CP mining approach, distances traveled by patients can be reduced substantially as compared to using a baseline method. In a second case study, when using our approach for reconstructing a hospital and incorporating expert knowledge into the planning, existing layouts can be improved

Cognitive workload reduction in hospital information systems

Order sets are a critical component in hospital information systems that are expected to substantially reduce physicians’ physical and cognitive workload and improve patient safety. Order sets represent time intervalclustered order items, such as medications prescribed at hospital admission, that are administered to patients during their hospital stay. In this paper, we develop a mathematical programming model and an exact and a heuristic solution procedure with the objective of minimizing physicians’ cognitive workload associated with prescribing order sets. Furthermore, we provide structural insights into the problem which lead us to a valid lower bound on the order set size. In a case study using order data on Asthma patients with moderate complexity from a major pediatric hospital, we compare the hospital’s current solution with the exact and heuristic solutions on a variety of performance metrics. Our computational results confirm our lower bound and reveal that using a time interval decomposition approach substantially reduces computation times for the mathematical program, as does a K−means clustering based decomposition approach which, however, does not guarantee optimality because it violates the lower bound. The results of comparing the mathematical program with the current order set configuration in the hospital indicates that cognitive workload can be reduced by about 20.2% by allowing 1 to 5 order sets, respectively. The comparison of the K−means based decomposition with the hospital’s current configuration reveals a cognitive workload reduction of about 19.5%, also by allowing 1 to 5 order sets, respectively. We finally provide a decision support system to help practitioners analyse the current order set configuration, the results of the mathematical program and the heuristic approach

Machine learning approaches for early DRG classification and resource allocation

Recent research has highlighted the need for upstream planning in healthcare service delivery systems, patient scheduling, and resource allocation in the hospital inpatient setting. This study examines the value of upstream planning within hospital-wide resource allocation decisions based on machine learning (ML) and mixed-integer programming (MIP), focusing on prediction of diagnosis-related groups (DRGs) and the use of these predictions for allocating scarce hospital resources. DRGs are a payment scheme employed at patients’ discharge, where the DRG and length of stay determine the revenue that the hospital obtains. We show that early and accurate DRG classification using ML methods, incorporated into an MIP-based resource allocation model, can increase the hospital’s contribution margin, the number of admitted patients, and the utilization of resources such as operating rooms and beds. We test these methods on hospital data containing more than 16,000 inpatient records and demonstrate improved DRG classification accuracy as compared to the hospital’s current approach. The largest improvements were observed at and before admission, when information such as procedures and diagnoses is typically incomplete, but performance was improved even after a substantial portion of the patient’s length of stay, and under multiple scenarios making different assumptions about the available information. Using the improved DRG predictions within our resource allocation model improves contribution margin by 2.9% and the utilization of scarce resources such as operating rooms and beds from 66.3% to 67.3% and from 70.7% to 71.7%, respectively. This enables 9.0% more nonurgent elective patients to be admitted as compared to the baseline

Hospital-wide therapist scheduling and routing: exact and heuristic methods

In this paper, we address the problem of scheduling and routing physical therapists hospital-wide. At the beginning of a day, therapy jobs are known to a hospital's physical therapy scheduler who decides for each therapy job when, where and by which therapist a job is performed. If a therapist is assigned to a sequence which contains two consecutive jobs that must take place in different treatment rooms, then transfer times must be considered. We propose three approaches to solve the problem. First, an Integer Program (IP) simultaneously schedules therapies and routes therapists. Second, a cutting plane algorithm iteratively solves the therapy scheduling problem without routing constraints and adds cuts to exclude schedules which have no feasible routes. Since hospitals are interested in obtaining quick solutions, we also propose a heuristic algorithm, which schedules therapies sequentially by simultaneously checking routing and resource constraints. Using real-world data from a hospital, we compare the performance of the three approaches. Our computational analysis reveals that our IP formulation fails to solve test, which have more than~30 jobs, to optimality in an acceptable solution time. In contrast, the cutting plane algorithm can solve instances with more than 100 jobs optimally. The heuristic approach obtains good solutions for large real-world instances within fractions of a second

Predictive and Prescriptive Analytics for Multi-Site Modeling of Frail and Elderly Patient Services

Recent research has highlighted the potential of linking predictive and prescriptive analytics. However, it remains widely unexplored how both paradigms could benefit from one another to address today's major challenges in healthcare. One of these is smarter planning of resource capacities for frail and elderly inpatient wards, addressing the societal challenge of an aging population. Frail and elderly patients typically suffer from multimorbidity and require more care while receiving medical treatment. The aim of this research is to assess how various predictive and prescriptive analytical methods, both individually and in tandem, contribute to addressing the operational challenges within an area of healthcare that is growing in demand. Clinical and demographic patient attributes are gathered from more than 165,000 patient records and used to explain and predict length of stay. To that extent, we employ Classification and Regression Trees (CART) analysis to establish this relationship. On the prescriptive side, deterministic and two-stage stochastic programs are developed to determine how to optimally plan for beds and ward staff with the objective to minimize cost. Furthermore, the two analytical methodologies are linked by generating demand for the prescriptive models using the CART groupings. The results show the linked methodologies provided different but similar results compared to using averages and in doing so, captured a more realistic real-world variation in the patient length of stay. Our research reveals that healthcare managers should consider using predictive and prescriptive models to make more informed decisions. By combining predictive and prescriptive analytics, healthcare managers can move away from relying on averages and incorporate the unique characteristics of their patients to create more robust planning decisions, mitigating risks caused by variations in demand

Modelling the Accessibility of Adult Psychology Services Using Discrete Event Simulation

With a growing number of people seeking treatment for mental health problems, mental health services are consequently coming under increased pressure resulting in longer waiting times and worsening of mental health problems. Service underfunding, overworked staff, and the looming threat of further demand due to the COVID-19 pandemic only add to the concerns. Hence it is imperative the efficiencies of these services are maximised to allow better access to quality treatment. We created a Discrete Event Simulation model to replicate the current clinical approach taken in an adult psychology clinic in the U.K.'s National Health Service. The model identifies bottlenecks in the service, and provides results on how different staffing scenarios could alleviate challenges