Scheduling admissions and reducing variability in bed demand

Team Size and Composition in Home Healthcare: Quantitative Insights and Six Model-Based Principles

The aim of this constructive study was to develop model-based principles to provide guidance to managers and policy makers when making decisions about team size and composition in the context of home healthcare. Six model-based principles were developed based on extensive data analysis and in close interaction with practice. In particular, the principles involve insights in capacity planning, travel time, available effective capacity, contract types, and team manageability. The principles are formalized in terms of elementary mathematical models that capture the essence of decision-making. Numerical results based on real-life scenarios reveal that efficiency improves with team size, albeit more prominently for smaller teams due to diminishing returns. Moreover, it is demonstrated that the complexity of managing and coordinating a team becomes increasingly more difficult as team size grows. An estimate for travel time is provided given the size and territory of a team, as well as an upper bound for the fraction of full-time contracts, if split shifts are to be avoided. Overall, it can be concluded that an ideally sized team should serve (at least) around a few hundreds care hours per week.

Appointment Pathways: Yield Management via Cause-and-Effect Modeling in the Outpatient Setting at Mayo Clinic

Patients have multiple outpatient appointments for various reasons. Analyzing patients' related appointments provides insight into referral patterns, leading to recommendations for ideal care and more efficient planning. We model these appointments with causal graphs via Judea Pearl's causal graph approach. Once we define the causal relationships in the appointment data, we leverage a graph database and visualization software to investigate valuable patterns and relationships in patient care over time. The Pathways tool allows yield management at specialty, provider, or appointment levels. Leaders use this tool to anticipate a patient's downstream appointments; the tool provides insights into staffing and the impact of growing demand.

Physician-Customized Strategies for Reducing Outpatient Waiting Time in South Korea Using Queueing Theory and Probabilistic Metamodels

The time a patient spends waiting to be seen by a healthcare professional is an important determinant of patient satisfaction in outpatient care. Hence, it is crucial to identify parameters that affect the waiting time and optimize it accordingly. First, statistical analysis was used to validate the effective parameters. However, no parameters were found to have significant effects with respect to the entire outpatient department or to each department. Therefore, we studied the improvement of patient waiting times by analyzing and optimizing effective parameters for each physician. Queueing theory was used to calculate the probability that patients would wait for more than 30 min for a consultation session. Using this result, we built metamodels for each physician, formulated an effective method to optimize the problem, and found a solution to minimize waiting time using a non-dominated sorting genetic algorithm (NSGA-II). On average, we obtained a 30% decrease in the probability that patients would wait for a long period. This study shows the importance of customized improvement strategies for each physician.

Design and comparison of scheduling strategy for teleconsultation

BACKGROUND

Telemedicine is playing an increasingly more important role in disease diagnosis and treatment. The market of telemedicine application is continuously promoted, thus bringing some issues on telemedicine operations management.

OBJECTIVE

We aimed to compare the teleconsultation scheduling performance of newly designed proactive strategy and existing static strategy and explore the decision-making under different conditions.

METHODS

We developed a discrete-event simulation model based on practical investigation to describe the existing static scheduling strategy of teleconsultation. The static strategy model was verified by comparing it with the historical data. Then a new proactive strategy was proposed, whose average waiting time, variance of waiting time and completed numbers were compared with the static strategy.

RESULTS

The analysis indicated that the proactive strategy performed better than static under the current resource allocation. Furthermore, we explored the impact on the system of both strategies varying arrival rate and experts' shift time.

CONCLUSIONS

Under different shift times and arrival rates, the managers of telemedicine center should select different strategy. The experts' shift time had a significant impact on all system performance indicators. Therefore, if managers wanted to improve the system performance to a greater extent, they needed to reduce the shift time as much as possible.

Explicit results on conditional distributions of generalized exponential mixtures

For independent exponentially distributed random variables $X_i$ , $i\in {\mathcal{N}}$ , with distinct rates ${\lambda}_i$ we consider sums $\sum_{i\in\mathcal{A}} X_i$ for $\mathcal{A}\subseteq {\mathcal{N}}$ which follow generalized exponential mixture distributions. We provide novel explicit results on the conditional distribution of the total sum $\sum_{i\in {\mathcal{N}}}X_i$ given that a subset sum $\sum_{j\in \mathcal{A}}X_j$ exceeds a certain threshold value $t>0$ , and vice versa. Moreover, we investigate the characteristic tail behavior of these conditional distributions for $t\to\infty$ . Finally, we illustrate how our probabilistic results can be applied in practice by providing examples from both reliability theory and risk management.

Integrated Scheduling and Capacity Planning with Considerations for Patients' Length-of-Stays

Motivated by the shortcoming of current hospital scheduling and capacity planning methods which often model different units in isolation, we introduce the first dynamic multi-day scheduling model that integrates information about capacity usage at more than one location in a hospital. In particular, we analyze the first dynamic model that accounts for patients' length-of-stay and downstream census in scheduling decisions. Via a simple and innovative variable transformation, we show that the optimal number of patients to be allowed in the system is increasing in the state of the system and in the downstream capacity. Moreover, the total system cost exhibits decreasing marginal returns as the capacity increases at any location independently of another location. Through numerical experiments on realistic data, we show that there is substantial value in making integrated scheduling decisions. In contrast, localized decision rules that only focus on a single location of a hospital can result in up to 60% higher expenses.

Levelling bed occupancy: reconfiguring surgery schedules via simulation

PURPOSE

The purpose of this paper is to present simulation modelling to reconfigure a 700-bed Hong Kong hospital's master surgery schedule (MSS), aiming to improve patient flow, capacity management and resource allocation through levelling bed occupancy within the hospital.

DESIGN/METHODOLOGY/APPROACH

A discrete-event simulation model was developed to understand how changes to the MSS would affect bed occupancy, thereby providing business intelligence for short- and long-term hospital planning. A decision tool was subsequently developed for hospital managers to test different scenarios.

FINDINGS

Simulation modelling showed that significant bed occupancy levelling could be achieved through small and practicable changes to the MSS. Optimisation routines conducted using the simulation model then gave additional insights into how the schedule should be revamped for the long term.

PRACTICAL IMPLICATIONS

The authors show how operations research methods are useful for guiding hospital operational planning. The authors show that a data-driven and evidence-based model enables hospital managers to critically explore various scheduling changes, while also providing a scientific common ground for discussion among important stakeholders. It is a crucial step forward when adopting advanced analytics for Hong Kong hospital operational planning.

ORIGINALITY/VALUE

The authors provide a robust method for evaluating the relationship between Hong Kong hospital's MSS and its bed occupancy. Through simulating various changes to the surgical schedule, valuable and practicable insights were made available for hospital managers to make short- and longer-term changes that enhance the system's overall efficiency and service quality.

Factors impacting technology adoption in hospital bed logistics

Purpose

The purpose of this paper is to refine and expand technology adoption theory for a healthcare logistics setting by combining the technology–organization–environment framework with a business process management (BPM) perspective. The paper identifies and ranks factors impacting the decision to implement instances of technologies in healthcare logistics processes.

Design/methodology/approach

A multiple case study is carried out at five Danish hospitals to investigate the bed logistics process. A combined technology adoption and BPM lens is applied to gain an understanding of the reasoning behind technology adoption.

Findings

A set of 17 factors impacting the adoption of technologies within healthcare logistics was identified. The impact factors perceived as most important to the adoption of technologies in healthcare logistics processes relate to quality, employee work conditions and employee engagement.

Research limitations/implications

This paper seeks to understand how managers can use knowledge about impact factors to improve processes through technology adoption. The findings of this study provide insights about the factors impacting the adoption of technologies in healthcare logistics processes. Differences in perceived importance of factors enable ranking of impact factors, and prioritization of changes to be implemented. The study is limited to five hospitals, but is expected to be representative of public hospitals in developed countries and applicable to similar processes.

Originality/value

The study contributes to the empirical research within the field of BPM and technology adoption in healthcare. Furthermore, the findings of this study enable managers to make an informed decision about technology adoption within a healthcare logistics setting.

Multi-objective admission planning problem: a two-stage stochastic approach

Effective admission planning can improve inpatient throughput and waiting times, resulting in better quality of service. The uncertainty in the patient arrival and the availability of resources makes the patient's allocation difficult to manage. Thus, in the admission process hospitals aim to accomplish targets of resource utilization and to lower the cost of service. Both objectives are related and in conflict. In this paper, we present a bi-objective stochastic optimization model to study the trade-off between the resource utilization and the cost of service, taking into account demand and capacity uncertainties. Real data from the surgery and medical areas of a Chilean public hospital are used to illustrate the approach. The results show that the solutions of our approach outperform the actual practice in the Chilean hospital.

A Capacity Allocation Planning Model for Integrated Care and Access Management

The prevailing first-come-first-served approach to outpatient appointment scheduling ignores differing urgency levels, leading to unnecessarily long waits for urgent patients. In data from a partner healthcare organization, we found in some departments that urgent patients were inadvertently waiting longer for an appointment than non-urgent patients. This paper develops a capacity allocation optimization methodology that reserves appointment slots based on urgency in a complicated, integrated care environment where multiple specialties serve multiple types of patients. This optimization reallocates network capacity to limit access delays (indirect waiting times) for initial and downstream appointments differentiated by urgency. We formulate this problem as a queueing network optimization and approximate it via deterministic linear optimization to simultaneously smooth workloads and guarantee access delay targets. In a case study of our industry partner we demonstrate the ability to (1) reduce urgent patient mean access delay by 27% with only a 7% increase in mean access delay for non-urgent patients, and (2) increase throughput by 31% with the same service levels and overtime.

The Boarding Patient: Effects of ICU and Hospital Occupancy Surges on Patient Flow

Patients admitted to a hospital's intensive care unit (ICU) often endure prolonged boarding within the ICU following receipt of care, unnecessarily occupying a critical care bed, and thereby delaying admission for other incoming patients due to bed shortage. Using patient-level data over two years at two major academic medical centers, we estimate the impact of ICU and ward occupancy levels on ICU length of stay (LOS), and test whether simultaneous "surge occupancy" in both areas impacts overall ICU length of stay. In contrast to prior studies that only measure total LOS, we split LOS into two individual periods based on physician requests for bed transfers. We find that "service time" (when critically ill patients are stabilized and treated) is unaffected by occupancy levels. However, the less essential "boarding time" (when patients wait to exit the ICU) is accelerated during periods of high ICU occupancy and, conversely, prolonged when hospital ward occupancy levels are high. When the ICU and wards simultaneously encounter bed occupancies in the top quartile of historical levels-which occurs 5% of the time-ICU boarding increases by 22% compared to when both areas experience their lowest utilization, suggesting that ward bed availability dominates efforts to accelerate ICU discharges to free up ICU beds. We find no adverse effects of high occupancy levels on ICU bouncebacks, in-hospital deaths, or 30-day hospital readmissions, which supports our finding that the largely discretionary boarding period fluctuates with changing bed occupancy levels.

Emergency overcrowding and access block: A smaller problem than we think

OBJECTIVES

Emergency department (ED) access block, the inability to provide timely care for high acuity patients, is the leading safety concern in First World EDs. The main cause of ED access block is hospital access block with prolonged boarding of inpatients in emergency stretchers. Cumulative emergency access gap, the product of the number of arriving high acuity patients and their average delay to reach a care space, is a novel access measure that provides a facility-level estimate of total emergency care delays. Many health leaders believe these delays are too large to be solved without substantial increases in hospital capacity. Our objective was to quantify cumulative emergency access blocks (the problem) as a fraction of inpatient capacity (the potential solution) at a large sample of Canadian hospitals.

METHODS

In this cross-sectional study, we collated 2015 administrative data from 25 Canadian hospitals summarizing patient inflow and delays to ED care space. Cumulative access gap for high acuity patients was calculated by multiplying the number of Canadian Triage Acuity Scale (CTAS) 1-3 patients by their average delay to reach a care space. We compared cumulative ED access gap to available inpatient bed hours to estimate fractional access gap.

RESULTS

Study sites included 16 tertiary and 9 community EDs in 12 cities, representing 1.79 million patient visits. Median ED census (interquartile range) was 66,300 visits per year (58,700-80,600). High acuity patients accounted for 70.7% of visits (60.9%-79.0%). The mean (SD) cumulative ED access gap was 46,000 stretcher hours per site per year (± 19,900), which was 1.14% (± 0.45%) of inpatient capacity.

CONCLUSION

ED access gaps are large and jeopardize care for high acuity patients, but they are small relative to hospital operating capacity. If access block were viewed as a "whole hospital" problem, capacity or efficiency improvements in the range of 1% to 3% could profoundly mitigate emergency care delays.

Using the M/G/∞ queueing model to predict inpatient family medicine service census and resident workload

The number and timing of unplanned admissions to inpatient teaching services vary. Recent changes to resident duty hours make it essential to maximize learning experiences and balance workload on these services. Queueing theory provides a mechanism for understanding and planning for the variations in admissions and daily census. Daily admissions, length of stay, and daily census were modeled for a teaching inpatient family medicine service over 46 months using an M/G/∞ queueing model. Q–Q plots and a Kolmogorov–Smirnov test were used to check the fit of actual data to the model. Admissions and daily census followed a Poisson distribution (λ = 3.28 and λ = 8.28, respectively), while length-of-stay followed a lognormal distribution (µ = 0.49, σ2 = 0.83). The M/G/∞ queueing model proved useful for predicting overflow admission frequency, defining expected resident workload in terms of patient-days, and determining hospital unit size requirements.

The probability of readmission within 30 days of hospital discharge is positively associated with inpatient bed occupancy at discharge--a retrospective cohort study

BACKGROUND

Previous work has suggested that given a hospital's need to admit more patients from the emergency department (ED), high inpatient bed occupancy may encourage premature hospital discharges that favor the hospital's need for beds over patients' medical interests. We argue that the effects of such action would be measurable as a greater proportion of unplanned hospital readmissions among patients discharged when the hospital was full than when not. In response, the present study tested this hypothesis by investigating the association between inpatient bed occupancy at the time of hospital discharge and the 30-day readmission rate.

METHODS

The sample included all inpatient admissions from the ED at a 420-bed emergency hospital in southern Sweden during 2011-2012 that resulted in discharge before 1 December 2012. The share of unplanned readmissions within 30 days was computed for levels of inpatient bed occupancy of <95%, 95-100%, 100-105% and >105% at the hour of discharge. A binary logistic regression model was constructed to adjust for age, time of discharge, and other factors that could affect the outcome.

RESULTS

In all, 32,811 visits were included in the study, 9.9% of which resulted in an unplanned readmission within 30 days of discharge. The proportion of readmissions was 9.0% for occupancy levels of <95% at the patient's discharge, 10.2% for 95-100% occupancy, 10.8% for 100-105% occupancy, and 10.5% for >105% occupancy (p = 0.0001). Results from the multivariate models show that the OR (95% CI) of readmission was 1.11 (1.01-1.22) for patients discharged at 95-100% occupancy, 1.17 (1.06-1.29) at 100-105% occupancy, and 1.15 (0.99-1.34) at >105% occupancy.

CONCLUSIONS

Results indicate that patients discharged from inpatient wards at times of high inpatient bed occupancy experience an increased risk of unplanned readmission within 30 days of discharge.

A simulation optimization approach for resource allocation in an emergency department

The emergency department (ED) is a primary health care unit and one of the main entrances to the hospital system where appropriate, timely and good performance can save lives. Lack of sufficient resources, such as beds and qualified health care professionals, are major stumbling blocks to providing timely and suitable services; but resources availability and moving towards the ideal situation without attention to budget restrictions is neither practical nor achievable. In this study, simulation optimization is used to finding the best configuration in ED resources (e.g., Bed, Nurse, and GP) that affects a patient's length of stay, subject to budget constraints. Simulation is used to analyze the system and estimate target function an optimization model is then solved under different budget constraints. By considering the current budget, the new configuration of 20 inpatient beds, 3 nurses and 1 GP, with 554.4 minutes of a patient's length of stay shows 8.1% length of stay (LOS) improvement. Whilst with a maximum 35.5 budget units allocation of 20 inpatient beds, 4 nurses and 3 GPs a 9.5% decrease in LOS is proposed.

Associations between in-hospital bed occupancy and unplanned 72-h revisits to the emergency department: a register study

Background

A possible downstream effect of high in-hospital bed occupancy is that patients in the emergency department (ED) who would benefit from in-hospital care are denied admission. The present study aimed at evaluating this hypothesis through investigating associations between in-hospital bed occupancy at the time of presentation in the ED and the probability for unplanned 72-hour (72-h) revisits to the ED among patients discharged at index. A second outcome was unplanned 72-h revisits resulting in admission.

Methods

All visits to the ED of a 420-bed emergency hospital in southern Sweden between 1 January 2011 and 31 December 2012, which did not result in admission, death, or transfer to another hospital were included. Revisiting fractions were computed for in-hospital occupancy intervals <85%, 85% to 90%, 90% to 95%, 95% to 100%, 100% to 105%, and ≥105%. Multivariate models were constructed in an attempt to take confounding factors from, e.g., presenting complaints, age, referral status, and triage priority into account.

Results

Included in the study are 81,878 visits. The fraction of unplanned 72-h revisits/unplanned 72-h revisits resulting in admission was 5.8%/1.4% overall, 6.2%/1.4% for occupancy <85%, 6.4%/1.5% for occupancy 85% to 90%, 5.8%/1.4% for occupancy 90% to 95%, 6.0%/1.6% for occupancy 95% to 100%, 5.4%/1.6% for occupancy 100% to 105%, and 4.9%/1.4% for occupancy ≥105%.

In the multivariate models, a trend to lower probability of unplanned 72-h revisits was observed at occupancy ≥105% compared to occupancy <95% (OR 0.88, CI 0.76 to 1.01). No significant associations between in-hospital occupancy at index and the probability of making unplanned 72-h revisits resulting in admission were observed.

Conclusions

The lack of associations between in-hospital occupancy and unplanned 72-h revisits does not support the hypothesis that ED patients are inappropriately discharged when in-hospital beds are scarce. The results are reassuring as they indicate that physicians are able to make good decisions, also while resources are constrained.

Scalable approximate policies for Markov decision process models of hospital elective admissions

OBJECTIVE

To demonstrate the feasibility of using stochastic simulation methods for the solution of a large-scale Markov decision process model of on-line patient admissions scheduling.

METHODS

The problem of admissions scheduling is modeled as a Markov decision process in which the states represent numbers of patients using each of a number of resources. We investigate current state-of-the-art real time planning methods to compute solutions to this Markov decision process. Due to the complexity of the model, traditional model-based planners are limited in scalability since they require an explicit enumeration of the model dynamics. To overcome this challenge, we apply sample-based planners along with efficient simulation techniques that given an initial start state, generate an action on-demand while avoiding portions of the model that are irrelevant to the start state. We also propose a novel variant of a popular sample-based planner that is particularly well suited to the elective admissions problem.

RESULTS

Results show that the stochastic simulation methods allow for the problem size to be scaled by a factor of almost 10 in the action space, and exponentially in the state space. We have demonstrated our approach on a problem with 81 actions, four specialities and four treatment patterns, and shown that we can generate solutions that are near-optimal in about 100s.

CONCLUSION

Sample-based planners are a viable alternative to state-based planners for large Markov decision process models of elective admissions scheduling.

A framework to analyze hospital-wide patient flow logistics: evidence from an Italian comparative study

Through a comparative study of six Italian hospitals, the paper develops and tests a framework to analyze hospital-wide patient flow performance. The framework adopts a system-wide approach to patient flow management and is structured around three different levels: (1) the hospital, (2) the pipelines (possible patient journeys within the hospital) and (3) the production units (physical spaces, such as operating rooms, where service delivery takes places). The focus groups and the data analysis conducted within the study support that the model is a useful tool to investigate hospital-wide implications of patient flows. The paper provides also evidence about the causes of hospital patient flow problems. Particularly, while shortage of capacity does not seem to be a relevant driver, our data shows that patient flow variability caused by inadequate allocation of capacity does represent a key problem. Results also show that the lack of coordination between different pipelines and production units is critical. Finally, the problem of overlapping between elective and unscheduled cases can be solved by setting aside a certain level of capacity for unexpected peaks.