Can we accurately forecast non-elective bed occupancy and admissions in the NHS?:A time-series MSARIMA analysis of longitudinal data from an NHS Trust

OBJECTIVES: The main objective of the study was to develop more accurate and precise short-term forecasting models for admissions and bed occupancy for an NHS Trust located in Bristol, England. Subforecasts for the medical and surgical specialties, and for different lengths of stay were realised DESIGN: Autoregressive integrated moving average models were specified on a training dataset of daily count data, then tested on a 6-week forecast horizon. Explanatory variables were included in the models: day of the week, holiday days, lagged temperature and precipitation. SETTING: A secondary care hospital in an NHS Trust in South West England. PARTICIPANTS: Hospital admissions between September 2016 and March 2020, comprising 1291 days. PRIMARY AND SECONDARY OUTCOME MEASURES: The accuracy of the forecasts was assessed through standard measures, as well as compared with the actual data using accuracy thresholds of 10% and 20% of the mean number of admissions or occupied beds. RESULTS: The overall Autoregressive Integrated Moving Average (ARIMA) admissions forecast was compared with the Trust’s forecast, and found to be more accurate, namely, being closer to the actual value 95.6% of the time. Furthermore, it was more precise than the Trust’s. The subforecasts, as well as those for bed occupancy, tended to be less accurate compared with the overall forecasts. All of the explanatory variables improved the forecasts. CONCLUSIONS: ARIMA models can forecast non-elective admissions in an NHS Trust accurately on a 6-week horizon, which is an improvement on the current predictive modelling in the Trust. These models can be readily applied to other contexts, improving patient flow

Estimating the waiting time of multi-priority emergency patients with downstream blocking

To characterize the coupling effect between patient flow to access the emergency department (ED) and that to access the inpatient unit (IU), we develop a model with two connected queues: one upstream queue for the patient flow to access the ED and one downstream queue for the patient flow to access the IU. Building on this patient flow model, we employ queueing theory to estimate the average waiting time across patients. Using priority specific wait time targets, we further estimate the necessary number of ED and IU resources. Finally, we investigate how an alternative way of accessing ED (Fast Track) impacts the average waiting time of patients as well as the necessary number of ED/IU resources. This model as well as the analysis on patient flow can help the designer or manager of a hospital make decisions on the allocation of ED/IU resources in a hospital

DISEÑO DE UN MODELO DE MEDICIÓN DEL TIEMPO DE CICLO EN LA OPTIMIZACIÓN DE UNA CADENA DE SUMINISTRO (DESIGN OF A MODEL MEASUREMENT OF CYCLE TIME IN THE OPTIMIZATION OF A SUPPLY CHAIN)

ResumenLos mercados globalizados y competitivos obligan a una gestión de la cadena de suministro, con el fin de cumplir con las expectativas de los clientes. En la toma de decisiones se han implementado los modelos matemáticos, destacando los relacionados con líneas de espera. En el presente trabajo se vinculó la teoría de colas con la medición del tiempo de ciclo en una cadena de suministro, en la disminución del tiempo de recolección de tarimas de una empresa arrendadora, cuando éstas son desocupadas en los supermercados. En las pruebas realizadas se observó una optimización del tiempo de carga logrando no solo un beneficio global para la empresa. Por lo que este trabajo será de utilidad para los administradores y responsables de la gestión de la cadena de suministro.Palabra(s) Clave: Cadena de suministro, Modelo matemático, Teoría de colas, Tiempo de ciclo. AbstractGlobalized and competitive markets require supply chain management in order to meet customer expectations. In decision-making, mathematical models have been implemented, highlighting those related to waiting lines. In the present work, the queuing theory was linked in the measurement of the cycle time in a supply chain, in the reduction of the time of collection of pallets of a leasing company, when these are vacated in the supermarkets. In the tests carried out, an optimization of the loading time was observed, achieving not only a global benefit for the company. So this work will be useful for managers and managers of the supply chain management.Keywords: Cycle time, Mathematical model, Queueing theory, Supply chain

Petri Nets Validation of Markovian Models of Emergency Department Arrivals

International audienceModeling of hospital’s Emergency Departments (ED) is vital for optimisation of health services offered to patients that shows up at an ED requiring treatments with different level of emergency. In this paper we present a modeling study whose contribution is twofold: first, based on a dataset relative to the ED of an Italian hospital, we derive different kinds of Markovian models capable to reproduce, at different extents, the statistical character of dataset arrivals; second, we validate the derived arrivals model by interfacing it with a Petri net model of the services an ED patient undergoes. The empirical assessment of a few key performance indicators allowed us to validate some of the derived arrival process model, thus confirming that they can be used for predicting the performance of an ED

A scalable forecasting framework to predict COVID-19 hospital bed occupancy

The coronavirus disease 2019 (COVID-19) pandemic has led to capacity problems in many hospitals around the world. During the peak of new infections in Germany in April 2020 and October to December 2020, most hospitals had to cancel elective procedures for patients because of capacity shortages. We present a scalable forecasting framework with a Monte Carlo simulation to forecast the short-term bed occupancy of patients with confirmed and suspected COVID-19 in intensive care units and regular wards. We apply the simulation to different granularity and geographical levels. Our forecasts were a central part of the official weekly reports of the Bavarian State Ministry of Health and Care, which were sent to key decision makers in the individual ambulance districts from May 2020 to March 2021. Our evaluation shows that the forecasting framework delivers accurate forecasts despite data availability and quality issues

Development and implementation of a real time statistical control method to identify the start and end of the winter surge in demand for paediatric intensive care

Winter surge management in intensive care is hampered by the annual variability in the winter surge. We aimed to develop a real-time monitoring system that could promptly identify the start, and accurately predict the end, of the winter surge in a paediatric intensive care (PIC) setting. We adapted a statistical process control method from the stock market called “Bollinger bands” that compares current levels of demand for PIC services to thresholds based on the medium term average demand. Algorithms to identify the start and end of the surge were developed for a specific PIC service: the North Thames Children's Acute Transport Service (CATS) using eight winters of data (2005–12) to tune the algorithms and one winter to test the final method (2013/14). The optimal Bollinger band thresholds were 1.2 and 1 standard deviations above and below a 41-day moving average of demand respectively. A simple linear model was found to predict the end of the surge and overall demand volume as soon as the start had been identified. Applying the method to the validation winter of 2013/14 showed excellent performance, with the surge identified from 18th November 2013 to 4th January 2014. An Excel tool running the algorithms has been in use within CATS since September 2014. There were three factors which facilitated the successful implementation of this tool: the perceived problem was pressing and identified by the clinical team; there was close clinical engagement throughout and substantial effort was made to develop an easy-to-use Excel tool for sustainable use

A genetic algorithm for dynamic scheduling in emergency departments with priorities

A hospital is a very complex environment and its management is a hard task. The point we explore in this thesis is the management of the patient flow for the Emergency Department. The main contribution of the thesis is twofold: on the one hand, we design a model of the Emergency Department as close as possible to the real environment; on the other hand, we design a genetic algorithm for finding the optimal schedule of patients’ care. The choice of this approach is due to both the dynamic nature of the environment and the tight constraints on computational time, which favour the use of an any-time algorithm. We show through simulation that the model is sound and that the genetic algorithm is effective for the scheduling problem and could be easily applied to a real Emergency Departmen