A novel healthcare resource allocation decision support tool: A forecasting-simulation-optimization approach

TL;DR: This work developed a model that linked each and every service and specialty including A&E, and outpatient and inpatient services, with the aim of developing a linear optimization model to estimate the required bed capacity and staff needs of a mid-size hospital in England.

Abstract: The increasing pressures on the healthcare system in the UK are well documented. The solution lies in making best use of existing resources (e.g. beds), as additional funding is not available. Incr...

Summary

1. Introduction

• Demand at National Health Service (NHS) hospitals in England has been increasing significantly over the past decade.
• Many simulation-optimisation methods have been developed with the aim of determining optimal solutions for their decision variables (e.g. number of operating rooms and beds or staffing cost).
• Optimisation techniques, such as mathematical programming and heuristic algorithms, are able to provide an exact configuration for the better, and simulation techniques, such as Discrete Event Simulation (DES) and System Dynamics (SD), are able to tell possible outcomes of a scenario.

3. The proposed hybrid framework: FSO approach

• The following three methodologies are combined to develop a forecastingsimulation-optimization (FSO) approach for the purpose of optimizing the level of resources of an NHS Trust: forecasting, DES and integer linear programming.
• The second component of the proposed methodology is to develop a generic hospital simulation model that integrates all specialties (i.e. A&E, outpatient, and inpatient services) and interactions to capture the stochastic behaviour of the hospital.
• The forecasting techniques used in their hybrid framework enable conversion from generic data sources to useful information.
• An optimisation model is attached to their framework as it finds the optimum number of beds, doctors, and nurses for specialties.
• Activity related data at PAH (i.e. the number of admissions to inpatient, outpatient and A&E services) is derived from the national Hospital Episode Statistics (HES) dataset after an extensive data preparation process.

3.1. Demand forecasting

• A decision support system (DSS) is developed to identify better forecasting methods and time periods for each specialty of the hospital.
• Using MASE, 64 best forecasting models are selected out of 760 models, comprising 38 for outpatient specialties demand, 25 for inpatient specialties, and 1 for A&E.
• Elective patients, or inpatient, processes generally require scheduling, admission and bed management.
• Black-box and white-box validations were used to validate their DES model.
• The parameters of the integer linear programming are defined as follows: NDPs: Number of discharged patients at specialty s, BOR: Bed occupancy rate (assumed to be annual bed occupancy rate of the hospital) TARGET: Target level of bed occupancy rate (assumed to be 85% according to the literature), NBs:.

4. A case study: Reallocating number of beds and optimizing staffing levels

• The authors applied the FSO approach to PAH and provided inputs from four types of resources: Local data, forecasting, simulation and the literature (see Table 4 for a breakdown of beds by specialty).
• Average length of stay and average revenue are inputs generated by the generic hospital simulation model.
• The remaining specialties require additional beds to cope with the overcapacity running, for example, general medicine (by 30 beds), cardiology (by 6 beds), geriatric medicine (by 39 beds) and obstetrics (by 5 beds).
• A sensitivity analysis was also carried out, increasing the forecasted demand (i.e. above the base model).
• A new metric known as Demand Coverage Ratio (DCR) is developed for the purpose of measuring the percentage of patients admitted to the hospital and discharged using the available resources of each specialty.

4.2. Optimized number of staff

• Figures 5 and 6 show the relationship between bed occupancy rate and total number of consultants, and bed occupancy rate and total number of nurses, respectively.
• As seen in Table 5, the required number of consultants and nurses in all inpatient services, are determined by assuming that all staff are in full time employment (i.e. 1 FTE).
• The increasing pressures on the healthcare system in the UK and other parts of the world are well documented.

Figures

Figure 1. The structure of the FSO approach along with the relationships of inputsoutputs

Table 3. Best performing Forecasting methods for the inpatient specialities; ARIMA: Autoregressive integrated moving average, ES: Exponential smoothing, SLR: Stepwise linear regression, STLF: Seasonal and trend decomposition by loess forecasting

Figure 5. Relationship between BOR and total number of consultants

Table 4. Input values of the FSO approach. ENB: Existing number of beds, ALoS: Average length of stay, NAP: Number of admitted patients, AR: Average revenue

Table 7. Number of nurses depending on different FTE ratios for the base model. FTE: Full time equivalence, Case Mix is 50% with 1.0 FTE, 30% with 0.8 FTE, 20% with 0.5 FTE

Table 1. Detailed information about studies related to simulation-optimization modelling in healthcare settings. ABS: Agent based simulation, BDU: Bed daily utilization, DES: Discrete event simulation, GP: Goal programming, ILP: Integer linear programming, INLP: Integer nonlinear programming, IP: Integer programming, Max: Maximization, Min: Minimization, MIP: Mixed integer programming, NG: Not given, NSGA II: Non-dominated sorting genetic algorithm II, O: Optimization, OR: Operating room, PIOA: Prevalence and incidence optimization algorithm, S: Simulation, SSA: Simultaneous search algorithm, SBSA: Sequential bisection search algorithm, VBA: Visual basic for application

Figure 4. Analysis results with total number of beds, DCR and BOR

Figure 3. Comparison of results with the current situation. Specialties are 1) General surgery, 2) Trauma & orthopaedics, 3) General medicine, 4) Cardiology, 5) Paediatrics, 6) Geriatric medicine, 7) Obstetrics, 8) Gynaecology and 9) Others

Table 5. The results of the FSO approach for the base model. NDEP: Number of discharged elective patients, NDNEP: Number of discharged non-elective patients, BOR: Bed occupancy rate, NB: Number of beds, NC: Number of consultants, NN: Number of nurses

Figure 2. Outline illustration of the whole hospital conceptualized model

Table 6. Number of consultants depending on different FTE ratios for the base model. FTE: Full time equivalence, Case Mix is 50% with 1.0 FTE, 30% with 0.8 FTE, 20% with 0.5 FTE

Table 2. Forecast accuracy values (mean absolute scaled error) for the general surgery inpatient elective and non-elective speciality. ARIMA: Autoregressive integrated moving average, ES: Exponential smoothing, SLR: Stepwise Linear Regression, STLF: Seasonal and trend decomposition by loess forecasting, TS: Training Set, VS: Validation Set

Figure 6. Relationship between BOR and total number of nurses

Full text

1
A novel healthcare resource allocation decision support tool: A
forecasting-simulation-optimization approach
Muhammed Ordu
a
*, Eren Demir
b
, Chris Tofallis
b
and Murat M. Gunal
c
a
Department of Industrial Engineering, Faculty of Engineering, Osmaniye Korkut Ata
University, Osmaniye, Turkey
b
Hertfordshire Business School, University of Hertfordshire, Hatfield, United Kingdom;
c
Barbaros Naval Science and Engineering Institute, National Defence University,
Istanbul, Turkey
*Corresponding Author: Osmaniye Korkut Ata University, Faculty of Engineering,
Department of Industrial Engineering, 80000, Osmaniye, Turkey,
muhammedordu@osmaniye.edu.tr
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
This is an accepted manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 03 Feb 2020,
available online: https://doi.org/10.1080/01605682.2019.1700186.

2
A novel healthcare resource allocation decision support tool: a
forecasting-simulation-optimization approach
The increasing pressures on the healthcare system in the UK are well
documented. The solution lies in making best use of existing resources (e.g.
beds), as additional funding is not available. Increasing demand and capacity
shortages are experienced across all specialties and services in hospitals.
Modelling at this level of detail is a necessity, as all the services are
interconnected, and cannot be assumed to be independent of each other. Our
review of the literature revealed two facts; First an entire hospital model is rare,
and second, use of multiple OR techniques are applied more frequently in recent
years. Hybrid models which combine forecasting, simulation and optimization
are becoming more popular. We developed a model that linked each and every
service and specialty including A&E, and outpatient and inpatient services, with
the aim of, 1) forecasting demand for all the specialties, 2) capturing all the
uncertainties of patient pathway within a hospital setting using discrete event
simulation, and 3) developing a linear optimization model to estimate the
required bed capacity and staff needs of a mid-size hospital in England (using
essential outputs from simulation). These results will bring a different perspective
to key decision makers with a decision support tool for short and long term
strategic planning to make rational and realistic plans, and highlight the benefits
of hybrid models.
Keywords: Healthcare, decision support system, forecasting, discrete event
simulation, integer linear programming
1. Introduction
Demand at National Health Service (NHS) hospitals in England has been increasing
significantly over the past decade. The estimates show that there has been a 26% and
32% increase in accident & emergency (A&E) and inpatient hospital admissions from
2010/11 to 2017/18, respectively (National Health Services England, 2018a and 2018b).
The increasing demand for services is closely linked to worsening prevailing conditions
and an expanding elderly population, that often has multiple complex conditions, (such
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
This is an accepted manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 03 Feb 2020,
available online: https://doi.org/10.1080/01605682.2019.1700186.

3
as diabetes and dementia), and which forms the highest demand for beds (The King’s
Fund, 2012). Advancements in technology and medicine have led to improvements in
healthcare, greatly reducing length of stays in hospital and increasing the number of
day-cases (or outpatient); however hospital beds remain fundamental resources for all
health systems.
Despite a sharp growth in demand, the number of beds has continued to decline.
In 2000 there were an average of 3.8 beds per 1,000 people, whereas this had dropped to
2.4 beds by 2015. Between 2006/07 and 2015/16 the number of overnight beds has
decreased by over a fifth. As a result, the average bed occupancy rates have increased
over time, with rates for general and acute wards, and mental health, now peaking at
over 91% (BMA, 2017). Hospitals are expected to aim for an 85% bed occupancy rate,
whereas they are increasingly operating at very high levels of occupancy, particularly
during the winter period.
The implications of high bed occupancy rates are widespread, and include, 1) it
creates a backlog in emergency departments (Nuffield Trust, 2016), 2) patients can be
placed on clinically inappropriate wards, which may affect the patient experience and
the quality of care they receive (Goulding, 2015), and 3) evidence suggests that high
occupancy rates increases the rate of hospital acquired infections, which may lead to
temporary closure of beds or wards (Kaier, 2012).
Due to severe budget cuts in the NHS, hospitals do not have the necessary
funding to increase capacity, either in the form of beds or staff. Therefore, hospital
management needs to find efficient and effective ways of utilising existing resources.
This may mean the management doing things differently, a shift from the conventional
decision-making process to a more evidence-based approach (a behavioural change).
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
This is an accepted manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 03 Feb 2020,
available online: https://doi.org/10.1080/01605682.2019.1700186.

4
A hospital is a complex system made up of 25 or more specialties providing
treatment within inpatient, outpatient and A&E services. There are numerous
departments and wards within each specialty, with staff including consultants, nurses,
healthcare assistances, and technicians. Therefore, determining the most effective use of
resources (predominantly beds, consultants and nurses) is a major challenge.
The literature around developing models for healthcare providers is rich and
vast. Many simulation-optimisation methods have been developed with the aim of
determining optimal solutions for their decision variables (e.g. number of operating
rooms and beds or staffing cost). Previous and current models in the literature typically
maximized the number of admissions and financial outputs, or minimized length of
stay, waiting time and costs in healthcare settings. In the majority of instances these
models have focused on modelling a service, department or a specialty, however no
models have tackled current and future bed occupancy (and other key metrics of
interest) at the entire hospital level (details in the literature review below). A model for
a single service (or a few) would not be adequate to determine the required capacity for
all specialties within a hospital.
A comprehensive entire hospital modelling framework is necessary that
combines all the specialties and services within a single decision support system (DSS).
Such an integrated DSS should be able to: 1) forecast demand for all specialties within
inpatient, outpatient and A&E, 2) capture the entire hospital patient pathway at a
sufficient level of detail, and 3) optimise the required bed capacity and the required
number of consultants and nurses.
Such a DSS is able to answer many key questions beyond capacity requirements.
For example, a hospital may experience a sharp increase in activity. The forecasts will
generate the expected activity to be integrated into the simulation model, whereas the
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
This is an accepted manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 03 Feb 2020,
available online: https://doi.org/10.1080/01605682.2019.1700186.

5
simulation will capture all the uncertainties around the dynamics of the hospital, ranging
from time related activities (e.g. length of stay, waiting times, and treatment duration) to
hospital finances (revenue, cost and surplus), with the aim of testing a wide range of
scenarios around impact of change. The simulation has limitations around establishing
the optimal capacity requirements. This is where the optimisation becomes a valuable
tool to estimate the exact bed requirements (along with consultant and nurse hours)
subject to constraints (e.g. targeted bed occupancy rate).
The merger of these techniques, optimisation and simulation, creates more
power in decision making. Optimisation techniques, such as mathematical programming
and heuristic algorithms, are able to provide an exact configuration for the better, and
simulation techniques, such as Discrete Event Simulation (DES) and System Dynamics
(SD), are able to tell possible outcomes of a scenario. Hybrid modelling approaches are
becoming more popular in today’s complex decision-making environment.
The core objectives of this study are as follows:
(1) Develop an innovative approach combining DES and forecasting demand and
capacity in healthcare settings. To our knowledge, the literature does not have an
extensive study that forecasts demand for all types of attendances/admissions of
each specialty which then integrates these demand inputs within an entire
generic hospital simulation model.
(2) Develop a linear optimisation algorithm to determine the required bed capacity
and staff requirements to meet the needs of local populations. A number of
essential outputs from the simulation model will be fed into the optimisation
model.
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
This is an accepted manuscript of an article published by Taylor & Francis in Journal of the Operational Research Society on 03 Feb 2020,
available online: https://doi.org/10.1080/01605682.2019.1700186.