Balancing the NHS balanced scorecard!

In the UK, the split between opposition and supporters views of the National Health Service (NHS) performance ratings system is growing. Objective argument and consensus would be facilitated if a methodology was developed which showed the cause and effect relationships between the components of the performance rating system. The NHS hospital trust performance ratings data used in 2002 and 2003 were downloaded from the Department of Health performance rating website. Structural equation modelling was used to construct a causal-loop diagram showing the cause and effect relationships between the 16 common performance indicators in the two years. Scenario testing suggests that indicators of delayed transfer of care and of data quality are compromised if emergency readmissions performance is improved.     

An evaluation of the applicability of system dynamics to patient flow modelling

The objective of this research is to determine whether Systems Dynamics (SD) is a beneficial method for modelling hospital patient flow from a strategic planning perspective. While discrete event simulation has frequently been used as a tool for analysing and improving patient flow in health care settings, the desire to assess and understand patient flow and resource demand from a more strategic, and therefore aggregate, perspective led to the use of SD. To evaluate the suitability of such an approach, a model was developed in collaboration with the General Campus at The Ottawa Hospital with particular attention paid to the delays experienced by patients in the emergency department. The modelling techniques used, model validation and scenarios tested with the model are discussed, accompanied by comments regarding the appropriateness of SD for such a model.     

Examining the feasibility of using a modelling tool to assess resilience across a health-care system and assist with decisions concerning service reconfiguration

Changes in medical practice, demographic shifts and financial pressures are all examples of factors that may contribute to demand for periodic changes in the configuration of health services. When reconfiguring a service, health planners often take into account projected demand for services, patient access criteria and budgetary constraints (among other things), but typically give little consideration regarding its resilience to deliver services during and after external disruptions to its capability to deliver. In this paper we discuss a study conducted in response to a direct request from the National Health Service (NHS) Resilience Project within the Department of Health to explore the feasibility of assessing resilience across local services within the NHS and developing a computer software tool to assess resilience of different service reconfigurations. We give an account of the modelling process used, including the analytical framework we developed using both optimisation and heuristic methods, and an illustrative example of usage of a prototype software tool. We also highlight the key lessons that emerged during this project, which may be helpful to OR analysts working on similar projects regarding resilience in the public sector.     

Modelling for the planning and management of bed capacities in hospitals

The internal dynamics of a hospital represent a complex non-linear structure. Planning and management of bed capacities must be evaluated within an environment of uncertainty, variability and limited resources. A common approach is to plan and manage capacities based on simple deterministic spreadsheet calculations. This paper demonstrates that these calculations typically do not provide the appropriate information and result in underestimating true bed requirements. More sophisticated, flexible and necessarily detailed capacity models are needed. The development and use of such a simulation model is presented in this paper. The modelling work, in conjunction with a major UK NHS Trust, considers various types of patient flows, at the individual patient level, and resulting bed needs over time. The consequence of changes in capacity planning policies and management of existing capacities can be readily examined. The work has highlighted the need for evaluating hospital bed capacities in light of both bed occupancies and refused admission rates. The relationship between occupancy and refusals is complex and often overlooked by hospital managers.     

Patient flow-based allocation of inpatient resources: A case study

The paper considers the allocation of inpatient resources such as beds, operating theatres and nursing staff to specialties within a hospital setting. It describes an allocation procedure that takes patient flows as its starting point and enables an evaluation of combined impacts on the different resources involved. The paper is written in the format of a case study, dealing with a hospital that had serious problems with the utilization of beds and was faced with many admission-stops. However, the method can be used to a wide range of resource management problems in hospitals and can contribute to improving flexibility in the use of hospital resources.     

Overcoming the barriers: a qualitative study of simulation adoption in the NHS

This paper addresses a key issue in the health OR literature, namely the apparent failure of OR modelling to become embedded and widely implemented within healthcare organisations. The research presented here is a case study to evaluate the adoption of one particular simulation modelling tool, Scenario Generator (S:G), which was developed by the SIMUL8 Corporation in a PPI partnership with the UK's National Health Service (NHS) Institute for Innovation and Improvement. The study involved semi-structured interviews with employees of 28 Primary Care Trusts who had all been engaged in some way with the initiative, with participants classified as ‘Not Started’, ‘Given Up’ and ‘Actively Using’. This paper presents a brief summary of barriers and facilitators to the successful use of the S:G software, but its main purpose is to focus more broadly on factors influencing the successful adoption of simulation tools in general within healthcare organisations. The insights gained in this study are relevant to improving the uptake of OR modelling in general within the NHS.     

A simulation-based study of a NHS Walk-in Centre

This paper describes a simulation-based project to help North Mersey Community National Health Service Trust to design and plan the operation of a NHS Walk-in Centre. The simulation model developed of this multi-service facility was used to facilitate managers and health professionals to recognize existing problems and potential future problems, and to investigate ideas for their ‘solution’. In the fast-moving NHS where initiatives to improve access, such as walk-in centres, are a recent development and where no two centres are the same, ideas for best practice borrowed from elsewhere can be quickly tested for suitability in the local situation.     

A multi-objective model to determine efficient resource levels in a medical assessment unit

This paper details models that determine the efficient allocation of resources on a medical assessment unit (MAU) of a general hospital belonging to the National Health Service (NHS) UK. The MAU was established to improve the quality of care given to acute medical patients on admission, and also provide the organizational means of rapid assessment and investigation in order to avoid unnecessary admissions. To analyse the performance of the MAU, doctors, nurses and beds are considered as the three main resources. Then a model is developed using the goal programming approach in multiobjective decision making and solved to deal with MAU performance. The developed model is solved under three different sets of patient admissions with the same resource levels using past data from the MAU. The results of the model are used to analyse the needed resource levels. Conclusions as to the appropriate staffing levels and functions of the MAU are drawn.     

Waiting list behaviour and the consequences for NHS targets

The United Kingdom's National Health Service (NHS) is investing considerable resources in reducing patient waiting times for elective treatment. This paper describes the development of a waiting list model and its use in a simulation to assess management options. Simulation usually assumes that waiting is adequately described by simple queuing disciplines, typically first-in-first-out. However, waiting in the United Kingdom's NHS is a more complex phenomenon. The waiting list behaviour is explored through an analysis of the changes in waiting time distributions for elective orthopaedics in one Scottish Health Board, NHS Fife. The evolving distributions suggest that there have been substantial changes in priorities in response to the various NHS targets. However, in the short or medium term, the form of the distribution appears reasonably stable, providing a basis for estimating future waiting times in different scenarios. A model of the waiting behaviour and prioritization in the appointment allocations was embedded in a simulation of the complete elective orthopaedic patient journey from referral, through outpatients and diagnostics to surgery. The model has been used to explore the consequences of various management options in the context of the NHS target that no patient should wait more than 18 weeks between referral and treatment.     

Logical Analysis of Legislation Using Flow Diagrams

The Department of the Environment/Department of Transport (DOE/DTp) OR group uses flow diagrams to analyse legislation. Taking the bus deregulation sections of the 1985 Transport Act as the main example, this paper shows how a complex course of action prescribed in legal language may be simply represented by a series of yes/no questions. Traffic Area staff who implement the legislation have the diagrams as working guidelines to resolve their own, potentially conflicting, interpretations.     

A TIME SERIES APPROACH TO STOCK-RECRUITMENT ANALYSIS: TRANSFER FUNCTION NOISE MODELLING

Perceived relationships between stock size and recruitment have long been a corner-stone of fisheries management. These relationships are often used to design harvest strategies for ensuring that sufficient spawning stock exists to generate desired levels of recruitment in subsequent years. However, existing models fail to recognize and exploit the autocorrelation structure of both the recruitment and stock time series. The time series approach to modelling stock and recruitment presented in this paper takes this autocorrelation structure into account. The performance of the time series model is compared to existing stock-recruitment models using North Sea herring and Pacific halibut data.     

OR and the challenge to improve the NHS: modelling for insight and improvement in in-patient flows

This paper considers efforts to improve in-patient flows, a particularly urgent issue in the National Health Service (NHS). The context is described and related to reasons why OR has been making relatively little contribution. The paper argues that large complex models may often be unnecessary and even get in the way of providing clear insight and guidance for problem owners. The importance of understanding the generic working of systems to lead to improvement, and the limitations of simply describing them, is stressed. It is demonstrated that some very simple models can be of significant practical value in understanding and managing complex systems, changing mindsets and driving collection and use of operationally valuable data. Recommendations for more effective engagement with the NHS are offered.     

Flow equivalence,hyperbolic systems and a new zeta function for flows

We analyze the dynamics of diffeomorphisms in terms of their suspension flows. For many Axion A diffeomorphisms we find simplest representatives in their flow equivalence class and so reduce flow equivalence to conjugacy. The zeta functions of maps in a flow equivalence class are correlated with a zeta function ζ _H for their suspended flow. This zeta function is defined for any flow with only finitely many closed orbits in each homology class, and is proven rational for Axiom A flows. The flow equivalence of Anosov diffeomorphisms is used to relate the spectrum of the induced map on first homology to the existence of fixed points. For Morse-Smale maps, we extend a result of Asimov on the geometric index. Partially supported by MCS 76-08795.     

Maximal flow network modelling of production bottleneck problems

This paper considers the analysis of process networks with bottlenecks and shows how they may be regarded as simple multi-source maximal flow linear programming problems. We surveyed over 30 Production/Operations Management and management science/OR textbooks, finding that only iterative trial-and-error procedures are now being suggested for this kind of analysis. The maximal flow network approach is easier for complex problems and also allows several advantages not available in the trial-and-error approaches. This paper also discusses the use of a simple linear programming sensitivity result called radial change. The modelling approach suggested here can provide new ideas for improving system capacity following the application of Theory of Constraints techniques.     

Localized Stable Manifolds for Whiskered Tori in Coupled Map Lattices with Decaying Interaction

In this paper we consider lattice systems coupled by local interactions. We prove invariant manifold theorems for whiskered tori (we recall that whiskered tori are quasi-periodic solutions with exponentially contracting and expanding directions in the linearized system). The invariant manifolds we construct generalize the usual (strong) (un)stable manifolds and allow us to consider also non-resonant manifolds. We show that if the whiskered tori are localized near a collection of specific sites, then so are the invariant manifolds. We recall that the existence of localized whiskered tori has recently been proven for symplectic maps and flows in Fontich et al. (J Diff Equ, 2012), but our results do not need that the systems are symplectic. For simplicity we will present first the main results for maps, but we will show that the result for maps imply the results for flows. It is also true that the results for flows can be proved directly following the same ideas.     

Staff optimization for time-dependent acute patient flow

The emergency department is a key element of acute patient flow, but due to high demand and an alternating rate of arriving patients, the department is often challenged by insufficient capacity. Proper allocation of resources to match demand is, therefore, a vital task for many emergency departments.Constrained by targets on patient waiting time, we consider the problem of minimizing the total amount of staff-resources allocated to an emergency department. We test a matheuristic approach to this problem, accounting for both patient flow and staff scheduling restrictions. Using a continuous-time Markov chain, patient flow is modeled as a time-dependent queueing network where inhomogeneous behavior is evaluated using the uniformization method. Based on this modeling approach, we recursively evaluate and allocate staff to the system using integer linear programming until the waiting time targets are respected in all queues of the network. By comparing to discrete-event simulations of the associated system, we show that this approach is adequate for both modeling and optimizing the patient flow. In addition, we demonstrate robustness to the service time distribution and the associated system with multiple classes of patients.     

Modelling variations in hospital service delivery based on real time locating information

Variations in service delivery have been identified as a major challenge to the success of process improvement studies in service departments of hospital such as radiology. Largely, these variations are due to inherent system level factors, i.e., system variations such as unavailability of resources (nurse, bed, doctors, and equipment). These system variations are largely unnecessary/unwarranted and mostly lead to longer waiting times, delays, and lowered productivity of the service units. There is limited research on identifying system variations and modelling them for service improvements within hospital. Therefore, this paper proposes a modelling methodology to model system variations in radiology based on real time locating system (RTLS) tracking data. The methodology employs concepts from graph theory to identify and represent system variations. In particular, edge coloured directed multi-graphs (ECDMs) are used to model system variations which are reflected in paths adopted by staff, i.e., sequence of rooms/areas traversed while delivering services. The main steps of the methodology are: (i) identifying the most standard path followed by staff for service delivery; (ii) filtering the redundant events in RTLS tracking database for analysis; (iii) identifying rooms/areas of hospital site involved in the service delivery; (iv) determining patterns of paths adopted by staff from filtered tracking database; and, (v) representation of patterns in graph based model called as edge coloured directed multigraphs (ECDMs) of a role. A case study of MR scanning process is utilized to illustrate the implementation of the proposed methodology for modelling system variations reflected in the paths adopted by staff.     

Market share in a post-entry game

This paper investigates the dynamics of market share within a contemporary, real life, entry deterrence situation in the provision of National Health Service (NHS) pathology services. The major conclusion is that the previous Government's initiatives did not succeed in promoting competition in markets where existing NHS providers were operating significantly more efficiently than their neighbours. Evidence suggests managers were influenced more by potential competition from a new private sector entrant than by actual competition among existing providers. The effect of a new entrant is modelled as a perturbation of a pre-existing stable equilibrium in a seeming oligopoly influenced by market forces subject to Government regulation. Economic analysis of the market share which a new entry might gain shows that, on the assumptions made and contrary to expectations, the likely impact of Government regulation of NHS prices would be an increase in price per test in most of the market. Nevertheless the policy objective of improving quality at value for money prices was achieved for the near-monopoly provider within our case study area.     

Utilizing buffer management to improve performance in a healthcare environment

For over 50 years, the United Kingdom’s National Health Service has aspired to provide universal access to quality health care. However, as evidenced by huge backlogs and lengthy waiting times for many services, the NHS is showing the strain of accommodating rising contemporary expectations within a constrained budget. This paper describes the concept of buffer management, its origins in manufacturing applications, and how it can be applied to generate improvements in health care systems. The successful implementation of buffer management is illustrated with recent applications in the Accident and Emergency departments and the hospital admissions process of three NHS facilities.