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.     

Hospital Waiting List Management Models

This paper describes work carried out with hospital consultants in Lancaster District Health Authority to develop and use computerized waiting list management models. The ‘what if?’ models produced have been found to be a very useful tool in the constructive debate about problems faced by consultants and managers, and of the options available to them.     

Location of services and the impact on healthcare quality: insights from a simulation of a musculoskeletal physiotherapy service

Many healthcare systems are being redesigned to deliver local care with more services within the community. Relocation may enhance access but other aspects of healthcare quality should also be considered, notably waiting times and equity of care. This study examined a musculoskeletal physiotherapy service using a discrete-event simulation with simple heuristics to model patient behaviour. This combination provided an effective mechanism for incorporating the individuality of the patients in the flows along the patient pathways, subject to the varying availabilities of key resources. In particular, it captured the feedback that is critical in system performance, especially where waiting times are important. The model recognised the heterogeneity of patient attitudes and demonstrated how the behaviour of a relatively small proportion can affect the experience of all patients. The study suggested that, with careful operational management, more care could be delivered locally while exploiting many of the benefits of a centralised service.     

Using OR to support the development of an integrated musculo-skeletal service

This paper discusses the question of how operational research in general, and discrete event simulation in particular, can help to meet management challenges in hospital-based orthopaedics medicine. It focuses on the reduction of waiting times for elective patients, both for a first outpatient appointment and for the subsequent commencement of in-patient treatment. The research is based on a series of projects carried out by students from the Department of Management Science, University Strathclyde in Stobhill Hospital and the Glasgow Royal Infirmary between 1999 and 2003. An increasingly detailed and complex simulation model was developed for the musculo-skeletal service provided by these hospitals. The paper discusses the application of a modelling methodology—based on the idea of requisite models evolving over time—that is participatory, iterative and focused on enhancing the clients' understanding of the main performance drivers of the service. It concludes that this methodology fits well with successful strategies to sustain reductions in waiting times.     

Efficiency and welfare implications of managed public sector hospital waiting lists

A queuing model for public health service waiting lists is developed, and the implications for patient welfare of different systems for managing the waiting list are analysed. If patients are admitted to hospital on a first-come-first-served basis, a welfare gain is achieved by moving from a system of implicit to one of explicit rationing of access to the waiting list. If individual waiting times and hospital admissions are dependent on clinical priority, a further welfare gain is achievable without the use of explicit rationing, by reallocating the total waiting time from the more towards the less seriously ill. On efficiency and welfare criteria, a maximum waiting time guarantee does not appear to be a desirable development.     

The Impact of Operational Research on Agriculture

The paper shows that agriculture is one of the United Kingdom's largest industries. It would therefore be expected that O.R. could have made a significant contribution to decision making. But achievements in practice have been disappointingly small. The industry comprises of a large number of small individual businesses which do not permit specialisation in management functions. Consequently, technical advice and much R and D is provided from public funds. O.R. applications for agriculture have mainly been developed by Universities, Colleges, State Advisory Services and QUANGOS.The paper discusses some techniques used in agriculture—linear programming, dynamic programming and simulation—and outlines some problems encountered with these. Other techniques have had limited uptake and application. Reasons for the disappointing impact of O.R. are discussed as a set of problems-those specific to farmers and their systems; those specific to computer use; problems in recruiting and training O.R. specialists and problems in communication.     

M/M/1 Queueing systems with inventory

We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/∞-system. All authors were supported by DAAD/KBN grant number D/02/32206.     

Modelling toolkit to assist with introducing a stepped care system design in mental health care

We describe a modelling toolkit that was developed with the aim of assisting those responsible for introducing stepped care systems to local mental health services in the UK. The toolkit was pre-populated with real patient flow data collected from four sites that piloted the stepped care system design. Two analytical models were developed and coded as part of the toolkit to provide insights concerning workload, patient throughput, and changes in waiting times and waiting list size. An interface was built to allow users to specify their own stepped care system and input their own estimates or data of service demands and capacities at different steps. Despite the challenges and limitations, the use of modelling to inform the design of new service configurations is an important step in the right direction and we would recommend this as a reasonable way forward.     

Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service

The paper proposes Bayesian framework in an M/G/1 queuing system with optional second service. The semi-parametric model based on a finite mixture of Gamma distributions is considered to approximate both the general service and re-service times densities in this queuing system. A Bayesian procedure based on birth-death MCMC methodology is proposed to estimate system parameters, predictive densities and some performance measures related to this queuing system such as stationary system size and waiting time. The approach is illustrated with several numerical examples based on various simulation studies.     

A Hospital Throughput Model in the Context of Long Waiting Lists

In a public health system, one of the problems is the size of the waiting list for admission to hospital. This research involves establishing a method of analysing the general surgery waiting list problem at hospital and district level. While there are many aspects to such a study, this paper concentrates on a linear programming model to plan the aggregate throughput of the general surgical department. Preliminary results from applying the techniques to actual health districts in the United Kingdom are reported.     

System dynamics mapping of acute patient flows

Department of Health staff wished to use systems modelling to discuss acute patient flows with groups of NHS staff. The aim was to assess the usefulness of system dynamics (SD) in a healthcare context and to elicit proposals concerning ways of improving patient experience. Since time restrictions excluded simulation modelling, a hybrid approach using stock/flow symbols from SD was created. Initial interviews and hospital site visits generated a series of stock/flow maps. A ‘Conceptual Framework’ was then created to introduce the mapping symbols and to generate a series of questions about different patient paths and what might speed or slow patient flows. These materials formed the centre of three workshops for NHS staff. The participants were able to propose ideas for improving patient flows and the elicited data was subsequently employed to create a finalized suite of maps of a general acute hospital. The maps and ideas were communicated back to the Department of Health and subsequently assisted the work of the Modernization Agency.     

Algorithmic methods for multi-server queues with group arrivals and exponential services

We discuss algorithms for the computation of the steady-state features of the c-server queue with exponential service times and bounded group arrivals. While our methods are valid for general interarrival time distributions, we treat in detail the simplifications obtained by using a distribution of phase type. Oueue length densities at times prior to arrivals and at arbitrary times are obtained in a modified matrix-geometric form. Their means and variances are found in computationally tractable forms. We also present algorithmic methods for the waiting time and the virtual waiting time distributions of a customer in a group and obtain the means and variances of these distributions in tractable forms. Numerical examples show that the effects of changing various parameters of the queuing model may so be examined at a small computational cost.     

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.     

Analysis via goal programming of the minimum achievable stay in surgical waiting lists

In this paper, a Goal Programming model is developed in order to study the possibility of decreasing the length of stay on the waiting list of a hospital that belongs to the Spanish Health Service. First, a problem is solved to determine the optimal planning for one year, so as to make the maximum waiting time decrease to six months (at present, some operations have a waiting list of more than a year). Afterwards, two other problems are solved in order to determine the impact that a further reduction of the waiting time (four months) would have on the requirements of extra resources for the hospital. The particular problem for the Trauma service is described in detail, but global results are shown and commented.     

Assessment of a 7-day turn-around for the reporting of cervical smear results using discrete event simulation

A discrete event simulation (DES) model has been used to analyse options with the potential to facilitate a 7-day turn-around of cervical screening results in England, with the aim of reducing the anxiety experienced by the participants. Detailed information regarding the cervical screening process collected from the NHS Cancer Screening Programme, research papers, current national guidelines and five cytology laboratories in England was used to inform a DES model representing a typical laboratory. A number of options for change were evaluated. The simulation model suggested that it would be feasible to improve the result turn-around times from 95% within 11 weeks to 95% within 2 weeks; and from an average current result turn-around time of around 6 weeks, to over 50% within 7 days. Moreover, the options for change should be cost saving in the long term.     

Pricing Occupation-Time Options in a Mixed-Exponential Jump-Diffusion Model

In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of intervals.     

Modeling the transplant waiting list: A queueing model with reneging

Motivated by the problem of organ allocation, we develop a queueing model with reneging that provides a stylistic representation of the transplant waiting list. The model assumes that there are several classes of patients, several classes of organs, and patient reneging due to death. We focus on randomized organ allocation policies and develop closed-form asymptotic expressions for the stationary waiting time, stationary waiting time until transplantation, and fraction of patients who receive transplantation for each patient class. Analysis of these expressions identifies the main factors that underlie the performance of the transplant waiting list and demonstrates that queueing models can prove useful when evaluating the organ allocation system. This revised version was published online in June 2006 with corrections to the Cover Date.     

Waiting times in a two-queue model with exhaustive and Bernoulli service

This paper deals with waiting times in a two-queue polling system in which one queue is served according to the Bernoulli service discipline and the other one attains exhaustive service. Exact results are derived for the LST's of the waiting time distributions via an iteration scheme. Based on those results the mean waiting times are expressed in the system parameters.     

Response times in gated M/G/1 queues: The processor-sharing case

A class of single server queues with Poisson arrivals and a gated server is considered. Whenever the server becomes idle the gate separating it from the waiting line opens, admitting all the waiting customers into service, and then closes again. The batch admitted into service may be served according to some arbitrary scheme. The equilibrium waiting time distribution is provided for the subclass of conservative schemes with arbitrary service times and the processor-sharing case is treated in some detail to produce the equilibrium time-in-service and response time distributions, conditional on the length of required service. The LIFO and random order of service schemes and the case of compound Poisson arrivals are treated briefly as examples of the effectiveness of the proposed method of analysis. All distributions are provided in terms of their Laplace transforms except for the case of exponential service times where the L.T. of the waiting time distribution is inverted. The first two moments of the equilibrium waiting and response times are provided for most treated cases and in the exponential service times case the batch size distribution is also presented.